Date: Thu, 26 Feb 15 01:23:53 GMT
Subject: math-ph daily 11 new + 6 crosses received   by eprepget 

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received   by eprepget from  Tue 24 Feb 15 21:00:00 GMT  to  Wed 25 Feb 15 21:00:00 GMT
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arXiv:1502.06985
Date: Mon, 5 Jan 2015 13:20:57 GMT   (722kb)

Title: The hyperbolic field theory on the plane of double variable
Authors: Dmitry Pavlov and Sergey Kokarev
Categories: math-ph math.MP
Comments: 51 pages, 27 figures
Journal-ref: Hypercomplex Numbers in Geometry and Physics, 1(13), No.7, 2010,
  pp.78-126 (In Russian)
\\
  By analogy to the theory of harmonic fields on the complex plane, we build
the theory of wave-like fields on the plane of double variable. We construct
the hyperbolic analogues of point vortices, sources, vortice-sources and their
higher-order multipole generalizations. We examine the physical aspects and the
possibility of extension to the space of polynumbers of higher dimensions.
\\ ( http://arxiv.org/abs/1502.06985 ,  722kb)
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arXiv:1502.07033
Date: Wed, 25 Feb 2015 02:46:12 GMT   (5kb)

Title: Addendum to "Barotropic FRW cosmologies with Chiellini damping"
Authors: Haret C. Rosu, Stefan C. Mancas, Pisin Chen
Categories: math-ph math.MP
Comments: 4 pages
\\
  For non-zero cosmological constant Lambda, we show that the barotropic FRW
cosmologies as worked out in the comoving time lead in the radiation-dominated
case to scale factors of identical form as for the Chiellini dissipative scale
factors in conformal time obtained recently by us in Phys. Lett. A 379 (2015)
882-887. This is due to the Ermakov equation which is obtained in this case.
For zero cosmological constant, several textbook solutions are provided as
particular cases of Lambda different from zero
\\ ( http://arxiv.org/abs/1502.07033 ,  5kb)
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arXiv:1502.07047
Date: Wed, 25 Feb 2015 04:20:39 GMT   (23kb)

Title: The Vlasov-Poisson dynamics as the mean-field limit of rigid charges
Authors: Dustin Lazarovici
Categories: math-ph math.AP math.MP
\\
  This paper treats the validity problem of the non-relativistic Vlasov-Poisson
system in 3 dimensions. It is shown that the Vlasov-Poisson dynamics can be
derived as a combined mean-field and point-particle limit of an N-particle
Coulomb system of rigid charges. This requires a sufficiently fast convergence
of the initial empirical distributions. If the electron-radius doesn't decrease
faster than $N^{-\frac{1}{5}+\epsilon}$, the corresponding initial
configurations are shown to be typical.
\\ ( http://arxiv.org/abs/1502.07047 ,  23kb)
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arXiv:1502.07078
Date: Wed, 25 Feb 2015 08:18:49 GMT   (140kb,D)

Title: Common eigenfunctions of commuting differential operators of rank 2
Authors: Vardan Oganesyan
Categories: math-ph math.MP
Comments: 6 pages
\\
  In this paper we find coomon eigenfunctions of commuting differential
operators of rank 2 with polynomial coefficients in some partial cases.
\\ ( http://arxiv.org/abs/1502.07078 ,  140kb)
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arXiv:1502.07107
Date: Wed, 25 Feb 2015 10:12:05 GMT   (9kb)

Title: Schroedinger operators with n positive eigenvalues: an explicit
  construction involving complex valued potentials
Authors: S. Richard, J. Uchiyama, T. Umeda
Categories: math-ph math.MP math.SP
Comments: 8 pages
\\
  An explicit construction is provided for embedding n positive eigenvalues in
the spectrum of a Schroedinger operator on the half-line with a Dirichlet
boundary condition at the origin. The resulting potential is of von
Neumann-Wigner type, but can be real valued as well as complex valued.
\\ ( http://arxiv.org/abs/1502.07107 ,  9kb)
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arXiv:1502.07147
Date: Wed, 25 Feb 2015 12:19:39 GMT   (61kb,D)

