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ISSN: 2523-0212 (online) 2616-4906 (Print)
ISSN: 2616-8111 (online) 2616-8103 (Print)
ISSN: 2617-9687 (online) 2617-9679 (Print)
ISSN: 2618-0758 (online) 2618-074X (Print)
ISSN: 2617-9709 (online) 2617-9695 (Print)
ISSN: 2791-0814 (online) 2791-0806 (Print)
Open Journal of Mathematical Science (OMS)
ISSN: 2523-0212 (online) 2616-4906 (Print)
Open Journal of Mathematical Analysis (OMA)
ISSN: 2616-8111 (online) 2616-8103 (Print)
Open Journal of Discrete Applied Mathematics (ODAM)
ISSN: 2617-9687 (online) 2617-9679 (Print)
Ptolemy Journal of Chemistry (PJC)
ISSN: 2618-0758 (online) 2618-074X (Print)
Engineering and Applied Science Letters (EASL)
ISSN: 2617-9709 (online) 2617-9695 (Print)
Trends in Clinical and Medical Sciences (TCMS)
ISSN: 2791-0814 (online) 2791-0806 (Print)
This paper studies the movement of a molecule in two types of cell complexes: the square tiling and the hexagonal one. This movement from a cell \(i\) to a cell \(j\) is referred to as an homogeneous Markov chain. States with the same stochastic behavior are grouped together using symmetries of states deduced from groups acting on the cellular complexes. This technique of lumpability is effective in forming new chains from the old ones without losing the primitive properties and simplifying tedious calculations. Numerical simulations are performed using R software to determine the impact of the shape of the tiling and other parameters on the achievement of the equilibrium. We start from small square tiling to small hexagonal tiling before comparing the results obtained for each of them. In this paper, only continuous Markov chains are considered. In each tiling, the molecule is supposed to leave the central cell and move into the surrounding cells.
In this work, we are concerned with a problem for a viscoelastic wave equation with strong damping, nonlinear source and distributed delay terms. We show the exponential growth of solution with \(L_{p}\)-norm, i.e., \(\lim\limits_{t\rightarrow \infty}\Vert u\Vert_p^p \rightarrow \infty\).
A new recursion in only one variable allows very simple verifications of Bressoud’s polynomial identities, which lead to the Rogers-Ramanujan identities. This approach might be compared with an earlier approach due to Chapman. Applying the \(q\)-Chu-Vandermonde convolution, as suggested by Cigler, makes the computations particularly simple and elementary. The same treatment is also applied to the Santos polynomials and perhaps more polynomials from a list of Rogers-Ramanujan like polynomials [1].
Let \(0<k\in\mathbb{Z}\). A reinterpretation of the proof of existence of Hamilton cycles in the middle-levels graph \(M_k\) induced by the vertices of the \((2k+1)\)-cube representing the \(k\)- and \((k+1)\)-subsets of \(\{0,\ldots,2k\}\) is given via an associated dihedral quotient graph of \(M_k\) whose vertices represent the ordered (rooted) trees of order \(k+1\) and size \(k\).
Let \(G\) be a simple graph. A total dominator coloring of \(G\) is a proper coloring of the vertices of \(G\) in which each vertex of the graph is adjacent to every vertex of some color class. The total dominator chromatic number \(\chi_d^t(G)\) of \(G\) is the minimum number of colors among all total dominator coloring of \(G\). In this paper, we study the total dominator chromatic number of some graphs with specific construction. Also we compare \(\chi_d^t(G)\) with \(\chi_d^t(G-e)\), where \(e\in E(G)\).
As a generalization of KU-algebras, the notion of pseudo-KU algebras is introduced in 2020 by the author (D. A. Romano. Pseudo-UP algebras, An introduction. Bull. Int. Math. Virtual Inst., 10(2)(2020), 349-355). Some characterizations of pseudo-KU algebras are established in that article. In addition, it is shown that each pseudo-KU algebra is a pseudo-UP algebra. In this paper it is a concept developed of pseudo-KU algebras in more detail and it has identified some of the main features of this type of universal algebras such as the notions of pseudo-subalgebras, pseudo-ideals, pseudo-filters and pseudo homomorphisms. Also, it has been shown that every pseudo-KU algebra is a pseudo-BE algebra. In addition, a congruence was constructed on a pseudo-KU algebra generated by a pseudo-ideal and shown that the corresponding factor-structure is and pseudo-KU algebra as well.
In this article, modified difference-type estimator for the population mean in two-phase sampling scheme using two auxiliary variables has been proposed. The mean squared error of the proposed estimator has also been derived using large sample approximation. The efficiency comparison conditions for the proposed estimator in comparison with other existing estimators in which the proposed estimator performed better than the other relevant existing estimators have been given.
Let \(G = (V,E)\) be a simple connected undirected graph. In this paper, we define generalized the Liouville’s and Möbius functions of a graph \(G\) which are the sum of Liouville \(\lambda\) and Möbius \(\mu\) functions of the degree of the vertices of a graph denoted by \(\Lambda(G)=\sum\limits_{v\in V(G)}\lambda(deg(v))\) and \(M(G)=\sum\limits_{v\in V(G)}\mu(deg(v))\), respectively. We also determine the Liouville’s and Möbius functions of some standard graphs as well as determining the relationships between the two functions with their proofs. The sum of generalized the Liouville and Möbius functions extending over the divisor d of degree of vertices of graphs is also given.
In this paper, we introduce a symmetric function in order to derive a new generating functions of bivariate Pell Lucas polynomials. We define complete homogeneous symmetric functions and give generating functions for Gauss Fibonacci polynomials, Gauss Lucas polynomials, bivariate Fibonacci polynomials, bivariate Lucas polynomials, bivariate
Jacobsthal polynomials and bivariate Jacobsthal Lucas polynomials.
We establish the strong generalized solution of the second mixed problem for an Euler-Poisson-Darboux equation in which the free term has the form: \(\gamma(t) u(x_0,t_0)\) where \(u(x,t)\) is the unknown function sought at the point \((x_0,t_0).\)
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