Tamkang Journal of Mathematics https://journals.math.tku.edu.tw/index.php/TKJM <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> Tamkang University en-US Tamkang Journal of Mathematics 0049-2930 A Brief introduction of Professor Yurko https://journals.math.tku.edu.tw/index.php/TKJM/article/view/3346 Sergey Buterin Copyright (c) 2019 https://creativecommons.org/licenses/by-nc-sa/4.0 2019-09-03 2019-09-03 50 3 i ii 10.5556/j.tkjm.50.2019.3346 Inverse Problems for Sturm-Liouville Differential Operators on Closed Sets https://journals.math.tku.edu.tw/index.php/TKJM/article/view/3343 <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> V. Yurko Copyright (c) 2019-09-02 2019-09-02 50 3 199 206 10.5556/j.tkjm.50.2019.3343 An inverse spectral problem for Sturm-Liouville-type integro-differential operators with robin boundary conditions https://journals.math.tku.edu.tw/index.php/TKJM/article/view/3347 <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> Sergey Buterin Copyright (c) 2019-09-02 2019-09-02 50 3 207 221 10.5556/j.tkjm.50.2019.3347 The eigenvalues’ function of the family of Sturm-Liouville operators and the inverse problems https://journals.math.tku.edu.tw/index.php/TKJM/article/view/3352 <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> Tigran Harutyunyan Copyright (c) 2019-09-02 2019-09-02 50 3 233 252 10.5556/j.tkjm.50.2019.3352 An inverse problem for the second-order integro-differential pencil https://journals.math.tku.edu.tw/index.php/TKJM/article/view/3348 <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> Natalia P. Bondarenko Copyright (c) 2019-09-02 2019-09-02 50 3 223 231 10.5556/j.tkjm.50.2019.3348 Integral transforms connected with differential systems with a singularity. https://journals.math.tku.edu.tw/index.php/TKJM/article/view/3353 <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> Mikhail Ignatiev Copyright (c) 2019-09-02 2019-09-02 50 3 253 268 10.5556/j.tkjm.50.2019.3353 The formula for the regularized trace of the Sturm-Liouville operator with a logarithmic potential https://journals.math.tku.edu.tw/index.php/TKJM/article/view/3354 <p>We have obtained a regularized trace formula for the Sturm-Liouville operator on a semi-axis with a logarithmic potential.</p> Khabir Kabirovich Ishkin Leisan Gainullovna Valiullina Copyright (c) 2019-09-02 2019-09-02 50 3 269 280 10.5556/j.tkjm.50.2019.3354 An inverse spectral problem for Sturm-Liouville operators with singular potentials on arbitrary compact graphs https://journals.math.tku.edu.tw/index.php/TKJM/article/view/3356 <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> S. V. Vasiliev Copyright (c) 2019-09-02 2019-09-02 50 3 293 305 10.5556/j.tkjm.50.2019.3356 The partial inverse nodal problem for differential pencils on a finite interval https://journals.math.tku.edu.tw/index.php/TKJM/article/view/3359 <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> Y. P. Wang Yiteng Hu Chung-Tsun Shieh Copyright (c) 2019-09-02 2019-09-02 50 3 307 319 Inverse spectral problem for the matrix Sturm-Liouville operator with the general separated self-adjoint boundary conditions https://journals.math.tku.edu.tw/index.php/TKJM/article/view/3360 <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> Xiao-Chuan Xu Copyright (c) 2019-09-02 2019-09-02 50 3 321 336 10.5556/j.tkjm.50.2019.3360 Inverse nodal problem for nonlocal differential operators https://journals.math.tku.edu.tw/index.php/TKJM/article/view/3361 <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> Xin-Jian Xu Chuan-Fu Yang Copyright (c) 2019-09-02 2019-09-02 50 3 337 347 10.5556/j.tkjm.50.2019.3361 Inverse problem for Sturm-Liouville operators on a curve https://journals.math.tku.edu.tw/index.php/TKJM/article/view/3368 <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> Andrey Aleksandrovich Golubkov Yulia Vladimirovna Kuryshova Copyright (c) 2019-09-02 2019-09-02 50 3 349 359 10.5556/j.tkjm.50.2019.3368 On the Integration of the matrix modified Korteweg-de Vries equation with a self-consistent source https://journals.math.tku.edu.tw/index.php/TKJM/article/view/3355 <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> G. U. Urazboev A. K. Babadjanova Copyright (c) 2019-09-03 2019-09-03 50 3 281 291 10.5556/j.tkjm.50.2019.3355