Title: Muttalib--Borodin ensembles in random matrix theory --- realisations and
  correlation functions
Authors: Peter J. Forrester and Dong Wang
Categories: math-ph math.CA math.MP math.PR
Comments: 42 pages, 4 figures
MSC-class: 60B20, 15B52, 82D35, 30E10
\\
  Muttalib--Borodin ensembles are characterised by the pair interaction term in
the eigenvalue probability density function being of the form $\prod_{1 \le j <
k \le N}(\lambda_k - \lambda_j) (\lambda_k^\theta - \lambda_j^\theta)$. We
study the Laguerre and Jacobi versions of this model --- so named by the form
of the one-body interaction terms --- and show that for $\theta \in \mathbb
Z^+$ they can be realised as the eigenvalue PDF of certain random matrices with
Gaussian entries. For general $\theta > 0$, realisations in terms of the
eigenvalue PDF of ensembles involving triangular matrices are given. In the
Laguerre case this is a recent result due to Cheliotis, although our derivation
is different. We make use of a generalisation of a double contour integral
formulas for the correlation functions contained in a paper by Adler, van
Moerbeke and Wang to analyse the global density (which we also analyse by
studying characteristic polynomials), and the hard edge scaled correlation
functions. For the global density functional equations for the corresponding
resolvents are obtained; solving this gives the moments in terms of
Fuss--Catalan numbers (Laguerre case --- a known result) and particular
binomial coefficients (Jacobi case). For $\theta \in \mathbb Z^+$ the Laguerre
and Jacobi cases are closely related to the squared singular values for
products of $\theta$ standard Gaussian random matrices, and truncations of
unitary matrices, respectively. At the hard edge the double contour integral
formulas provide a double contour integral form of the scaled correlation
kernel obtained by Borodin in terms of Wright's Bessel function.
\\ ( http://arxiv.org/abs/1502.07147 ,  61kb)
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arXiv:1502.07175
Date: Wed, 25 Feb 2015 14:24:48 GMT   (21kb)

Title: Some results on the dynamics and transition probabilities for non
  self-adjoint hamiltonians
Authors: Fabio Bagarello
Categories: math-ph math.MP
Comments: in press in Annals of Physics
\\
  We discuss systematically several possible inequivalent ways to describe the
dynamics and the transition probabilities of a quantum system when its
hamiltonian is not self-adjoint. In order to simplify the treatment, we mainly
restrict our analysis to finite dimensional Hilbert spaces. In particular, we
propose some experiments which could discriminate between the various
possibilities considered in the paper. An example taken from the literature is
discussed in detail.
\\ ( http://arxiv.org/abs/1502.07175 ,  21kb)
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arXiv:1502.07205
Date: Wed, 25 Feb 2015 15:39:32 GMT   (12kb)

Title: Note on a Family of Monotone Quantum Relative Entropies
Authors: Andreas Deuchert, Christian Hainzl, Robert Seiringer
Categories: math-ph math.FA math.MP
Comments: 19 pages
\\
  Given a convex function $\varphi$ and two hermitian matrices $A$ and $B$,
Lewin and Sabin study in [M. Lewin, J. Sabin, {\it A Family of Monotone Quantum
Relative Entropies}, Lett. Math. Phys. \textbf{104} (2014), 691-705.] the
relative entropy defined by $\mathcal{H}(A,B)=\tr [ \varphi(A) - \varphi(B) -
\varphi'(B)(A-B) ]$. Amongst other things, they prove that the so-defined
quantity is monotone if and only if $\varphi'$ is operator monotone. The
monotonicity is then used to properly define $\mathcal{H}(A,B)$ for
self-adjoint bounded operators acting on an infinite-dimensional Hilbert space
by a limiting procedure. More precisely, for an increasing sequence of
finite-dimensional projections $\lbrace P_n \rbrace_{n=1}^{\infty}$ with $P_n
\to 1$ strongly, the limit $\lim_{n \to \infty} \mathcal{H}(P_n A P_n, P_n B
P_n)$ is shown to exist and to be independent of the sequence of projections
$\lbrace P_n \rbrace_{n=1}^{\infty}$. The question whether this sequence
converges to its "obvious" limit, namely $\tr [ \varphi(A)- \varphi(B) -
\varphi'(B)(A-B) ]$, has been left open. We answer this question in principle
affirmatively and show that $\lim_{n \to \infty} \mathcal{H}(P_n A P_n, P_n B
P_n) = \tr[ \varphi(A) - \varphi(B) - \frac{\text{d}}{\text{d} \alpha} \varphi(
\alpha A + (1-\alpha)B )|_{\alpha = 0} ]$. If the operators $A$ and $B$ are
regular enough, that is $(A-B)$, $\varphi(A)-\varphi(B)$ and $\varphi'(B)(A-B)$
are trace-class, the identity $\tr[ \varphi(A) - \varphi(B) -
\frac{\text{d}}{\text{d} \alpha} \varphi( \alpha A + (1-\alpha)B )|_{\alpha =
0} ] = \tr [ \varphi(A)- \varphi(B) - \varphi'(B)(A-B) ]$ holds.
\\ ( http://arxiv.org/abs/1502.07205 ,  12kb)
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arXiv:1502.07219
Date: Wed, 25 Feb 2015 16:02:11 GMT   (18kb)

