In this paper, we study the existence and multiplicity of solutions for Dirichlet singular elliptic problems involving the $p(x)$-Laplace equation with critical growth. The technical approach is mainly based on the variational method combined with the genus theory.
{"title":"Results of singular Direchelet problem involving the $p(x)$-laplacian with critical growth","authors":"H. Belaouidel, M. Haddaoui, N. Tsouli","doi":"10.5269/bspm.52984","DOIUrl":"https://doi.org/10.5269/bspm.52984","url":null,"abstract":"In this paper, we study the existence and multiplicity of solutions for Dirichlet singular elliptic problems involving the $p(x)$-Laplace equation with critical growth. The technical approach is mainly based on the variational method combined with the genus theory.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46837321","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}
In this paper, we discuss the implementation and numerical aspects of the Matlab solver designed for the solution of Low Protein Model (LPD). In this paper, we study the existence and uniqueness of the weak solution and we try to write some codes in Matlab which are based on Euler’s Method and several technics of programmation. subject to an initial condition dM dt = µL − δM, (2) L(0) = 0 and M (0) = 0. (3) The code is based on Euler’s Method and several technics of programmation.
{"title":"Implementation and numerical aspects of the matlab solver designed for the solution of low protein model","authors":"Meraihi Mouna","doi":"10.5269/bspm.51826","DOIUrl":"https://doi.org/10.5269/bspm.51826","url":null,"abstract":"In this paper, we discuss the implementation and numerical aspects of the Matlab solver designed for the solution of Low Protein Model (LPD). In this paper, we study the existence and uniqueness of the weak solution and we try to write some codes in Matlab which are based on Euler’s Method and several technics of programmation. subject to an initial condition \u0000dM \u0000dt = µL − δM, (2) \u0000L(0) = 0 and M (0) = 0. (3) \u0000The code is based on Euler’s Method and several technics of programmation.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45227253","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}
In this work, we research geometrical interpretation involved with the energy by ED-frame field of first and second kind on orientable hypersurface in E⁴. We explore the geometric properties of some graphics by way of energy. We apply totally diverse discussion and approach to illustrate bending energy functional for ED-frame field of first and second kind. Moreover, we have an original and satisfactorily association among energy of the curve on orientable hypersurface in E⁴.
{"title":"A new version of energy and elastica for curves with extended darboux frame","authors":"V. Asil, T. Körpınar, Y. Ünlütürk","doi":"10.5269/bspm.51025","DOIUrl":"https://doi.org/10.5269/bspm.51025","url":null,"abstract":"In this work, we research geometrical interpretation involved with the energy by ED-frame field of first and second kind on orientable hypersurface in E⁴. We explore the geometric properties of some graphics by way of energy. We apply totally diverse discussion and approach to illustrate bending energy functional for ED-frame field of first and second kind. Moreover, we have an original and satisfactorily association among energy of the curve on orientable hypersurface in E⁴.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44368962","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}
The current article introduces the notion of asymptotically lacunary $(Delta^n,mu)$-statistical equivalent sequence in the settings of a probabilistic norm $N$. Furthermore, the article presents the concepts of asymptotically $(Delta^n,mu)$-strongly Ces'{a}ro equivalent sequences and asymptotically $(Delta^n,mu)$-strongly Ces'{a}ro Orlicz equivalent sequences in the theory of probabilistic normed spaces and also investigates their various properties including some inclusion relations as well as some equivalent conditions in this new settings.
{"title":"Asymptotically lacunary µ-statistical equivalence of generalized difference sequences in probabilistic normed spaces","authors":"R. Haloi, M. Sen, B. Tripathy","doi":"10.5269/bspm.51915","DOIUrl":"https://doi.org/10.5269/bspm.51915","url":null,"abstract":"The current article introduces the notion of asymptotically lacunary $(Delta^n,mu)$-statistical equivalent sequence in the settings of a probabilistic norm $N$. Furthermore, the article presents the concepts of asymptotically $(Delta^n,mu)$-strongly Ces'{a}ro equivalent sequences and asymptotically $(Delta^n,mu)$-strongly Ces'{a}ro Orlicz equivalent sequences in the theory of probabilistic normed spaces and also investigates their various properties including some inclusion relations as well as some equivalent conditions in this new settings.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45705906","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}
This article is concerned with the existence and uniqueness of solutions of a nonlinear neutral conformable fractional differential system with infinite delay, involving conformable fractional derivative. Additionally, we study the Ulam--Hyres stability, Ulam--Hyres--Mittag--Leffler stability, Ulam--Hyres--Mittag--Leffler--Rassias stability for the solutions of considered system using Picard operator. For application of the theory, we add an example at the end.
