Eurasian Mathematical Journal
https://emj.enu.kz/index.php/main
<p>ISSN <strong>2077-9879</strong></p> <p>Founded in 2010 by the L.N. Gumilyov Eurasian National University in cooperetion with the M.V. Lomonosov Moscow State University the Peoplesʼ Friendship University of Russia the University of Padua (RUDN University)</p> <p>Supported by the ISAAC (International Society for Analysis, its Applications and Computation) and by the Kazakhstan Mathematical Society</p> <p>Registered by Ministry of Culture and information of Republic of Kazakhstan. First registration certificate No.10330-Ж from 25.09.2009</p> <p>Second registration certificate No.14167-Ж from 18.02.2014</p> <p>Aim: Publication of carefully selected original research papers in all areas of mathematics written by mathematicians first of all from Europe and Asia. However papers by mathematicians from other continents are also welcome. From time to time Eurasian Mathematical Journal will also publish survey papers.</p> <p>Periodicity: 4 issues in a year.</p> <p>A working language: English.</p> <p>Web-page of EMJ: www.emj.enu.kz</p> <p>E-mail adress: eurasianmj@yandex.kz</p> <p> </p> <p>Published by the L.N. Gumilyov Eurasian National University, Astana, Kazakhstan</p> <p>The contents of the EMJ are indexed in: Scopus; Web of Science (ESCI); Mathematical Reviews, MathSciNet (American Mathematical Society, USA); Zentrablatt Math (ZMATH, Germany); Referativnyi Zhurnal-Matematika, Math-Net.Ru (Russia).</p> <p>The EMJ is included in the list of journals recommended by the Committee for Control of Education and Science (Ministry of Education and Science of the Republic of Kazakhstan) and in the list of journals recommended by the Higher Attestation Commission (Ministry of Education and Science of the Russian Federation).</p>en-USEurasian Mathematical Journal2077-9879Time optimal control problem with integral constraint for the heat transfer process
https://emj.enu.kz/index.php/main/article/view/3
<p>In the present paper a mathematical model of thermocontrol processes is studied. Several convectors are installed on the disjoint subsets Г<sub>k</sub> of the wall ∂Ω of a volume Ω and each convector produces a hot or cold flow with magnitude equal to µk(t), which are control functions, and on the surface <em>∂Ω \ Γ, Γ = ∪Γ<sub>k</sub></em>, a heat exchange occurs by the Newton law. The control functions <em>µ<sub>k</sub>(t)</em> are subjected to an integral constraint. The problem is to find control functions to transfer the state of the process to a given state. A necessary and sufficient condition is found for solvability of this problem. An equation for the optimal transfer time is found, and an optimal control function is constructed explicitly</p>Shavkat AlimovGafurjan Ibragimov
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2024-04-082024-04-08151Applications of λ-truncations to the study of local and global solvability of nonlinear equations
https://emj.enu.kz/index.php/main/article/view/4
<p>In this paper, we consider the equation <img src="http://10.255.61.4:3292/public/site/images/admin/mceclip1.png"> in a neighbourhood of a given point <img src="http://10.255.61.4:3292/public/site/images/admin/mceclip2.png">, where <em>F</em> is a given continuous mapping between finite-dimensional real spaces. We study a class of polynomial mappings and show that these polynomials satisfy certain regularity assumptions. We show that if a <em>λ</em>-truncation of <em>F</em> at <img src="http://10.255.61.4:3292/public/site/images/admin/mceclip3.png">¯ belongs to the considered class of polynomial mappings then for every <img src="http://10.255.61.4:3292/public/site/images/admin/mceclip0-b63ced4048d7d21fc4fc2e03ddac41a8.png"> close to <img src="http://10.255.61.4:3292/public/site/images/admin/mceclip1-7dfb53f53f06342c1858193b2c1d4ca3.png"> there exists a solution to the equation <img src="http://10.255.61.4:3292/public/site/images/admin/mceclip4.png"> that is close to <img src="http://10.255.61.4:3292/public/site/images/admin/mceclip2.png">. For polynomial mappings satisfying the regularity conditions we study their stability to bounded continuous perturbations.</p>Aram ArutyunovSergey Zhukovskiy
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2024-04-082024-04-08151A problem with gellerstedt conditions on different characteristics for a mixed loaded equation of the second kind
https://emj.enu.kz/index.php/main/article/view/10
<p>This work is devoted to a formulation and an investigation of a boundary value problem with Gellerstedt conditions on different characteristics for the loaded parabolic-hyperbolic type equation of the second kind. By using the extremum principle and the method of energy integrals, there are proved the uniqueness of solution of the formulated problem, and the existence of a solution to the problem - by the method integral equations.</p>Bozor IslomovDildora Nasirova
