Date: Fri, 1 Mar 13 01:08:11 GMT Subject: math daily 77 new + 20 crosses received ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Send any comments regarding submissions directly to submitter. ------------------------------------------------------------------------------ See http://front.math.ucdavis.edu/ for a math specific front-end or point your web browser at http://arxiv.org/ for the generic front-end. To unsubscribe, e-mail To: math@arXiv.org, Subject: cancel ------------------------------------------------------------------------------ received from Wed 27 Feb 13 21:00:00 GMT to Thu 28 Feb 13 21:00:00 GMT ------------------------------------------------------------------------------ \\ arXiv:1302.7011 Date: Wed, 27 Feb 2013 21:38:24 GMT (8886kb) Title: Some knots in S^1 x S^2 with lens space surgeries Authors: Kenneth L. Baker, Dorothy Buck, Ana G. Lecuona Categories: math.GT Comments: 35 pages, 32 figures MSC-class: 57M27 \\ We propose a classification of knots in S^1 x S^2 that admit a longitudinal surgery to a lens space. Any lens space obtainable by longitudinal surgery on some knots in S^1 x S^2 may be obtained from a Berge-Gabai knot in a Heegaard solid torus of S^1 x S^2, as observed by Rasmussen. We show that there are yet two other families of knots: those that lie on the fiber of a genus one fibered knot and the `sporadic' knots. All these knots in S^1 x S^2 are both doubly primitive and spherical braids. This classification arose from generalizing Berge's list of doubly primitive knots in S^3, though we also examine how one might develop it using Lisca's embeddings of the intersection lattices of rational homology balls bounded by lens spaces as a guide. We conjecture that our knots constitute a complete list of doubly primitive knots in S^1 x S^2 and reduce this conjecture to classifying the homology classes of knots in lens spaces admitting a longitudinal S^1 x S^2 surgery. \\ ( http://arxiv.org/abs/1302.7011 , 8886kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7013 Date: Wed, 27 Feb 2013 21:50:57 GMT (92kb,D) Title: Alzheimer's disease: analysis of a mathematical modelincorporating the role of prions Authors: Mohamed Helal, Erwan Hingant, Laurent Pujo-Menjouet, Glenn F. Webb Categories: math.CA math.AP MSC-class: 35F61, 92B05, 34L30 \\ We introduce a mathematical model of the in vivo progression of Alzheimer's disease with focus on the role of prions in memory impairment. Our model consists of differential equations that describe the dynamic formation of {\beta}-amyloid plaques based on the concentrations of A{\beta} oligomers, PrPC proteins, and the A{\beta}-x-PrPC complex, which are hypothesized to be responsible for synaptic toxicity. We prove the well-posedness of the model and provided stability results for its unique equilibrium, when the polymerization rate of {\beta}-amyloid is constant and also when it is described by a power law. \\ ( http://arxiv.org/abs/1302.7013 , 92kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7015 Date: Wed, 27 Feb 2013 22:05:30 GMT (290kb,D) Title: The geometry of lightlike surfaces in Minkowski space Authors: Brian Carlsen and Jeanne N. Clelland Categories: math.DG \\ We investigate the geometric properties of lightlike surfaces in the Minkowski space $\R^{2,1}$, using Cartan's method of moving frames to compute a complete set of local invariants for such surfaces. Using these invariants, we give a complete local classification of lightlike surfaces of constant type in $\R^{2,1}$ and construct new examples of such surfaces. \\ ( http://arxiv.org/abs/1302.7015 , 290kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7019 Date: Wed, 27 Feb 2013 22:35:50 GMT (1614kb,D) Title: A bigroupoid's topology Authors: David Michael Roberts Categories: math.AT math.CT math.GN Comments: 26 pages, 8 figures. Preliminary version, comments welcome \\ The fundamental bigroupoid of a space captures its homotopy 2-type. When the space is semilocally 2-connected, we can lift the construction to a bigroupoid internal to the category of spaces, such that the invariants of the topological bigroupoid corresponding to the path components and first two homotopy groups are discrete. In fact more is true, in that the topologised fundamental bigroupoid is locally trivial in a way analogous to the case of topological groupoids. \\ ( http://arxiv.org/abs/1302.7019 , 1614kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7022 Date: Wed, 27 Feb 2013 22:54:45 GMT (23kb) Title: Foward the theory of Sobolev's mappings on the plane Authors: R. Salimov Categories: math.CV \\ The paper is devoted to the study of homeomoephisms with finite distortion on the plane with use of the modulus techniques. \\ ( http://arxiv.org/abs/1302.7022 , 23kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7024 Date: Wed, 27 Feb 2013 23:07:42 GMT (43kb) Title: Level set percolation for random interlacements and the Gaussian free field Authors: Pierre-Fran\c{c}ois Rodriguez Categories: math.PR math-ph math.MP Comments: 33 pages, 1 figure MSC-class: 60G15, 60G55, 60G60, 60K35, 82B43 \\ We consider continuous-time random interlacements on Z^d, d greater or equal to 3, and investigate the percolation model where a site x of Z^d is occupied if the total amount of time spent at x by all the trajectories of the interlacement at level u > 0 exceeds some given non-negative parameter, and empty otherwise. Thus, the set of occupied sites forms a subset of the interlacement at level u. We also investigate percolation properties of empty sites. A recent isomorphism theorem enables us to "translate" some of the relevant questions into the language of level-set percolation for the Gaussian free field on Z^d, d greater or equal to 3, for which useful tools have been developed. We also gain new insights of independent interest concerning "two-sided" level-set percolation, where a site x of Z^d is occupied if and only if the absolute value of the field variable at that site exceeds a given non-negative level. \\ ( http://arxiv.org/abs/1302.7024 , 43kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7030 Date: Wed, 27 Feb 2013 23:33:45 GMT (244kb) Title: Quadratic differentials as stability conditions Authors: Tom Bridgeland, Ivan Smith Categories: math.AG math.DS math.RT Comments: 123 pages; 38 figures MSC-class: 14F05, 32G15 \\ We prove that moduli spaces of meromorphic quadratic differentials with simple zeroes on compact Riemann surfaces can be identified with spaces of stability conditions on a class of CY3 triangulated categories defined using quivers with potential associated to triangulated surfaces. We relate the finite-length trajectories of such quadratic differentials to the stable objects of the corresponding stability condition. \\ ( http://arxiv.org/abs/1302.7030 , 244kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7035 Date: Wed, 27 Feb 2013 23:54:55 GMT (51kb,D) Title: Lipschitz inverse shadowing for nonsingular flows Authors: Dmitry Todorov Categories: math.DS Comments: 17 pages, 9 figures MSC-class: 37C50, 34D30 \\ We prove that Lipschitz inverse shadowing for nonsingular flows is equivalent to structural stability. \\ ( http://arxiv.org/abs/1302.7035 , 51kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7040 Date: Thu, 28 Feb 2013 00:25:01 GMT (9kb) Title: On matrix inequalities between the power means: counterexamples Authors: Koenraad M.R. Audenaert and Fumio Hiai Categories: math.FA Comments: 15 pages MSC-class: 15A45, 47A64 \\ We prove that the known sufficient conditions on the real parameters $(p,q)$ for which the matrix power mean inequality $((A^p+B^p)/2)^{1/p} \le ((A^q+B^q)/2)^{1/q}$ holds are indeed best possible. The proof is done by constructing $2 \times 2$ counterexamples. \\ ( http://arxiv.org/abs/1302.7040 , 9kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7044 Date: Thu, 28 Feb 2013 00:44:59 GMT (24kb) Title: Current Density Impedance Imaging of an Anisotropic Conductivity in a Known Conformal Class Authors: Nicholas Hoell, Amir Moradifam, Adrian Nachman Categories: math.AP \\ We present a procedure for recovering the conformal factor of an anisotropic conductivity matrix in a known conformal class in a domain in Euclidean space of dimension greater than or equal to 2. The method requires one internal measurement, together with a priori knowledge of the conformal class (local orientation) of the conductivity matrix. This problem arises in the coupled-physics medical imaging modality of Current Density Impedance Imaging (CDII) and the assumptions on the data are suitable for measurements determinable from cross-property based couplings of the two imaging modalities CDII and Diffusion Tensor Imaging (DTI). We show that the corresponding electric potential is the unique solution of a constrained minimization problem with respect to a weighted total variation functional defined in terms of the physical data. Further, we show that the associated equipotential surfaces are area minimizing with respect to a Riemannian metric obtained from the data. The results are also extended to allow the presence of perfectly conducting and/or insulating inclusions. \\ ( http://arxiv.org/abs/1302.7044 , 24kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7050 Date: Thu, 28 Feb 2013 01:21:29 GMT (11kb) Title: Note on Solution Regularity of the Generalized Magnetohydrodynamic Equations with Partial Dissipation Authors: Chuong V. Tran, Xinwei Yu, Zhichun Zhai Categories: math.AP Comments: 10 pages. Nonlinear Analysis TMA, to appear \\ In this brief note we study the $n$-dimensional magnetohydrodynamic equations with hyper-viscosity and zero resistivity. We prove global regularity of solutions when the hyper-viscosity is sufficiently strong. \\ ( http://arxiv.org/abs/1302.7050 , 11kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7053 Date: Thu, 28 Feb 2013 01:38:08 GMT (18kb) Title: Elliptic Springer Theory Authors: David Ben-Zvi and David Nadler Categories: math.RT math.QA Comments: 13 pages. Comments welcome! \\ We introduce an elliptic version of the Grothendieck-Springer sheaf and establish elliptic analogues of the basic results of Springer theory. From a geometric perspective, our constructions specialize geometric Eisenstein series to the resolution of degree zero, semistable G-bundles by degree zero B-bundles over an elliptic curve E. From a representation theory perspective, they produce a full embedding of representations of the elliptic or double affine Weyl group into perverse sheaves with nilpotent characteristic variety on the moduli of G-bundles over E. The resulting objects are principal series examples of elliptic character sheaves, objects expected to play the role of character sheaves for loop groups. \\ ( http://arxiv.org/abs/1302.7053 , 18kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7055 Date: Thu, 28 Feb 2013 02:06:06 GMT (368kb) Title: A variation on Heawood-list-coloring for graphs on surfaces Authors: Joan P. Hutchinson Categories: math.CO Comments: 10 pages MSC-class: 05C10, 05C15 \\ We prove a variation on Heawood-list-coloring for graphs on surfaces, modeled on Thomassen's planar 5-list-coloring theorem. For epsilon>0 define the Heawood number to be H(epsilon)=Floor((7+Sqrt[24*epsilon+1])/2). We prove that, except for epsilon=3, every graph embedded on a surface of Euler genus epsilon>0 with a distinguished face F can be list-colored when the vertices of F have (H(epsilon)-2)-lists and all other vertices have H(epsilon)-lists unless the induced subgraph on the vertices of F contains the complete graph on H(epsilon)-1 vertices. \\ ( http://arxiv.org/abs/1302.7055 , 368kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7061 Date: Thu, 28 Feb 2013 02:52:38 GMT (28kb) Title: Existence of strong solutions to the steady Navier-Stokes equations for a compressible heat-conductive fluid with large forces Authors: Changsheng Dou, Song Jiang and Yong-Fu Yang Categories: math.AP math-ph math.MP Comments: 30 pages \\ We prove that there exists a strong solution to the Dirichlet boundary value problem for the steady Navier-Stokes equations of a compressible heat-conductive fluid with large external forces in a bounded domain $R^d (d = 2, 3)$, provided that the Mach number is appropriately small. At the same time, the low Mach number limit is rigorously verified. The basic idea in the proof is to split the equations into two parts, one of which is similar to the steady incompressible Navier-Stokes equations with large forces, while another part corresponds to the steady compressible heat-conductive Navier-Stokes equations with small forces. The existence is then established by dealing with these two parts separately, establishing uniform in the Mach number a priori estimates and exploiting the known results on the steady incompressible Navier-Stokes equations. \\ ( http://arxiv.org/abs/1302.7061 , 28kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7062 Date: Thu, 28 Feb 2013 02:52:49 GMT (34kb) Title: Interior regularity of fully nonlinear degenerate elliptic equations, I: Bellman equations with constant coefficients Authors: Wei Zhou Categories: math.AP math.OC math.PR Comments: The author would appreciate any comments and suggestions on the manuscript MSC-class: 35B65, 35J60, 35J70, 60H30, 93E20 \\ This is the first of a series of papers on the interior regularity of fully nonlinear degenerate elliptic equations. We consider a stochastic optimal control problem in which the diffusion coefficients, drift coefficients and discount factor are independent of the spacial variables. Under suitable assumptions, for $k=0,1$, when the terminal and running payoffs are globally $C^{k,1}$, we obtain the $C^{k,1}$-smoothness of the value function, which yields the existence and uniqueness of the solution to the associated Dirichlet problem for the degenerate Bellman equation. \\ ( http://arxiv.org/abs/1302.7062 , 34kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7064 Date: Thu, 28 Feb 2013 03:01:25 GMT (15kb) Title: On the Hausdorff dimension of countable intersections of certain sets of normal numbers Authors: Bill Mance Categories: math.NT Comments: 15 pages, 1 figure \\ We show that the set of numbers that are $Q$-distribution normal but not simply $Q$-ratio normal has full Hausdorff dimension. It is further shown under some conditions that countable intersections of sets of this form still have full Hausdorff dimension even though they are not winning sets (in the sense of W. Schmidt). As a consequence of this, we construct