Title: Functorial Quantum Field Theory in the Riemannian setting
Authors: Santosh Kandel
Categories: math-ph math.MP
Comments: Feedback welcome!
\\
  We construct examples of Functorial Quantum Field Theories in the Riemannian
setting by quantizing free massive bosons.
\\ ( http://arxiv.org/abs/1502.07219 ,  18kb)
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arXiv:1502.07235
Date: Wed, 25 Feb 2015 16:39:29 GMT   (363kb)

Title: Derivation of Ray Optics Equations in Photonic Crystals Via a
  Semiclassical Limit
Authors: Giuseppe De Nittis and Max Lein
Categories: math-ph math.MP
Comments: 39 pages
\\
  In this work we present a novel approach to the ray optics limit: we rewrite
the dynamical Maxwell equations in Schr\"odinger form and prove Egorov-type
theorems, a robust semiclassical technique. We implement this scheme for
periodic light conductors, photonic crystals, thereby making the quantum-light
analogy between semiclassics for the Bloch electron and ray optics in photonic
crystals rigorous. Our main results, Theorems 3.3 and 4.1, give a ray optics
limit for quadratic observables and, among others, apply to local averages of
energy density, the Poynting vector and the Maxwell stress tensor. Ours is the
first rigorous derivation of ray optics equations which include all sub-leading
order terms, some of which are also new to the physics literature. While the
ray optics limit we prove initially (Theorem 3.3) applies to photonic crystals
of any topological class, we also consider the ray optics limit for real
electromagnetic fields propagating in non-gyrotropic photonic crystals. Such an
extension is non-trivial, because the ray optic limit for real fields is
necessarily a multiband problem.
\\ ( http://arxiv.org/abs/1502.07235 ,  363kb)
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arXiv:1502.07293
Date: Wed, 25 Feb 2015 18:36:31 GMT   (160kb,D)

Title: A superintegrable discrete oscillator and two-variable Meixner
  polynomials
Authors: Julien Gaboriaud, Vincent X. Genest, Jessica Lemieux and Luc Vinet
Categories: math-ph math.MP
Comments: 14 pages, 4 figures
\\
  A superintegrable, discrete model of the quantum isotropic oscillator in
two-dimensions is introduced. The system is defined on the regular,
infinite-dimensional $\mathbb{N}\times \mathbb{N}$ lattice. It is governed by a
Hamiltonian expressed as a seven-point difference operator involving three
parameters. The exact solutions of the model are given in terms of the
two-variable Meixner polynomials orthogonal with respect to the negative
trinomial distribution. The constants of motion of the system are constructed
using the raising and lowering operators for these polynomials. They are shown
to generate an $\mathfrak{su}(2)$ invariance algebra. The two-variable Meixner
polynomials are seen to support irreducible representations of this algebra. In
the continuum limit, where the lattice constant tends to zero, the standard
isotropic quantum oscillator in two dimensions is recovered. The limit process
from the two-variable Meixner polynomials to a product of two Hermite
polynomials is carried out by involving the bivariate Charlier polynomials.
\\ ( http://arxiv.org/abs/1502.07293 ,  160kb)
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arXiv:1401.6800 (*cross-listing*)
Date: Mon, 27 Jan 2014 10:56:50 GMT   (124kb,D)
Date (revised v2): Sat, 9 Aug 2014 13:19:11 GMT   (153kb,D)
Date (revised v3): Wed, 3 Dec 2014 18:26:35 GMT   (153kb,D)
Date (revised v4): Thu, 5 Feb 2015 08:52:42 GMT   (153kb,D)

