Abstract: We discuss the painleve analysis of the variable coefficient of the Burgers equation. Next discuss the symmetries of the variable coefficient of the Burgers equation. We classify one-dimensional and two-dimensional subalgebras of the Burgers equation. Further reduction of these equations to second order equations....
Abstract: In this paper, we have defined the concept $k^{*}$-continuous function in ideal closure spaces. In particular, the properties of open and closed maps, composite of $k^{*}$-continuous functions, characterization of $k^{*}$-homeomorphic functions in ideal closure spaces are explained in detail. Keywords: $k^{*}$-continuous functions, open map, closed map,...
Abstract: The aim of this paper is to apply generalized Kummer's theorem and generalized Dixon's theorem due to Lavoie et al. to establish two general integrals involving Humbert's functions of two variables $ \varPhi_2 $, $ \varPsi_2 $ and Kummer's function $ {}_1F_1 $. Some interesting...
Abstract: Wang and Yeh proved that if $P(x)$ is a polynomial with non-negative and nondecreasing coefficients, then $P(x + d)$ is unimodal for any $d > 0$. A mode of a unimodal polynomial $f(x) = a_0 + a_1x +\cdots+a_mx^m$ is an index $k$ such that...
Abstract: Presented dynamical behavior of a prey--predator system where both prey and predator populations are affected by diseases with susceptible--infected. We also analysis the system of equilibrium point and stability analysis. A system of four differential equation susceptible--infected prey species and predator species has been proposed...
Abstract: The main purpose of the present paper is to introduce and study some weaker forms of continuity in bitopological ordered spaces .Such as pairwise $I$-continuous maps, pairwise $D$-continuous maps, pairwise $B$-continuous maps, pairwise $I$-open maps, pairwise $D$-open maps, pairwise $B$-open maps, pairwise $I$-closed maps,...
Abstract: We present a local convergence analysis for a multi-point family of high order methods in order to approximate a solution of a nonlinear equation in a Banach space setting. The convergence ball and error estimates are given for these methods under H$\ddot{o}$lder continuity conditions....
Abstract: In this paper, we prove some fixed point theorems with the notions of compatible mappings of type$(R)$, of type $(\chi)$ and of type $(E)$ using implicit relations in fuzzy metric space. Keywords: Fuzzy metric space, Compatible mappings, Compatible mappings of type $(R)$, of type $(\chi)$, of...
Abstract: In this paper, the concept of fuzzy simply* Lindelof spaces is introduced and several characterizations of fuzzy simply* Lindelof spaces are given. The conditions under which fuzzy simply* Lindelof spaces become fuzzy simply Lindelof spaces, are obtained. Keywords: Fuzzy nowhere dense set, fuzzy first category set,...
Abstract: New method of generating prime numbers through quantization of discrete geometrical space is proposed. It is shown that quantization of the geometrical space results in stratification of the space into subspaces in such a way that to each subspace a distinct indivisible line is associated....
Abstract: This study develops a mathematical model for two-dimensional solute transport in a semi-infinite heterogeneous porous medium. The geological formation is initially not solute free. The nature of pollutants is considered conservative and gives out from space and time-dependent pulse type point source. Dispersion coefficient is...
Abstract: In this work, we have developed two-point iterative methods with three function evaluations reaching more than fourth order convergence. Furthermore, we show that with the same number of function evaluations we can develop higher order two-point methods of order $r+3$, where $r$ is a...
Abstract: In this present paper we obtain certain results on multivalent analytic functions, as an application of the principle of subordination, with fixed second coefficient. The influence of the second coefficient of $p$-valent analytic functions is realized in the results obtained. Keywords: Analytic functions, $p-$valent starlike...
Abstract: Connectivity and diagnosability play an important role in measuring the fault tolerance of interconnection networks. As a topology structure of interconnection networks, the $n$-dimensional crossed cube $CQ_{n}$ has many good properties. In this paper, we study the 2-extra connectivity and 2-extra diagnosability of $CQ_{n}$. We...
Abstract: In this paper, the notion of neutrosophic soft metric space $(NSMS)$ is introduced in terms of neutrosophic soft points and several related properties, structural characteristics have been investigated. Then the convergence of sequence in neutrosophic soft metric space is defined and illustrated by examples....
Abstract: A nonlinear rational difference equation $x_{n+1}=ax_{n}+\dfrac{\alpha +\beta x_{n-k}}{A+Bx_{n-k}},\;\;\;n=0,1,...,$ of higher order is considered to apprehend the dynamics viz. the invariant intervals, periodic solutions, the character of semi-cycles and global asymptotic stability. {\Large \noindent }Here all the parameters $a$, $% \alpha $, $\beta $ and $A$,...
Abstract: In this paper, we consider the averaging principle for the general uncertain differential equations under a Lipschitz condition. The solutions of convergence in mean square and convergence in uncertain measure between standard uncertain differential equation and the corresponding averaged uncertain delay differential equation are considered....
Abstract: In the present paper, a new class of generalized $(s,m,\varphi)$-preinvex Godunova-Levin function of the second kind is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula are given. Moreover, by using new identity via classical integrals some Hermite-Hadamard, Simpson...
Abstract: The space $r^q(u,p,s)$ of non-absolute type have recently been introduced and studied (see, M. F. Rahman and A. B. M. R. Karim, Generalized Riesz sequence space of non-absolute type and some matrix mappings, Pure and Applied Math. Journal, 4(3)(2015), 90-95). In the present paper, we...
Abstract: If $P(z):=\sum_{j=0}^{n} \alpha_{j}z^{j}$ be a polynomial of degree n such that $ \alpha_{j}=a_{j}+ib_{j} $ where $a_{j}$ and $b_{j}$, j=0,1,...,n are real numbers. In this paper, we prove some extensions and generalizations of the classical results of the well known Enestr\"{o}m-Kakeya theorem by imposing restrictions on...