http://eastwestmath.org/index.php/ewm/issue/feedEast West Math2024-03-05T16:00:11+08:00Trung, Nguyen Hoang Baonhbtrung@ntt.edu.vnOpen Journal Systemshttp://eastwestmath.org/index.php/ewm/article/view/485STRUCTURES OF POWER DIGRAPHS ASSOCIATED WITH xpk ≡ y (mod n) WHERE p IS AN ODD PRIME2024-02-27T12:47:05+08:00Ratinan Boonklurbratinan.b@chula.ac.thPinkaew Siriwongpinkaew.s@tsu.ac.th<p><span class="fontstyle0">Let </span><span class="fontstyle2">k </span><span class="fontstyle0">and </span><span class="fontstyle2">n </span><span class="fontstyle0">be positive integers and </span><span class="fontstyle2">p </span><span class="fontstyle0">be an odd prime. A power </span><span class="fontstyle0">digraph </span><span class="fontstyle2">G</span><span class="fontstyle0">(</span><span class="fontstyle2">p</span><span class="fontstyle3">k</span><span class="fontstyle2">; n</span><span class="fontstyle0">) for which the vertex set is </span><span class="fontstyle4">f</span><span class="fontstyle0">0</span><span class="fontstyle2">; </span><span class="fontstyle0">1</span><span class="fontstyle2">; </span><span class="fontstyle0">2</span><span class="fontstyle2">; : : : ; n </span><span class="fontstyle4">- </span><span class="fontstyle0">1</span><span class="fontstyle4">g </span><span class="fontstyle0">and (</span><span class="fontstyle2">u; v</span><span class="fontstyle0">) </span><span class="fontstyle0">is a directed edge from a vertex </span><span class="fontstyle2">u </span><span class="fontstyle0">to a vertex </span><span class="fontstyle2">v </span><span class="fontstyle0">if </span><span class="fontstyle2">u</span><span class="fontstyle3">p</span><span class="fontstyle5">k </span><span class="fontstyle4">≡ </span><span class="fontstyle2">v </span><span class="fontstyle0">(mod </span><span class="fontstyle2">n</span><span class="fontstyle0">). We </span><span class="fontstyle0">study the structures of this power digraphs. Moreover, we provide some interesting results when </span><span class="fontstyle2">p </span><span class="fontstyle0">is 3</span><span class="fontstyle2">; </span><span class="fontstyle0">5 or 7.</span></p>2024-02-27T00:00:00+08:00Copyright (c) 2024 East West Mathhttp://eastwestmath.org/index.php/ewm/article/view/486EXISTENCE OF THREE WEAK SOLUTIONS FOR THE KIRCHHOFF-TYPE PROBLEM WITH MIXED BOUNDARY CONDITION IN A VARIABLE SOBOLEV SPACE2024-02-27T12:59:17+08:00Junichi Aramakiaramaki@hctv.ne.jp<p><span class="fontstyle0">In this paper, we consider the Kirchhoff-type problem for a class of nonlinear operators containing </span><span class="fontstyle2">p</span><span class="fontstyle0">(</span><span class="fontstyle3">·</span><span class="fontstyle0">)-Laplacian and mean curvature operator with mixed boundary conditions. More precisely, we are concerned with the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary. We show the existence of at least three weak solutions according to hypotheses on given functions and values of parameters.</span></p>2024-02-27T00:00:00+08:00Copyright (c) 2024 East West Mathhttp://eastwestmath.org/index.php/ewm/article/view/487ON THE COFINITENESS OF IN DIMENSION < 2 LOCAL COHOMOLOGY MODULES FOR A PAIR OF IDEALS2024-02-27T14:26:11+08:00Ngo Thi Ngoanhoangnv@utc.edu.vnNguyen Van Hoanghoangnv@utc.edu.vnNguyen Huy Hoanghoangnv@utc.edu.vn<p><span class="fontstyle0">In this note, we prove the cofiniteness of local cohomology modules </span><span class="fontstyle2">H</span><span class="fontstyle3">i I;J</span><span class="fontstyle0">(</span><span class="fontstyle2">N</span><span class="fontstyle0">) with respect to a pair of ideals (</span><span class="fontstyle2">I; J</span><span class="fontstyle0">) for all </span><span class="fontstyle2">i < t </span><span class="fontstyle0">and </span><span class="fontstyle0">the finiteness of (0 :</span><span class="fontstyle3">H</span><span class="fontstyle4">t I;J </span><span class="fontstyle5">(</span><span class="fontstyle3">N</span><span class="fontstyle5">) </span><span class="fontstyle2">I</span><span class="fontstyle0">) and Ext</span><span class="fontstyle5">1 </span><span class="fontstyle3">R</span><span