Title: Functional Approach to Electrodynamics of Media
Authors: R. Starke and G. A. H. Schober
Categories: cond-mat.mtrl-sci math-ph math.MP physics.class-ph
Comments: accepted by Photonics and Nanostructures - Fundamentals and
  Applications
\\
  In this paper, we put forward a new approach to electrodynamics of materials.
Based on the identification of induced electromagnetic fields as the
microscopic counterparts of polarization and magnetization, we systematically
employ the mutual functional dependencies of induced, external and total field
quantities. This allows for a unified, relativistic description of the
electromagnetic response without assuming the material to be composed of
electric or magnetic dipoles. Using this approach, we derive universal
(material-independent) relations between electromagnetic response functions
such as the dielectric tensor, the magnetic susceptibility and the microscopic
conductivity tensor. Our formulae can be reduced to well-known identities in
special cases, but more generally include the effects of inhomogeneity,
anisotropy, magnetoelectric coupling and relativistic retardation. If combined
with the Kubo formalism, they would also lend themselves to the ab initio
calculation of all linear electromagnetic response functions.
\\ ( http://arxiv.org/abs/1401.6800 ,  153kb)
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arXiv:1502.07095 (*cross-listing*)
Date: Wed, 25 Feb 2015 09:27:41 GMT   (36kb)

Title: Algebraic analysis on scalar generalized Verma modules of Heisenberg
  parabolic type I.: $A_n$-series
Authors: Libor K\v{r}i\v{z}ka, Petr Somberg
Categories: math.RT math-ph math.AP math.DG math.FA math.MP
MSC-class: 53A30, 22E47, 33C45, 58J70
\\
  In the present article, we combine some techniques in the harmonic analysis
together with the geometric approach given by modules over sheaves of rings of
twisted differential operators ($\mathcal{D}$-modules), and reformulate the
composition series and branching problems for objects in the
Bernstein-Gelfand-Gelfand parabolic category $\mathcal{O}^\mathfrak{p}$
geometrically realized on certain orbits in the generalized flag manifolds. The
general framework is then applied to the scalar generalized Verma modules
supported on the closed Schubert cell of the generalized flag manifold $G/P$
for $G={\rm SL}(n+2,\mathbb{C})$ and $P$ the Heisenberg parabolic subgroup, and
the algebraic analysis gives a complete classification of
$\mathfrak{g}'_r$-singular vectors for all
$\mathfrak{g}'_r=\mathfrak{sl}(n-r+2,\mathbb{C})\,\subset\,
\mathfrak{g}=\mathfrak{sl}(n+2,\mathbb{C})$, $n-r > 2$. A consequence of our
results is that we classify ${\rm SL}(n-r+2,\mathbb{C})$-covariant differential
operators acting on homogeneous line bundles over the complexification of the
odd dimensional CR-sphere $S^{2n+1}$ and valued in homogeneous vector bundles
over the complexification of the CR-subspheres $S^{2(n-r)+1}$.
\\ ( http://arxiv.org/abs/1502.07095 ,  36kb)
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arXiv:1502.07151 (*cross-listing*)
Date: Wed, 25 Feb 2015 12:30:58 GMT   (17kb)

Title: Spinless Aharonov-Bohm problem in curved space
Authors: Edilberto O. Silva, S\'ergio C. Ulhoa, Fabiano M. Andrade, Cleverson
  Filgueiras, R. G. G. Amorin
Categories: quant-ph math-ph math.MP
\\
  The dynamics of a spinless charged particle under the influence of a magnetic
field in curved space is considered. We chose the surface as being a cone
defined by a line element in polar coordinates. The geometry of this line
element establishes that the motion of the particle can occur on the surface of
a cone or an anti-cone. As a consequence of the nontrivial topology of the cone
and also because of two-dimensional confinement, the geometric potential should
be taken into account. At first, we establish the conditions for the particle
describing a circular path in such a context. Because of the presence of the
geometric potential, which contains a singular term, we use the self-adjoint
extension method in order to describe the dynamics in all space including the
singularity. Expressions are obtained for the bound state energies and wave
functions.
\\ ( http://arxiv.org/abs/1502.07151 ,  17kb)
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arXiv:1502.07194 (*cross-listing*)
Date: Wed, 25 Feb 2015 15:13:51 GMT   (25kb)

