http://journals.math.tku.edu.tw/index.php/TKJM/issue/feedTamkang Journal of Mathematics2017-02-22T09:24:54+08:00Editorial Officeeo-tkjm@mail2.tku.edu.twOpen Journal Systems<h2>Welcome to Tamkang Journal of Mathematics</h2><strong>Aims and Scope</strong><br /><div>To promote research interactions between local and overseas researchers, the Department has been publishing an international mathematics journal, the Tamkang Journal of Mathematics. The journal started as a biannual journal in 1970 and is devoted to high-quality original research papers in pure and applied mathematics. In 1985 it has become a quarterly journal.</div>http://journals.math.tku.edu.tw/index.php/TKJM/article/view/1838On K-extending modules2017-02-16T09:22:36+08:00Tayyebeh Amouzegart.amoozegar@yahoo.comLet $M$ be a right $R$-module and $S=End_R(M)$. We call $M$ a $\mathcal{K}$-extending module if for every element $\phi\in S$, Ker$\phi$ is essential in a direct summand of $M$. In this paper we investigate these modules. We give a characterization of $\mathcal{K}$-extending modules. We prove that if $M$ is a projective self-generator module, then $M$ is a $\mathcal{K}$-extending module and every finitely generated projective right ideal of $S$ is a summand if and only if $S$ is semiregular and $\Delta(M)=Jac(S)$, where $\Delta(M)=\{f\in S \mid Ker f\leq^e M \}$ if and only if $M$ is $Z(M)$-$\mathcal{I}$-lifting.2017-03-30T00:00:00+08:00http://journals.math.tku.edu.tw/index.php/TKJM/article/view/1842A remark on the number of distinct prime divisors of integers2017-02-16T09:22:37+08:00Mehdi Hassanimehdi.hassani@znu.ac.irWe study the asymptotic formula for the sum $\sum_{n\leqslant x}\o(n)$ where $\o(n)$ denotes the number of distinct prime divisors of $n$, and we perform some computations which detect curve patterns in the distribution of a related sequence.2017-03-30T00:00:00+08:00http://journals.math.tku.edu.tw/index.php/TKJM/article/view/2036Coefficients of strongly alpha-convex and alpha-logarithmicaly convex functions2017-02-16T09:22:37+08:00Derek Keith Thomasd.k.thomas@swansea.ac.ukLet the function $f$ be analytic in $D=\{z:|z|<1\}$ and be given by $f(z)=z+\sum_{n=2}^{\infty}a_{n}z^{n}$. For $0< \beta \le 1$, denote by $C (\beta)$ and $S^*(\beta)$ the classes of strongly convex functions and strongly starlike functions respectively. For $0\le \alpha \le1$ and $0< \beta \le 1$, let $M(\alpha, \beta)$ be the class of strongly alpha-convex functions defined by $\left|\arg \Big((1-\alpha) \dfrac{zf'(z)}{f(z)}\Big)+\alpha (1+\dfrac{zf''(z)}{f'(z)})^{}\Big)\right|< \dfrac{\pi \beta }{2}$, and $M^{*}(\alpha, \beta)$ the class of strongly alpha-logarithmically convex functions defined by $\left|\arg\Big( \Big( \dfrac{zf'(z)}{f(z)}\Big)^{1-\alpha}\Big(1+\dfrac{zf''(z)}{f'(z)}\Big)^{\alpha}\Big)\right|< \dfrac{\pi \beta }{2}$. We give sharp bounds for the initial coefficients of $f\in M(\alpha,\beta)$ and $f\in M^{*}(\alpha,\beta)$, and for the initial coefficients of the inverse function $f^{-1}$ of $f\in M(\alpha,\beta)$ and $f\in M^{*}(\alpha,\beta)$. These results generalise and unify known coefficient inequalities for $C (\beta)$ and $S^*(\beta)$2017-03-30T00:00:00+08:00http://journals.math.tku.edu.tw/index.php/TKJM/article/view/2136Global existence and quenching for a damped hyperbolic MEMS equation with the fringing field2017-02-16T09:22:37+08:00Tosiya Miyasitask109685@mail.doshisha.ac.jpWe study a damped hyperbolic MEMS equation with the fringing field.It arises in the Micro-Electro Mechanical System(MEMS) devices. We give some criteria for global existence and quenching of the solution.First we establish a time-local solution by a contraction mapping theorem. This procedure is standard.Next we show that there exists a global solution for the small parameter and