We show that e, π and other remarkable real numbers are limits of E-computable sequences of rational numbers having a polynomial rate of convergence (as usual, E denotes the second Grzegorczyk class). However, only the rational numbers are limits of E-computable sequences of rational numbers with an exponential rate of convergence

The aim of this paper is to present a PSPACE algorithm which yields a finite graph of exponential size and which describes the set of all solutions of equations in free groups as well as the set of all solutions of equations in free monoids with involution in the presence of rational constraints. This became possible due to the recently invented recompression technique of the second author. He ...

Integrable models of resonant interaction of two or more waves in 1+1 dimensions are known to be of applicative interest in several areas. Here we consider a system of three coupled wave equations which includes as special cases the vector nonlinear Schrödinger equations and the equations describing the resonant interaction of three waves. The Darboux-Dressing construction of soliton solutions ...

Optical soliton solutions in a magneto-optical waveguide and other exact are investigated for the coupled system of nonlinear Biswas–Milovic equation with Kudryashov’s law using extended F-expansion method. Various types extracted, such as dark solutions, singular dark–singular combo soliton, Jacobi elliptic periodic hyperbolic rational exponential Weierstrass solutions. The obtained different ...

In multi-hop cellular networks, the existence of a communication link between the mobile station and the base station is not required: a mobile station that has no direct connection with a base station can use other mobile stations as relays. Compared with conventional (single-hop) cellular networks, this new generation can lead to a better usage of the available spectrum and to a reduction of ...

In multi-hop cellular networks, the existence of a communication link between the mobile station and the base station is not required: a mobile station that has no direct connection with a base station can use other mobile stations as relays. Compared with conventional (single-hop) cellular networks, this new generation can lead to a better usage of the available spectrum and to a reduction of ...

This paper researches the accuracy of the Differential Transformation Method (DTM) for solving the Holling Tanner models which are described as two-dimensional system of ODES with quadratic and rational nonlinearities. Numerical results are compared to those obtained by the fourth-order Runge-Kutta method to illustrate the preciseness and effectiveness of the proposed method. The direct symboli...

This paper challenges the conventional wisdom dominating social sciences and philosophy regarding temporal discounting, practice of discounting value future utility when making decisions. Although there are sharp disagreements about a kind standard model has arisen, one that begins with normative how we should make intertemporal comparisons utility. demands in so far as is rational discounts ut...

A discounted-sum automaton (NDA) is a nondeterministic finite automaton with edge weights, valuing a run by the discounted sum of visited edge weights. More precisely, the weight in the i-th position of the run is divided by λ, where the discount factor λ is a fixed rational number greater than 1. The value of a word is the minimal value of the automaton runs on it. Discounted summation is a co...