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2024-04-082024-04-08151Asymptotics of the solution of parabolic problems with nonsmooth boundary functions
https://emj.enu.kz/index.php/main/article/view/11
<p>In this paper, we construct the asymptotics of the solution to a singularly perturbed parabolic problem with a nonsmooth boundary layer function. In contrast to works devoted to this direction, our asymptotics contains only one boundary layer function, which is the product of parabolic and exponential boundary layer functions. Our approach allows us to construct a classical solution without applying smoothing procedures</p>Asan OmuralievElla Abylaeva
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2024-04-082024-04-08151On the associated spaces of the weighted altered cesaro space
https://emj.enu.kz/index.php/main/article/view/12
<p>We study weighted altered Ces`aro space <img src="http://10.255.61.4:3292/public/site/images/admin/mceclip0-a88bf79b20f79e6aa1a50b13db8a40d5.png">, which is a non-ideal enlargement of the usual Ces`aro space. We prove the connection of this space with one weighted Sobolev space of the first order on real line and give characterizations of associate spaces of this space.</p>Dmitrii Prokhorov
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2024-04-082024-04-08151Concinnity of dynamic inequalities designed on calculus of time scales
https://emj.enu.kz/index.php/main/article/view/13
<p>We present some reverse dynamic inequalities of Radon’s and Bergstr¨om’s type on time scales in general form. The extension of Clarkson’s dynamic inequality on time scales is also given. Our further investigations explore some dynamic inequalities by using Kantorovich’s and Specht’s ratios. The calculus of time scales unifies and extends continuous results and their corresponding discrete and quantum analogues.</p>Muhammad Jibril Shahab SahirFaryal Chaudhry
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2024-04-082024-04-08151Porosity in the context of hypergroups
https://emj.enu.kz/index.php/main/article/view/14
<p>In this paper we show that the set of all elements <img src="http://10.255.61.4:3292/public/site/images/admin/mceclip0-9ecc89fe11547202e43f2dae25055a90.png"> for which <img src="http://10.255.61.4:3292/public/site/images/admin/mceclip1-73a4c33db2aeeeb08c81281807a7efc7.png"> for a center element <img src="http://10.255.61.4:3292/public/site/images/admin/mceclip2-8eaff47e98b28cf294da2548652f92a4.png">, is <img src="http://10.255.61.4:3292/public/site/images/admin/mceclip3-cc230cb5e35cf62ceb70870dfdbb8ec4.png">-c-lower porous, where <img src="http://10.255.61.4:3292/public/site/images/admin/mceclip4-668d692a9893bc1d28c982734ad1501b.png"> is a non-compact unimodular hypergroup and <em>B</em> is some special symmetric compact neighborhood of the identity element. As an application, we give some new equivalent condition for the finiteness of a discrete Hermitian hypergroup. Moreover, we give some sufficient conditions for the set of all pairs <img src="http://10.255.61.4:3292/public/site/images/admin/mceclip5.png"> in <img src="http://10.255.61.4:3292/public/site/images/admin/mceclip6.png"> for which for a center element <img src="http://10.255.61.4:3292/public/site/images/admin/mceclip7.png">, is a <img src="http://10.255.61.4:3292/public/site/images/admin/mceclip3-cc230cb5e35cf62ceb70870dfdbb8ec4.png">-c-lower porous, where <img src="http://10.255.61.4:3292/public/site/images/admin/mceclip8.png"> with <img src="http://10.255.61.4:3292/public/site/images/admin/mceclip9.png">. Also, we show that the complement of this set is spaceable in <img src="http://10.255.61.4:3292/public/site/images/admin/mceclip10.png">.</p> <div id="gtx-trans" style="position: absolute; left: 597px; top: 98px;"> <div class="gtx-trans-icon"> </div> </div>Seyyed Mohammad TabatabaieAli Reza Bagheri SalecHaneen Ridha Jameel Allami
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2024-04-082024-04-08151Finite groups with given systems of propermutable subgroups
https://emj.enu.kz/index.php/main/article/view/15
<p>Let H be a subgroup of a finite group G. Then we say that H is propermutable in G provided G has a subgroup B such that G = NG(H)B and H permutes with all subgroups of B. In this paper, we present new properties of propermutable subgroups. Also we provide new information on the structure of a group with propermutable Sylow (Hall, maximal) subgroups and a group G = AB with propermutable subgroups A and B.</p>Alexander Trofimuk
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2024-04-082024-04-08151