Title: Quantum toroidal gl(1) and Bethe ansatz
Authors: B. Feigin, M. Jimbo, T. Miwa, and E. Mukhin
Categories: math.QA math-ph math.MP
Comments: Latex, 25 pages
\\
  We establish the method of Bethe ansatz for the XXZ type model obtained from
the R-matrix associated to quantum toroidal gl(1). We do that by using shuffle
realizations of the modules and by showing that the Hamiltonian of the model is
obtained from a simple multiplication operator by taking an appropriate
quotient. We expect this approach to be applicable to a wide variety of models.
\\ ( http://arxiv.org/abs/1502.07194 ,  25kb)
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arXiv:1502.07195 (*cross-listing*)
Date: Wed, 25 Feb 2015 15:13:54 GMT   (22kb)

Title: Generalized Graph States Based on Hadamard Matrices
Authors: Shawn X Cui, Nengkun Yu, Bei Zeng
Categories: quant-ph math-ph math.MP
Comments: 16 pages, 11 figures
\\
  Graph states are widely used in quantum information theory, including
entanglement theory, quantum error correction, and one-way quantum computing.
Graph states have a nice structure related to a certain graph, which is given
by either a stabilizer group or an encoding circuit, both can be directly given
by the graph. To generalize graph states, whose stabilizer groups are abelian
subgroups of the Pauli group, one approach taken is to study non-abelian
stabilizers. In this work, we propose to generalize graph states based on the
encoding circuit, which is completely determined by the graph and a Hadamard
matrix. We study the entanglement structures of these generalized graph states,
and show that they are all maximally mixed locally. We also explore the
relationship between the equivalence of Hadamard matrices and local equivalence
of the corresponding generalized graph states. This leads to a natural
generalization of the Pauli $(X,Z)$ pairs, which characterizes the local
symmetries of these generalized graph states. Our approach is also naturally
generalized to construct graph quantum codes which are beyond stabilizer codes.
\\ ( http://arxiv.org/abs/1502.07195 ,  22kb)
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arXiv:1502.07294 (*cross-listing*)
Date: Wed, 25 Feb 2015 18:37:51 GMT   (66kb)

Title: Spin covers of maximal compact subgroups of Kac-Moody groups and
  spin-extended Weyl groups
Authors: David Ghatei and Max Horn and Ralf K\"ohl and Sebastian Wei{\ss}
Categories: math.GR math-ph math.MP
\\
  Let G be a split real Kac-Moody group of arbitrary type and let K be its
maximal compact subgroup, i.e. the subgroup of elements fixed by a
Cartan-Chevalley involution of G. We construct non-trivial spin covers of K,
thus confirming a conjecture by Damour and Hillmann (arXiv:0906.3116). For
irreducible simply laced diagrams and for all spherical diagrams these spin
covers are two-fold central extensions of K. For more complicated irreducible
diagrams these spin covers are central extensions by a finite 2-group of
possibly larger cardinality. Our construction is amalgam-theoretic and makes
use of the generalized spin representations of maximal compact subalgebras of
split real Kac-Moody algebras studied in arXiv:1110.5576. Our spin covers
contain what we call spin-extended Weyl groups which admit a presentation by
generators and relations obtained from the one for extended Weyl groups by
relaxing the condition on the generators so that only their eighth powers are
required to be trivial.
\\ ( http://arxiv.org/abs/1502.07294 ,  66kb)
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arXiv:1304.8122 (*cross-listing*)
replaced with revised version Tue, 24 Feb 2015 21:53:49 GMT   (58kb)

Title: New perturbative method for solving the gravitational N-body problem in
  the general theory of relativity
Authors: Slava G. Turyshev and Viktor T. Toth
Categories: gr-qc math-ph math.MP
Comments: revtex4, 48 pages. arXiv admin note: text overlap with
  arXiv:1109.1796
\\ ( http://arxiv.org/abs/1304.8122 ,  58kb)
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arXiv:1312.2892
replaced with revised version Wed, 25 Feb 2015 09:52:47 GMT   (760kb,D)

Title: Biorthogonal ensembles with two-particle interactions
Authors: Tom Claeys and Stefano Romano
Categories: math-ph math.CA math.CV math.MP
Comments: 28 pages, 6 figures
MSC-class: 60B20, 42C05, 35Q15
Journal-ref: Nonlinearity 27 (2014), 2419-2443
\\ ( http://arxiv.org/abs/1312.2892 ,  760kb)
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arXiv:1406.4702 (*cross-listing*)
replaced with revised version Wed, 25 Feb 2015 00:01:16 GMT   (665kb)