many explicit examples of numbers that are simultaneously distribution normal but not simply ratio normal with respect to certain countable families of basic sequences. Additionally, we prove that some related sets are either winning sets or sets of the first category. \\ ( http://arxiv.org/abs/1302.7064 , 15kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7066 Date: Thu, 28 Feb 2013 03:22:19 GMT (5kb) Title: Integral mean estimates for the polar derivative of a polynomial Authors: N. A. Rather and Suhail Gulzar Categories: math.CV Comments: 8 pages MSC-class: 30A10, 30C10, 30E10, 30C15 \\ Let $ P(z) $ be a polynomial of degree $ n $ having all zeros in $|z|\leq k$ where $k\leq 1,$ then it was proved by Dewan \textit{et al} that for every real or complex number $\alpha$ with $|\alpha|\geq k$ and each $r\geq 0$ $$ n(|\alpha|-k)\left\{\int\limits_{0}^{2\pi}\left|P\left(e^{i\theta}\right)\right|^r d\theta\right\}^{\frac{1}{r}}\leq\left\{\int\limits_{0}^{2\pi}\left|1+ke^{i\theta}\right|^r d\theta\right\}^{\frac{1}{r}}\underset{|z|=1}{Max}|D_\alpha P(z)|. $$ \indent In this paper, we shall present a refinement and generalization of above result and also extend it to the class of polynomials $P(z)=a_nz^n+\sum_{\nu=\mu}^{n}a_{n-\nu}z^{n-\nu},$ $1\leq\mu\leq n,$ having all its zeros in $|z|\leq k$ where $k\leq 1$ and thereby obtain certain generalizations of above and many other known results. \\ ( http://arxiv.org/abs/1302.7066 , 5kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7069 Date: Thu, 28 Feb 2013 03:35:18 GMT (21kb) Title: Learning Theory in the Arithmetic Hierarchy Authors: Achilles Beros Categories: math.LO cs.LG cs.LO Comments: 19 pages MSC-class: 03D80, 68Q32 \\ We consider the arithmetic complexity of index sets of uniformly computably enumerable families learnable under different learning criteria. We determine the exact complexity of these sets for the standard notions of finite learning, learning in the limit, behaviorally correct learning and anomalous learning in the limit. In proving the $\Sigma_5^0$-completeness result for behaviorally correct learning we prove a result of independent interest; if a uniformly computably enumerable family is not learnable, then for any computable learner there is a $\Delta_2^0$ enumeration witnessing failure. \\ ( http://arxiv.org/abs/1302.7069 , 21kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7071 Date: Thu, 28 Feb 2013 03:46:34 GMT (163kb) Title: Generalized Multiscale Finite Element Method. Symmetric Interior Penalty Coupling Authors: Y. Efendiev, J. Galvis, R. Lazarov, M. Moon, and M. Sarkis Categories: math.NA \\ Motivated by applications to numerical simulation of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose three different finite element spaces on the coarse mesh. The first space is based on a local eigenvalue problem that uses a weighted $L_2-$norm for computing the "mass" matrix. The second space is generated by amending the eigenvalue problem of the first case with a term related to the penalty. The third choice is based on generation of a large space of snapshots and subsequent selection of a subspace of a reduced dimension. The approximation with these spaces is based on the discontinuous Galerkin finite element method framework. We investigate the stability and derive error estimates for the methods and further experimentally study their performance on a representative number of numerical examples. \\ ( http://arxiv.org/abs/1302.7071 , 163kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7074 Date: Thu, 28 Feb 2013 03:58:36 GMT (18kb) Title: A null space property approach to compressed sensing with frames Authors: Xuemei Chen, Rongrong Wang Categories: cs.IT math.FA math.IT \\ An interesting topic in compressive sensing concerns problems of sensing and recovering signals with sparse representations in a dictionary. In this note, we study conditions of An interesting topic in compressive sensing concerns problems of sensing and recovering signals with sparse representations in a dictionary. In this note, we study conditions of sensing matrices A for the l_1-synthesis method to accurately recovery sparse, or nearly sparse signals in a given dictionary D. In particular, we propose a dictionary based null space property (D-NSP) which, to the best of our knowledge, is the first sufficient and necessary condition for the success of the l_1 recovery. This new property is then utilized to detect some of those dictionaries whose sparse families cannot be compressed universally. Moreover, when the dictionary is full spark, we show that AD being NSP, which is well-known to be only sufficient for stable recovery via l_1-synthesis method, is indeed necessary as well. \\ ( http://arxiv.org/abs/1302.7074 , 18kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7076 Date: Thu, 28 Feb 2013 04:18:26 GMT (15kb) Title: Combinatorial characterizations of the Cohen-Macaulayness of the second power of edge ideals Authors: Do Trong Hoang, Nguyen Cong Minh and Tran Nam Trung Categories: math.AC math.CO Comments: 16 pages, to appear in JCTA MSC-class: 13D45, 05C90, 05E40, 05E45 \\ Let $I(G)$ be the edge ideal of a simple graph $G$. In this paper, we will give sufficient and necessary combinatorial conditions of $G$ in which the second symbolic and ordinary power of its edge ideal are Cohen-Macaulay (resp. Buchsbaum, generalized Cohen-Macaulay). As an application of our results, we will classify all bipartite graphs in which the second (symbolic) powers are Cohen-Macaulay (resp. Buchsbaum, generalized Cohen-Macaulay). \\ ( http://arxiv.org/abs/1302.7076 , 15kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7077 Date: Thu, 28 Feb 2013 04:18:59 GMT (11kb) Title: Interior regularity of fully nonlinear degenerate elliptic equations, II: real and complex Monge-Amp\`ere equations Authors: Wei Zhou Categories: math.AP math.DG math.PR Comments: The author would appreciate any comments and suggestions on the manuscript MSC-class: 35J96, 32W20, 35B65, 35J70, 60H30 \\ We first obtain the interior $C^{1,1}$-regularity and solvability for the degenerate real Monge-Amp\`ere equation in a bounded, $C^3$-smooth and strictly convex domain in $\mathbb R^d$ ($d\ge2$), assuming that the boundary data is only globally $C^{1,1}$, and the $d$-th root of the nonnegative right-hand side is globally $C^{0,1}$ and convex after adding $K|x|^2$ for some constant $K$. Then we establish the interior $C^{1,1}$-regularity and solvability for the degenerate complex Monge-Amp\`ere equation in a bounded, $C^3$-smooth and strictly pseudoconvex domain in $\mathbb C^d$, under the global $C^{1,1}$-regularity assumption on the boundary data and the $d$-th root of the nonnegative right-hand side. Since the derivatives may blow up along non-tangent directions at the boundary under our regularity assumptions on the boundary data, we also estimate the derivatives up to second order in both problems. Our technique is probabilistic by following Krylov's approach. The result in the real case extends N. Trudinger and J. Urbas's interior $C^{1,1}$-regularity result for the homogeneous case [N. Trudinger and J. Urbas, Bull. Austral. Math. Soc., 30(3): 321~334, 1984.] in the sense of considering the nonnegative right-hand side. The result in the complex case generalizes E. Bedford and B. A. Taylor's interior $C^{1,1}$-regularity result in a ball [E. Bedford and B. A. Taylor, Invent. Math., 37(1): 1~44, 1976.] by allowing the domain be any bounded, sufficiently smooth and strictly pseudoconvex one. \\ ( http://arxiv.org/abs/1302.7077 , 11kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7079 Date: Thu, 28 Feb 2013 04:35:57 GMT (25kb) Title: Compact embedding in the space of piecewise H1 functions Authors: Sheng Zhang Categories: math.NA MSC-class: 65N30, 46E35, 74S05 \\ We prove a compact embedding theorem in a class of spaces of piecewise H1 functions subordinated to a class of shape regular, but not necessarily quasi-uniform triangulations of a polygonal domain. This result generalizes the Rellich--Kondrachov theorem. It is used to prove generalizations to piecewise functions of nonstandard Poincar\'e--Friedrichs inequalities. It can be used to prove Korn inequalities for piecewise functions associated with elastic shells. \\ ( http://arxiv.org/abs/1302.7079 , 25kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7083 Date: Thu, 28 Feb 2013 04:50:56 GMT (174kb) Title: Quantification of uncertainty from high-dimensional experimental data Authors: Lionel Mathelin Categories: math.NA stat.ME \\ This paper discusses a methodology for determining a functional representation of a random process from a collection of pointwise samples. This situation typically arises when experimental data are used to estimate some quantities in a form suitable for their subsequent use in a numerical simulation as initial and/or boundary conditions. The present work specifically focuses onto random quantities lying in a high dimensional stochastic space in the context of limited amount of information. The proposed approach involves a procedure for the selection of an approximation basis and the evaluation of the associated coefficients. The selection of the approximation basis relies on the a priori choice of the High-Dimensional Model Representation format combined with a modified Least Angle Regression technique. The resulting basis then provides the structure for the actual approximation basis, possibly using different functions, more parsimonious and nonlinear in its coefficients. To evaluate the coefficients, both an alternate least squares and an alternate weighted total least squares methods are employed. Examples are provided for the approximation of a random variable in a high-dimensional space as well as the estimation of a random field. Stochastic dimensions up to 100 are considered, with an amount of information as low as about 3 samples per dimension, and robustness of the approximation is demonstrated w.r.t. noise in the dataset. The computational cost of the solution method is shown to scale only linearly with the cardinality of the a priori basis and exhibits a (N_q)^s, 2 <= s <= 3, dependence with the number N_q of samples in the dataset. The provided numerical experiments illustrate the ability of the present approach to derive an accurate approximation from scarce experimental data even in the presence of noise. \\ ( http://arxiv.org/abs/1302.7083 , 174kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7084 Date: Thu, 28 Feb 2013 05:00:58 GMT (25kb) Title: Ill-posedness of the incompressible Navier-Stokes equations in $\dot{F}^{-1,q}_{\infty}({R}^3)$ Authors: C. Deng and X. Yao Categories: math.AP Comments: 19. arXiv admin note: text overlap with arXiv:1302.5785 \\ In this paper, authors show the ill-posedness of 3D incompressible Navier-Stokes equations in the critical Triebel-Lizorkin spaces $ \dot{F}^{-1,q}_{\infty} (\mathbb{R}^3) $ for any $ q>2 $ in the sense that arbitrarily small initial data of $ \dot{F}^{-1,q}_{\infty}(\mathbb{R}^3) $ can lead the corresponding solution to become arbitrarily large after an arbitrarily short time. In view of the well-posedness of 3D-incompressible Navier-Stokes equations in $ BMO^{-1} $ (i.e. the Triebel-Lizorkin space $ \dot{F}^{-1,2}_{\infty}(\mathbb{R}^3) $) by Koch and Tataru, our work completes a dichotomy of well-posedness and ill-posedness in the Triebel-Lizorkin space framework depending on $ q=2 $ or $ q>2 $. \\ ( http://arxiv.org/abs/1302.7084 , 25kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7092 Date: Thu, 28 Feb 2013 06:04:32 GMT (301kb,D) Title: On Concept of Mechanical System Authors: Al Cheremensky Categories: math-ph math.MP Comments: arXiv admin note: text overlap with arXiv:1012.3633 MSC-class: 68T40, 70B10 \\ The paper gives a screw axiomatics of rational mechanics, namely: 1. introduces the main measures of mechanics: the mass measure, the scalar and (vector) screw measures of motion, the (vector) screw measure of impressed action, the increment velocity of the vector measure of motion, the (vector) screw measure of constraint action; 2. postulates the (stronger) local integral form of conservation law for the vector measuare of motion (fundamental principle of dynamics), and 3. defines the central concept of rational mechanics {mechanical system being realized in the form of all classical mechanical systems (mass-points, rigid bodies, continua, point-bodies, etc.). The presentation is based on new notions of vector calculus -- homogeneous and inhomogeneous vector and tensor slider-functions and screw measures. \\ ( http://arxiv.org/abs/1302.7092 , 301kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7095 Date: Thu, 28 Feb 2013 06:27:19 GMT (9kb) Title: Hattori-Stallings trace and character Authors: Yang Han Categories: math.KT math.RA math.RT Comments: 11 pages MSC-class: 16G10, 16E30, 18E30, 18G10 \\ It is shown that Hattori-Stallings trace induces a homomorphism of abelian groups, called Hattori-Stallings character, from the $K_1$-group of endomorphisms of the perfect derived category of an algebra to its zero-th Hochschild homology, which provides a new proof of Igusa-Liu-Paquette Theorem, i.e., the strong no loop conjecture for finite-dimensional elementary algebras, on the level of complexes. Moreover, the Hattori-Stallings traces of projective bimodules and one-sided projective bimodules are studied, which provides another proof of Igusa-Liu-Paquette Theorem on the level of modules. \\ ( http://arxiv.org/abs/1302.7095 , 9kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7098 Date: Thu, 28 Feb 2013 07:03:51 GMT (29kb) Title: The influence of boundary conditions on the contact problem in a 3D Navier-Stokes Flow Authors: David G\'erard-Varet (IMJ), Matthieu Hillairet (CEREMADE, ICJ), Chao Wang (IMJ) Categories: math.AP Comments: 34 p \\ We consider the free fall of a sphere above a wall in a viscous incompressible fluid. We investigate the influence of boundary conditions on the finite-time occurrence of contact between the sphere and the wall. We prove that slip boundary conditions enable to circumvent the "no-collision" paradox associated with no-slip boundary conditions. We also examine the case of mixed boundary conditions. \\ ( http://arxiv.org/abs/1302.7098 , 29kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7099 Date: Thu, 28 Feb 2013 07:04:35 GMT (36kb) Title: Community Detection in Random Networks Authors: Ery Arias-Castro (Math Dept, UCSD), Nicolas Verzelen (MISTEA) Categories: math.ST stat.ML stat.TH \\ We formalize the problem of detecting a community in a network into testing whether in a given (random) graph there is a subgraph that is unusually dense. We observe an undirected and unweighted graph on N nodes. Under the null hypothesis, the graph is a realization of an Erd\"os-R\'enyi graph with probability p0. Under the (composite) alternative, there is a subgraph of n nodes where the probability of connection is p1 > p0. We derive a detection lower bound for detecting such a subgraph in terms of N, n, p0, p1 and exhibit a test that achieves that lower bound. We do this both when p0 is known and unknown. We also consider the problem of testing in polynomial-time. As an aside, we consider the problem of detecting a clique, which is intimately related to the planted clique problem. Our focus in this paper is in the quasi-normal regime where n p0 is either bounded away from zero, or tends to zero slowly. \\ ( http://arxiv.org/abs/1302.7099 , 36kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7101 Date: Thu, 28 Feb 2013 07:15:58 GMT (11kb) Title: Representations of the Yokonuma-Temperley-Lieb algebra Authors: Maria Chlouveraki Categories: math.RT Comments: 10 pages MSC-class: 20C08, 05E10, 16S80 \\ We determine the representations of the Yokonuma-Temperley-Lieb algebra, which is defined as a quotient of the Yokonuma-Hecke algebra by generalising the construction of the classical Temperley-Lieb algebra. \\ ( http://arxiv.org/abs/1302.7101 , 11kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7105 Date: Thu, 28 Feb 2013 07:42:59 GMT (14kb) Title: Taylor approximations of operator functions Authors: Anna Skripka Categories: math.FA Comments: 12 pages \\ This survey on approximations of perturbed operator functions addresses recent advances and some of the successful methods. \\ ( http://arxiv.org/abs/1302.7105 , 14kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7109 Date: Thu, 28 Feb 2013 08:34:19 GMT (17kb) Title: Reconstructing multisets over commutative groupoids, with an application to a reconstruction problem for functions of several arguments (the case of affine functions) Authors: Erkko Lehtonen Categories: math.CO Comments: 17 pages \\ A reconstruction problem is formulated for multisets over commutative groupoids. The cards of a multiset are obtained by replacing a pair of its elements by their sum. Necessary and sufficient conditions for the reconstructibility of multisets are determined. These results find an application in a different kind of reconstruction problem for functions of several arguments and identification minors: classes of linear or affine functions over nonassociative semirings are shown to be weakly reconstructible. Moreover, affine functions of sufficiently large arity over finite fields are reconstructible. \\ ( http://arxiv.org/abs/1302.7109 , 17kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7116 Date: Thu, 28 Feb 2013 09:05:12 GMT (10kb) Title: Projections of orbital measures, Gelfand-Tsetlin polytopes, and splines Authors: Grigori Olshanski Categories: math.RT Comments: 12 pages; to appear in Journal of Lie Theory \\ The unitary group U(N) acts by conjugations on the space H(N) of NxN Hermitian matrices, and every orbit of this action carries a unique invariant probability measure called an orbital measure. Consider the projection of the space H(N) onto the real line assigning to an Hermitian matrix its (1,1)-entry. Under this projection, the density of the pushforward of a generic orbital measure is a spline function with N knots. This fact was pointed out by Andrei Okounkov in 1996, and the goal of the paper is to propose a multidimensional generalization. Namely, it turns out that if instead of the (1,1)-entry we cut out the upper left matrix corner of arbitrary size KxK, where K=2,...,N-1, then the pushforward of a generic orbital measure is still computable: its density is given by a KxK determinant composed from one-dimensional splines. The result can also be reformulated in terms of projections of the Gelfand-Tsetlin polytopes. \\ ( http://arxiv.org/abs/1302.7116 , 10kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7118 Date: Thu, 28 Feb 2013 09:11:57 GMT (1706kb) Title: Asymptotics of Discrete Chebyshev Polynomials Authors: J. H. Pan and Prof. Roderick Wong Categories: math.CV Comments: 32 pages, 8 figures \\ The discrete Chebyshev polynomials $t_n(x,N)$ are orthogonal with respect to a distribution, which is a step function with jumps one unit at the points $x=0,1,\cdots, N-1$, $N$ being a fixed positive integer. By using a double integral representation, we have recently obtained asymptotic expansions for $t_{n}(aN,N+1)$ in the double scaling limit, namely, $N\rightarrow\infty$ and $n/N\rightarrow b$, where $b\in (0,1)$ and $a\in(-\infty,\infty)$; see [Studies in Appl. Math. \textbf{128} (2012), 337-384]. In the present paper, we continue to investigate the behaviour of these polynomials when the parameter $b$ approaches the endpoints of the interval $(0,1)$. While the case $b\rightarrow 1$ is relatively simple (since it is very much like the case when $b$ is fixed), the case $b\rightarrow 0$ is quite complicated. The discussion of the latter case is divided into several subcases, depending on the quantities $n$, $x$ and $xN/n^2$, and different special functions have been used as approximants, including Airy, Bessel and Kummer functions. \\ ( http://arxiv.org/abs/1302.7118 , 1706kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7119 Date: Thu, 28 Feb 2013 09:12:22 GMT (19kb) Title: Symmetries of trivial systems of ODEs of mixed order Authors: Boris Doubrov and Igor Zelenko Categories: math.DG Comments: 28 pages MSC-class: 17B70, 34A26, 34A34, 34C14, 53C10 \\ We compute symmetry algebras of a system of two equations y^(k)=z^(l)=0, where 2<=k t$ for all $t > 0$, we perform an explicit construction of a process $X$ which is Brownian motion in its own filtration and that hits zero for the first time at $V(\tau)$, where $\tau := \inf\{t>0: Z_t =0\}$. We also provide the semimartingale decomposition of $X$ under the filtration jointly generated by $X$ and $Z$. Our construction relies on a combination of enlargement of filtration and filtering techniques. The resulting process $X$ may be viewed as the analogue of a 3-dimensional Bessel bridge starting from 1 at time 0 and ending at 0 at the random time $V(\tau)$. We call this {\em a dynamic Bessel bridge} since $V(\tau)$ is not known in advance. Our study is motivated by insider trading models with default risk, where the insider observes the firm's value continuously on time. \\ ( http://arxiv.org/abs/1302.7128 , 25kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7130 Date: Thu, 28 Feb 2013 09:59:25 GMT (17kb) Title: Order estimates of the best $n$-term orthogonal trigonometric approximations of the classes ${\cal F}_{q}^{\psi}$ of periodic functions in the integral metrics Authors: Andriy L. Shidlich Categories: math.CA Comments: 23 pages, in Russian MSC-class: 41A46 ACM-class: G.1.2 \\ We obtain order estimates in the spaces $L_p$ of the best $n$-term trigonometric orthogonal approximations of the classes ${\cal F}_{q}^{\psi}$ of periodic functions, whose Fourier coefficients decrease faster then any power function. We also obtain order estimates of the quantities of approximations by $n$-term Greedy approximants of such classes in the spaces $L_p$. \\ ( http://arxiv.org/abs/1302.7130 , 17kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7141 Date: Thu, 28 Feb 2013 10:27:47 GMT (23kb) Title: The union-closed sets conjecture almost holds for almost all random bipartite graphs Authors: Henning Bruhn and Oliver Schaudt Categories: math.CO \\ Frankl's union-closed sets conjecture states that in every finite union-closed set of sets, there is an element that is contained in at least half of the member-sets (provided there are at least two members). The conjecture has an equivalent formulation in terms of graphs: In every bipartite graph with least one edge, both colour classes contain a vertex belonging to at most half of the maximal stable sets. We prove that, for every fixed edge-probability, almost every random bipartite graph almost satisfies Frankl's conjecture. \\ ( http://arxiv.org/abs/1302.7141 , 23kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7146 Date: Thu, 28 Feb 2013 10:47:12 GMT (31kb) Title: Dispersive perturbations of Burgers and hyperbolic equations I : local theory Authors: Felipe Linares, Didier Pilod and Jean-Claude Saut Categories: math.AP Comments: 31 pages \\ The aim of this paper is to show how a weakly dispersive perturbation of the inviscid Burgers equation improve (enlarge) the space of resolution of the local Cauchy problem. More generally we will review several problems arising from weak dispersive perturbations of nonlinear hyperbolic equations or systems. \\ ( http://arxiv.org/abs/1302.7146 , 31kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7156 Date: Thu, 28 Feb 2013 11:19:14 GMT (17kb) Title: Basic properties of ultrafunctions Authors: Vieri Benci and Lorenzo Luperi Baglini Categories: math.FA Comments: 25 pages MSC-class: 26E30, 26E35, 46F30 \\ Ultrafunctions are a particular class of functions defined on a non-Archimedean field. They provide generalized solutions to functional equations which do not have any solutions among the real functions or the distributions. In this paper we analyze sistematically some basic properties of the spaces of ultrafunctions. \\ ( http://arxiv.org/abs/1302.7156 , 17kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7159 Date: Thu, 28 Feb 2013 12:03:56 GMT (3371kb,D) Title: Noise-induced canard and mixed-mode oscillations in large stochastic networks with multiple timescales Authors: Jonathan Touboul and Maciej Krupa and Mathieu Desroches Categories: math.DS nlin.CD \\ We investigate the dynamics of large stochastic networks with different timescales and nonlinear mean-field interactions. After deriving the limit equations for a general class of network models, we apply our results to the celebrated Wilson-Cowan system with two populations with or without slow adaptation, paradigmatic example of nonlinear mean-field network. This system has the property that the dynamics of the mean of the solution exactly satisfies an ODE. This reduction allows to show that in the mean-field limit and in multiple populations with multiple timescales, noise induces canard explosions and Mixed-Mode Oscillations on the mean of the solution. This sheds new light on the qualitative effects of noise and sensitivity to precise noise values in large stochastic networks. We further investigate finite-sized networks and show that systematic differences with the mean-field limits arise in bistable regimes (where random switches between different attractors occur) or in mixed-mode oscillations, were the finite-size effects induce early jumps due to the sensitivity of the attractor. \\ ( http://arxiv.org/abs/1302.7159 , 3371kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7163 Date: Thu, 28 Feb 2013 12:14:51 GMT (37kb) Title: Highly symmetric 2-plane fields on 5-manifolds and Heisenberg 5-group holonomy Authors: Travis Willse Categories: math.DG Comments: 36 pages \\ Nurowski showed that any generic 2-plane field $D$ on a 5-manifold $M$ determines a natural conformal structure $c_D$ on $M$; these conformal structures are exactly those (on oriented $M$) whose normal conformal holonomy is contained in the (split, real) simple Lie group $G_2$. Graham and Willse showed that for real-analytic $D$ the same holds for the holonomy of the real-analytic Fefferman-Graham ambient metric of $c_D$, and that both holonomy groups are equal to $G_2$ for almost all $D$. We investigate here independently interesting plane fields for which the associated holonomy groups are a proper subset of $G_2$. Cartan solved the local equivalence problem for 2-plane fields $D$ and constructed the fundamental curvature tensor $A$ for these objects. He furthermore described locally all $D$ whose infinitesimal symmetry algebra has rank at least 6 and gave a local quasi-normal form, depending on a single function of one variable, for those that satisfy a natural degeneracy condition on $A$. We show that the conformal structures $c_D$ induced by these plane fields via Nurowski's construction are always almost Einstein, that we can write their ambient metrics explicitly, and that the holonomy groups associated to $c_D$ are always the Heisenberg 5-group, which here acts indecomposably but not irreducibly. We show also that similar results hold for the related class of 2-plane fields defined on suitable jet spaces by the ODEs $z'(x) = F(y"(x))$ satisfying a simple genericity condition. \\ ( http://arxiv.org/abs/1302.7163 , 37kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7189 Date: Thu, 28 Feb 2013 13:19:28 GMT (37kb) Title: On the stability of the boundary trace of the polynomial L^2-projection on triangles and tetrahedra (extended version) Authors: Jens Markus Melenk and Tobias Wurzer Categories: math.NA Report-no: ASC-report 25/2012 \\ For the reference triangle or tetrahedron $T$, we study the stability properties of the $L^2(T)$-projection $\Pi_N$ onto the space of polynomials of degree $N$. We show $\|\Pi_N u\|_{L^2(\partial T)}^2 \leq C \|u\|_{L^2(T)} \|u\|_{H^1(T)}$. This implies optimal convergence rates for the approximation error $\|u - \Pi_N u\|_{L^2(\partial T)}$ for all $u \in H^k(T)$, $k > 1/2$. \\ ( http://arxiv.org/abs/1302.7189 , 37kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7198 Date: Thu, 28 Feb 2013 14:06:59 GMT (69kb) Title: Difference Galois theory of linear differential equations Authors: Lucia Di Vizio, Charlotte Hardouin and Michael Wibmer Categories: math.AC math.AG math.DS math.RA Comments: 42 pages MSC-class: 12H05, 12H10, 12F10 \\ We develop a Galois theory for linear differential equations equipped with the action of an endomorphism. This theory is aimed at studying the difference algebraic relations among the solutions of a linear differential equation. The Galois groups here are linear difference algebraic groups, i.e., matrix groups defined by algebraic difference equations. \\ ( http://arxiv.org/abs/1302.7198 , 69kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7199 Date: Thu, 28 Feb 2013 14:08:45 GMT (5kb) Title: A strong law of large numbers for branching processes: almost sure spine events Authors: Simon C. Harris and Matthew I. Roberts Categories: math.PR