Theory and Applications of Mathematics & Computer Science https://uav.ro/applications/se/journal/index.php/TAMCS <!-- /* Font Definitions */ @font-face {font-family:"Cambria Math"; panose-1:2 4 5 3 5 4 6 3 2 4;} @font-face {font-family:Calibri; panose-1:2 15 5 2 2 2 4 3 2 4;} @font-face {font-family:Tahoma; panose-1:2 11 6 4 3 5 4 4 2 4;} @font-face {font-family:"Century Schoolbook"; panose-1:2 4 6 4 5 5 5 2 3 4;} /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {margin-top:0in; margin-right:0in; margin-bottom:10.0pt; margin-left:0in; line-height:115%; font-size:11.0pt; font-family:"Calibri","sans-serif";} a:link, span.MsoHyperlink {color:blue; text-decoration:underline;} a:visited, span.MsoHyperlinkFollowed {color:purple; text-decoration:underline;} em {font-weight:bold; font-style:normal;} p.MsoAcetate, li.MsoAcetate, div.MsoAcetate {mso-style-link:"Balloon Text Char"; margin:0in; margin-bottom:.0001pt; font-size:8.0pt; font-family:"Tahoma","sans-serif";} p.msopapdefault, li.msopapdefault, div.msopapdefault {mso-style-name:msopapdefault; margin-right:0in; margin-bottom:10.0pt; margin-left:0in; line-height:115%; font-size:12.0pt; font-family:"Times New Roman","serif";} p.msochpdefault, li.msochpdefault, div.msochpdefault {mso-style-name:msochpdefault; margin-right:0in; margin-left:0in; font-size:10.0pt; font-family:"Times New Roman","serif";} span.BalloonTextChar {mso-style-name:"Balloon Text Char"; mso-style-link:"Balloon Text"; font-family:"Tahoma","sans-serif";} .MsoChpDefault {font-size:10.0pt;} .MsoPapDefault {margin-bottom:10.0pt; line-height:115%;} @page Section1 {size:8.5in 11.0in; margin:1.0in 1.0in 1.0in 1.0in;} div.Section1 {page:Section1;} --> <div class="Section1"> <p class="MsoNormal" style="text-align: justify; text-indent: .5in; line-height: normal; margin: 12.0pt 0in 12.0pt 0in;"><strong><span style="font-size: 13.0pt; font-family: 'Century Schoolbook','serif'; color: #000000;"> Theory Appl. Math. Comput. Sci. <br>An International Journal Focused on Fuzzy Methods</span></strong></p> <p class="MsoNormal" style="text-align: justify; text-indent: .5in; line-height: normal; margin: 12.0pt 0in .0001pt 0in;"><strong><span style="font-size: 13.0pt; font-family: 'Century Schoolbook','serif'; color: #000000;">ISSN 2067-2764; E-ISSN 2247-6202</span></strong></p> <p>&nbsp;</p> <p class="MsoNormal" style="text-align: justify; text-indent: .5in; line-height: normal; margin: 12.0pt 0in .0001pt 0in;"><strong><span style="font-size: 13.0pt; font-family: 'Century Schoolbook','serif'; color: #000000;"> Journal Scope </span></strong></p> <p class="MsoNormal" style="text-align: justify; text-indent: .5in; line-height: normal; margin: 12.0pt 0in .0001pt 0in;"><strong><span style="font-size: 13.0pt; font-family: 'Century Schoolbook','serif'; color: #b91b0f;">The journal “Theory and Applications of Mathematics &amp; Computer Science (TAMCS)” publishes high-quality original articles and state-of-the-art surveys in the areas of pure and applied mathematics and computer science, but giving a preference in presenting works in the theory and applications of fuzzy sets and systems in the areas of mathematics, artificial intelligence and control.</span></strong></p> <p>&nbsp;</p> <p class="MsoNormal" style="text-align: justify; text-indent: .5in; line-height: normal; margin: 12.0pt 0in .0001pt 0in;"><strong><span style="font-size: 13.0pt; font-family: 'Century Schoolbook','serif'; color: #000000;"> Journal Topics </span></strong></p> <p class="MsoListParagraphCxSpFirst" style="mso-add-space: auto; text-align: justify; text-indent: -.25in; mso-list: l1 level1 lfo2; margin: 12.0pt 0in 12.0pt 3.5in;"><!-- [if !supportLists]--><span style="font-size: 13.0pt; mso-bidi-font-size: 12.0pt; font-family: Wingdings; mso-fareast-font-family: Wingdings; mso-bidi-font-family: Wingdings; color: #b91b0f; mso-bidi-font-weight: bold;"><span style="mso-list: Ignore;">v</span></span><!--[endif]--><strong><span style="font-size: 13.0pt; mso-bidi-font-size: 12.0pt; font-family: 'Century Schoolbook','serif'; mso-fareast-font-family: 'Times New Roman'; color: #b91b0f;">Fuzzy mathematics</span></strong></p> <p class="MsoListParagraphCxSpMiddle" style="mso-add-space: auto; text-align: justify; text-indent: -.25in; mso-list: l1 level1 lfo2; margin: 12.0pt 0in 12.0pt 3.5in;"><!