Stationary Boltzmann equation: an approach via Morse theory

In this paper we study the unidimensional Stationary Boltzmann Equation by an approach via Morse theory. We define a functional J whose critical points coincide with the solutions of the Stationary Boltzmann Equation. By the calculation of Morse index of J’’0(0)h and the critical groups C2(J, 0) and C2(J, ∞) we prove that J has two different critical points u1 and u2 different from 0, that is, solutions of Boltzmann Equation.

Laplacian integral graphs with a given degree sequence constraint

Let G be a graph on n vertices. The Laplacian matrix of G, denoted by L(G), is defined as L(G) = D(G) −A(G), where A(G) is the adjacency matrix of G and D(G) is the diagonal matrix of the vertex degrees of G. A graph G is said to be L-integral if all eigenvalues of the matrix L(G) are integers. In this paper, we characterize all Lintegral non-bipartite graphs among all connected graphs with at most two vertices of degree larger than or equal to three.

Power domination in splitting and degree splitting graph

A vertex set S is called a power dominating set of a graph G if every vertex within the system is monitored by the set S following a collection of rules for power grid monitoring. The power domination number of G is the order of a minimal power dominating set of G. In this paper, we solve the power domination number for splitting and degree splitting graph.

New Hermite-Hadamard type inequalities for m and (α, m)-convex functions on the coordinates via generalized fractional integrals

In this paper, we obtained a new Hermite-Hadamard type inequality for functions of two independent variables that are m-convex on the coordinates via some generalized Katugampola type fractional integrals. We also established a new identity involving the second order mixed partial derivatives of functions of two independent variables via the generalized Katugampola fractional integrals. Using the identity, we established some new Hermite-Hadamard type inequalities for functions whose second order mixed partial derivatives in absolute value at some powers are (α, m)-convex on the coordinates. Our results are extensions of some earlier results in the literature for functions of two variables.

Domination in the entire nilpotent element graph of a module over a commutative ring

Let R be a commutative ring with unity and M be a unitary R module. Let Nil(M) be the set of all nilpotent elements of M. The entire nilpotent element graph of M over R is an undirected graph E(G(M)) with vertex set as M and any two distinct vertices x and y are adjacent if and only if x + y ∈ Nil(M). In this paper we attempt to study the domination in the graph E(G(M)) and investigate the domination number as well as bondage number of E(G(M)) and its induced subgraphs N(G(M)) and Non(G(M)). Some domination parameters of E(G(M)) are also studied. It has been showed that E(G(M)) is excellent, domatically full and well covered under certain conditions.

The paradox of heat conduction, influence of variable viscosity, and thermal conductivity on magnetized dissipative Casson fluid with stratification models

The boundary layer flow of temperature-dependent variable thermal conductivity and dynamic viscosity on flow, heat, and mass transfer of magnetized and dissipative Casson fluid over a slenderized stretching sheet has been studied. The model explores the Cattaneo-Christov heat flux paradox instead of the Fourier’s law plus the stratifications impact. The variable temperature-dependent plastic dynamic viscosity and thermal conductivity were assumed to vary as a linear function of temperature. The governing systems of equations in PDEs were transformed into non-linear ordinary differential equations using the suitable similarity transformations, hence the approximate solutions were obtained using Chebyshev Spectral Collocation Method (CSCM). Effects of pertinent flow parameters on concentration, temperature, and velocity profiles are presented graphically and tabled, therein, thermal relaxation and wall thickness parameters slow down the distribution of the flowing fluid. A rise in Casson parameter, temperature-dependent thermal conductivity, and velocity power index parameter increases the skin friction thus leading to a decrease in energy and mass gradient at the wall, also, temperature gradient attain maximum within 0.2 - 1.0 variation of Casson parameter.

A note on convolution operators on Riesz Bounded variation spaces

We show some estimates and approximation results of operators of convolution type defined on Riesz Bounded variation spaces in Rn. We also state some embedding results that involve the collection of generalized absolutely continuous functions.

On the domination polynomial of a digraph: a generation function approach

Let G be a directed graph on n vertices. The domination polynomial of G is the polynomial D(G, x) =∑ni=0 d(G, i)xi, where d(G, i) is the number of dominating sets of G with i vertices. In this paper, we prove that the domination polynomial of G can be obtained by using an ordinary generating function. Besides, we show that our method is useful to obtain the minimum-weighted dominating set of a graph.

Fixed point theorems in the study of positive strict set-contractions

The author uses fixed point index properties and Inspired by the work in Benmezai and Boucheneb (see Theorem 3.8 in [3]) to prove new fixed point theorems for strict set-contraction defined on a Banach space and leaving invariant a cone.

Linear maps on ℬ(ℋ) preserving some operator properties

In this paper, for a complex Hilbert space ℋ with dim ℋ ≥ 2, we study the linear maps on ℬ(ℋ), the bounded linear operators on ℋ, that preserves projections and idempotents. As a result, we characterize the linear maps on ℬ(ℋ) that preserves involutions in both directions.