Comments: 6 pages MSC-class: 60J80 \\ We demonstrate a novel strong law of large numbers for branching processes, with a simple proof via measure-theoretic manipulations and spine theory. Roughly speaking, any sequence of events that eventually occurs almost surely for the spine entails the almost sure convergence of a certain sum over particles in the population. \\ ( http://arxiv.org/abs/1302.7199 , 5kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7203 Date: Thu, 28 Feb 2013 14:13:07 GMT (28kb) Title: Accurate eigenvalue decomposition of arrowhead matrices and applications Authors: Nevena Jakovcevic Stor, Ivan Slapnicar and Jesse L. Barlow Categories: math.NA MSC-class: 65F15 \\ We present a new algorithm for solving an eigenvalue problem for a real symmetric arrowhead matrix. The algorithm computes all eigenvalues and all components of the corresponding eigenvectors with high relative accuracy in $O(n^{2})$ operations. The algorithm is based on a shift-and-invert approach. Double precision is eventually needed to compute only one element of the inverse shifted matrix. Each eigenvalue and the corresponding eigenvector can be computed separately, which makes the algorithm adaptable for parallel computing. Our results extend to Hermitian arrowhead matrices, real symmetric diagonal-plus-rank-one matrices and singular value decomposition of real triangular arrowhead matrices. \\ ( http://arxiv.org/abs/1302.7203 , 28kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7204 Date: Mon, 25 Feb 2013 16:28:10 GMT (194kb) Title: Polynomial over Associative D-Algebra Authors: Aleks Kleyn Categories: math.GM Comments: English text - 20 pages; Russian text - 21 pages MSC-class: 16-02, 12-02 \\ In the paper I considered algebra of polynomials over associative D-algebra with unit. Using the tensor notation allows to simplify the representation of polynomial. I considered questions related to divisibility of polynomial of any power over polynomial of power 1. \\ ( http://arxiv.org/abs/1302.7204 , 194kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7207 Date: Thu, 28 Feb 2013 14:34:52 GMT (27kb) Title: G-convergence of linear differential equations Authors: Marcus Waurick Categories: math.FA Comments: 27 pages Report-no: AN-03-2013 MSC-class: 34L99, 34E13, 34A08, 35B27, 35Q61, 45A05 \\ We discuss $G$-convergence of linear integro-differential-algebaric equations in Hilbert spaces. We show under which assumptions it is generic for the limit equation to exhibit memory effects. Moreover, we investigate which classes of equations are closed under the process of $G$-convergence. The results have applications to the theory of homogenization. As an example we treat Maxwell's equation with the Drude-Born-Fedorov constitutive relation. \\ ( http://arxiv.org/abs/1302.7207 , 27kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7208 Date: Sat, 23 Feb 2013 21:49:38 GMT (45kb) Title: Sharper estimates for Chebyshev's functions $\vartheta$ and $\psi$ Authors: Sadegh Nazardonyavi, Semyon Yakubovich Categories: math.NT Comments: After finishing this article we realized that some of the theorems of this article was found by Pierre Dusart. In this article we give the proofs with more details. The proof essentially similar to those of Rosser and Shoenfeld papers in this area \\ In this article we present some improved results for Chebyshev's functions $\vartheta$ and $\psi$ using the new zero-free region obtained by H. Kadiri and the calculated the first $10^{13}$ zeros of the Riemann zeta function on the critical line by Xavier Gourdon. The methods in the proofs are similar to those of Rosser-Shoenfeld papers on this subject. \\ ( http://arxiv.org/abs/1302.7208 , 45kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7209 Date: Thu, 28 Feb 2013 14:39:51 GMT (20kb) Title: Exponential Stability for Linear Evolutionary Equations Authors: Sascha Trostorff Categories: math.AP math.FA Report-no: MATH-AN-04-2013 MSC-class: 35B35, 35B40, 47N20, 35F16 \\ We give an approach to exponential stability within the framework of evolutionary equations due to [R. Picard. A structural observation for linear material laws in classical mathematical physics. Math. Methods Appl. Sci., 32(14):1768-1803,2009]. We derive sufficient conditions for exponential stability in terms of the material law operator, which is defined via an analytic and bounded operator-valued function and give an estimate for the expected decay rate. The results are illustrated by three examples: differential-algebraic equations, partial differential equations with finite delay and parabolic integro-differential equations. \\ ( http://arxiv.org/abs/1302.7209 , 20kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7213 Date: Thu, 28 Feb 2013 14:51:11 GMT (463kb,D) Title: Gromov width of non-regular coadjoint orbits of U(n), SO(2n) and SO(2n+1) Authors: Milena Pabiniak Categories: math.SG Comments: 23 pages, 14 figures MSC-class: 53D99 \\ Let G be a compact connected Lie group G and T its maximal torus. The coadjoint orbit O_lambda through lambda in Lie(T)^* is canonically a symplectic manifold. Therefore we can ask the question about its Gromov width. In many known cases the Gromov width is exactly the minimum over the set {< alpha_j^{\vee},lambda > ; alpha_j^{\vee} a coroot and < alpha_j^{\vee},lambda > positive}. We show that the Gromov width of coadjoint orbits of the unitary group and of most of the coadjoint orbits of the special orthogonal group is at least the above minimum. The proof uses the torus action coming from the Gelfand-Tsetlin system. \\ ( http://arxiv.org/abs/1302.7213 , 463kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7219 Date: Thu, 28 Feb 2013 14:59:25 GMT (29kb) Title: Nonlocal porous medium equation: Barenblatt profiles and other weak solutions Authors: Piotr Biler, Cyril Imbert (CEREMADE), Grzegorz Karch Categories: math.AP Comments: 28 pages \\ A degenerate nonlinear nonlocal evolution equation is considered; it can be understood as a porous medium equation whose pressure law is nonlinear and nonlocal. We show the existence of sign changing weak solutions to the corresponding Cauchy problem. Moreover, we construct explicit compactly supported self-similar solutions which generalize Barenblatt profiles --- the well-known solutions of the classical porous medium equation. \\ ( http://arxiv.org/abs/1302.7219 , 29kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7222 Date: Thu, 28 Feb 2013 15:03:40 GMT (32kb) Title: Homogenization of high-contrast and non symmetric conductivities for non periodic columnar structures Authors: Mohamed Camar-Eddine (IRMAR, INSA Rennes), Laurent Pater (IRMAR) Categories: math.AP Comments: 28 pages \\ In this paper we determine, in dimension three, the effective conductivities of non periodic high-contrast two-phase cylindrical composites, placed in a constant magnetic field, without any assumption on the geometry of their cross sections. Our method, in the spirit of the H-convergence of Murat-Tartar, is based on a compactness result and the cylindrical nature of the microstructure. The homogenized laws we obtain extend those of the periodic fibre-reinforcing case of [M. Briane and L. Pater. Homogenization of high-contrast two-phase conductivities perturbed by a magnetic field. Comparison between dimension two and dimension three. J. Math. Anal. Appl., 393 (2) (2012), 563 -589] to the case of periodic and non periodic composites with more general transversal geometries. \\ ( http://arxiv.org/abs/1302.7222 , 32kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7223 Date: Thu, 28 Feb 2013 15:09:22 GMT (14kb) Title: Restriction Theorems for Principal Bundles and Some Consequences Authors: Sudarshan Gurjar Categories: math.AG Comments: 13 pages MSC-class: 14D06, 14F05 \\ The aim of this paper is to give a proof of the restriction theorems for principal bundles with a reductive algebraic group as structure group in arbitrary characteristic. Let $G$ be a reductive algebraic group over any field $k=\bar{k}$, let $X$ be a smooth projective variety over $k$, let $H$ be a very ample line bundle on $X$ and let $E$ be a semistable (resp. stable) principal $G$-bundle on $X$ w.r.t. $H$. The main result of this paper is that the restriction of $E$ to a general smooth curve which is a complete intersection of ample hypersurfaces of sufficiently high degree's is again semistable (resp. stable). \\ ( http://arxiv.org/abs/1302.7223 , 14kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7227 Date: Thu, 28 Feb 2013 15:12:29 GMT (69kb) Title: Randomly Trapped Random Walks Authors: G\'erard Ben Arous, Manuel Cabezas, Ji\v{r}\'i \v{C}ern\'y, Roman Royfman Categories: math.PR Comments: 2 figures, 56 pages MSC-class: 60K37, 60F17 \\ We introduce a general model of trapping for random walks on graphs. We give the possible scaling limits of these "Randomly Trapped Random Walks" on Z. These scaling limits include the well known Fractional Kinetics process, the Fontes-Isopi-Newman singular diffusion as well as a new broad class we call Spatially Subordinated Brownian Motions. We give sufficient conditions for convergence and illustrate these on two important examples. \\ ( http://arxiv.org/abs/1302.7227 , 69kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7228 Date: Thu, 28 Feb 2013 15:12:31 GMT (9kb) Title: Applications of a new separator theorem for string graphs Authors: Jacob Fox and Janos Pach Categories: math.CO cs.CG cs.DM Comments: 7 pages MSC-class: 05C62, 05C10, 05C35, 05C55, 05D10 \\ An intersection graph of curves in the plane is called a string graph. Matousek almost completely settled a conjecture of the authors by showing that every string graph of m edges admits a vertex separator of size O(\sqrt{m}\log m). In the present note, this bound is combined with a result of the authors, according to which every dense string graph contains a large complete balanced bipartite graph. Three applications are given concerning string graphs G with n vertices: (i) if K_t is not a subgraph of G for some t, then the chromatic number of G is at most (\log n)^{O(\log t)}; (ii) if K_{t,t} is not a subgraph of G, then G has at most t(\log t)^{O(1)}n edges,; and (iii) a lopsided Ramsey-type result, which shows that the Erdos-Hajnal conjecture almost holds for string graphs. \\ ( http://arxiv.org/abs/1302.7228 , 9kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7229 Date: Thu, 28 Feb 2013 15:15:28 GMT (33kb) Title: A p-adic Eisenstein measure for vector-weight automorphic forms Authors: Ellen Eischen Categories: math.NT \\ We construct a p-adic Eisenstein measure with values in the space of vector-weight p-adic automorphic forms on certain unitary groups. This measure allows us to p-adically interpolate special values of certain vector-weight C-infinity automorphic forms, including Eisenstein series, as their weights vary. \\ ( http://arxiv.org/abs/1302.7229 , 33kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7235 Date: Thu, 28 Feb 2013 15:38:03 GMT (14kb) Title: Existence and Destruction of Kantorovich Main Continuous Solutions of Nonlinear Integral Equations Authors: Denis N. Sidorov Categories: math.OC math-ph math.MP MSC-class: 45D05, 35B44, 49K15 ACM-class: G.1.9 \\ The sufficient conditions are obtained for existence of the main solution of the nonlinear Volterra integral equation of the second kind on the semi-axis and on a finite interval. The method for computation of this boundary interval is designed. Beyond such integral the solution has the blow-up. The efficiency of proposed technique is demonstrated on concrete examples. \\ ( http://arxiv.org/abs/1302.7235 , 14kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7237 Date: Thu, 28 Feb 2013 15:56:30 GMT (17kb) Title: Stability of Asymptotics of Christoffel-Darboux Kernels Authors: Jonathan Breuer, Yoram Last, and Barry Simon Categories: math.SP math-ph math.CA math.MP \\ We study the stability of convergence of the Christoffel-Darboux kernel, associated with a compactly supported measure, to the sine kernel, under perturbations of the Jacobi coefficients of the measure. We prove stability under variations of the boundary conditions and stability in a weak sense under $\ell^1$ and random $\ell^2$ diagonal perturbations. We also show that convergence to the sine kernel at $x$ implies that $\mu(\{x\})=0$. \\ ( http://arxiv.org/abs/1302.7237 , 17kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7238 Date: Mon, 25 Feb 2013 16:57:31 GMT (31kb) Title: On Bubbling of Linearly Ordered Sets. Part I Authors: Maria Viktorovna Droganova, Valentin Vankov Iliev Categories: math.GN Comments: 38 pages MSC-class: 06A11, 06A75, 54F05 \\ Given a loset I, every surjective map p: A ---> I endows the set A with a structure of preordered set by "replacing" the elements of I with their inverse images via p considered as "bubbles" (sets endowed with an equivalence relation), lifting the structure of loset on A, and "agglutinating" this structure with the bubbles. Every bubbling A of a structure of loset I is a structure of preordered set A (not necessarily complete) whose preorder has negatively transitive asymmetric part and every such structure on a given set A can be obtained by bubbling up of certain structure of a loset I, intrinsically encoded in A. In other words, the difference between linearity and negative transitivity is constituted of bubbles. As a consequence of this characterization, under certain natural topological conditions on the preordered set A furnished with its interval topology, the existence of a continuous generalized utility function on A is proved. \\ ( http://arxiv.org/abs/1302.7238 , 31kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7247 Date: Thu, 28 Feb 2013 16:30:16 GMT (151kb) Title: Stopping strategies and gambler's ruin problem Authors: T.J. van Uem Categories: math.PR Comments: 15 pages \\ We obtain absorption probabilities and expected time until absorption for different stopping strategies in gambler's ruin problem using the concept of multiple function barriers \\ ( http://arxiv.org/abs/1302.7247 , 151kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7249 Date: Thu, 28 Feb 2013 16:39:26 GMT (234kb) Title: The dynamics of semigroups of transcendental entire functions Authors: Dinesh Kumar and Sanjay Kumar Categories: math.DS Comments: 7 pages, work in progress MSC-class: 37F10, 30D05 \\ In this paper we consider the dynamics associated with an arbitrary semigroup of transcendental entire functions. Fatou-Julia theory is