Ukrains’kyi Matematychnyi Zhurnal最新文献

{"title":"Geometry of multilinear forms on a normed space <mml:math>\u0000<mml:mrow>\u0000\t<mml:msup>\u0000\t\t<mml:mi>ℝ</mml:mi>\u0000\t\t<mml:mi>m</mml:mi>\u0000\t</mml:msup>\u0000</mml:mrow>\u0000</mml:math>","authors":"Sung Guen Kim","doi":"10.3842/umzh.v76i5.7476","DOIUrl":"https://doi.org/10.3842/umzh.v76i5.7476","url":null,"abstract":"<jats:p>UDC 514.1\u0000For every <mml:math>\u0000<mml:mrow>\u0000\t<mml:mi>m</mml:mi>\u0000\t<mml:mo>≥</mml:mo>\u0000\t<mml:mn>2</mml:mn>\u0000\t<mml:mo>,</mml:mo>\u0000</mml:mrow>\u0000</mml:math> let <mml:math>\u0000<mml:mrow>\u0000\t<mml:msubsup>\u0000\t\t<mml:mi>ℝ</mml:mi>\u0000\t\t<mml:mrow>\u0000\t\t\t<mml:mo>‖</mml:mo>\u0000\t\t\t<mml:mo>⋅</mml:mo>\u0000\t\t\t<mml:mo>‖</mml:mo>\u0000\t\t</mml:mrow>\u0000\t\t<mml:mi>m</mml:mi>\u0000\t</mml:msubsup>\u0000</mml:mrow>\u0000</mml:math> be <mml:math>\u0000<mml:mrow>\u0000\t<mml:msup>\u0000\t\t<mml:mi>ℝ</mml:mi>\u0000\t\t<mml:mi>m</mml:mi>\u0000\t</mml:msup>\u0000</mml:mrow>\u0000</mml:math> with a norm <mml:math>\u0000<mml:mrow>\u0000\t<mml:mo>‖</mml:mo>\u0000\t<mml:mo>⋅</mml:mo>\u0000\t<mml:mo>‖</mml:mo>\u0000</mml:mrow>\u0000</mml:math> such that its unit ball has finitely many extreme points. For every <mml:math>\u0000<mml:mrow>\u0000\t<mml:mi>n</mml:mi>\u0000\t<mml:mo>≥</mml:mo>\u0000\t<mml:mn>2</mml:mn>\u0000\t<mml:mo>,</mml:mo>\u0000</mml:mrow>\u0000</mml:math> we focus our attention on the description of the sets of extreme and exposed points of the closed unit balls of <mml:math>\u0000<mml:mrow>\u0000\t<mml:mi>ℒ</mml:mi>\u0000\t<mml:msup>\u0000\t\t<mml:mo>(</mml:mo>\u0000\t\t<mml:mi>n</mml:mi>\u0000\t</mml:msup>\u0000\t<mml:msubsup>\u0000\t\t<mml:mi>ℝ</mml:mi>\u0000\t\t<mml:mrow>\u0000\t\t\t<mml:mo>‖</mml:mo>\u0000\t\t\t<mml:mo>⋅</mml:mo>\u0000\t\t\t<mml:mo>‖</mml:mo>\u0000\t\t</mml:mrow>\u0000\t\t<mml:mi>m</mml:mi>\u0000\t</mml:msubsup>\u0000\t<mml:mo form=\"postfix\">)</mml:mo>\u0000</mml:mrow>\u0000</mml:math> and <mml:math>\u0000<mml:mrow>\u0000\t<mml:msub>\u0000\t\t<mml:mi>ℒ</mml:mi>\u0000\t\t<mml:mi>s</mml:mi>\u0000\t</mml:msub>\u0000\t<mml:msup>\u0000\t\t<mml:mo>(</mml:mo>\u0000\t\t<mml:mi>n</mml:mi>\u0000\t</mml:msup>\u0000\t<mml:msubsup>\u0000\t\t<mml:mi>ℝ</mml:mi>\u0000\t\t<mml:mrow>\u0000\t\t\t<mml:mo>‖</mml:mo>\u0000\t\t\t<mml:mo>⋅</mml:mo>\u0000\t\t\t<mml:mo>‖</mml:mo>\u0000\t\t</mml:mrow>\u0000\t\t<mml:mi>m</mml:mi>\u0000\t</mml:msubsup>\u0000\t<mml:mo form=\"postfix\">)</mml:mo>\u0000</mml:mrow>\u0000</mml:math>, where <mml:math>\u0000<mml:mrow>\u0000\t<mml:mi>ℒ</mml:mi>\u0000\t<mml:msup>\u0000\t\t<mml:mo>(</mml:mo>\u0000\t\t<mml:mi>n</mml:mi>\u0000\t</mml:msup>\u0000\t<mml:msubsup>\u0000\t\t<mml:mi>ℝ</mml:mi>\u0000\t\t<mml:mrow>\u0000\t\t\t<mml:mo>‖</mml:mo>\u0000\t\t\t<mml:mo>⋅</mml:mo>\u0000\t\t\t<mml:mo>‖</mml:mo>\u0000\t\t</mml:mrow>\u0000\t\t<mml:mi>m</mml:mi>\u0000\t</mml:msubsup>\u0000\t<mml:mo form=\"postfix\">)</mml:mo>\u0000</mml:mrow>\u0000</mml:math> is the space of <mml:math>\u0000<mml:mrow>\u0000\t<mml:mi>n</mml:mi>\u0000</mml:mrow>\u0000</mml:math>-linear forms on <mml:math>\u0000<mml:mrow>\u0000\t<mml:msubsup>\u0000\t\t<mml:mi>ℝ</mml:mi>\u0000\t\t<mml:mrow>\u0000\t\t\t<mml:mo>‖</mml:mo>\u0000\t\t\t<mml:mo>⋅</mml:mo>\u0000\t\t\t<mml:mo>‖</mml:mo>\u0000\t\t</mml:mrow>\u0000\t\t<mml:mi>m</mml:mi>\u0000\t</mml:msubsup>\u0000</mml:mrow>\u0000</mml:math> and <mml:math>\u0000<mml:mrow>\u0000\t<mml:msub>\u0000\t\t<mml:mi>ℒ</mml:mi>\u0000\t\t<mml:mi>s</mml:mi>\u0000\t</mml:msub>\u0000\t<mml:msup>\u0000\t\t<mml:mo>(</mml:mo>\u0000\t\t<mml:mi>n</mml:mi>\u0000\t</mml:msup>\u0000\t<mml:msubsup>\u0000\t\t<mml:mi>ℝ</mml:mi>\u0000\t\t<mml:mrow>\u0000\t\t\t<mml:mo>‖</mml:mo>\u0000\t\t\t<mml:mo>⋅</mml:mo>\u0000\t\t\t<mml:mo>‖</mml:mo>\u0000\t\t</mml:mrow>\u0000\t\t<mml:mi>m</mml:mi>\u0000\t</mml:msubsup>\u0000\t<mml:mo form=\"postfix\">)</mml:mo>\u0000</mml:mrow>\u0000</mml:math> is the subspace of <mml:math>\u0000<mml:mrow>\u0000\t<mml:mi>ℒ</mml:mi>\u0000\t<mml:msup>\u0000\t\t<mml:mo>(</mml:mo>\u0000\t\t<mml:mi>n</mml:mi>\u0000\t</mml:msup>\u0000\t<mml:msubsup>\u0000\t\t<mml:mi>ℝ</mml:mi>\u0000\t\t<mml:mrow>\u0000\t\t\t<mml:mo>‖</mml:mo>\u0000\t\t\t<mml:mo>⋅</mml:mo>\u0000\t\t\t<mml:mo>‖</mml:mo>\u0000\t\t</mml:mrow>\u0000\t\t<mml:mi>m</mml:mi>\u0000\t</mml:msubsup>\u0000\t<mml:mo form=\"postfix\">)</mml:mo>\u0000</mml:","PeriodicalId":163365,"journal":{"name":"Ukrains’kyi Matematychnyi Zhurnal","volume":"115 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141682706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Алфавітний покажчик 75-го тому „Українського математичного журналу”","authors":".. Editorial board","doi":"10.3842/umzh.v75i12.8069","DOIUrl":"https://doi.org/10.3842/umzh.v75i12.8069","url":null,"abstract":"","PeriodicalId":163365,"journal":{"name":"Ukrains’kyi Matematychnyi Zhurnal","volume":"102 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139630274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"1d piecewise smooth map: exploring a model of investment dynamics under financial frictions with three types of investment projects","authors":"I. Sushko, L. Gardini, Kiminori Matsuyama","doi":"10.3842/umzh.v75i12.7721","DOIUrl":"https://doi.org/10.3842/umzh.v75i12.7721","url":null,"abstract":"UDC 517.9\u0000We consider a 1D continuous piecewise smooth map, which depends on seven parameters. Depending on the values of parameters, it may have up to six branches. This map was proposed by Matsuyama [Theor. Econ., 8, 623–651 (2013); Section 5].  It describes the macroeconomic dynamics of investment and credit fluctuations in which three types of investment projects compete in the financial market.  We introduce a partitioning of the parameter space according to different branch configurations of the map and illustrate this partitioning for a specific parameter setting.  Then we present an example of the bifurcation structure in a parameter plane, which includes periodicity regions related to superstable cycles. Several bifurcation curves are obtained analytically, in particular, the border-collision bifurcation curves of  fixed points. We show that the intersection point of two  curves of this kind is an organizing center from which infinitely many other bifurcation curves are originated.","PeriodicalId":163365,"journal":{"name":"Ukrains’kyi Matematychnyi Zhurnal","volume":"80 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139536953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Використання другого методу Ляпунова для отримання умов стійкості в системах з квадратичною правою частиною","authors":"D. Khusainov, A. Shatyrko, B. Puza, V. Novotna","doi":"10.3842/umzh.v75i12.7655","DOIUrl":"https://doi.org/10.3842/umzh.v75i12.7655","url":null,"abstract":"УДК 517.929\u0000За