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Asymptotic estimates on the time derivative of entropy on a Riemannian manifold
the time derivative entropy Riemannian manifold
2010/11/23
We consider the entropy of the solution to the heat equation on a Riemannian manifold. When the manifold is compact, we provide two estimates on the rate of change of the entropy in terms of the lower...
On correlation function of high moments of Wigner random matrices
correlation function Wigner random matrices
2010/11/23
We consider the Wigner ensemble of Hermitian n-dimensional random matrices and study the correlation function K(s',s") of their moments in the limit when the numbers s', s" of the moments are proporti...
Nash Problem for quotient surface singularities
Nash Problem quotient surface singularities
2010/11/22
We give an affirmative answer to Nash Problem for quotient surface singularities, in particular for the icosahedral singularity $E_8$.
I present an inverse function theorem for differentiable maps between Frechet spaces which contains the classical theorem of Nash and Moser as a particular case. In contrast to the latter, the proof ...
Polytopes, Hopf algebras and Quasi-symmetric functions
Polytopes Hopf algebras Quasi-symmetric functions
2010/11/11
In this paper we use the technique of Hopf algebras and quasi-symmetric functions to study the combinatorial polytopes. Consider the free abelian group $\mathcal{P}$ generated by all combinatorial po...
Wigner quantization of some one-dimensional Hamiltonians
Wigner quantization one-dimensional Hamiltonians
2010/11/15
Recently, several papers have been dedicated to the Wigner quantization of different Hamiltonians. In these examples, many interesting mathematical and physical properties have been shown. Among those...
Productivity of sequences with respect to a given weight function
Productivity weight function
2010/11/11
Given a function f: N --> (omega+1)-{0}, we say that a faithfully indexed sequence {a_n: n in N} of elements of a topological group G is: (i) f-Cauchy productive (f-productive) provided that the seque...
For n > 2, the Dehn functions of Aut(F_n) and Out(F_n) are exponential.
On functional relations for the alternating analogues of Tornheim's double zeta function
Tornheim's double zeta function
2010/11/18
We give two functional relations for the alternating analogues of Tornheim's double zeta function. Using the functional relations, we give new proofs of some evaluation formulas found by H. Tsumura fo...
Eigenfunctions and Very Singular Similarity Solutions of Odd-Order Nonlinear Dispersion PDEs
Eigenfunctions Very Singular Similarity Solutions Odd-Order Nonlinear Dispersion PDEs
2010/11/11
Asymptotic properties of solutions of odd-order nonlinear dispersion equations are studied. The global in time similarity solutions, which lead to eigenfunctions of the rescaled ODEs, are constructed....
Jacob's ladders, Bessel's functions and the asymptotic solutions of a new class of nonlinear integral equations
Jacob's ladders Bessel's functions the asymptotic solutions
2010/11/19
It is shown in this paper that there is a connection between the Riemann zeta-function $\zf$ and the Bessel's functions. In this direction, a new class of the nonlinear integral equations is introduce...
A number of mathematical methods have been shown to model the zeroes of $L$-functions with remarkable success, including the Ratios Conjecture and Random Matrix Theory. In order to understand the str...
Concerning the $L^4$ norms of typical eigenfunctions on compact surfaces
typical eigenfunctions compact surfaces
2010/11/8
Let $(M,g)$ be a two-dimensional compact boundaryless Riemannian manifold with Laplacian, $\Delta_g$. If $e_\lambda$ are the associated eigenfunctions of $\sqrt{-\Delta_g}$ so that $-\Delta_g e_\lamb...
On combinatorial invariance of the cohomology of Milnor fiber of arrangements and Catalan equation over function field
Milnor fiber arrangements Catalan equation function field
2010/11/8
We show that for arrangements of lines with points of multiplicity at most three, the cohomology of Milnor fiber is determined only by the combinatorics of arrangement. The proof depends on enumeratio...
On Reliability Function of BSC with Noisy Feedback
Reliability Function BSC with Noisy Feedback
2010/11/15
For information transmission a binary symmetric channel is used. There is also another noisy binary symmetric channel (feedback channel), and the transmitter observes without delay all the outputs of...