used to investigate the dynamics of these semigroups. Several results of the dynamics associated with iteration of a transcendental entire function have been extended to transcendental semigroup case. We also investigate the dynamics of conjugate semigroups and Abelian transcendental semigroups. \\ ( http://arxiv.org/abs/1302.7249 , 234kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7252 Date: Thu, 28 Feb 2013 16:44:23 GMT (17kb) Title: Stability results for some fully nonlinear eigenvalue estimates Authors: Francesco Della Pietra and Nunzia Gavitone Categories: math.AP \\ In this paper, we give some stability estimates for the Faber-Krahn inequality relative to the eigenvalues of Hessian operators \\ ( http://arxiv.org/abs/1302.7252 , 17kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7261 Date: Thu, 28 Feb 2013 17:12:23 GMT (28kb) Title: On the structure of phase transition maps for three or more coexisting phases Authors: Nicholas D. Alikakos Categories: math.AP math.DG Comments: 22 pages, 6 figures MSC-class: 35J47, 49Q20, 53A10 \\ This paper is partly based on a lecture delivered by the author at the ERC workshop "Geometric Partial Differential Equations" held in Pisa in September 2012. What is presented here is an expanded version of that lecture. \\ ( http://arxiv.org/abs/1302.7261 , 28kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7264 Date: Thu, 28 Feb 2013 17:16:53 GMT (961kb) Title: A Practical Cooperative Multicell MIMO-OFDMA Network Based on Rank Coordination Authors: Bruno Clerckx, Heunchul Lee, Young-Jun Hong and Gil Kim Categories: cs.IT math.IT Comments: IEEE Transactions or Wireless Communications, Accepted for Publication \\ An important challenge of wireless networks is to boost the cell edge performance and enable multi-stream transmissions to cell edge users. Interference mitigation techniques relying on multiple antennas and coordination among cells are nowadays heavily studied in the literature. Typical strategies in OFDMA networks include coordinated scheduling, beamforming and power control. In this paper, we propose a novel and practical type of coordination for OFDMA downlink networks relying on multiple antennas at the transmitter and the receiver. The transmission ranks, i.e.\ the number of transmitted streams, and the user scheduling in all cells are jointly optimized in order to maximize a network utility function accounting for fairness among users. A distributed coordinated scheduler motivated by an interference pricing mechanism and relying on a master-slave architecture is introduced. The proposed scheme is operated based on the user report of a recommended rank for the interfering cells accounting for the receiver interference suppression capability. It incurs a very low feedback and backhaul overhead and enables efficient link adaptation. It is moreover robust to channel measurement errors and applicable to both open-loop and closed-loop MIMO operations. A 20% cell edge performance gain over uncoordinated LTE-A system is shown through system level simulations. \\ ( http://arxiv.org/abs/1302.7264 , 961kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7265 Date: Thu, 28 Feb 2013 17:23:12 GMT (21kb) Title: An Inverse problem for the Magnetic Schr\"odinger Operator on a Half Space with partial data Authors: Valter Pohjola Categories: math.AP math-ph math.MP Comments: This is the article version of a Licentiate thesis. arXiv admin note: text overlap with arXiv:1104.0789 by other authors MSC-class: 35R30 \\ In this paper we prove uniqueness for an inverse boundary value problem for the magnetic Schr\"odinger equation in a half space, with partial data. We prove that the curl of the magnetic potential $A$, when $A\in W_{comp}^{1,\infty}(\ov{\R^3_{-}},\R^3)$, and the electric pontetial $q \in L_{comp}^{\infty}(\ov{\R^3_{-}},\C)$ are uniquely determined by the knowledge of the Dirichlet-to-Neumann map on parts of the boundary of the half space. \\ ( http://arxiv.org/abs/1302.7265 , 21kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7267 Date: Thu, 28 Feb 2013 17:42:14 GMT (28kb) Title: Rank change in Poisson dynamical systems Authors: Vivek Narayanan and P. J. Morrison Categories: math-ph math.MP \\ It is shown in this paper how a connection may be made between the symmetry generators of the Hamiltonian (or potential) invariant under a symmetry group $G$, and the subcasimirs that come about when the rank of the Poisson structure of a dynamical system drops by an even integer. This {\em kinematics-dynamics} connection is made by using the algebraic geometry of the orbit space in the vicinity of rank change, and the extra null eigenvectors of the mass matrix (Hessian with respect to symmetry generators) of the Hamiltonian (or potential). Some physical interpretations of this point of view include a control-theoretic prescription to study stability on various symplectic leaves of the Poisson structure. Methods of Invariant Theory are utilized to provide parametrization for the leaves of a Poisson dynamical system for the case where a compact Lie group acts properly on the phase space, which is assumed to be modeled by Poisson geometry. \\ ( http://arxiv.org/abs/1302.7267 , 28kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7271 Date: Tue, 5 Feb 2013 12:41:49 GMT (13kb) Title: On the Orbits of the Magnetized Kepler Problems in Dimension $2k+1$ Authors: Zhanqiang Bai, Guowu Meng, Erxiao Wang Categories: math-ph math.MP Comments: 13 pages \\ It is demonstrated that, for the recently introduced classical magnetized Kepler problems in dimension $2k+1$, the non-colliding orbits in the "external configuration space" $\mathbb R^{2k+1}\setminus\{\mathbf 0\}$ are all conics, moreover, a conic orbit is an ellipse, a parabola, and a branch of a hyperbola according as the total energy is negative, zero, and positive. It is also demonstrated that the Lie group ${\mr {SO}}^+(1,2k+1)\times {\bb R}_+$ acts transitively on both the set of oriented elliptic orbits and the set of oriented parabolic orbits. \\ ( http://arxiv.org/abs/1302.7271 , 13kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7282 Date: Thu, 28 Feb 2013 18:49:24 GMT (185kb) Title: An almost existence theorem for non-contractible periodic orbits in cotangent bundles Authors: Pedro A. S. Salom\~ao (IME USP), Joa Weber (UNICAMP) Categories: math.SG math.DS Comments: 9 pages, 4 figures MSC-class: 37-06 (Primary) 70H12 (Secondary) \\ Assume M is a closed connected smooth manifold and H:T^*M->R a smooth proper function bounded from below. Suppose the sublevel set {H=d the level set {H=s} carries a periodic orbit z of the Hamiltonian system (T^*M,\omega_0,H) representing \alpha. Examples show that the condition that {H1$; the function has an $A_1$ majorant; for any $p>1$ the function belongs to $L^p_w$ for some $A_p$ weight $w$. We also examine the case of functions defined on ${\mathbb R}^n$ and give characterizations of the union of $L^p_w$ over $w$ in $A_p$ and when a function has an $A_1$ majorant on all of ${\mathbb R}^n$. \\ ( http://arxiv.org/abs/1302.7315 , 18kb) %-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%- ------------------------------------------------------------------------------ \\ arXiv:1301.1977 (*cross-listing*) Date: Wed, 9 Jan 2013 21:00:03 GMT (1118kb,D) Title: M-Theoretic Derivations of 4d-2d Dualities: From a Geometric Langlands Duality for Surfaces, to the AGT Correspondence, to Integrable Systems Authors: Meng-Chwan Tan Categories: hep-th math.AG math.QA math.RT nlin.SI Comments: 188 pp + appendix \\ In Part I, we extend our analysis in [arXiv:0807.1107], and show that a mathematically conjectured geometric Langlands duality for complex surfaces in [1], and its generalizations -- which relate some cohomology of the moduli space of certain ("ramified") G-instantons to the integrable representations of the Langlands dual of certain affine (sub) G-algebras, where G is any compact Lie group -- can be derived, purely physically, from the principle that the spacetime BPS spectra of string-dual M-theory compactifications ought to be equivalent. In Part II, to the setup in Part I, we introduce Omega-deformation via fluxbranes and add half-BPS boundary defects via M9-branes, and show that the celebrated AGT correspondence in [2, 3], and its generalizations -- which essentially relate, among other things, some equivariant cohomology of the moduli space of certain ("ramified") G-instantons to the integrable representations of the Langlands dual of certain affine W-algebras -- can likewise be derived from the principle that the spacetime BPS spectra of string-dual M-theory compactifications ought to be equivalent. In Part III, we consider various limits of our setup in Part II, and connect our story to chiral fermions and integrable systems. Among other things, we derive the Nekrasov-Okounkov conjecture in [4] -- which relates the topological string limit of the dual Nekrasov partition function for pure G to the integrable representations of the Langlands dual of an affine G-algebra -- and also demonstrate that the Nekrasov-Shatashvili limit of the "fully-ramified" Nekrasov instanton partition function for pure G is a simultaneous eigenfunction of the quantum Toda Hamiltonians associated with the Langlands dual of an affine G-algebra. Via the case with matter, we also make contact with Hitchin systems and the "ramified" geometric Langlands correspondence for curves. \\ ( http://arxiv.org/abs/1301.1977 , 1118kb) ------------------------------------------------------------------------------ \\ arXiv:1302.3227 (*cross-listing*) Date: Wed, 13 Feb 2013 21:00:05 GMT (780kb,D) Title: A Topological Chern-Simons Sigma Model and New Invariants of Three-Manifolds Authors: Yuan Luo, Meng-Chwan Tan Categories: hep-th math.GT math.QA Comments: 44 pages \\ We construct a topological Chern-Simons sigma model on a Riemannian three-manifold M with gauge group G whose hyperkahler target space X is equipped with a G-action. Via a perturbative computation of its partition function, we obtain new topological invariants of M that define new weight systems which are characterized by both Lie algebra structure and hyperkahler geometry. In canonically quantizing the sigma model, we find that the partition function on certain M can be expressed in terms of Chern-Simons knot invariants of M and the intersection number of certain G-equivariant cycles in the moduli space of G-covariant maps from M to X. We also construct supersymmetric Wilson loop operators, and via a perturbative computation of their expectation value, we obtain new knot invariants of M that define new knot weight systems which are also characterized by both Lie algebra structure and hyperkahler geometry. \\ ( http://arxiv.org/abs/1302.3227 , 780kb) ------------------------------------------------------------------------------ \\ arXiv:1302.6716 (*cross-listing*) Date: Wed, 27 Feb 2013 10:45:44 GMT (28kb,D) Title: "Quantum" linearization of Painlev\'{e} equations as a component of their $L,A$ pairs Authors: Bulat Suleimanov Categories: nlin.SI hep-th math-ph math.CA math.MP quant-ph Comments: 10 pages Journal-ref: Ufa Mathematical Journal 2012, V.2, p.127-136 ( translaited from Ufimski Mathematicheskii Jhurnal, 2012, v.2, p.127-135 (in russian)) \\ The procedure of the "quantum" linearization of the Hamiltonian ordinary differential equations with one degree of freedom is introduced. It is offered to be used for the classification of integrable equations of the Painleve type. By this procedure and all natural numbers $n$ we construct the solutions $\Psi(\hbar,t,x,n)$ to the non-stationary Shr\"{o}dinger equation with the Hamiltonian $H = (p^2+q^2)/2$ which tend to zero as $x\to\pm\infty$. On the curves $x=q_n (\hbar, t) $ defined by the old Bohr-Sommerfeld quantization rule the solutions satisfy the relation $i\hbar \Psi '_x\equiv p_n (\hbar, t) \Psi $, where $p_n (\hbar, t) = (q_n (\hbar, t)) '_t $ is the classical momentum corresponding to the harmonic $q_n (\hbar, t) $. \\ ( http://arxiv.org/abs/1302.6716 , 28kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7047 (*cross-listing*) Date: Thu, 28 Feb 2013 00:53:02 GMT (203kb,D) Title: Nonuniqueness of the C operator in PT-symmetric quantum mechanics Authors: Carl M. Bender and Mariagiovanna Gianfreda Categories: hep-th math-ph math.MP quant-ph Comments: 16 pages, 5 figures \\ The C operator in PT-symmetric quantum mechanics satisfies a system of three simultaneous algebraic operator equations, $C^2=1$, $[C,PT]=0$, and $[C,H]=0$. These equations are difficult to solve exactly, so perturbative methods have been used in the past to calculate C. The usual approach has been to express the Hamiltonian as $H=H_0+\epsilon H_1$, and to seek a solution for C in the form $C=e^Q P$, where $Q=Q(q,p)$ is odd in the momentum p, even in the coordinate q, and has a perturbation expansion of the form $Q=\epsilon Q_1+\epsilon^3 Q_3+\epsilon^5 Q_5+\ldots$. [In previous work it has always been assumed that the coefficients of even powers of $\epsilon$ in this expansion would be absent because their presence would violate the condition that $Q(p,q)$ is odd in p.] In an earlier paper it was argued that the C operator is not unique because the perturbation coefficient $Q_1$ is nonunique. Here, the nonuniqueness of C is demonstrated at a more fundamental level: It is shown that the perturbation expansion for Q actually has the more general form $Q=Q_0+\epsilon Q_1+\epsilon^2 Q_2+\ldots$ in which {\it all} powers and not just odd powers of $\epsilon$ appear. For the case in which $H_0$ is the harmonic-oscillator Hamiltonian, $Q_0$ is calculated exactly and in closed form and it is shown explicitly to be nonunique. The results are verified by using powerful summation procedures based on analytic continuation. It is also shown how to calculate the higher coefficients in the perturbation series for Q. \\ ( http://arxiv.org/abs/1302.7047 , 203kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7057 (*cross-listing*) Date: Thu, 28 Feb 2013 02:11:58 GMT (10kb) Title: A new integrable problem with a quartic integral in the dynamics of a rigid body Authors: Hamad M. Yehia and Adel A. Elmandouh Categories: nlin.SI math-ph math.MP Comments: This work will appear shortly in "Journal of Physics A: Mathematical and Theoretical" \\ We consider the problem of motion of a rigid body about a fixed point under the action of an axisymmetric combination of potential and gyroscopic forces. We introduce a new integrable case, valid on zero level of the cyclic integral, that generalizes the known case of motion of a body in liquid due to Chaplygin and its subsequent generalization by Yehia. Apart from certain singular potential terms, the new case involves finite potential and gyroscopic forces, which admit physical interpretation as resulting from interaction of mass, magnetized parts and electric charges on the body with gravitational, electric and magnetic fields. \\ ( http://arxiv.org/abs/1302.7057 , 10kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7070 (*cross-listing*) Date: Thu, 28 Feb 2013 03:43:08 GMT (301kb) Title: Sound localization using compressive sensing Authors: Hong Jiang, Boyd Mathews and Paul Wilford Categories: cs.SD cs.IT math.IT Comments: 9 pages, 7 figures Journal-ref: Proc. SENSORNETS, 2012, pp.159-166 \\ In a sensor network with remote sensor devices, it is important to have a method that can accurately localize a sound event with a small amount of data transmitted from the sensors. In this paper, we propose a novel method for localization of a sound source using compressive sensing. Instead of sampling a large amount of data at the Nyquist sampling rate in time domain, the acoustic sensors take compressive measurements integrated in time. The compressive measurements can be used to accurately compute the location of a sound source. \\ ( http://arxiv.org/abs/1302.7070 , 301kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7085 (*cross-listing*) Date: Thu, 28 Feb 2013 05:05:34 GMT (740kb,D) Title: Maximum Differential Coloring of Caterpillars and Spiders Authors: A. Das, M. Geyer, M. Kaufmann, S. Kobourov, S. Veeramoni Categories: cs.DM math.CO Comments: 12 pages. 