-- [if !supportLists]--><span style="font-size: 13.0pt; mso-bidi-font-size: 12.0pt; font-family: Wingdings; mso-fareast-font-family: Wingdings; mso-bidi-font-family: Wingdings; color: #b91b0f; mso-bidi-font-weight: bold;"><span style="mso-list: Ignore;">v</span></span><!--[endif]--><strong><span style="font-size: 13.0pt; mso-bidi-font-size: 12.0pt; font-family: 'Century Schoolbook','serif'; mso-fareast-font-family: 'Times New Roman'; color: #b91b0f;">Artificial intelligence</span></strong></p> <p class="MsoListParagraphCxSpMiddle" style="mso-add-space: auto; text-align: justify; text-indent: -.25in; mso-list: l1 level1 lfo2; margin: 12.0pt 0in 12.0pt 3.5in;"><!-- [if !supportLists]--><span style="font-size: 13.0pt; mso-bidi-font-size: 12.0pt; font-family: Wingdings; mso-fareast-font-family: Wingdings; mso-bidi-font-family: Wingdings; color: #b91b0f; mso-bidi-font-weight: bold;"><span style="mso-list: Ignore;">v</span></span><!--[endif]--><strong><span style="font-size: 13.0pt; mso-bidi-font-size: 12.0pt; font-family: 'Century Schoolbook','serif'; mso-fareast-font-family: 'Times New Roman'; color: #b91b0f;"> Fuzzy control systems</span></strong></p> <p class="MsoListParagraphCxSpMiddle" style="mso-add-space: auto; text-align: justify; text-indent: -.25in; mso-list: l1 level1 lfo2; margin: 12.0pt 0in 12.0pt 3.5in;"><!-- [if !supportLists]--><span style="font-size: 13.0pt; mso-bidi-font-size: 12.0pt; font-family: Wingdings; mso-fareast-font-family: Wingdings; mso-bidi-font-family: Wingdings; color: #b91b0f; mso-bidi-font-weight: bold;"><span style="mso-list: Ignore;">v</span></span><!--[endif]--><strong><span style="font-size: 13.0pt; mso-bidi-font-size: 12.0pt; font-family: 'Century Schoolbook','serif'; mso-fareast-font-family: 'Times New Roman'; color: #b91b0f;">Functional analysis</span></strong></p> <p class="MsoListParagraphCxSpLast" style="mso-add-space: auto; text-align: justify; text-indent: -.25in; mso-list: l1 level1 lfo2; margin: 12.0pt 0in 12.0pt 3.5in;"><!-- [if !supportLists]--><span style="font-size: 13.0pt; mso-bidi-font-size: 12.0pt; font-family: Wingdings; mso-fareast-font-family: Wingdings; mso-bidi-font-family: Wingdings; color: #b91b0f; mso-bidi-font-weight: bold;"><span style="mso-list: Ignore;">v</span></span><!--[endif]--><strong><span style="font-size: 13.0pt; mso-bidi-font-size: 12.0pt; font-family: 'Century Schoolbook','serif'; mso-fareast-font-family: 'Times New Roman'; color: #b91b0f;">Operator theory</span></strong></p> <p class="MsoListParagraphCxSpFirst" style="mso-add-space: auto; text-align: justify; text-indent: -.25in; mso-list: l1 level1 lfo2; margin: 12.0pt 0in 12.0pt 3.5in;"><!-- [if !supportLists]--><span style="font-size: 13.0pt; mso-bidi-font-size: 12.0pt; font-family: Wingdings; mso-fareast-font-family: Wingdings; mso-bidi-font-family: Wingdings; color: #b91b0f; mso-bidi-font-weight: bold;"><span style="mso-list: Ignore;">v</span></span><!--[endif]--><strong><span style="font-size: 13.0pt; mso-bidi-font-size: 12.0pt; font-family: 'Century Schoolbook','serif'; mso-fareast-font-family: 'Times New Roman'; color: #b91b0f;"> Differential equations</span></strong></p> <p>&nbsp;</p> <p>&nbsp;</p> <p class="MsoNormal" style="text-align: justify; line-height: 200%; margin: 0in 35.3pt .0001pt 0in;">&nbsp;</p> <p class="MsoNormal" style="text-align: justify; line-height: 200%; margin: 0in 35.3pt .0001pt 0in;">&nbsp;</p> <p class="MsoNormal" style="text-align: justify; line-height: 200%; margin: 0in 35.3pt .0001pt 0in;"><strong><span style="font-size: 13.0pt; line-height: 200%; font-family: 'Century Schoolbook','serif'; color: #b91b0f;">Abstracting / Indexing in:</span></strong></p> <p>&nbsp;<strong><strong><strong><span style="font-size: 13.0pt; line-height: 200%; font-family: 'Arial Black','sans-serif'; color: #c00000;">Mathematical Reviews® (MathSciNet®)&nbsp;</span></strong></strong></strong></p> <strong><strong><strong> <br><img src="/applications/se/journal/public/site/images/admin/zbmath.gif" alt=""> <span