допомогою апарату прямого методу Ляпунова з функцією у класі квадратичних форм для нелінійних систем диференціальних рівнянь другого й третього порядку побудовано алгебраїчні достатні умови стійкості тривіальних розв’язків. ","PeriodicalId":163365,"journal":{"name":"Ukrains’kyi Matematychnyi Zhurnal","volume":"38 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139536603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Олександр Миколайович Шарковський (07.12.1936–21.11.2022)","authors":"A. F. Ivanov, Yu. L. Maistrenko, O. Romanenko","doi":"10.3842/umzh.v75i12.7913","DOIUrl":"https://doi.org/10.3842/umzh.v75i12.7913","url":null,"abstract":"","PeriodicalId":163365,"journal":{"name":"Ukrains’kyi Matematychnyi Zhurnal","volume":"24 39","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139631028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamics of one-dimensional maps and Gurtin–Maccamy's population model. Part I. Asymptotically constant solutions","authors":"Franco Herrera, S.N. Trofimchuk","doi":"10.3842/umzh.v75i12.7678","DOIUrl":"https://doi.org/10.3842/umzh.v75i12.7678","url":null,"abstract":"UDC 517.9\u0000Motivated by the recent work by  Ma and Magal [Proc. Amer. Math. Soc. (2021); https://doi.org/10.1090/proc/15629] on  the global stability property of  the Gurtin–MacCamy's population model, we consider a family of scalar nonlinear convolution equations with unimodal nonlinearities.  In particular, we  relate the Ivanov and Sharkovsky analysis  of singularly perturbed delay differential equations in [https://doi.org/10.1007/978-3-642-61243-5_5] with the asymptotic behavior of solutions of the  Gurtin–MacCamy's system. According the classification proposed in  [https://doi.org/10.1007/978-3-642-61243-5_5], we can distinguish three fundamental  kinds of continuous solutions of our equations, namely, solutions of the asymptotically constant type, relaxation type  and turbulent type. We present various conditions assuring that all solutions belong to the first of these three classes. In the setting of unimodal convolution  equations, these conditions suggest a generalized version of the famous Wright's conjecture.","PeriodicalId":163365,"journal":{"name":"Ukrains’kyi Matematychnyi Zhurnal","volume":"30 33","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139630850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamics of a random Hopfield neural lattice model with adaptive synapses and delayed Hebbian learning","authors":"Xiaoying Han, P. Kloeden","doi":"10.3842/umzh.v75i12.7594","DOIUrl":"https://doi.org/10.3842/umzh.v75i12.7594","url":null,"abstract":"UDC 517.9\u0000A Dong–Hopfield neural lattice model with random external forcing and delayed response to the evolution of interconnection weights is developed and studied.   The interconnection weights evolve according to the Hebbian learning rule with a decay term and contribute to  changes in the states after a short delay.  The lattice system is  first reformulated as a coupled functional-ordinary differential equation system on an appropriate product space.  Then the solution of the system is shown to exist and be unique. Furthermore  it is shown that the system of equations  generates a continuous random dynamical system.  