6 pages appendix, 10 figures \\ We study the maximum differential coloring problem, where an n- vertex graph must be labeled with the numbers 1, ..., n such that the minimum difference between the two labels of any edge is maximized. As it is NP-Hard to find the optimal labels for general graphs, we consider special sub-classes: caterpillars, spiders, and extended stars. We first prove new upper bounds for maximum differential coloring for spiders and regular caterpillars. Using these new bounds, we prove that the Miller-Pritikin labeling scheme for forests is optimal for regular caterpillars and for spider graphs. We then present a label- ing scheme for general caterpillars which is at most \Delta + O(1) away from the optimal labeling where \Delta is the maximum number of legs of any spine vertex in the caterpillar. Finally we present new optimal labeling schemes for regular caterpillars and for sub-classes of spider graphs. \\ ( http://arxiv.org/abs/1302.7085 , 740kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7111 (*cross-listing*) Date: Thu, 28 Feb 2013 08:40:40 GMT (43kb) Title: Syllogisms in Rudimentary Linear Logic, Diagrammatically Authors: Ruggero Pagnan Categories: cs.LO math.LO \\ We present a reading of the traditional syllogistics in a fragment of the propositional intuitionistic multiplicative linear logic and prove that with respect to a diagrammatic logical calculus that we introduced in a previous paper, a syllogism is provable in such a fragment if and only if it is diagrammatically provable. We extend this result to syllogistics with complemented terms \`a la De Morgan, with respect to a suitable extension of the diagrammatic reasoning system for the traditional case and a corresponding reading of such De Morgan style syllogistics in the previously referred to fragment of linear logic. \\ ( http://arxiv.org/abs/1302.7111 , 43kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7135 (*cross-listing*) Date: Thu, 28 Feb 2013 10:10:41 GMT (15kb) Title: Fields and Laplacians on Quantum Geometries Authors: Johannes Th\"urigen Categories: gr-qc hep-th math-ph math.MP Comments: 3 pages, submitted to the Proceedings of the 13th Marcel Grossmann Meeting (MG13), Stockholm, July 1-7, 2012 Report-no: AEI-2013-063 \\ In fundamentally discrete approaches to quantum gravity such as loop quantum gravity, spin-foam models, group field theories or Regge calculus observables are functions on discrete geometries. We present a bra-ket formalism of function spaces and discrete calculus on abstract simplicial complexes equipped with geometry and apply it to the mentioned theories of quantum gravity. In particular we focus on the quantum geometric Laplacian and discuss as an example the expectation value of the heat kernel trace from which the spectral dimension follows. \\ ( http://arxiv.org/abs/1302.7135 , 15kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7142 (*cross-listing*) Date: Thu, 28 Feb 2013 10:31:06 GMT (83kb) Title: Holonomy Operator and Quantization Ambiguities on Spinor Space Authors: Etera R. Livine Categories: gr-qc math-ph math.MP Comments: 14 pages \\ We construct the holonomy-flux operator algebra in the recently developed spinor formulation of loop gravity. We show that, when restricting to SU(2)-gauge invariant operators, the familiar grasping and Wilson loop operators are written as composite operators built from the gauge-invariant `generalized ladder operators' recently introduced in the U(N) approach to intertwiners and spin networks. We comment on quantization ambiguities that appear in the definition of the holonomy operator and use these ambiguities as a toy model to test a class of quantization ambiguities which is present in the standard regularization and definition of the Hamiltonian constraint operator in loop quantum gravity. \\ ( http://arxiv.org/abs/1302.7142 , 83kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7144 (*cross-listing*) Date: Thu, 28 Feb 2013 10:44:53 GMT (19kb) Title: Multi-time Lagrangian 1-forms for families of B\"acklund transformations. Toda-type systems Authors: Raphael Boll, Matteo Petrera, Yuri B. Suris Categories: nlin.SI math-ph math.MP Comments: 27 pp \\ General Lagrangian theory of discrete one-dimensional integrable systems is illustrated by a detailed study of B\"acklund transformations for Toda-type systems. Commutativity of B\"acklund transformations is shown to be equivalent to consistency of the system of discrete multi-time Euler-Lagrange equations. The precise meaning of the commutativity in the periodic case, when all maps are double-valued, is established. It is shown that gluing of different branches is governed by the so called superposition formulas. The closure relation for the multi-time Lagrangian 1-form on solutions of the variational equations is proved for all Toda-type systems. Superposition formulas are instrumental for this proof. The closure relation was previously shown to be equivalent to the spectrality property of B\"acklund transformations, i.e., to the fact that the derivative of the Lagrangian with respect to the spectral parameter is a common integral of motion of the family of B\"acklund transformations. We relate this integral of motion to the monodromy matrix of the zero curvature representation which is derived directly from equations of motion in an algorithmic way. This serves as a further evidence in favor of the idea that B\"acklund transformations serve as zero curvature representations for themselves. \\ ( http://arxiv.org/abs/1302.7144 , 19kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7192 (*cross-listing*) Date: Thu, 28 Feb 2013 13:45:05 GMT (29kb) Title: Weak and strong no-arbitrage conditions for continuous financial markets Authors: Claudio Fontana Categories: q-fin.PR math.PR Comments: 25 pages MSC-class: 60G44, 60H05, 91B70, 91G10 \\ We propose a unified analysis of a whole spectrum of no-arbitrage conditions for financial market models based on continuous semimartingales. In particular, we focus on no-arbitrage conditions weaker than the classical notions of No Arbitrage and No Free Lunch with Vanishing Risk. We provide a complete characterisation of all no-arbitrage conditions, linking their validity to the existence and to the properties of (weak) martingale deflators and to the characteristics of the discounted asset price process. \\ ( http://arxiv.org/abs/1302.7192 , 29kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7193 (*cross-listing*) Date: Thu, 28 Feb 2013 13:56:18 GMT (325kb,D) Title: Matrix-free GPU implementation of a preconditioned conjugate gradient solver for anisotropic elliptic PDEs Authors: Eike Mueller, Xu Guo, Robert Scheichl, Sinan Shi Categories: cs.NA cs.DC math.NA Comments: 18 pages, 7 figures MSC-class: 65F10, 65N22, 65Y05, 65Y10 ACM-class: G.1.3; I.3.1; D.1.3 \\ Many problems in geophysical and atmospheric modelling require the fast solution of elliptic partial differential equations (PDEs) in "flat" three dimensional geometries. In particular, an anisotropic elliptic PDE for the pressure correction has to be solved at every time step in the dynamical core of many numerical weather prediction models, and equations of a very similar structure arise in global ocean models, subsurface flow simulations and gas and oil reservoir modelling. The elliptic solve is often the bottleneck of the forecast, and an algorithmically optimal method has to be used and implemented efficiently. Graphics Processing Units have been shown to be highly efficient for a wide range of applications in scientific computing, and recently iterative solvers have been parallelised on these architectures. We describe the GPU implementation and optimisation of a Preconditioned Conjugate Gradient (PCG) algorithm for the solution of a three dimensional anisotropic elliptic PDE for the pressure correction in NWP. Our implementation exploits the strong vertical anisotropy of the elliptic operator in the construction of a suitable preconditioner. As the algorithm is memory bound, performance can be improved significantly by reducing the amount of global memory access. We achieve this by using a matrix-free implementation which does not require explicit storage of the matrix and instead recalculates the local stencil. Global memory access can also be reduced by rewriting the algorithm using loop fusion and we show that this further reduces the runtime on the GPU. We demonstrate the performance of our matrix-free GPU code by comparing it to a sequential CPU implementation and to a matrix-explicit GPU code which uses existing libraries. The absolute performance of the algorithm for different problem sizes is quantified in terms of floating point throughput and global memory bandwidth. \\ ( http://arxiv.org/abs/1302.7193 , 325kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7194 (*cross-listing*) Date: Wed, 27 Feb 2013 05:59:29 GMT (48kb) Title: Normalization of Polynomials in Algebraic Invariants of Three-Dimensional Orthogonal Geometry Authors: Hongbo Li Categories: cs.SC math.RA \\ In classical invariant theory, the Gr\"obner base of the ideal of syzygies and the normal forms of polynomials of invariants are two core contents. To improve the performance of invariant theory in symbolic computing of classical geometry, advanced invariants are introduced via Clifford product. This paper addresses and solves the two key problems in advanced invariant theory: the Gr\"obner base of the ideal of syzygies among advanced invariants, and the normal forms of polynomials of advanced invariants. These results beautifully extend the straightening of Young tableaux to advanced invariants. \\ ( http://arxiv.org/abs/1302.7194 , 48kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7234 (*cross-listing*) Date: Thu, 28 Feb 2013 15:34:55 GMT (40kb) Title: Source integrals of asymptotic multipole moments Authors: Norman G\"urlebeck Categories: gr-qc math-ph math.MP Comments: 9 pages, 1 figure, contribution to the proceedings of the conference "Relativity and Gravitation - 100 Years after Einstein in Prague", June 25-29, 2012, Prague \\ We derive source integrals for multipole moments that describe the behaviour of static and axially symmetric spacetimes close to spatial infinity. We assume isolated non-singular sources but will not restrict the matter content otherwise. Some future applications of these source integrals of the asymptotic multipole moments are outlined as well. \\ ( http://arxiv.org/abs/1302.7234 , 40kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7246 (*cross-listing*) Date: Thu, 28 Feb 2013 16:29:08 GMT (264kb,D) Title: An analytic multi-currency model with stochastic volatility and stochastic interest rates Authors: Alessandro Gnoatto and Martino Grasselli Categories: q-fin.PR math.PR q-fin.CP MSC-class: 91G20, 91G30 \\ We introduce a tractable multi-currency model with stochastic volatility and correlated stochastic interest rates that takes into account the smile in the FX market and the evolution of yield curves. The pricing of vanilla options on FX rates can be performed effciently through the FFT methodology thanks to the affinity of the model. A joint calibration exercise of the implied volatility surfaces of a triangle of FX rates shows the flexibility of our framework in dealing with the typical symmetries that characterize the FX market. Our framework is also able to describe many non trivial links between FX rates and interest rates: a second calibration exercise highlights the ability of the model to fit simultaneously FX implied volatilities while being coherent with interest rate products. \\ ( http://arxiv.org/abs/1302.7246 , 264kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7286 (*cross-listing*) Date: Thu, 28 Feb 2013 19:05:23 GMT (766kb) Title: Quantum recurrence of a subspace and operator-valued Schur functions Authors: J. Bourgain, F.A. Gr\"unbaum, L. Vel\'azquez, J. Wilkening Categories: quant-ph math-ph math.MP Comments: 40 pages, 8 figures \\ A notion of monitored recurrence for discrete-time quantum processes was recently introduced in [Commun. Math. Phys., DOI 10.1007/s00220-012-1645-2] (see also arXiv:1202.3903) taking the initial state as an absorbing one. We extend this notion of monitored recurrence to absorbing subspaces of arbitrary finite dimension. The generating function approach leads to a connection with the well-known theory of operator-valued Schur functions. This is the cornerstone of a spectral characterization of subspace recurrence that generalizes some of the main results in the above mentioned paper. The spectral decomposition of the unitary step operator driving the evolution yields a spectral measure, which we project onto the subspace to obtain a new spectral measure that is purely singular iff the subspace is recurrent, and consists of a pure point spectrum with a finite number of masses precisely when all states in the subspace have a finite expected return time. This notion of subspace recurrence also links the concept of expected return time to an Aharonov-Anandan phase that, in contrast to the case of state recurrence, can be non-integer. Even more surprising is the fact that averaging such geometrical phases over the absorbing subspace yields an integer with a topological meaning, so that the averaged expected return time is always a rational number. Moreover, state recurrence can occasionally give higher return probabilities than subspace recurrence, a fact that reveals once more the counterintuitive behavior of quantum systems. All these phenomena are illustrated with explicit examples, including as a natural application the analysis of site recurrence for coined walks. \\ ( http://arxiv.org/abs/1302.7286 , 766kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7292 (*cross-listing*) Date: Thu, 28 Feb 2013 19:28:32 GMT (331kb,D) Title: Accelerated density matrix expansions for Born-Oppenheimer molecular dynamics Authors: Emanuel H. Rubensson and Anders M. N. Niklasson Categories: physics.comp-ph math.NA Comments: 22 pages, 7 figures Report-no: LA-UR-13-21340 MSC-class: 65F60, 65F15 \\ An accelerated polynomial expansion scheme to construct the density matrix in quantum mechanical molecular dynamics simulations is proposed. The scheme is based on recursive density matrix expansions, e.g. [Phys. Rev. B. 66 (2002), p. 155115], which are accelerated by a scale-and-fold technique [J. Chem. Theory Comput. 