After the social learning models were proposed, finding solutions to the games becomes a well-defined mathematical question. However, almost all papers on the games and their applications are based on solutions built either upon an ad-hoc argument or a twisted Bayesian analysis of the games. Here, we present logical gaps in those solutions and offer an exact solution of our own. We also introdu...

One of the promising lightwave network architectures is the multihop lightwave networks based on wavelength division multiplexing (WDM). In this architecture, separate channels created by assigning different wavelengths between node pairs define the logical connectivity. This logical topology is independent of the underlying physical topology and can be adaptively changed according to the chang...

We investigate exact solutions and the asymptotic dynamics for Friedmann-Lema\^{\i}tre-Robertson-Walker universe with nonzero spatial curvature in fourth-order modified teleparallel gravitational theory known as $f\left( T, B\right) $ theory. show that field equations admit a minisuperspace description, they can reproduce any form of scale factor. Moreover, we calculate equilibrium points analy...

We study the performance of distance-three surface code layouts under realistic multi-parameter noise models. We first calculate their thresholds under depolarizing noise. We then compare a Pauli-twirl approximation of amplitude and phase damping to amplitude and phase damping. We find the approximate channel results in a pessimistic estimate of the logical error rate, indicating the realistic ...

The design of multiple-choice questions (MCQs) to assess students’ knowledge and abilities is a delicate task. A well designed test is in fact required to meet some fundamental requirements, some concerning linguistic aspects and others being of a more logical nature. This paper presents a system that can be used to assist the designer of logical test items, i.e. questions aiming at verifying l...

We reexamine the three-body problem in the framework of general relativity. The Newtonian N-body problem admits choreographic solutions, where a solution is called choreographic if every massive particle moves periodically in a single closed orbit. One is a stable figure-eight orbit for a three-body system, which was found first by Moore (1993) and rediscovered with its existence proof by Chenc...

For all μ > 0, a locally Lipschitz continuous map f with xf (x) > 0, x ∈ R\{0}, is constructed, such that the scalar equation ẋ (t) = −μx (t)−f (x (t− 1)) with delayed negative feedback has an infinite number of periodic orbits. All periodic solutions defining these orbits oscillate slowly around 0 in the sense that they admit at most one sign change in each interval of length of 1. Moreover, i...

In the paper we present a survey on the mathematical modeling of nonconvex and nonsmooth problems arising in the mathematical theory of contact mechanics which is a growing field in engineering and scientific computing. The approach to such problems is based on the notion of hemivariational inequality and our presentation focuses on three aspects. First we present the ideas leading to inequalit...