The object of the paper is to establish convergence throughout the entire complex plane of sequences of rational functions of prescribed types which satisfy a certain degree of approximation to the function aeyz on the disk \z\ S p. It is assumed that the approximating rational functions have a bounded number of free poles. Estimates are given for the degree of best approximation to the exponen...

We generalize the Toda lattice (or Toda chain) equation to the square lattice, i.e., we construct an integrable nonlinear equation for a scalar field taking values on the square lattice and depending on a continuous (time) variable, characterized by an exponential law of interaction in both discrete directions of the square lattice. We construct the Darboux-Bäcklund transformations for such lat...

Rational proofs, introduced by Azar and Micali (STOC 2012), are a variant of interactive proofs in which the prover is rational, and may deviate from the protocol for increasing his reward. Guo et al. (ITCS 2014) demonstrated that rational proofs are relevant to delegation of computation. By restricting the prover to be computationally bounded, they presented a one-round delegation scheme with ...

Abstract: This study proposes new C rational cubic spline interpolant of the form cubic/quadratic with three shape parameters to preserves the geometric properties of the given data sets. Sufficient conditions for the positivity and data constrained modeling of the rational interpolant are derived on one parameter while the remaining two parameters can further be utilized to change and modify t...

Background: One of social problems which has affected our society and resulted in problems for different groups of people is drug abuse. This issue indicates a serious psychological, physical and social problem in community. Social skills have positive and successful influences in prevention of substance abuse. This includes the ability to explain events correctly and then appropriate decision ...

If the universe is ( or a slice of ) AdS5 space with 3-branes, the 5-dimensional GUT scale on each brane can be indetified as the 5-dimensional Planck scale, but, the 4-dimensional Planck scale is generated from the low 4-dimensional GUT scale exponentially in our world. The 4-dimensional GUT scales and Planck scale are related to the 5-dimensional GUT scales and Planck scale by exponential fac...

We construct non-Abelian analogs for some KdV type equations, including the (rational form of) exponential Calogero--Degasperis equation and generalizations of Schwarzian equation. Equations differential substitutions under study contain arbitrary parameters.