style="font-size: 13.0pt; line-height: 115%; font-family: 'Century Schoolbook','serif'; color: #b91b0f;"><span style="font-size: 13.0pt; font-family: 'Century Schoolbook','serif'; color: #b91b0f;"><img src="/applications/se/journal/public/site/images/admin/centralProquest.jpg" alt=""> <img src="/applications/se/journal/public/site/images/admin/03-16_EBSCOhost_3.gif" alt="" width="214" height="68"> </span></span></strong></strong></strong> <p>&nbsp;</p> <p class="MsoNormal" style="text-align: justify; line-height: 200%; margin: 0in 35.3pt .0001pt 0in;">&nbsp;</p> <p class="MsoNormal" style="text-align: justify; line-height: 200%; margin: 0in 35.3pt .0001pt 0in;"><strong><strong><span style="font-size: 14.0pt; line-height: 200%; font-family: 'Century Schoolbook','serif'; color: #0975bf;">Urlich’s Periodicals Directory.</span></strong></strong></p> </div> <div class="Section1"><br> <p class="MsoNormal" style="line-height: normal;">&nbsp;</p> <p class="MsoNormal"><strong>&nbsp;</strong></p> </div> EDITURA UNIVERSITĂŢII “AUREL VLAICU” ARAD en-US Theory and Applications of Mathematics & Computer Science 2067-2764 <p><strong>Copyright Policies</strong></p> <p>All authors must sign the Transfer of Copyright agreement before the article can be published. This transfer agreement enables EDITURA UNIVERSITĂŢII "AUREL VLAICU" ARAD, ROMANIA&nbsp; to protect the copyrighted material for the authors, but does not relinquish the authors' proprietary rights. The copyright transfer covers the exclusive rights to reproduce and distribute the article, including reprints, photographic reproductions, microfilm or any other reproductions of similar nature and translations. Authors are responsible for obtaining from the copyright holder permission to reproduce any figures for which copyright exists.</p> Realizers of Partially Ordered Multisets https://uav.ro/applications/se/journal/index.php/TAMCS/article/view/186 <p>In this paper, the concept of a realizer of an ordered set is generalized for ordered multisets. The ordered multiset structure is defined via the ordering induced by a partially ordered base set. The notion of realizers is shown to be well defined for the proposed multiset structure. Consequently, some analogous results on realizers are obtained in the multiset setting.</p> F. Balogun D. Singh Y. Tella Copyright (c) 2020 Theory and Applications of Mathematics & Computer Science https://creativecommons.org/licenses/by-nc-nd/4.0 2020-08-28 2020-08-28 10 2 1 6 Properties of Linearly Independent Solutions of Second Order Linear Differential Equations https://uav.ro/applications/se/journal/index.php/TAMCS/article/view/187 <p><img src="/applications/se/journal/public/site/images/admin/Capture1.JPG"></p> Mohammed Amin Abdellaoui Benharrat Belaïdi Copyright (c) 2020 Theory and Applications of Mathematics & Computer Science https://creativecommons.org/licenses/by-nc-nd/4.0 2020-08-29 2020-08-29 10 2 7 26 A Finite Difference Approach to the Solution of Elliptic Boundary value Problems with Nonlocal Boundary Condition in PDEs https://uav.ro/applications/se/journal/index.php/TAMCS/article/view/188 <p>In the article Poisson equation and corresponding boundary value problem with nonlocal boundary condition in two dimension space is considered. A numerical technique based on the finite difference method is proposed for the approximate solution of a considered problem. The computational results in numerical experiment on linear and nonlinear model test problems are presented to validate the proposed idea. Theoretically analyzed and established the convergence of the proposed method.</p> Pramod Kumar Pandey Copyright (c) 2020 Theory and Applications of Mathematics & Computer Science https://creativecommons.org/licenses/by-nc-nd/4.0 2020-09-13 2020-09-13 10 2 27 38 An Application of Generalized Bessel functions on Two Subclasses of Analytic Functions https://uav.ro/applications/se/journal/index.php/TAMCS/article/view/190 <p>Two subclasses H(β<sub>1</sub>,β<sub>1</sub>,...,β<em><sub>k</sub></em>;α) and G(β<sub>1</sub>,β<sub>1</sub>,...,β<em><sub>k</sub></em>;α) of analytic functions are introduced. The main object of this paper is to find necessary and sufficient conditions for generalized Bessel functions of first kind <em>z</em>(2 − <em>u<sub>p</sub></em>(<em>z</em>)) to be in these classes. Furthermore, we consider an integral operator related to the generalized Bessel functions.