Finally, the existence of random attractors for the random dynamical system generated by the Dong–Hopfield model is established.","PeriodicalId":163365,"journal":{"name":"Ukrains’kyi Matematychnyi Zhurnal","volume":"24 36","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139631030","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the balanced pantograph equation of mixed type","authors":"G. Derfel, B. V. Brunt","doi":"10.3842/umzh.v75i12.7654","DOIUrl":"https://doi.org/10.3842/umzh.v75i12.7654","url":null,"abstract":"<jats:p>UDC 517.9\u0000We consider the balanced pantograph equation (BPE) <mml:math>\u0000<mml:mrow>\u0000\t<mml:msup>\u0000\t\t<mml:mi>y</mml:mi>\u0000\t\t<mml:mo>′</mml:mo>\u0000\t</mml:msup>\u0000\t<mml:mrow>\u0000\t\t<mml:mo form=\"prefix\">(</mml:mo>\u0000\t\t<mml:mi>x</mml:mi>\u0000\t\t<mml:mo form=\"postfix\">)</mml:mo>\u0000\t</mml:mrow>\u0000\t<mml:mo>+</mml:mo>\u0000\t<mml:mi>y</mml:mi>\u0000\t<mml:mrow>\u0000\t\t<mml:mo form=\"prefix\">(</mml:mo>\u0000\t\t<mml:mi>x</mml:mi>\u0000\t\t<mml:mo form=\"postfix\">)</mml:mo>\u0000\t</mml:mrow>\u0000\t<mml:mo>=</mml:mo>\u0000\t<mml:mstyle displaystyle=\"true\">\u0000\t\t<mml:munderover>\u0000\t\t\t<mml:mo>∑</mml:mo>\u0000\t\t\t<mml:mrow>\u0000\t\t\t\t<mml:mi>k</mml:mi>\u0000\t\t\t\t<mml:mo>=</mml:mo>\u0000\t\t\t\t<mml:mn>1</mml:mn>\u0000\t\t\t</mml:mrow>\u0000\t\t\t<mml:mi>m</mml:mi>\u0000\t\t</mml:munderover>\u0000\t</mml:mstyle>\u0000\t<mml:msub>\u0000\t\t<mml:mi>p</mml:mi>\u0000\t\t<mml:mi>k</mml:mi>\u0000\t</mml:msub>\u0000\t<mml:mi>y</mml:mi>\u0000\t<mml:mrow>\u0000\t\t<mml:mo form=\"prefix\">(</mml:mo>\u0000\t\t<mml:msub>\u0000\t\t\t<mml:mi>a</mml:mi>\u0000\t\t\t<mml:mi>k</mml:mi>\u0000\t\t</mml:msub>\u0000\t\t<mml:mi>x</mml:mi>\u0000\t\t<mml:mo form=\"postfix\">)</mml:mo>\u0000\t</mml:mrow>\u0000\t<mml:mo>,</mml:mo>\u0000</mml:mrow>\u0000</mml:math> where <mml:math>\u0000<mml:mrow>\u0000\t<mml:msub>\u0000\t\t<mml:mi>a</mml:mi>\u0000\t\t<mml:mi>k</mml:mi>\u0000\t</mml:msub>\u0000\t<mml:mo>,</mml:mo>\u0000\t<mml:msub>\u0000\t\t<mml:mi>p</mml:mi>\u0000\t\t<mml:mi>k</mml:mi>\u0000\t</mml:msub>\u0000\t<mml:mo>></mml:mo>\u0000\t<mml:mn>0</mml:mn>\u0000</mml:mrow>\u0000</mml:math> and <mml:math>\u0000<mml:mrow>\u0000\t<mml:mstyle displaystyle=\"true\">\u0000\t\t<mml:munderover>\u0000\t\t\t<mml:mo>∑</mml:mo>\u0000\t\t\t<mml:mrow>\u0000\t\t\t\t<mml:mi>k</mml:mi>\u0000\t\t\t\t<mml:mo>=</mml:mo>\u0000\t\t\t\t<mml:mn>1</mml:mn>\u0000\t\t\t</mml:mrow>\u0000\t\t\t<mml:mi>m</mml:mi>\u0000\t\t</mml:munderover>\u0000\t</mml:mstyle>\u0000\t<mml:msub>\u0000\t\t<mml:mi>p</mml:mi>\u0000\t\t<mml:mi>k</mml:mi>\u0000\t</mml:msub>\u0000\t<mml:mo>=</mml:mo>\u0000\t<mml:mn>1.</mml:mn>\u0000</mml:mrow>\u0000</mml:math> It is known that if <mml:math>\u0000<mml:mrow>\u0000\t<mml:mi>K</mml:mi>\u0000\t<mml:mo>=</mml:mo>\u0000\t<mml:mstyle displaystyle=\"true\">\u0000\t\t<mml:munderover>\u0000\t\t\t<mml:mo>∑</mml:mo>\u0000\t\t\t<mml:mrow>\u0000\t\t\t\t<mml:mi>k</mml:mi>\u0000\t\t\t\t<mml:mo>=</mml:mo>\u0000\t\t\t\t<mml:mn>1</mml:mn>\u0000\t\t\t</mml:mrow>\u0000\t\t\t<mml:mi>m</mml:mi>\u0000\t\t</mml:munderover>\u0000\t</mml:mstyle>\u0000\t<mml:msub>\u0000\t\t<mml:mi>p</mml:mi>\u0000\t\t<mml:mi>k</mml:mi>\u0000\t</mml:msub>\u0000\t<mml:mi>ln</mml:mi>\u0000\t<mml:msub>\u0000\t\t<mml:mi>a</mml:mi>\u0000\t\t<mml:mi>k</mml:mi>\u0000\t</mml:msub>\u0000\t<mml:mo>≤</mml:mo>\u0000\t<mml:mn>0</mml:mn>\u0000</mml:mrow>\u0000</mml:math> then, under mild technical conditions, the BPE does not have bounded solutions that are not constant, whereas for <mml:math>\u0000<mml:mrow>\u0000\t<mml:mi>K</mml:mi>\u0000\t<mml:mo>></mml:mo>\u0000\t<mml:mn>0</mml:mn>\u0000</mml:mrow>\u0000</mml:math> these solutions exist.  