Title: Structure of finite-RSB asymptotic Gibbs measures in the diluted spin
  glass models
Authors: Dmitry Panchenko
Categories: math.PR math-ph math.MP
MSC-class: 60K35, 60G09, 82B44
\\ ( http://arxiv.org/abs/1406.4702 ,  665kb)
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arXiv:1407.5180
replaced with revised version Wed, 25 Feb 2015 14:30:26 GMT   (35kb)

Title: Canonoid and Poissonoid Transformations, Symmetries and BiHamiltonian
  Structures
Authors: Giovanni Rastelli and Manuele Santoprete
Categories: math-ph math.MP
Comments: 34 pages, no figures
MSC-class: 53D05, 37K10, 53D17
\\ ( http://arxiv.org/abs/1407.5180 ,  35kb)
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arXiv:1408.0444
replaced with revised version Tue, 24 Feb 2015 23:26:17 GMT   (25kb)

Title: Quantum dilogarithms and partition q-series
Authors: Akishi Kato and Yuji Terashima
Categories: math-ph hep-th math.CO math.MP math.QA
Comments: 24 pages, published version
MSC-class: 13F60, 16G20, 05E15, 33C80
DOI: 10.1007/s00220-015-2323-y
\\ ( http://arxiv.org/abs/1408.0444 ,  25kb)
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arXiv:1409.0435
replaced with revised version Wed, 25 Feb 2015 09:45:31 GMT   (86kb,D)

Title: Asymptotics for Toeplitz determinants: perturbation of symbols with a
  gap
Authors: Christophe Charlier and Tom Claeys
Categories: math-ph math.CA math.CV math.MP
Comments: 28 pages, 5 figures
Journal-ref: J. Math. Phys 56 (2015), 022705
\\ ( http://arxiv.org/abs/1409.0435 ,  86kb)
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arXiv:1409.3723
replaced with revised version Wed, 25 Feb 2015 13:52:49 GMT   (14kb)

Title: Relativistic covariance of Ohm's law
Authors: R. Starke, G. A. H. Schober
Categories: math-ph cond-mat.mtrl-sci gr-qc math.MP
Comments: minor corrections
\\ ( http://arxiv.org/abs/1409.3723 ,  14kb)
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arXiv:1411.3835 (*cross-listing*)
replaced with revised version Wed, 25 Feb 2015 10:56:12 GMT   (21kb)

Title: Recovering quantum graph spectrum from vertex data
Authors: Jonathan Rohleder
Categories: math.SP math-ph math.MP
Comments: Revised version
\\ ( http://arxiv.org/abs/1411.3835 ,  21kb)
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arXiv:1411.5718 (*cross-listing*)
replaced with revised version Wed, 25 Feb 2015 16:56:06 GMT   (54kb,D)

Title: Inequalities for the quantum privacy
Authors: M. A. S Trindade and E. Pinto
Categories: quant-ph math-ph math.MP
Comments: 9 pages and 4 figures
\\ ( http://arxiv.org/abs/1411.5718 ,  54kb)
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arXiv:1412.5945
replaced with revised version Wed, 25 Feb 2015 11:40:57 GMT   (87kb,D)

Title: Algebraic QFT in Curved Spacetime and quasifree Hadamard states: an
  introduction
Authors: Igor Khavkine and Valter Moretti
Categories: math-ph gr-qc math.MP
Comments: v2: minor corrections, added reference to older work by Sahlmann and
  Verch. v1: 59 pages, 4 figures. arXiv admin note: text overlap with
  arXiv:1008.1776 by other authors
\\ ( http://arxiv.org/abs/1412.5945 ,  87kb)
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arXiv:1502.05756 (*cross-listing*)
replaced with revised version Wed, 25 Feb 2015 10:23:55 GMT   (13kb,D)

Title: Noncommutative Borsuk-Ulam-type conjectures
Authors: Paul F. Baum, Ludwik Dabrowski and Piotr M. Hajac
Categories: math.QA math-ph math.GN math.MP
Comments: 10 pages, 1 figure
\\ ( http://arxiv.org/abs/1502.05756 ,  13kb)
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