Tamkang Journal of Mathematics 2019-09-04T02:24:41+00:00 Editorial Office Open Journal Systems <p><strong>Welcome to Tamkang Journal of Mathematics </strong><span lang="en"><strong><span lang="en"><span lang="en"><br><br><strong>~Hot News~ </strong><br><strong>Tamkang Journal of Mathematics(TKJM) is included in Emerging Sources Citation Index (ESCI)</strong> <br><br><img src="/public/201709_ESCI_toTKJM.jpg" alt="TKJM in ESCI" width="469" height="220"><br><br><br><strong>Aims and Scope</strong><br></span></span></strong></span></p> <p>&nbsp;</p> <p>&nbsp;</p> <p>&nbsp;</p> <p>&nbsp;</p> <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 &nbsp;in pure and applied mathematics. In 1985 it has become a quarterly journal.</div> A Brief introduction of Professor Yurko 2019-09-03T11:15:07+00:00 Sergey Buterin 2019-09-03T02:30:04+00:00 Copyright (c) 2019 Inverse Problems for Sturm-Liouville Differential Operators on Closed Sets 2019-09-03T11:20:54+00:00 V. Yurko <p>Second-order differential operators on closed sets (time scales) are considered. Properties of their spectral characteristics are obtained and inverse problems are studied, which consists in recovering the operators from their spectral characteristics. We establish the uniqueness and develop constructive algorithms for the solution of the inverse problems.</p> 2019-09-02T00:00:00+00:00 Copyright (c) An inverse spectral problem for Sturm-Liouville-type integro-differential operators with robin boundary conditions 2019-09-03T11:20:22+00:00 Sergey Buterin <p>The perturbation of the Sturm--Liouville differential operator on a finite interval with Robin boundary conditions by a convolution operator is considered. The inverse problem of recovering the convolution term along with one boundary condition from the spectrum is studied, provided that the Sturm--Liouville potential as well as the other boundary condition are known a priori. The uniqueness of solution for this inverse problem is established along with necessary and sufficient conditions for its solvability. The proof is constructive and gives an algorithm for solving the inverse problem.</p> 2019-09-02T00:00:00+00:00 Copyright (c) The eigenvalues’ function of the family of Sturm-Liouville operators and the inverse problems 2019-09-03T11:19:17+00:00 Tigran Harutyunyan <p>We study the direct and inverse problems for the family of Sturm-Liouville operators, generated by fixed potential q and the family of separated boundary conditions. We prove that the union of the spectra of all these operators can be represented as a smooth surface (as the values of a real analytic function of two variables), which has specific properties. We call this function ”the eigenvalues function of the family of Sturm-Liouville operators (EVF)”. From the properties of this function we select those, which are sufficient for a function of two variables be the EVF a family of Sturm-Liouville operators.</p> 2019-09-02T06:53:18+00:00 Copyright (c) An inverse problem for the second-order integro-differential pencil 2019-09-03T11:18:46+00:00 Natalia P. Bondarenko <p>We consider the second-order (Sturm-Liouville) integro-differential pencil with polynomial dependence on the spectral parameter in a boundary condition. The inverse problem is solved, which consists in reconstruction of the convolution kernel and one of the polynomials in the boundary condition by using the eigenvalues and the two other polynomials. We prove uniqueness of solution, develop a constructive algorithm for solving the inverse problem, and obtain necessary and sufficient conditions for its solvability.</p> 2019-09-02T06:53:37+00:00 Copyright (c) Integral transforms connected with differential systems with a singularity. 2019-09-03T11:18:14+00:00 Mikhail Ignatiev <p>We consider some integral transforms with the kernels expressed in terms of solutions of the system of differential equations \( y'=(x^{-1}A+B)y, \) where \(A\) and \(B\) are constant \(n\times n\), \(n&gt;2\) , matrices. We study analytical and asymptotical properties of such transforms. We also study the transforms as operators acting in some functional spaces.