class="fontstyle0">(</span><span class="fontstyle2">R=I; H</span><span class="fontstyle3">I;J t </span><span class="fontstyle0">(</span><span class="fontstyle2">N</span><span class="fontstyle0">)) provided that</span></p> <p><span class="fontstyle0">Ext</span><span class="fontstyle3">i R</span><span class="fontstyle0">(</span><span class="fontstyle2">R=I; N</span><span class="fontstyle0">) is finitely generated for all </span><span class="fontstyle2">i </span><span class="fontstyle6">≤ </span><span class="fontstyle2">t </span><span class="fontstyle0">+ 1 and </span><span class="fontstyle2">H</span><span class="fontstyle3">I;J i </span><span class="fontstyle0">(</span><span class="fontstyle2">N</span><span class="fontstyle0">) is in dimension </span><span class="fontstyle2">< </span><span class="fontstyle0">2 for all </span><span class="fontstyle2">i < t</span><span class="fontstyle0">, where </span><span class="fontstyle2">t </span><span class="fontstyle6">≥ </span><span class="fontstyle0">1 is an integer (here, </span><span class="fontstyle2">N </span><span class="fontstyle0">is not necessarily finitely generated over </span><span class="fontstyle2">R</span><span class="fontstyle0">). This extends the results of Bahmanpour-Naghipour [5, Thm 2.6], Bahmanpour-Naghipour-Sedghi [4, Thm 2.8] and H-N [16, Thm 1.1].</span> </p>2024-02-27T14:25:49+08:00Copyright (c) 2024 East West Mathhttp://eastwestmath.org/index.php/ewm/article/view/488PICARD OPERATORS IN STRONG b-TVS CONE METRIC SPACES2024-03-05T15:57:32+08:00Bui The Hunghungbt@tnue.edu.vnDoan Trong Hieuhieupci@gmail.com<p><span class="fontstyle0">Let </span><span class="fontstyle2">X </span><span class="fontstyle0">be a topological space. A mapping </span><span class="fontstyle2">T </span><span class="fontstyle0">: </span><span class="fontstyle2">X </span><span class="fontstyle3">! </span><span class="fontstyle2">X </span><span class="fontstyle0">is called a Picard operator if </span><span class="fontstyle2">T </span><span class="fontstyle0">has a unique fixed point ¯ </span><span class="fontstyle2">x </span><span class="fontstyle3">2 </span><span class="fontstyle2">X </span><span class="fontstyle0">and for any </span><span class="fontstyle2">x </span><span class="fontstyle3">2 </span><span class="fontstyle2">X</span><span class="fontstyle0">, the sequence of iterates </span><span class="fontstyle3">f</span><span class="fontstyle2">T </span><span class="fontstyle4">n</span><span class="fontstyle2">x</span><span class="fontstyle3">g </span><span class="fontstyle0">converge to ¯ </span><span class="fontstyle2">x</span><span class="fontstyle0">. In this paper, we give new results concerning the existence of Picard operators in strong </span><span class="fontstyle2">b</span><span class="fontstyle0">-TVS cone metric space. Our result is an extension of Sh. Rezapuor and R. Hamlbarani [19]</span> </p>2024-02-27T00:00:00+08:00Copyright (c) 2024 East West Mathhttp://eastwestmath.org/index.php/ewm/article/view/489MATHEMATICAL LITERACY FOR DIGITAL ERA: REVIEW OF MATHEMATICAL THINKING AND COMPUTATIONAL THINKING FOR CURRICULUM DEVELOPMENT2024-03-05T16:00:11+08:00Maitree Inprasithainprasithacrme@kku.ac.thMasami Isodaisoda@criced.tsukuba.ac.jpRoberto Arayaroberto.araya.schulz@gmail.com<p><span class="fontstyle0">In the Era of AI and Data Science under the fourth industrial revolution, Mathematical Capitalism (Ministry of Economy, Trade and Industry, Japan., 2019 [32]) becomes a key issue in Education up to higher education in this changing society. Mathematical Thinking provides the grand for Informatics as a school subject that develops computational thinking. This article confirmed mathematics as the key literacy subject in school and re-viewed it as universal literacy in the era through the confirmation of mathematical thinking and value are a necessary component of general competency in the era. This claim is illustrated by the historical meaning of mathematics, the current aims of mathematics education, and re-viewed the meaning of mathematics education for the digital society <br></span></p>2024-02-27T14:32:26+08:00Copyright (c) 2024 East West Math