initial value. Finally, we deal with the quenching result for the large parameter.2017-03-30T00:00:00+08:00http://journals.math.tku.edu.tw/index.php/TKJM/article/view/2188Liar’s domination in graphs under some operations2017-02-16T09:22:37+08:00Sergio Jr. Rosales Canoyserge_canoy@yahoo.comCarlito Bancoyo Balandracarlito_balandra@yahoo.comA set $S\subseteq V(G)$ is a liar's dominating set ($lds$) of graph $G$ if $|N_G[v]\cap S|\geq 2$ for every $v\in V(G)$ and $|(N_G[u]\cup N_G[v])\cap S|\geq 3$ for any two distinct vertices $u,v \in V(G)$. The liar's domination number of $G$, denoted by $\gamma_{LR}(G)$, is the smallest cardinality of a liar's dominating set of $G$. In this paper we study the concept of liar's domination in the join, corona, and lexicographic product of graphs.2017-03-30T00:00:00+08:00http://journals.math.tku.edu.tw/index.php/TKJM/article/view/2264Sturm-Liouville differential operators with deviating argument2017-02-16T09:22:37+08:00Vjacheslav Anatoljevich Yurkoyurkova@info.sgu.ruSergey Alexandrovich Buterinbuterinsa@info.sgu.ruMilenko Pikulapikulam1947@gmail.comNon-selfadjoint second-order differential operators with a constant delay are studied. We establish properties of the spectral characteristics and investigate the inverse problem of recovering operators from their spectra. For this inverse problem the uniqueness theorem is proved.2017-03-30T00:00:00+08:00http://journals.math.tku.edu.tw/index.php/TKJM/article/view/2274Approximation of generalized Riemann solutions to compressible Euler-Poisson equations of isothermal flows in spherically symmetric space-times2017-02-22T09:24:54+08:00John Meng-Kai Hongjhong@math.ncu.edu.twReyna Marsya Quitareynaquita2905@gmail.comIn this paper, we consider the compressible Euler-Poisson system in spherically symmetric space-times. This system, which describes the conservation of mass and momentum of physical quantity with attracting gravitational potential, can be written as a $3\times 3$ mixed-system of partial differential systems or a $2\times 2$ hyperbolic system of balance laws with $global$ source. We show that, by the equation for the conservation of mass, Euler-Poisson equations can be transformed into a standard $3\times 3$ hyperbolic system of balance laws with $local$ source. The generalized approximate solutions to the Riemann problem of Euler-Poisson equations, which is the building block of generalized Glimm scheme for solving initial-boundary value problems, are provided as the superposition of Lax's type weak solutions of the associated homogeneous conservation laws and the perturbation terms solved by the linearized hyperbolic system with coefficients depending on such Lax solutions.2017-03-30T00:00:00+08:00http://journals.math.tku.edu.tw/index.php/TKJM/article/view/2271Levitin-Polyak well-posedness of completely generalized mixed variational inequalities in reflexive banach spaces2017-02-16T09:22:38+08:00Lu-Chuan Cengzenglc@hotmail.comChing-Feng Wencfwen@kmu.edu.twLet $X$ be a real reflexive Banach space. In this paper, we first introduce the concept of Levitin-Polyak well-posedness of a completely generalized mixed variational inequality in $X$, and establish some characterizations of its Levitin-Polyak well-posedness. Under suitable conditions, we prove that the Levitin-Polyak well-posedness of a completely generalized mixed variational inequality is equivalent both to the Levitin-Polyak well-posedness of a corresponding inclusion problem and to the Levitin-Polyak well-posedness of a corresponding fixed point problem. We also derive some conditions under which a completely generalized mixed variational inequality in $X$ is Levitin-Polyak well-posed. Our results improve, extend and develop the early and recent ones in the literature.2017-03-30T00:00:00+08:00