{"title":"Ulam's stability of conformable neutral fractional differential equations","authors":"Manzoor Ahmad, A. Zada","doi":"10.5269/bspm.51442","DOIUrl":"https://doi.org/10.5269/bspm.51442","url":null,"abstract":"This article is concerned with the existence and uniqueness of solutions of a nonlinear neutral conformable fractional differential system with infinite delay, involving conformable fractional derivative. Additionally, we study the Ulam--Hyres stability, Ulam--Hyres--Mittag--Leffler stability, Ulam--Hyres--Mittag--Leffler--Rassias stability for the solutions of considered system using Picard operator. For application of the theory, we add an example at the end.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47378987","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}
In this paper we introduce the concept of tension on an edge in a graph. The tension on an edge in a graph is the number of geodesics passing through it. We investigate some results and characterizations involving tensions on edges in graphs.
{"title":"Tension on an edge in a graph","authors":"K. Bhargava, N. N. Dattatreya, R. Rajendra","doi":"10.5269/bspm.51295","DOIUrl":"https://doi.org/10.5269/bspm.51295","url":null,"abstract":"In this paper we introduce the concept of tension on an edge in a graph. The tension on an edge in a graph is the number of geodesics passing through it. We investigate some results and characterizations involving tensions on edges in graphs.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42187591","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}
Preceding years predict IoT to be trend in technology domain as it possesses superior intelligence and methods to access data as well able to construct networks anywhere which we are witnessing today. Today IoT devices are well implemented and are a topic and product of interest for many. In midst of this S-IoT emerged which is understood as the added ingredient in IoT networks enables improvement in accessing data, its procession, real-time decisions, and many more new functions and all of this with an ideal price [1]. S-IoT led to the interesting development of enabling the Internet of things to be socially connected in a network with each other which permits them to socially interact with each other and have their respective profiles for their identification all similar to humans. This magical innovation-led internet networks to be more complicated. In this paper, we are modeling objects of S-Iot centered homes as network graphs with a medium domination number approach. The key notion here is to inspect the total number of objects connected that dominate every pair of objects in a network graph and the average value of this is defined as “the medium domination number”. We evaluated new results and relations along with further vulnerability methods and developed an algorithm of complexity O(n 2).
{"title":"Graph Modelling of Social Internet of Things (S-IoT) centered home automation using medium domination approach","authors":"Aaysha Khan, Jana Shafi","doi":"10.5269/bspm.51446","DOIUrl":"https://doi.org/10.5269/bspm.51446","url":null,"abstract":"Preceding years predict IoT to be trend in technology domain as it possesses superior intelligence and methods to access data as well able to construct networks anywhere which we are witnessing today. Today IoT devices are well implemented and are a topic and product of interest for many. In midst of this S-IoT emerged which is understood as the added ingredient in IoT networks enables improvement in accessing data, its procession, real-time decisions, and many more new functions and all of this with an ideal price [1]. S-IoT led to the interesting development of enabling the Internet of things to be socially connected in a network with each other which permits them to socially interact with each other and have their respective profiles for their identification all similar to humans. This magical innovation-led internet networks to be more complicated. In this paper, we are modeling objects of S-Iot centered homes as network graphs with a medium domination number approach. The key notion here is to inspect the total number of objects connected that dominate every pair of objects in a network graph and the average value of this is defined as “the medium domination number”. We evaluated new results and relations along with further vulnerability methods and developed an algorithm of complexity O(n 2).","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43569103","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}
In this paper, the study of the existence of a renormalized solution for quasilinear parabolicproblem with variable exponents and measure data. The model is: u_{t}-text{div}(leftvert nabla urightvert ^{p(x)-2}nabla u)+lambdaleftvert urightvert ^{p(x)-2}u=mutext{ } &text{in}hspace{0.5cm}Q=Omega times ]0,T[,u=0 & text{on}hspace{0.5cm}Sigma =partial Omega times ]0,T[, u(.,0)=u_{0}(.) & text{in}hspace{0.5cm}Omega, where $ lambda>0$ and $ T $ is any positive constant, $ muinmathcal{M}_{0}(Q) $ is any measure with bounded variation over $ Q=Omega times ]0,T[ $.
