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Abstract: It is shown that the original construction of polar codes suffices to achieve the symmetric capacity of discrete memoryless channels with arbitrary input alphabet sizes. It is shown that in ...
Abstract: We consider integrable discretizations of some soliton equations associated with the motions of plane curves: the Wadati-Konno-Ichikawa elastic beam equation, the complex Dym equation, and t...
Abstract: Here the Integral Value Transformations (IVTs) are considered to be Discrete Dynamical System map in the space\mathbb{N}_(0). In this paper, the dynamics of IVTs is deciphered through the li...
Abstract: It is suggest that a new fractal model for the Yang-Fourier transforms of discrete approximation based on local fractional calculus and the Discrete Yang-Fourier transforms are investigated ...
Abstract: The general topic of the present paper is to study the conservation for some structural property of a given problem when discretising this problem. Precisely we are interested with Lagrangia...
Abstract: Given a chain complex with the only modi?cation that each cell of the complex has a probability distribution assigned. We will call this complex - a random complex and what should be underst...
Abstract: C. Markett proved a Cohen type inequality for the classical Laguerre expansions in the appropriate weighted $L^{p}$ spaces. In this paper, we get a Cohen type inequality for the Fourier expa...
Abstract: Let $(\Omega,\mathscr{F},\mathbb{P})$ be a probability space and $\bS=\{\mathrm{S}_1,...,\mathrm{S}_K\}$ a discrete-topological space that consists of $K$ real $d$-by-$d$ matrices, where $K$...
Abstract: In this paper we give another proof of the fact that a random overlap array, which satisfies the Ghirlanda-Guerra identities and whose elements take values in a finite set, is ultrametric wi...
Abstract: Generalized uncertainty principle and breakdown of the spacetime continuum certainly represent two important results derived of various approaches related to quantum gravity and black hole p...
A group-theoretical approach for studying localized periodic and quasiperiodic vibrations in 2D and 3D lattice dynamical models is developed. This approach is demonstrated for the scalar mod- els on...
Abstract: The discrete non-linear Schrodinger (NLS) model in the presence of an integrable defect is examined. The problem is viewed from a purely algebraic point of view, starting from the fundamenta...
Abstract: We define the quadratic algebra su(2)_{\alpha} which is a one-parameter deformation of the Lie algebra su(2) extended by a parity operator. The odd-dimensional representations of su(2) (with...
Abstract: We outline a field theory on a multifractal spacetime. The measure in the action is characterized by a varying Hausdorff dimension and logarithmic oscillations governed by a fundamental phys...
Abstract: The linear canonical transformations of geometric optics on two-dimensional screens form the group $Sp(4,R)$, whose maximal compact subgroup is the Fourier group $U(2)_F$; this includes isot...

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