Demonstratio Mathematica最新文献

{"title":"Petri net analysis of a queueing inventory system with orbital search by the server","authors":"Lyes Ikhlef, Sedda Hakmi, Ouiza Lekadir, D. Aïssani","doi":"10.1515/dema-2022-0207","DOIUrl":"https://doi.org/10.1515/dema-2022-0207","url":null,"abstract":"Abstract In this article, a queueing inventory system with finite sources of demands, retrial demands, service time, lead time, ( s , S ) left(s,S) replenishment policy, and demands search from the orbit was studied. When the lead time is exponentially distributed (resp. lead time is generally distributed), generalized stochastic Petri net (GSPN) (resp. Markov regenerative stochastic Petri net [MRSPN]) is proposed for this inventory system. The quantitative analysis of this stochastic Petri net model was obtained by continuous time Markov chain for the GSPN model (resp. the supplementary variable method for the MRSPN model). The probability distributions are obtained, witch allowed us to compute performance measures and the expected cost rate of the studied system.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42186122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Increasing property and logarithmic convexity of functions involving Dirichlet lambda function","authors":"Feng Qi (祁锋), D. Lim","doi":"10.1515/dema-2022-0243","DOIUrl":"https://doi.org/10.1515/dema-2022-0243","url":null,"abstract":"Abstract In this article, with the help of an integral representation of the Dirichlet lambda function, by means of a monotonicity rule for the ratio of two integrals with a parameter, and by virtue of complete monotonicity and another property of an elementary function involving the exponential function, the authors find increasing property and logarithmic convexity of two functions containing the gamma function and the Dirichlet lambda function.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48986893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence of a solution to an infinite system of weighted fractional integral equations of a function with respect to another function via a measure of noncompactness","authors":"Anupam Das, Marija Paunović, Vahid Parvaneh, M. Mursaleen, Z. Bagheri","doi":"10.1515/dema-2022-0192","DOIUrl":"https://doi.org/10.1515/dema-2022-0192","url":null,"abstract":"Abstract In this article, some new generalizations of Darbo’s fixed-point theorem are given and the solvability of an infinite system of weighted fractional integral equations of a function with respect to another function is studied. Also, with the help of a proper example, we illustrate our findings.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48479805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On initial value problem for elliptic equation on the plane under Caputo derivative","authors":"Tran Thanh Binh, Bui Dinh Thang, Nguyen Duc Phuong","doi":"10.1515/dema-2022-0257","DOIUrl":"https://doi.org/10.1515/dema-2022-0257","url":null,"abstract":"Abstract In this article, we are interested to study the elliptic equation under the Caputo derivative. We obtain several regularity results for the mild solution based on various assumptions of the input data. In addition, we derive the lower bound of the mild solution in the appropriate space. The main tool of the analysis estimation for the mild solution is based on the bound of the Mittag-Leffler functions, combined with analysis in Hilbert scales space. Moreover, we provide a regularized solution for our problem using the Fourier truncation method. We also obtain the error estimate between the regularized solution and the mild solution. Our current article seems to be the first study to deal with elliptic equations with Caputo derivatives on the unbounded domain.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135262752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Small perturbations of critical nonlocal equations with variable exponents","authors":"Lulu Tao, Rui He, Sihua Liang","doi":"10.1515/dema-2023-0266","DOIUrl":"https://doi.org/10.1515/dema-2023-0266","url":null,"abstract":"Abstract In this article, we are concerned with the following critical nonlocal equation with variable exponents: <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"> <m:mfenced open=\"{\" close=\"\"> <m:mrow> <m:mtable displaystyle=\"true\"> <m:mtr> <m:mtd columnalign=\"left\"> <m:msubsup> <m:mrow> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mo>−</m:mo> <m:mi