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Tamkang Journal of Mathematics
Journal Prestige (SJR): 0.334

Citation Impact (citeScore): 1
Number of Followers: 0

This is an Open Access Journal

Open Access journal
ISSN (Print) 0049-2930 - ISSN (Online) 2073-9826
Published by Tamkang University

[2 journals]

Local distance antimagic chromatic number for the union of complete
bipartite graphs
- Authors: Nalliah M
  Pages: 281 - 291
  Abstract: Let G be a graph on p vertices and q edges with no isolated vertices. A bijection f : V → {1, 2, 3, ..., p} is called local distance antimagic labeling, if for any two adjacent vertices u and v, we have w(u) is not equal to w(v), where w(u) is the sum of all neighbour labels of u. The local distance antimagic chromatic number χlda(G) is defined to be the minimum number of colors taken overall colorings of G induced by local distance antimagic labelings of G. In this paper, we determine the graph G for the local distance antimagic chromatic number is 2.
  PubDate: 2022-08-21
  DOI: 10.5556/j.tkjm.54.2023.4804
  Issue No: Vol. 54, No. 4 (2022)
Fitted operator average finite difference method for singularly perturbed
delay parabolic reaction diffusion problems with non-local boundary
conditions
- Authors: Wakjira Tolassa Gobena, Gemechis File Duressa
  Pages: 293 - 312
  Abstract: This paper deals with numerical solution of singularly perturbed delay parabolic reaction diffusion problem having large delay on the spatial variable with non-local boundary condition. The solution of the problem exhibits parabolic boundary layer on both sides of the spatial domain and interior layer is also created. Introducing a fitting parameter into asymptotic solution and applying average finite difference approximation, a fitted operator finite difference method is developed for solving the problem under consideration. To treat the non-local boundary condition, Simpson's rule is applied. The stability and $\varepsilon$ uniform convergence analysis has been carried out. To validate the applicability of the scheme, numerical examples are presented and solved for different values of the perturbation parameter $\varepsilon$ and mesh sizes. The numerical results are tabulated in terms of maximum absolute errors and rate of convergence and it is observed that the present method is more accurate and shown to be second order Uniformly convergent in both direction, and it also improves the results of the methods existing in the literature.
  PubDate: 2022-10-14
  DOI: 10.5556/j.tkjm.54.2023.4175
  Issue No: Vol. 54, No. 4 (2022)
An exponentially fitted spline method for singularly perturbed parabolic
convection-diffusion problems with large time delay
- Authors: Naol Tufa Negero, Gemechis File Duressa
  Pages: 313 - 338
  Abstract: This paper deals with the numerical solutions of singularly perturbed parabolic convection-diffusion problems with a large delay in time. An exponentially fitted scheme is formulated using cubic splines method in equally-spaced grids. As the delay parameter is larger than the perturbation parameter, a special type of mesh is used for the temporal variable so that the shift lies on the nodal points and an exponentially fitted cubic spline method based on Crank-Nicolson's discretization scheme is developed. The obtained scheme is conditionally stable. Parameter-uniform error estimates are derived and it is shown that the method is ε-uniformly convergent of second-order accurate in both temporal direction and spatial direction. The proposed method provides more accurate solutions than an upwind finite difference scheme in a piecewise uniform mesh.
  PubDate: 2022-08-21
  DOI: 10.5556/j.tkjm.54.2023.3983
  Issue No: Vol. 54, No. 4 (2022)
On the Bari basis property for even-order differential operators with
involution
- Authors: Dmitry Polyakov
  Pages: 339 - 351
  Abstract: By using the method of similar operators we study even-order differential operators with involution. The domain of these operators are defined by periodic and antiperiodic~boundary conditions. We obtain estimates for spectral projections and we prove the Bari basis property for the system of eigenfunctions and associated functions
  PubDate: 2022-07-29
  DOI: 10.5556/j.tkjm.54.2023.4899
  Issue No: Vol. 54, No. 4 (2022)
Normalized null hypersurfaces in the Lorentz-Minkowski space satisfying
$L_r x =U x +b$
- Authors: Hans Fotsing Tetsing, Cyriaque Atindogbé, Ferdinand Nkageu
  Pages: 353 - 378
  Abstract: In the present paper, we classify all normalized null hypersurfaces
  $x: (M,g,N)\to\R^{n+2}_1$ endowed with UCC-normalization with vanishing
  $1-$form $\tau$, satisfying $L_r x =U x +b$ for some (field of)
  screen constant matrix $U\in \R^{(n+2)\times(n+2)}$ and vector
  $b\in\R^{n+2}_{1}$, where $L_r$ is the linearized operator of the
  $(r+1)th-$mean curvature of the normalized null hypersurface for
  $r=0,...,n$. For $r=0$, $L_0=\Delta^\eta$ is nothing but the
  (pseudo-)Laplacian operator on $(M, g, N)$. We prove that the lightcone
  $\Lambda_0^{n+1}$, lightcone cylinders $\Lambda_0^{m+1}\times\R^{n-m}$,
  $1\leq m\leq n-1$ and $(r+1)-$maximal Monge null hypersurfaces are the
  only UCC-normalized Monge null hypersurface with vanishing normalization
  $1-$form $\tau$ satisfying the above equation. In case $U$ is the (field of)
  scalar matrix $ \lambda I$, $\lambda\in\R$ and hence is constant on the whole
  $M$, we show that the only normalized Monge null hypersurfaces
  $x: (M,g,N)\to\R^{n+2}_1$ satisfying $\Delta^\eta x =\lambda x +b$, are
  open pieces of hyperplanes.
  PubDate: 2022-08-21
  DOI: 10.5556/j.tkjm.54.2023.4851
  Issue No: Vol. 54, No. 4 (2022)
Analyzing stability of equilibrium points in impulsive neural network
models involving generalized piecewise alternately advanced and retarded
argument
- Authors: Kuo-Shou Chiu
  Pages: 379 - 404
  Abstract: In this paper, we investigate the models of the impulsive cellular neural network with piecewise alternately advanced and retarded argument of generalized argument (in short IDEPCAG).
  To ensure the existence, uniqueness and global exponential stability of the equilibrium state, several new sufficient conditions are obtained.
  The method is based on utilizing Banach's fixed point theorem and a new IDEPCAG's Gronwall inequality.
  The criteria given are easy to check and when the impulsive effects do not affect, the results can be extracted from those of the non-impulsive systems.
  Typical numerical simulation examples are used to show the validity and effectiveness of proposed results.
  PubDate: 2022-07-29
  DOI: 10.5556/j.tkjm.54.2023.4740
  Issue No: Vol. 54, No. 4 (2022)

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