###### Applications of Stochastic Semigroups to Queueing Models

## Abstract

Non-markovian queueing systems can be extended to piecewise-deterministic Markov processes by appending supplementary variables to the system. Then their analysis leads to an infinite system of partial differential equations with an infinite number of variables and non-local boundary conditions. We show how one can study such systems by using the theory of stochastic semigroups.

###### Approximate Analytical Solutions to Conformable Modified Burgers Equation Using Homotopy Analysis Method

## Abstract

In this paper the authors aspire to obtain the approximate analytical solution of Modified Burgers Equation with newly defined conformable derivative by employing homotopy analysis method (HAM).

###### Complex Gleason Measures and the Nemytsky Operator

## Abstract

This work is devoted to the generalization of previous results on Gleason measures to complex Gleason measures. We develop a functional calculus for complex measures in relation to the Nemytsky operator. Furthermore we present and discuss the interpretation of our results with applications in the field of quantum mechanics. Some concrete examples and further extensions of several theorems are also presented.

###### D-Homothetically Deformed Kenmotsu Metric as a Ricci Soliton

## Abstract

In this paper we study the nature of Ricci solitons in *D*-homo-thetically deformed Kenmotsu manifolds. We prove that *η* -Einstein Kenmotsu metric as a Ricci soliton remains *η* -Einstein under *D*-homothetic deformation and the scalar curvature remains constant.

######
Exploring mod 2 *n*-queens games

## Abstract

We introduce a two player game on an n × n chessboard where queens are placed by alternating turns on a chessboard square whose availability is determined by the parity of the number of queens already on the board which can attack that square. The game is explored as well as its variations and complexity.

######
Extending the Applicability of the Super-Halley-Like Method Using *ω*-Continuous Derivatives and Restricted Convergence Domains

## Abstract

We present a local convergence analysis of the super-Halley-like method in order to approximate a locally unique solution of an equation in a Banach space setting. The convergence analysis in earlier studies was based on hypotheses reaching up to the third derivative of the operator. In the present study we expand the applicability of the super-Halley-like method by using hypotheses up to the second derivative. We also provide: a computable error on the distances involved and a uniqueness result based on Lipschitz constants. Numerical examples are also presented in this study.

###### Finite, Fiber- and Orientation-Preserving Group Actions on Totally Orientable Seifert Manifolds

## Abstract

In this paper we consider the finite groups that act fiber- and orientation-preservingly on closed, compact, and orientable Seifert manifolds that fiber over an orientable base space. We establish a method of constructing such group actions and then show that if an action satisfies a condition on the obstruction class of the Seifert manifold, it can be derived from the given construction. The obstruction condition is refined and the general structure of the finite groups that act via the construction is provided.

###### Insert a Root to Extract a Root of Quintic Quickly

## Abstract

The usual way of solving a solvable quintic equation has been to establish more equations than unknowns, so that some relation among the coefficients comes up, leading to the solutions. In this paper, a relation among the coefficients of a principal quintic equation is established by effecting a change of variable and inserting a root to the quintic equation, and then equating odd-powers of the resulting sextic equation to zero. This leads to an even-powered sextic equation, or equivalently a cubic equation; thus one needs to solve the cubic equation.

We break from this tradition, rather factor the even-powered sextic equation in a novel fashion, such that the inserted root is identified quickly along with one root of the quintic equation in a quadratic factor of the form, *u*
^{2}
*− g*
^{2} = (*u* + *g*)(*u − g*). Thus there is no need to solve any cubic equation. As an extra benefit, this root is a function of only one coefficient of the given quintic equation.

###### Inverse Ambiguous Functions and Automorphisms on Finite Groups

## Abstract

If *G* is a finite group, then a bijective function *f* : *G → G* is inverse ambiguous if and only if *f*(*x*)^{−1} = *f*
^{−1}(*x*) for all *x ∈ G*. We give a precise description when a finite group admits an inverse ambiguous function and when a finite group admits an inverse ambiguous automorphism.

###### Isomorphism Theorems for Coalgebras

## Abstract

Let *F* be an endofunctor of a category *C*. We prove isomorphism theorems for *F* -coalgebras under condition that the underlying category *C* is exact; that is, regular with exact sequences. Also, *F* is not assumed to preserve pullbacks.