mathvariant=\"normal\">Δ</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:mrow> <m:mrow> <m:mi>p</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo>,</m:mo> <m:mi>y</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:mrow> <m:mrow> <m:mi>s</m:mi> </m:mrow> </m:msubsup> <m:mi>u</m:mi> <m:mo>=</m:mo> <m:mi>λ</m:mi> <m:mi>f</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo>,</m:mo> <m:mi>u</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>+</m:mo> <m:msup> <m:mrow> <m:mo>∣</m:mo> <m:mi>u</m:mi> <m:mo>∣</m:mo> </m:mrow> <m:mrow> <m:mi>q</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>−</m:mo> <m:mn>2</m:mn> </m:mrow> </m:msup> <m:mi>u</m:mi> </m:mtd> <m:mtd columnalign=\"left\"> <m:mstyle> <m:mspace width=\"0.1em\" /> <m:mtext>in</m:mtext> <m:mspace width=\"0.1em\" /> </m:mstyle> <m:mspace width=\"0.33em\" /> <m:mi mathvariant=\"normal\">Ω</m:mi> <m:mo>,</m:mo> </m:mtd> </m:mtr> <m:mtr> <m:mtd columnalign=\"left\"> <m:mi>u</m:mi> <m:mo>=</m:mo> <m:mn>0</m:mn> </m:mtd> <m:mtd columnalign=\"left\"> <m:mstyle> <m:mspace width=\"0.1em\" /> <m:mtext>in</m:mtext> <m:mspace width=\"0.1em\" /> </m:mstyle> <m:mspace width=\"0.33em\" /> <m:msup> <m:mrow> <m:mi mathvariant=\"double-struck\">R</m:mi> </m:mrow> <m:mrow> <m:mi>N</m:mi> </m:mrow> </m:msup> <m:mo></m:mo> <m:mi mathvariant=\"normal\">Ω</m:mi> <m:mo>,</m:mo> </m:mtd> </m:mtr> </m:mtable> </m:mrow> </m:mfenced> </m:math> left{begin{array}{ll}{left(-Delta )}_{pleft(x,y)}^{s}u=lambda fleft(x,u)+{| u| }^{qleft(x)-2}u&amp; hspace{0.1em}text{in}hspace{0.1em}hspace{0.33em}Omega , u=0&amp; hspace{0.1em}text{in}hspace{0.1em}hspace{0.33em}{{mathbb{R}}}^{N}backslash Omega right,end{array}right. where <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"normal\">Ω</m:mi> <m:mo>⊂</m:mo> <m:msup> <m:mrow> <m:mi mathvariant=\"double-struck\">R</m:mi> </m:mrow> <m:mrow> <m:mi>N</m:mi> </m:mrow> </m:msup> </m:math> Omega subset {{mathbb{R}}}^{N} is a bounded domain with Lipschitz boundary, <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>N</m:mi> <m:mo>≥</m:mo> <m:mn>2</m:mn> </m:math> Nge 2 , <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>p</m:mi> <m:mo>∈</m:mo> <m:mi>C</m:mi> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:mi mathvariant=\"normal\">Ω</m:mi> <m:mo>×</m:mo> <m:mi mathvariant=\"normal\">Ω</m:mi> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:math> pin C(Omega times Omega ) is symmetric, <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>f</m:mi> <m:mo>:</m:mo> <m:mi>C</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi mathvariant=\"normal\">Ω</m:mi> <m:mo>×</m:m","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135263941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The behavior of hidden bifurcation in 2D scroll via saturated function series controlled by a coefficient harmonic linearization method","authors":"Zaamoune Faiza, Menacer Tidjani","doi":"10.1515/dema-2022-0211","DOIUrl":"https://doi.org/10.1515/dema-2022-0211","url":null,"abstract":"Abstract In this article, the behavior of hidden bifurcation in a two-dimensional (2D) scroll via saturated function series controlled by the coefficient harmonic linearization method is presented. A saturated function series approach for chaos generation. The systematic saturated function series methodicalness improved here can make multi-scroll and grid scroll chaotic attractors from a 3D linear autonomous system with a plain saturated function series supervisor. We have used a hidden bifurcation method in grid scroll., where the method of hidden bifurcation presented by Menacer, et al. in (2016) for Chua multi-scroll attractors. This additional parameter, which is absent from the initial problem, is perfectly adapted to unfold the structure of the multispiral chaotic attractor. The novelty of this article is twofold: first, the saturated function series model for hidden bifurcation in a 2 – D scroll; and second, the control of hidden bifurcation behavior by the value of the harmonic coefficient k 3 {k}_{3} .","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47695937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the stability of a strongly stabilizing control for degenerate systems in Hilbert spaces","authors":"Mohamed Hariri, Zohra Bouteffal, N. Beghersa, M. Benabdallah","doi":"10.1515/dema-2022-0238","DOIUrl":"https://doi.org/10.1515/dema-2022-0238","url":null,"abstract":"Abstract In this article, we explain how a recent Lyapunov theorem on stability plays a role in the study of the strong stabilizability problem in Hilbert spaces. We explore a degenerate controlled system and investigate the properties of a feedback control to stabilize such system in depth. The spectral theory of an appropriate pencil operator is used to generate robustness constraints for a stabilizing control.