In the present paper, we deal with a BPE of <em>mixed type</em>, i.e., <mml:math>\u0000<mml:mrow>\u0000\t<mml:msub>\u0000\t\t<mml:mi>a</mml:mi>\u0000\t\t<mml:mn>1</mml:mn>\u0000\t</mml:msub>\u0000\t<mml:mo><</mml:mo>\u0000\t<mml:mn>1</mml:mn>\u0000\t<mml:mo><</mml:mo>\u0000\t<mml:msub>\u0000\t\t<mml:mi>a</mml:mi>\u0000\t\t<mml:mi>m</mml:mi>\u0000\t</mml:msub>\u0000\t<mml:mo>,</mml:mo>\u0000</mml:mrow>\u0000</mml:math> and prove that, in this case, the BPE has a nonconstant solution <mml:math>\u0000<mml:mrow>\u0000\t<mml:mi>y</mml:mi>\u0000</mml:mrow>\u0000</mml:math> and that <mml:math>\u0000<mml:mrow>\u0000\t<mml:mi>y</mml:mi>\u0000\t<mml:mrow>\u0000\t\t<mml:mo form=\"prefix\">(</mml:mo>\u0000\t\t<mml:mi>x</mml:mi>\u0000\t\t<mml:mo","PeriodicalId":163365,"journal":{"name":"Ukrains’kyi Matematychnyi Zhurnal","volume":"38 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139536605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the solution manifolds for algebraic-delay systems","authors":"Hans-Otto Walther","doi":"10.3842/umzh.v75i12.7663","DOIUrl":"https://doi.org/10.3842/umzh.v75i12.7663","url":null,"abstract":"UDC 517.9\u0000Differential equations with state-dependent delays specify a semiflow of continuously differentiable solution operators, in general, only on an associated submanifold of the Banach space \u0000\u0000 \u0000 C\u0000 1\u0000 \u0000 \u0000 (\u0000 \u0000 [\u0000 -\u0000 h\u0000 ,0\u0000 ]\u0000 \u0000 ,\u0000 \u0000 R\u0000 n\u0000 \u0000 )\u0000 \u0000 .\u0000\u0000 We extend a recent result on the simplicity of these {it solution manifolds} to systems in which the delay is given by the state only implicitly in an extra equation. These algebraic delay systems appear in various applications. ","PeriodicalId":163365,"journal":{"name":"Ukrains’kyi Matematychnyi Zhurnal","volume":"23 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139630973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Novel compartmental VSLIT model used to analyze the dynamics of tuberculosis in Algeria and Ukraine and the assessment of vaccination and treatment effects","authors":"Bouchra Chennaf, Mohammed Salah Abdelouahab, René Lozi","doi":"10.3842/umzh.v75i12.7658","DOIUrl":"https://doi.org/10.3842/umzh.v75i12.7658","url":null,"abstract":"UDC 517.9\u0000Despite having low rates of tuberculosis (TB) mortality in many countries, like China, Europe, and the United States, other countries, like India continue to struggle to contain the epidemic. This study intends to examine the effects of vaccinations and treatments on the dynamics of TB in two countries, Ukraine and Algeria, with contrasted demographic profiles. A mathematical model called the VSLIT model is considered for this purpose. The stability of both disease-free and endemic equilibrium is discussed qualitatively. For numerical simulations,  the parameters are evaluated by the least squares approach according to the TB-reported data for Algeria and Ukraine from 1990 to 2020.","PeriodicalId":163365,"journal":{"name":"Ukrains’kyi Matematychnyi Zhurnal","volume":"24 17","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139631091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}