7 (2011), p. 1233]. The acceleration scheme requires interior eigenvalue estimates, which may be expensive and cumbersome to come by. Here we show how such eigenvalue estimates can be extracted from the recursive expansion by a simple and robust procedure at a negligible computational cost. Our method is illustrated with density functional tight-binding Born-Oppenheimer molecular dynamics simulations, where the computational effort is dominated by the density matrix construction. In our analysis we identify two different phases of the recursive polynomial expansion, the conditioning and purification phases, and we show that the acceleration represents an improvement of the conditioning phase, which typically gives a significant reduction of the computational cost. \\ ( http://arxiv.org/abs/1302.7292 , 331kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7297 (*cross-listing*) Date: Thu, 28 Feb 2013 19:39:56 GMT (49kb) Title: Defects in Cohomological Gauge Theory and Donaldson-Thomas Invariants Authors: Michele Cirafici Categories: hep-th math-ph math.AG math.MP Comments: 43 pages \\ Donaldson-Thomas theory on a Calabi-Yau can be described in terms of a certain six-dimensional cohomological gauge theory. We introduce a certain class of defects in this gauge theory which generalize surface defects in four dimensions. These defects are associated with divisors and are defined by prescribing certain boundary conditions for the gauge fields. We discuss generalized instanton moduli spaces when the theory is defined with a defect and propose a generalization of Donaldson-Thomas invariants. These invariants arise by studying torsion free coherent sheaves on Calabi-Yau varieties with a certain parabolic structure along a divisor, determined by the defect. We discuss the case of the affine space as a concrete example. In this case the moduli space of parabolic sheaves admits an alternative description in terms of the representation theory of a certain quiver. The latter can be used to compute the invariants explicitly via equivariant localization. We also briefly discuss extensions of our work to other higher dimensional field theories. \\ ( http://arxiv.org/abs/1302.7297 , 49kb) ------------------------------------------------------------------------------ \\ arXiv:1302.7314 (*cross-listing*) Date: Thu, 28 Feb 2013 20:50:26 GMT (562kb) Title: Torque Saturation in Bipedal Robotic Walking through Control Lyapunov Function Based Quadratic Programs Authors: Kevin Galloway, Koushil Sreenath, Aaron D. Ames and J.W. Grizzle Categories: cs.SY cs.RO math.OC \\ This paper presents a novel method for directly incorporating user-defined control input saturations into the calculation of a control Lyapunov function (CLF)-based walking controller for a biped robot. Previous work by the authors has demonstrated the effectiveness of CLF controllers for stabilizing periodic gaits for biped walkers, and the current work expands on those results by providing a more effective means for handling control saturations. The new approach, based on a convex optimization routine running at a 1 kHz control update rate, is useful not only for handling torque saturations but also for incorporating a whole family of user-defined constraints into the online computation of a CLF controller. The paper concludes with an experimental implementation of the main results on the bipedal robot MABEL. \\ ( http://arxiv.org/abs/1302.7314 , 562kb) %%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%% ------------------------------------------------------------------------------ \\ arXiv:math/0610050 replaced with revised version Thu, 28 Feb 2013 18:19:28 GMT (81kb) Title: The primes contain arbitrarily long polynomial progressions Authors: Terence Tao, Tamar Ziegler Categories: math.NT math.DS Comments: 82 pages, 1 figure. A minor error in the paper (concerning the definition of the polynomial forms condition, which had too weak of a requirement on the degree of the polynomials involved) has been fixed MSC-class: 11N13, 11B25, 374A5 Journal-ref: Acta Math. 201 (2008) 213-305 DOI: 10.1007/s11511-008-0032-5 \\ ( http://arxiv.org/abs/math/0610050 , 81kb) ------------------------------------------------------------------------------ \\ arXiv:0904.4746 replaced with revised version Thu, 28 Feb 2013 16:50:15 GMT (0kb,I) Title: Phase-space analysis and pseudodifferential calculus on the Heisenberg group Authors: Hajer Bahouri, Clotilde Fermanian-Kammerer (LAMA), Isabelle Gallagher (IMJ) Categories: math.AP Comments: This paper has been withdrawn by the authors. Please see arXiv:1005.0833 \\ ( http://arxiv.org/abs/0904.4746 , 0kb) ------------------------------------------------------------------------------ \\ arXiv:1001.1475 replaced with revised version Thu, 28 Feb 2013 09:27:46 GMT (26kb) Title: Presentations of Schutzenberger groups of minimal subshifts Authors: Jorge Almeida and Alfredo Costa Categories: math.GR math.DS Comments: To appear in Israel Journal of Mathematics. Corrects metadata field (abstract) of version of 27 Feb 2013 Report-no: CMUP 2010-1 and DMUC 10-01 MSC-class: 20E18 (Primary), 20M05, 37B10 (Secondary), 20M07 DOI: 10.1007/s11856-012-0139-4 \\ ( http://arxiv.org/abs/1001.1475 , 26kb) ------------------------------------------------------------------------------ \\ arXiv:1001.1707 replaced with revised version Thu, 28 Feb 2013 08:30:28 GMT (20kb) Title: A diagrammatic calculus of syllogisms Authors: Ruggero Pagnan Categories: math.LO math.CT MSC-class: 03B99 \\ ( http://arxiv.org/abs/1001.1707 , 20kb) ------------------------------------------------------------------------------ \\ arXiv:1004.4017 replaced with revised version Thu, 28 Feb 2013 17:51:39 GMT (231kb,D) Title: Optimal-Rate Code Constructions for Computationally Simple Channels Authors: Venkatesan Guruswami and Adam Smith Categories: cs.IT cs.CC math.IT Comments: 39 pages,1 figure. This version presents a simpler and stronger result for time-bounded channels, which subsumes two results in the previous versions (for log-space and poly-time channels) \\ ( http://arxiv.org/abs/1004.4017 , 231kb) ------------------------------------------------------------------------------ \\ arXiv:1005.0833 replaced with revised version Thu, 7 Feb 2013 08:57:28 GMT (110kb) Title: Phase-space analysis and pseudodifferential calculus on the Heisenberg group Authors: Hajer Bahouri, Clotilde Fermanian-Kammerer (LAMA), Isabelle Gallagher (IMJ) Categories: math.AP Comments: The definition of symbols has been made precise by specifying the regularity needed need $\lambda = 0$ \\ ( http://arxiv.org/abs/1005.0833 , 110kb) ------------------------------------------------------------------------------ \\ arXiv:1009.3862 replaced with revised version Thu, 28 Feb 2013 15:38:04 GMT (32kb,D) Title: Optimal stopping in a general framework Authors: Magdalena Kobylanski (LAMA), Marie-Claire Quenez (LPMA) Categories: math.PR Journal-ref: Electronic Journal of Probability 17, 72 (2012) 1-28 DOI: 10.1214 \\ ( http://arxiv.org/abs/1009.3862 , 32kb) ------------------------------------------------------------------------------ \\ arXiv:1010.0992 replaced with revised version Thu, 28 Feb 2013 13:26:23 GMT (0kb,I) Title: Ambikaehler geometry, ambitoric surfaces and Einstein 4-orbifolds Authors: Vestislav Apostolov, David M.J. Calderbank and Paul Gauduchon Categories: math.DG Comments: Replaced by arXiv:1302.6975 and arXiv 1302.6979, which contain more complete results MSC-class: 53C55, 53C25, 53B35, 32Q15, 14M25 \\ ( http://arxiv.org/abs/1010.0992 , 0kb) ------------------------------------------------------------------------------ \\ arXiv:1101.0226 replaced with revised version Thu, 28 Feb 2013 14:07:56 GMT (29kb) Title: On the derived functors of destabilization at odd primes Authors: Geoffrey Powell Categories: math.AT Comments: Significant revision (27 pages); accepted for publication in Acta Mathematica Vietnamica (AMV) MSC-class: 55S10 \\ ( http://arxiv.org/abs/1101.0226 , 29kb) ------------------------------------------------------------------------------ \\ arXiv:1101.5697 replaced with revised version Thu, 28 Feb 2013 05:27:46 GMT (14kb) Title: Recollements and Hochschild theory Authors: Yang Han Categories: math.RA math.KT math.RT Comments: 18 pages MSC-class: 16E40 (Primary) 16E35, 18E30 (Secondary) \\ ( http://arxiv.org/abs/1101.5697 , 14kb) ------------------------------------------------------------------------------ \\ arXiv:1108.2554 replaced with revised version Thu, 28 Feb 2013 16:29:12 GMT (12kb) Title: On VC-density over indiscernible sequences Authors: Vincent Guingona and Cameron Donnay Hill Categories: math.LO Comments: 12 pages MSC-class: 03C45 \\ ( http://arxiv.org/abs/1108.2554 , 12kb) ------------------------------------------------------------------------------ \\ arXiv:1110.2117 replaced with revised version Thu, 28 Feb 2013 12:44:09 GMT (37kb) Title: Skew products and random walks on the unit interval Authors: Victor Kleptsyn and Denis Volk Categories: math.DS Comments: 29 pages. Minor corrections and updated introduction MSC-class: 37C05, 37C20, 37C70, 37D20, 37D45 \\ ( http://arxiv.org/abs/1110.2117 , 37kb) ------------------------------------------------------------------------------ \\ arXiv:1111.4379 (*cross-listing*) replaced with revised version Thu, 28 Feb 2013 09:40:30 GMT (38kb) Title: Classification of Arbitrary Multipartite Entangled States under Local Unitary Equivalence Authors: Jun-Li Li and Cong-Feng Qiao Categories: quant-ph hep-ph math-ph math.MP Comments: 22 pages; published in J. Phys. A: Math. Theor Journal-ref: J. Phys. A: Math. Theor. 46, 075301 (2013) \\ ( http://arxiv.org/abs/1111.4379 , 38kb) ------------------------------------------------------------------------------ \\ arXiv:1112.3429 replaced with revised version Thu, 28 Feb 2013 05:34:12 GMT (31kb) Title: Non-orthogonal geometric realizations of Coxeter groups Authors: Xiang Fu Categories: math.RT MSC-class: 20F55 (Primary) 20F10, 20F65 (Secondary) \\ ( http://arxiv.org/abs/1112.3429 , 31kb) ------------------------------------------------------------------------------ \\ arXiv:1112.5689 replaced with revised version Wed, 27 Feb 2013 22:05:20 GMT (24kb) Title: Quasiderivative method for derivative estimates of solutions to degenerate elliptic equations Authors: Wei Zhou Categories: math.PR math.AP Comments: 37 pages. Remark 3.2 is added, in which an example is given showing that Assumption 3.2 is not only sufficient but also necessary under Assumption 3.1 MSC-class: 60H30, 60J60, 35J70, 35B65 \\ ( http://arxiv.org/abs/1112.5689 , 24kb) ------------------------------------------------------------------------------ \\ arXiv:1201.0646 (*cross-listing*) replaced with revised version Thu, 28 Feb 2013 14:28:35 GMT (882kb,D) Title: On the flexibility of the design of Multiple Try Metropolis schemes Authors: Luca Martino and Jesse Read Categories: stat.CO math.ST stat.ME stat.TH \\ ( http://arxiv.org/abs/1201.0646 , 882kb) ------------------------------------------------------------------------------ \\ arXiv:1201.3657 replaced with revised version Thu, 28 Feb 2013 15:53:14 GMT (30kb) Title: The Unstable Slice Filtration Authors: Pablo Pelaez Categories: math.KT math.AG math.AT Comments: 34 pages, added a comparison with the classical Postnikov tower. To appear in Transactions of the AMS MSC-class: 14, 55 \\ ( http://arxiv.org/abs/1201.3657 , 30kb) ------------------------------------------------------------------------------ \\ arXiv:1201.5792 replaced with revised version Thu, 28 Feb 2013 08:12:18 GMT (18kb,D) Title: Groebner bases of symmetric ideals Authors: Stefan Steidel Categories: math.AC Comments: 17 pages MSC-class: 13P10 (Primary), 68W10 (Secondary) ACM-class: G.4; I.1.2 \\ ( http://arxiv.org/abs/1201.5792 , 18kb) ------------------------------------------------------------------------------ \\ arXiv:1202.6408 replaced with revised version Thu, 28 Feb 2013 18:24:14 GMT (29kb) Title: Bimodules over Cartan MASAs in von Neumann Algebras, Norming Algebras, and Mercer's Theorem Authors: Jan Cameron, David R. Pitts and Vrej Zarikian Categories: math.OA Comments: 21 pages, paper is a completely reworked and expanded version of an earlier preprint with a similar title MSC-class: 47L30, 46L10, 46L07 \\ ( http://arxiv.org/abs/1202.6408 , 29kb) ------------------------------------------------------------------------------ \\ arXiv:1203.4955 replaced with revised version Thu, 28 Feb 2013 09:36:22 GMT (18kb) Title: Normal Bundle of Rational Curves and Waring Decomposition Authors: Alessandro Bernardi Categories: math.AG \\ ( http://arxiv.org/abs/1203.4955 , 18kb) ------------------------------------------------------------------------------ \\ arXiv:1203.5480 replaced with revised version Thu, 28 Feb 2013 07:48:50 GMT (9kb) Title: Estimates for the Initial Coefficients of Bi-univalent Functions Authors: S. Sivaprasad