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45401741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Properties of a subclass of analytic functions defined by Riemann-Liouville fractional integral applied to convolution product of multiplier transformation and Ruscheweyh derivative","authors":"A. Alb Lupaș, M. Acu","doi":"10.1515/dema-2022-0249","DOIUrl":"https://doi.org/10.1515/dema-2022-0249","url":null,"abstract":"Abstract The contribution of fractional calculus in the development of different areas of research is well known. This article presents investigations involving fractional calculus in the study of analytic functions. Riemann-Liouville fractional integral is known for its extensive applications in geometric function theory. New contributions were previously obtained by applying the Riemann-Liouville fractional integral to the convolution product of multiplier transformation and Ruscheweyh derivative. For the study presented in this article, the resulting operator is used following the line of research that concerns the study of certain new subclasses of analytic functions using fractional operators. Riemann-Liouville fractional integral of the convolution product of multiplier transformation and Ruscheweyh derivative is applied here for introducing a new class of analytic functions. Investigations regarding this newly introduced class concern the usual aspects considered by researchers in geometric function theory targeting the conditions that a function must meet to be part of this class and the properties that characterize the functions that fulfil these conditions. Theorems and corollaries regarding neighborhoods and their inclusion relation involving the newly defined class are stated, closure and distortion theorems are proved, and coefficient estimates are obtained involving the functions belonging to this class. Geometrical properties such as radii of convexity, starlikeness, and close-to-convexity are also obtained for this new class of functions.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49152583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On local fractional integral inequalities via generalized ( h ˜ 1 , h ˜ 2 ) left({tilde{h}}_{1},{tilde{h}}_{2}) -preinvexity involving local fractional integral operators with Mittag-Leffler kernel","authors":"M. Vivas-Cortez, Maria Bibi, M. Muddassar, S. Al-Sa'di","doi":"10.1515/dema-2022-0216","DOIUrl":"https://doi.org/10.1515/dema-2022-0216","url":null,"abstract":"Abstract Local fractional integral inequalities of Hermite-Hadamard type involving local fractional integral operators with Mittag-Leffler kernel have been previously studied for generalized convexities and preinvexities. In this article, we analyze Hermite-Hadamard-type local fractional integral inequalities via generalized ( h ˜ 1 , h ˜ 2 ) left({tilde{h}}_{1},{tilde{h}}_{2}) -preinvex function comprising local fractional integral operators and Mittag-Leffler kernel. In addition, two examples are discussed to ensure that the derived consequences are correct. As an application, we construct an inequality to establish central moments of a random variable.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43511074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On completeness of weak eigenfunctions for multi-interval Sturm-Liouville equations with boundary-interface conditions","authors":"H. Olğar","doi":"10.1515/dema-2022-0210","DOIUrl":"https://doi.org/10.1515/dema-2022-0210","url":null,"abstract":"Abstract The goal of this study is to analyse the eigenvalues and weak eigenfunctions of a new type of multi-interval Sturm-Liouville problem (MISLP) which differs from the standard Sturm-Liouville problems (SLPs) in that the Strum-Liouville equation is defined on a finite number of non-intersecting subintervals and the boundary conditions are set not only at the endpoints but also at finite number internal points of interaction. For the self-adjoint treatment of the considered MISLP, we introduced some self-adjoint linear operators in such a way that the considered multi-interval SLPs can be interpreted as operator-pencil equation. First, we defined a concept of weak solutions (eigenfunctions) for MISLPs with interface conditions at the common ends of the subintervals. Then, we found some important properties of eigenvalues and corresponding weak eigenfunctions. In particular, we proved that the spectrum is discrete and the system of weak eigenfunctions forms a Riesz basis in appropriate Hilbert space.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49041957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}