Authors:Moh.Ivan Azis Pages: 1 - 20 Abstract: The anisotropic-diffusion convection equation of spatially variable coefficients which is relevant for functionally graded media is discussed in this paper to find numerical solutions by using a combined Laplace transform and boundary element method. The variable coefficients equation is transformed to a constant coefficients equation. The constant coefficients equation is then Laplace-transformed so that the time variable vanishes. The Laplace-transformed equation is consequently written in a pure boundary integral equation which involves a time-free fundamental solution. The boundary integral equation is therefore employed to find numerical solutions using a standard boundary element method. Finally the results obtained are inversely transformed numerically using the Stehfest formula to get solutions in the time variable. The combined Laplace transform and boundary element method is easy to be implemented, efficient and accurate for solving unsteady problems of anisotropic functionally graded media governed by the diffusion convection equation. PubDate: 2023-02-01 DOI: 10.5556/j.tkjm.54.2023.4069 Issue No:Vol. 54, No. 1 (2023)
Authors:Bhawna Kohli Pages: 21 - 41 Abstract: In this paper, a multiobjective fractional bilevel programming problem is considered and optimality conditions using the concept of convexifactors are established for it. For this purpose, a suitable constraint qualification in terms of convexifactors is introduced for the problem. Further in the paper, notions of asymptotic pseudoconvexity, asymptotic quasiconvexity in terms of convexifactors are given and using them sufficient optimality conditions are derived. PubDate: 2023-02-01 DOI: 10.5556/j.tkjm.54.2023.3830 Issue No:Vol. 54, No. 1 (2023)
Authors:Alex M. Montes Pages: 43 - 55 Abstract: In this paper, via a variational approach, we show the existence of periodic traveling waves for a Kadomtsev-Petviashvili Boussinesq type system that describes the propagation of long waves in wide channels. We show that those periodic solutions are characterized as critical points of some functional, for which the existence of critical points follows as a consequence of the Mountain Pass Theorem and Arzela-Ascoli Theorem. PubDate: 2023-02-01 DOI: 10.5556/j.tkjm.54.2023.3971 Issue No:Vol. 54, No. 1 (2023)
Authors:Abdulhamit Ekinci, Seyit Temir Pages: 57 - 67 Abstract: In this paper, we study a new iterative scheme to approximate fixed point of Suzuki nonexpansive type mappings in Banach space. We also prove some weak and strong theorems for Suzuki nonexpansive type mappings. Numerical example is given to show the efficiency of new iteration process. The results obtained in this paper improve the recent ones announced by B. S. Thakur et al. \cite{Thakur}, Ullah and Arschad \cite{UA}. PubDate: 2023-02-01 DOI: 10.5556/j.tkjm.54.2023.3943 Issue No:Vol. 54, No. 1 (2023)
Authors:Tapatee Sahoo, Bijan Davvaz, Harikrishnan Panackal, Babushri Srinivas Kedukodi, Syam Prasad Kuncham Pages: 69 - 82 Abstract: Let $G$ be an $N$-group where $N$ is a (right) nearring. We introduce the concept of relative essential ideal (or $N$-subgroup) as a generalization of the concept of essential submodule of a module over a ring or a nearring. We provide suitable examples to distinguish the notions relative essential and essential ideals. We prove the important properties and obtain equivalent conditions for the relative essential ideals (or $N$-subgroups) involving the quotient. Further, we derive results on direct sums, complement ideals of $N$-groups and obtain their properties under homomorphism. PubDate: 2023-02-01 DOI: 10.5556/j.tkjm.54.2023.4136 Issue No:Vol. 54, No. 1 (2023)
Authors:Shariefuddin Pirzada, Saleem Khan Pages: 83 - 91 Abstract: Let $G$ be a connected graph with $n$ vertices, $m$ edges and having diameter $d$. The distance Laplacian matrix $D^{L}$ is defined as $D^L=$Diag$(Tr)-D$, where Diag$(Tr)$ is the diagonal matrix of vertex transmissions and $D$ is the distance matrix of $G$. The distance Laplacian eigenvalues of $G$ are the eigenvalues of $D^{L}$ and are denoted by $\delta_{1}, ~\delta_{1},~\dots,\delta_{n}$. In this paper, we obtain (a) the upper bounds for the sum of $k$ largest and (b) the lower bounds for the sum of $k$ smallest non-zero, distance Laplacian eigenvalues of $G$ in terms of order $n$, diameter $d$ and Wiener index $W$ of $G$. We characterize the extremal cases of these bounds. As a consequence, we also obtain the bounds for the sum of the powers of the distance Laplacian eigenvalues of $G$. PubDate: 2023-02-01 DOI: 10.5556/j.tkjm.54.2023.4120 Issue No:Vol. 54, No. 1 (2023)
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