Kumar, Virendra Kumar and V. Ravichandran Categories: math.CV Comments: 12 pages MSC-class: 30C45, 30C80 \\ ( http://arxiv.org/abs/1203.5480 , 9kb) ------------------------------------------------------------------------------ \\ arXiv:1204.4056 replaced with revised version Thu, 28 Feb 2013 07:40:50 GMT (10kb) Title: Quasi-morphisms on the group of area-preserving diffeomorphisms of the 2-disk via braid groups Authors: Tomohiko Ishida Categories: math.DS math.GR Comments: 8pages. The title of the paper has been changed, to appear in Proc. Amer. Math. Soc MSC-class: 37C15 (Primary), 37E30 (Secondary) \\ ( http://arxiv.org/abs/1204.4056 , 10kb) ------------------------------------------------------------------------------ \\ arXiv:1205.2050 replaced with revised version Thu, 28 Feb 2013 15:17:30 GMT (33kb) Title: On Maximal Green Sequences Authors: Thomas Br\"ustle, Gr\'egoire Dupont and Matthieu P\'erotin Categories: math.RT math.CO Comments: v2: Some proofs were clarified and improved. The article is substantially shorter, most of the examples and appendices were cut out. The reader may refer to http://arxiv.org/abs/1205.2050v1 for additional examples MSC-class: 13F60, 16G20, 81T60 \\ ( http://arxiv.org/abs/1205.2050 , 33kb) ------------------------------------------------------------------------------ \\ arXiv:1205.3816 (*cross-listing*) replaced with revised version Thu, 28 Feb 2013 06:49:36 GMT (50kb) Title: A Partially Ordered Structure and a Generalization of the Canonical Partition for General Graphs with Perfect Matchings Authors: Nanao Kita Categories: cs.DM math.CO Comments: 16 pages, no figures. arXiv admin note: text overlap with arXiv:1212.5960 \\ ( http://arxiv.org/abs/1205.3816 , 50kb) ------------------------------------------------------------------------------ \\ arXiv:1205.5450 replaced with revised version Thu, 28 Feb 2013 03:19:58 GMT (19kb) Title: Well-posedness results for the dispersion generalized Benjamin-Ono equation via the contraction principle Authors: Germ\'an Fonseca, Felipe Linares, Gustavo Ponce Categories: math.AP Comments: 22 pages \\ ( http://arxiv.org/abs/1205.5450 , 19kb) ------------------------------------------------------------------------------ \\ arXiv:1205.6536 replaced with revised version Thu, 28 Feb 2013 05:49:41 GMT (18kb) Title: The Eigenvalue Shift Technique and Its Eigenstructure Analysis of a Matrix Authors: Chun-Yueh Chiang, Matthew M. Lin Categories: math.NA \\ ( http://arxiv.org/abs/1205.6536 , 18kb) ------------------------------------------------------------------------------ \\ arXiv:1206.2473 replaced with revised version Thu, 28 Feb 2013 03:08:41 GMT (11kb) Title: On sums of prime subsets Authors: Zhen Cui, Hongze Li and Boqing Xue Categories: math.NT \\ ( http://arxiv.org/abs/1206.2473 , 11kb) ------------------------------------------------------------------------------ \\ arXiv:1206.5080 replaced with revised version Thu, 28 Feb 2013 16:52:17 GMT (18kb) Title: Upper triangular Toeplitz matrices and real parts of quasinilpotent operators Authors: Ken Dykema, Junsheng Fang and Anna Skripka Categories: math.OA math.FA Comments: 19 pages; for version 2 a few relatively minor corrections were made and the abstract improved; for version 3, a few comments and minor changes were made MSC-class: 15A60, 47B47 \\ ( http://arxiv.org/abs/1206.5080 , 18kb) ------------------------------------------------------------------------------ \\ arXiv:1207.1056 replaced with revised version Thu, 28 Feb 2013 11:45:02 GMT (494kb,D) Title: On adaptive wavelet estimation of a class of weighted densities Authors: Fabien Navarro, Christophe Chesneau, Jalal Fadili Categories: math.ST stat.TH MSC-class: 62G07, 62G20 \\ ( http://arxiv.org/abs/1207.1056 , 494kb) ------------------------------------------------------------------------------ \\ arXiv:1207.4263 replaced with revised version Thu, 28 Feb 2013 16:25:23 GMT (19kb) Title: Simultaneous Deformations of Lie Algebroids and Lie Subalgebroids Authors: Xiang Ji Categories: math-ph math.DG math.MP math.QA \\ ( http://arxiv.org/abs/1207.4263 , 19kb) ------------------------------------------------------------------------------ \\ arXiv:1207.4866 replaced with revised version Thu, 28 Feb 2013 14:48:22 GMT (975kb,D) Title: Predictive maintenance for the heated hold-up tank Authors: Beno\^ite de Saporta, Huilong Zhang Categories: math.OC Comments: arXiv admin note: text overlap with arXiv:1101.1740 \\ ( http://arxiv.org/abs/1207.4866 , 975kb) ------------------------------------------------------------------------------ \\ arXiv:1208.1424 replaced with revised version Thu, 28 Feb 2013 12:42:22 GMT (16kb) Title: On idempotent ultrafilters in higher-order reverse mathematics Authors: Alexander P. Kreuzer Categories: math.LO MSC-class: 03B30, 03F35, 03F60, 05D10 \\ ( http://arxiv.org/abs/1208.1424 , 16kb) ------------------------------------------------------------------------------ \\ arXiv:1208.3216 replaced with revised version Thu, 28 Feb 2013 04:18:14 GMT (18kb) Title: A stability conjecture for the unstable cohomology of SL_n Z, mapping class groups, and Aut(F_n) Authors: Thomas Church, Benson Farb, and Andrew Putman Categories: math.GT math.AT math.GR math.NT Comments: 18 pages \\ ( http://arxiv.org/abs/1208.3216 , 18kb) ------------------------------------------------------------------------------ \\ arXiv:1208.3831 replaced with revised version Thu, 28 Feb 2013 12:04:05 GMT (24kb) Title: The $\s$-Eulerian polynomials have only real roots Authors: Carla D. Savage and Mirk\'o Visontai Categories: math.CO Comments: Added a proof of a conjecture of Brenti (for Eulerian polynomials of type D) and a proof of a conjecture of Dilks, Petersen, and Stembridge (for affine Eulerian polynomials of type B) MSC-class: 05A05, 26C10 \\ ( http://arxiv.org/abs/1208.3831 , 24kb) ------------------------------------------------------------------------------ \\ arXiv:1209.5025 (*cross-listing*) replaced with revised version Wed, 27 Feb 2013 22:00:31 GMT (15kb) Title: Consensus on the Initial Global Majority by Local Majority Polling for a Class of Sparse Graphs Authors: Mohammed Amin Abdullah and Moez Draief Categories: cs.DC math.PR \\ ( http://arxiv.org/abs/1209.5025 , 15kb) ------------------------------------------------------------------------------ \\ arXiv:1210.7920 replaced with revised version Thu, 28 Feb 2013 17:05:55 GMT (255kb) Title: A note on Schwarzian derivatives and normal families Authors: Dinesh Kumar and Sanjay Kumar Categories: math.DS math.CV Comments: 5 pages MSC-class: 37F10 \\ ( http://arxiv.org/abs/1210.7920 , 255kb) ------------------------------------------------------------------------------ \\ arXiv:1211.0078 replaced with revised version Thu, 28 Feb 2013 16:34:15 GMT (54kb) Title: Full-featured peak reduction in right-angled Artin groups Authors: Matthew B. Day Categories: math.GR Comments: 71 pages, 1 figure. Figure fixed MSC-class: 20F36, 20F28 \\ ( http://arxiv.org/abs/1211.0078 , 54kb) ------------------------------------------------------------------------------ \\ arXiv:1211.3196 replaced with revised version Thu, 28 Feb 2013 10:02:37 GMT (15kb) Title: Maximum Likelihood Duality for Determinantal Varieties Authors: Jan Draisma and Jose Rodriguez Categories: math.AG MSC-class: 14m12, 62f12 \\ ( http://arxiv.org/abs/1211.3196 , 15kb) ------------------------------------------------------------------------------ \\ arXiv:1211.5425 replaced with revised version Thu, 28 Feb 2013 05:44:20 GMT (185kb) Title: A Cross-layer Perspective on Energy Harvesting Aided Green Communications over Fading Channels Authors: Tian Zhang, Wei Chen, Zhu Han, and Zhigang Cao Categories: cs.IT math.IT \\ ( http://arxiv.org/abs/1211.5425 , 185kb) ------------------------------------------------------------------------------ \\ arXiv:1211.6732 replaced with revised version Thu, 28 Feb 2013 19:43:07 GMT (42kb) Title: Equivariant Khovanov-Rozansky Homology and Lee-Gornik Spectral Sequence Authors: Hao Wu Categories: math.GT Comments: 43 pages, 7 figures. Third version: corrected mistakes; added new contents (exact couples, exterior algebra action and etc); changed the normalization of the torsion width MSC-class: 57M27 \\ ( http://arxiv.org/abs/1211.6732 , 42kb) ------------------------------------------------------------------------------ \\ arXiv:1211.6832 replaced with revised version Thu, 28 Feb 2013 18:39:36 GMT (13kb) Title: A Bicategory Approach to Differential Cohomology Authors: Markus Upmeier Categories: math.AT math.GT \\ ( http://arxiv.org/abs/1211.6832 , 13kb) ------------------------------------------------------------------------------ \\ arXiv:1212.0622 replaced with revised version Thu, 28 Feb 2013 02:20:38 GMT (9kb) Title: Another proof of Masuoka's Theorem for semisimple irreducible Hopf algebras Authors: Xingting Wang Categories: math.RA math.QA Comments: The same result was proved by A. Masuoka. His paper "Semisimplicity criteria for irreducible Hopf algebras in positive characteristic" was published in Proc. Amer. Math. Soc. 137(2009), no 6, 1925-1932 MSC-class: 16T05 \\ ( http://arxiv.org/abs/1212.0622 , 9kb) ------------------------------------------------------------------------------ \\ arXiv:1212.0834 replaced with revised version Thu, 28 Feb 2013 16:34:00 GMT (36kb,D) Title: Nonlinear elliptic Partial Differential Equations and p-harmonic functions on graphs Authors: Juan J. Manfredi, Adam M. Oberman, Alex P. Svirodov Categories: math.AP Comments: 19 pages, 2 figures MSC-class: 35J20, 35J60, 35J70 \\ ( http://arxiv.org/abs/1212.0834 , 36kb) ------------------------------------------------------------------------------ \\ arXiv:1212.1188 replaced with revised version Thu, 28 Feb 2013 18:36:58 GMT (3740kb) Title: Recursive bijections for Catalan objects Authors: Stefan Forcey, Mohammadmehdi Kafashan, Mehdi Maleki, Michael Strayer Categories: math.CO \\ ( http://arxiv.org/abs/1212.1188 , 3740kb) ------------------------------------------------------------------------------ \\ arXiv:1212.4333 replaced with revised version Thu, 28 Feb 2013 09:48:50 GMT (10kb) Title: A very smooth ride in a rough sea Authors: U. Frisch, V. Zheligovsky Categories: math.AP math-ph math.MP physics.flu-dyn Comments: 8 pp., 19 refs. Communications in Mathematical Physics, in press \\ ( http://arxiv.org/abs/1212.4333 , 10kb) ------------------------------------------------------------------------------ \\ arXiv:1212.6618 replaced with revised version Thu, 28 Feb 2013 08:27:30 GMT (133kb,D) Title: Integrability of Nonholonomically Coupled Oscillators Authors: Klas Modin, Olivier Verdier Categories: math.DS math.NA Comments: To appear in Discrete and Continuous Dynamical Systems - Series A (DCDS-A) \\ ( http://arxiv.org/abs/1212.6618 , 133kb) ------------------------------------------------------------------------------ \\ arXiv:1301.3993 replaced with revised version Thu, 28 Feb 2013 05:26:14 GMT (18kb) Title: On paired root systems of Coxeter groups Authors: Xiang Fu Categories: math.RT math.GR \\ ( http://arxiv.org/abs/1301.3993 , 18kb) ------------------------------------------------------------------------------ \\ arXiv:1301.4957 replaced with revised version Wed, 27 Feb 2013 21:09:58 GMT (25kb) Title: On automorphisms of blowups of projective manifolds Authors: Tuyen Trung Truong Categories: math.DS math.AG math.CV Comments: 27 pages. Slightly modified the statements and/or proofs of some results, added several new examples including one showing that the assumptions in the results in Section 2 can not be removed \\ ( http://arxiv.org/abs/1301.4957 , 25kb) ------------------------------------------------------------------------------ \\ arXiv:1302.1315 replaced with revised version Thu, 28 Feb 2013 14:58:09 GMT (20kb) Title: Counting matroids in minor-closed classes Authors: R.A. Pendavingh, J.G. van der Pol Categories: math.CO Comments: 13 pages, 3 figures \\ ( http://arxiv.org/abs/1302.1315 , 20kb) ------------------------------------------------------------------------------ \\ arXiv:1302.5143 (*cross-listing*) replaced with revised version Thu, 28 Feb 2013 00:17:02 GMT (49kb,D) Title: Multiplicity-free quantum 6j-symbols for U_q(sl_N) Authors: Satoshi Nawata and P. Ramadevi and Zodinmawia Categories: hep-th math-ph math.MP Comments: 4 pages,; v2 typos corrected Report-no: NIKHEF-2013-005 \\ ( http://arxiv.org/abs/1302.5143 , 49kb) ------------------------------------------------------------------------------ \\ arXiv:1302.5840 replaced with revised version Thu, 28 Feb 2013 20:56:40 GMT (12kb) Title: Lower $Q$-Homeomorphisms With Respect To $P$-Modulus And Orlicz-Sobolev Classes Authors: R. Salimov Categories: math.CV Comments: arXiv admin note: text overlap with arXiv:1012.5010 \\ ( http://arxiv.org/abs/1302.5840 , 12kb) ------------------------------------------------------------------------------ \\ arXiv:1302.6484 (*cross-listing*) replaced with revised version Thu, 28 Feb 2013 09:47:22 GMT (627kb,D) Title: Dynamic trajectory control of gliders Authors: Rui Dil\~ao and Jo\~ao Fonseca Categories: astro-ph.IM math.OC physics.space-ph Comments: 9 figures, Proceedings of the 2nd CEAS Specialist Conference on Guidance, Navigation & Control, Delft, 2013 \\ ( http://arxiv.org/abs/1302.6484 , 627kb) ------------------------------------------------------------------------------ \\ arXiv:1302.6945 replaced with revised version Thu, 28 Feb 2013 01:23:28 GMT (133kb) Title: Superfast Tikhonov Regularization of Toeplitz Systems Authors: Christopher Turnes (1), Doru Balcan (2), Justin Romberg (1) ((1) Georgia Institute of Technology, School of Electrical and Computer Engineering, (2) Georgia Institute of Technology, School of Interactive Computing) Categories: math.NA Comments: 26 pages, 6 figures, 3 tables, 2 algorithms Submitted to IEEE Transactions on Signal Processing on 25 Feb. 2013 \\ ( http://arxiv.org/abs/1302.6945 , 133kb) ------------------------------------------------------------------------------ \\ arXiv:1302.6958 replaced with revised version Thu, 28 Feb 2013 18:22:32 GMT (26kb) Title: Forward Brownian Motion Authors: Krzysztof Burdzy and Michael Scheutzow Categories: math.PR MSC-class: 60J65 \\ ( http://arxiv.org/abs/1302.6958 , 26kb) %%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%--- For general information on the new math archive (partitioned by keyword subject classification), see http://arXiv.org/new/math.html For subscribe options to combined math archives, e-mail To: math@arXiv.org, Subject: subscribe