Related papers: A Variant on the Feline Josephus Problem

Some time ago Wastlund reformulated the Basel problem in terms of a physical system using the proportionality of the apparent brightness of a star to the inverse square of its distance. Inspired by this approach, we give another physical…

Mortality is an instrument of natural selection. Evolutionary motivated theories imply its irreversibility and life history dependence. This is inconsistent with mortality data for protected populations. Accurate analysis yields mortality…

The purpose of this paper is to study a class of ill-posed differential equations. In some settings, these differential equations exhibit uniqueness but not existence, while in others they exhibit existence but not uniqueness. An example of…

In this paper we study the complexity of solving a problem when a solution of a similar instance is known. This problem is relevant whenever instances may change from time to time, and known solutions may not remain valid after the change.…

This paper attempts to explain the mystery behind an 18th elephant that appears in many popular legends involving the division of a herd of 17 elephants into groups in the ratio 1/2:1/3:1/9.

Many real-world optimisation problems involve dynamic and stochastic components. While problems with multiple interacting components are omnipresent in inherently dynamic domains like supply-chain optimisation and logistics, most research…

Mafia (also called Werewolf) is a party game. The participants are divided into two competing groups: citizens and a mafia. The objective is to eliminate the opponent group. The game consists of two consecutive phases (day and night) and a…

A nonlinear algebraic equation system of 5 variables is numerically solved, which is derived from the application of the Fourier transform to a differential equation system that allows modeling the behavior of the temperatures and the…

An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed.…

Motivated by the "tug-of-war" game studied in [12], we consider a "non-local" version of the game which goes as follows: at every step two players pick respectively a direction and then, instead of flipping a coin in order to decide which…

We consider the computational complexity of the question whether a certain strategy can be removed from a game by means of iterated elimination of dominated strategies. In particular, we study the influence of different definitions of…

In this paper, we consider a class of nonlinear fractional differential equations involving Hilfer derivative with boundary conditions. First, we obtain an equivalent integral for the given boundary value problem in weighted space of…

Most stars in the Universe are red dwarfs. They outnumber stars like our Sun by a factor of 5 and outlive them by another factor of 20 (population-weighted mean). When combined with recent observations uncovering an abundance of temperate,…

In a two-stage repeated classical game of prisoners' dilemma the knowledge that both players will defect in the second stage makes the players to defect in the first stage as well. We find a quantum version of this repeated game where the…

A comply/constrain game or a game with a Muller twist is a game where the next player is allowed to place constraints on opponent's next move. We develop a closed form formula for the Grundy value of the single-pile subtraction game where…

In the stable marriage problem, a set of men and a set of women are given, each of whom has a strictly ordered preference list over the acceptable agents in the opposite class. A matching is called stable if it is not blocked by any pair of…

The controversy concerning both the definition of the species and methods for inferring the boundaries and numbers of species has occupied biologists for centuries, and the debate itself has become known as the species problem. The modern…

We consider the problem of manipulating elections by cloning candidates. In our model, a manipulator can replace each candidate c by several clones, i.e., new candidates that are so similar to c that each voter simply replaces c in his vote…

We establish bounds on a finite separable extension of function fields in terms of the relative class number, thus reducing the problem of classifying extensions with a fixed relative class number to a finite computation. We also solve the…

In this paper, the solution of the multi-order differential equations, by using Mellin Transform, is proposed. It is shown that the problem related to the shift of the real part of the argument of the transformed function, arising when the…