</p> B.A. Frasin Copyright (c) 2020 Theory and Applications of Mathematics & Computer Science https://creativecommons.org/licenses/by-nc-nd/4.0 2020-11-13 2020-11-13 10 2 39 – 45 39 – 45 Elements of the Theory of Nested Named Sets https://uav.ro/applications/se/journal/index.php/TAMCS/article/view/192 <p>The goal of this paper is exploration of an important phenomenon called nesting, which plays a weighty role in many areas including mathematics and computer science. In mathematics, we can see nesting in algebraic and arithmetical expressions, in functions on rings of functions, in simplicial complexes, in various formulas, and other mathematical constructions. In computer science and technology, there are nested calls; nesting of several levels of subroutines; nesting in recursive calls; nested levels of parentheses in arithmetical expressions; nested blocks of imperative source code such as nested if-clauses, while-clauses or repeat-until clauses; nesting in information hiding; and nested data structures such as records, objects, classes, etc. Here we elaborate mathematical foundations for modeling and study of the systems with nesting as well as for measuring different attributes of nesting.</p> M. Burgin Copyright (c) 2020 Theory and Applications of Mathematics & Computer Science https://creativecommons.org/licenses/by-nc-nd/4.0 2020-12-07 2020-12-07 10 2 46–70 46–70 Possibility to Construct a Photonic Hypercomputer https://uav.ro/applications/se/journal/index.php/TAMCS/article/view/193 <p>On the basis of a theorem, in which an evanescent photon is a superluminal particle, the author considers the possibility of realizing a high performance computer system compared with conventional silicon processors. To realize such a quantum computer utilizing evanescent photons, we must replace electronic components with optical ones, and thus an equivalent optical transistor is required. This critical component for quantum computing can be created using meta-material circuits with a non-linear refractive index. Based on this optical computer system, utilizing metamaterial technology, it can be shown that superluminal computation, which is a new concept for hypercomputation, can be realized in the physical world.</p> Takaaki Musha Copyright (c) 2020 Theory and Applications of Mathematics & Computer Science https://creativecommons.org/licenses/by-nc-nd/4.0 2020-12-13 2020-12-13 10 2 71 84 Extensions of Stekloff and Almansi Inequalities to the Complex Integral https://uav.ro/applications/se/journal/index.php/TAMCS/article/view/194 <p>In this paper we establish some extensions of Stekloff and Almansi inequalities to the complex integral. Applications for bounding the complex <em>Čebyšev</em><em>&nbsp;functionalˇ </em>are also given.</p> S. S. Dragomir Copyright (c) 2020 Theory and Applications of Mathematics & Computer Science https://creativecommons.org/licenses/by-nc-nd/4.0 2020-12-28 2020-12-28 10 2 85 95 Strongly Invariant Submultigroups https://uav.ro/applications/se/journal/index.php/TAMCS/article/view/195 <p>In this paper, strongly invariant submultigroup idea was introduced as an extension of strongly invariant subgroup and its properties are presented. Specifically, it was proved that fully invariant direct factor of a multigroup is strongly invariant while on the diagonal submultigroup the reverse is the case. The idea was investigated on torsion, mixed and cyclic multigroups and established that every submultigroup of a torsion multigroup is strongly invariant, the intersection of torsion part of a mixed multigroup <em>A </em>is strongly invariant in <em>A </em>and a multigroup over a cyclic group of prime order is strongly invariant simple.</p> Usman Adamu Musa Adeku Ibrahim Copyright (c) 2020 Theory and Applications of Mathematics & Computer Science https://creativecommons.org/licenses/by-nc-nd/4.0 2020-12-31 2020-12-31 10 2 96 – 103 96 – 103