{"title":"The existence of renormalized solution for quasilinear parabolic problem with variable exponents and measure data","authors":"Fairouz Souileh, M. Maouni, K. Slimani","doi":"10.5269/bspm.51207","DOIUrl":"https://doi.org/10.5269/bspm.51207","url":null,"abstract":"In this paper, the study of the existence of a renormalized solution for quasilinear parabolicproblem with variable exponents and measure data. The model is: \u0000u_{t}-text{div}(leftvert nabla urightvert ^{p(x)-2}nabla u)+lambdaleftvert urightvert ^{p(x)-2}u=mutext{ } &text{in}hspace{0.5cm}Q=Omega times ]0,T[,u=0 & text{on}hspace{0.5cm}Sigma =partial Omega times ]0,T[, u(.,0)=u_{0}(.) & text{in}hspace{0.5cm}Omega, \u0000where $ lambda>0$ and $ T $ is any positive constant, $ muinmathcal{M}_{0}(Q) $ is any measure with bounded variation over $ Q=Omega times ]0,T[ $.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41443688","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}
Let G be a finite simple and undirected graph without isolated vertices. For any non-negative integers j and k, a subset D of V is called a pitchfork dominating set if every vertex in D dominates at least j and at most k vertices of V - D. A subset D -1 of V - D is an inverse pitchfork dominating set if it is a dominating set. The pitchfork domination number of G, denoted by pf (G) is a minimum cardinality over all pitchfork dominating sets in G. The inverse pitchfork domination number of G, denoted by pf-1 (G) is a minimum cardinality over all inverse pitchfork dominating sets in G. In this paper, pitchfork dominations and it's inverse are applied when j = 1 and k = 2 on some standard graphs such as: tadpole graph, lollipop graph, lollipop flower graph , daisy graph and Barbell graph.
{"title":"Applying the (1,2)-pitchfork domination and it's inverse on some special graphs","authors":"M. A. Abdlhusein","doi":"10.5269/bspm.52252","DOIUrl":"https://doi.org/10.5269/bspm.52252","url":null,"abstract":"Let G be a finite simple and undirected graph without isolated vertices. For any non-negative integers j and k, a subset D of V is called a pitchfork dominating set if every vertex in D dominates at least j and at most k vertices of V - D. A subset D -1 of V - D is an inverse pitchfork dominating set if it is a dominating set. The pitchfork domination number of G, denoted by pf (G) is a minimum cardinality over all pitchfork dominating sets in G. The inverse pitchfork domination number of G, denoted by pf-1 (G) is a minimum cardinality over all inverse pitchfork dominating sets in G. In this paper, pitchfork dominations and it's inverse are applied when j = 1 and k = 2 on some standard graphs such as: tadpole graph, lollipop graph, lollipop flower graph , daisy graph and Barbell graph.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42915504","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}
In this manuscript, the notion of soft topological groupoid is proposed by examining in a different perspective the notion of soft groupoid, which is defined as a parameterized family of the subgroupoids of a soft groupoid. In this context, topological groupoid structures are equipped with soft set theory and the category of soft topological groupoids is formed. Subsequently, the definition of soft topological subgroupoid is presented and all new notions given are strengthened by illustrative examples.
{"title":"A topological approach to soft groupoids","authors":"G. Oǧuz","doi":"10.5269/bspm.51392","DOIUrl":"https://doi.org/10.5269/bspm.51392","url":null,"abstract":"In this manuscript, the notion of soft topological groupoid is proposed by examining in a different perspective the notion of soft groupoid, which is defined as a parameterized family of the subgroupoids of a soft groupoid. In this context, topological groupoid structures are equipped with soft set theory and the category of soft topological groupoids is formed. Subsequently, the definition of soft topological subgroupoid is presented and all new notions given are strengthened by illustrative examples.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44729540","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}
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