</p> 2019-09-02T06:53:56+00:00 Copyright (c) The formula for the regularized trace of the Sturm-Liouville operator with a logarithmic potential 2019-09-03T11:17:42+00:00 Khabir Kabirovich Ishkin Leisan Gainullovna Valiullina <p>We have obtained a regularized trace formula for the Sturm-Liouville operator on a semi-axis with a logarithmic potential.</p> 2019-09-02T06:54:12+00:00 Copyright (c) An inverse spectral problem for Sturm-Liouville operators with singular potentials on arbitrary compact graphs 2019-09-03T11:17:11+00:00 S. V. Vasiliev <p>Sturm-Liouville differential operators with singular potentials on arbitrary com- pact graphs are studied. The uniqueness of recovering operators from Weyl functions is proved and a constructive procedure for the solution of this class of inverse problems is provided.</p> 2019-09-02T06:54:30+00:00 Copyright (c) The partial inverse nodal problem for differential pencils on a finite interval 2019-09-03T02:28:47+00:00 Y. P. Wang Yiteng Hu Chung-Tsun Shieh <p>In this paper, the partial inverse nodal problem for differential pencils with real-valued coefficients on a finite interval \([0,1]\) was studied. The authors showed that the coefficients \((q_{0}(x),q_{1}(x),h,H_0)\) of the differential pencil \(L_0\) can be uniquely determined by partial nodal data on the right(or, left) arbitrary subinterval \([a,b]\) of \([0,1].\) Finally, an example was given to verify the validity of the reconstruction algorithm for this inverse nodal problem.</p> 2019-09-02T06:54:47+00:00 Copyright (c) Inverse spectral problem for the matrix Sturm-Liouville operator with the general separated self-adjoint boundary conditions 2019-09-03T11:16:40+00:00 Xiao-Chuan Xu <p>In this work, we study the matrix Sturm-Liouville operator with the separated self-adjoint boundary conditions of general type, in terms of two unitary matrices. Some properties of the eigenvalues and the normalization matrices are given. Uniqueness theorems for determining the potential and the unitary matrices in the boundary conditions from the Weyl matrix, two characteristic matrices or one spectrum and the corresponding normalization matrices are proved.</p> 2019-09-02T06:55:18+00:00 Copyright (c) Inverse nodal problem for nonlocal differential operators 2019-09-03T11:16:08+00:00 Xin-Jian Xu Chuan-Fu Yang <p>Inverse nodal problem consists in constructing operators from the given zeros of<span class="Apple-converted-space">&nbsp; </span>their eigenfunctions. The problem of differential operators with nonlocal boundary condition appears, e.g., in scattering theory, diffusion processes and the other applicable fields. In this paper, we consider a class of differential operators with nonlocal boundary condition, and show that the potential function can be determined by nodal data.</p> 2019-09-02T06:55:35+00:00 Copyright (c) Inverse problem for Sturm-Liouville operators on a curve 2019-09-03T11:19:49+00:00 Andrey Aleksandrovich Golubkov Yulia Vladimirovna Kuryshova <p class="p1">he inverse spectral problem for the Sturm-Liouville equation with a piecewise-entire potential function and the discontinuity conditions for solutions on a rectifiable curve \(\gamma \subset \textbf{C}\) by the transfer matrix along this curve is studied. By the method of a unit transfer matrix the uniqueness of the solution to this problem is proved with the help of studying of the asymptotic behavior of the solutions to the Sturm-Liouville equation for large values of the spectral parameter module.</p> 2019-09-02T00:00:00+00:00 Copyright (c) On the Integration of the matrix modified Korteweg-de Vries equation with a self-consistent source 2019-09-04T02:24:41+00:00 G. U. Urazboev A. K. Babadjanova <p>In this work we deduce laws of the evolution of the scattering &nbsp;data for the matrix Zakharov Shabat system with the potential that is the solution of the matrix modied KdV equation with a self consistent source.</p> 2019-09-03T00:18:18+00:00 Copyright (c)