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":null,"pages":null},"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 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":null,"pages":null},"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}
We work with the notion of trace pseudospectra for an element in the matrix algebra. Many new interesting properties of the trace pseudospectrum have been discovered. In addition, we show an analogue of the spectral mapping theorem for trace pseudospectrum in the matrix algebra. Among other things, we illustrated the applicability of this concepts by a considerable number of examples.
{"title":"A new spectral approach in the matrix algebra: trace pseudospectrum","authors":"A. Ammar, A. Jeribi, K. Mahfoudhi","doi":"10.5269/bspm.48313","DOIUrl":"https://doi.org/10.5269/bspm.48313","url":null,"abstract":"We work with the notion of trace pseudospectra for an element in the matrix algebra. Many new interesting properties of the trace pseudospectrum have been discovered. In addition, we show an analogue of the spectral mapping theorem for trace pseudospectrum in the matrix algebra. Among other things, we illustrated the applicability of this concepts by a considerable number of examples.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41652416","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 purpose of the present paper is to introduce a new subclass of harmonic univalent functions associated with a $q$-Ruscheweyh derivative operator. A necessary and sufficient convolution condition for the functions to be in this class is obtained. Using this necessary and sufficient coefficient condition, results based on the extreme points, convexity and compactness for this class are also obtained.
{"title":"$q$-analogue of a class of harmonic functions","authors":"Omendra Mishra, S. Porwal","doi":"10.5269/bspm.52954","DOIUrl":"https://doi.org/10.5269/bspm.52954","url":null,"abstract":"The purpose of the present paper is to introduce a new subclass of harmonic univalent functions associated with a $q$-Ruscheweyh derivative operator. A necessary and sufficient convolution condition for the functions to be in this class is obtained. Using this necessary and sufficient coefficient condition, results based on the extreme points, convexity and compactness for this class are also obtained.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43689149","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 consider a multicompartment nonlinear epidemic model with temporary immunity and a saturated incidence rate. N(t) at time t, this population is divide into seven sub-classes. N(t) = S(t) + E(t) + I(t) + I1(t) + I2(t) + I3(t) + Q(t). where S(t),E(t); I(t); I(t); I1(t),I2(t); I3(t) and Q(t) denote the sizes of the population susceptible to disease, exposed, infectious members and quarantine members with the possibility of infection through temporary immunity, respectively.The stability of a disease-free status equilibrium and the existence of endemic equilibrium determined by the ratio called the basic reproductive number. The multicompartment non linear epidemic model with saturated rate has been studied the stochastic stability of the free disease equilibrium under certain conditions, and obtain the conditions of global attractivity of the infection.
{"title":"Stochastic stability and impulsive vaccination of multicompartment nonlinear epidemic model with incidence rate","authors":"Laid Chahrazed","doi":"10.5269/bspm.51981","DOIUrl":"https://doi.org/10.5269/bspm.51981","url":null,"abstract":"In this work, we consider a multicompartment nonlinear epidemic model with temporary immunity and a saturated incidence rate. N(t) at time t, this population is divide into seven sub-classes. N(t) = S(t) + E(t) + I(t) + I1(t) + I2(t) + I3(t) + Q(t). where S(t),E(t); I(t); I(t); I1(t),I2(t); I3(t) and Q(t) denote the sizes of the population susceptible to disease, exposed, infectious members and quarantine members with the possibility of infection through temporary immunity, respectively.The stability of a disease-free status equilibrium and the existence of endemic equilibrium determined by the ratio called the basic reproductive number. The multicompartment non linear epidemic model with saturated rate has been studied the stochastic stability of the free disease equilibrium under certain conditions, and obtain the conditions of global attractivity of the infection.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45416293","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 neighborhood structure can represent information or knowledge about relationships between a universe's object. In other words, such elements or objects are somewhat similar to that element in an element's neighborhood. Pawlak presented the idea of rough sets as useful tools for learning computer science and information systems. Neighborhood structures used this principle to be generalized and studied. This paper uses a neighborhood method to solve several rough set theory problems. By using a neighborhood of objects in the information system and illustrative examples to apply it, we introduce some new definitions of attributes, membership function and accuracy measurement. A decision making of our method gives an accurate decision and helps with decision correlation to calculate the accuracy of each attribute that builds an approach to decision making.
{"title":"Some membership functions via neighborhood systems: application to a rough set decision making","authors":"A. E. F. El Atik, A. Zedan","doi":"10.5269/bspm.51936","DOIUrl":"https://doi.org/10.5269/bspm.51936","url":null,"abstract":"The neighborhood structure can represent information or knowledge about relationships between a universe's object. In other words, such elements or objects are somewhat similar to that element in an element's neighborhood. Pawlak presented the idea of rough sets as useful tools for learning computer science and information systems. Neighborhood structures used this principle to be generalized and studied. This paper uses a neighborhood method to solve several rough set theory problems. By using a neighborhood of objects in the information system and illustrative examples to apply it, we introduce some new definitions of attributes, membership function and accuracy measurement. A decision making of our method gives an accurate decision and helps with decision correlation to calculate the accuracy of each attribute that builds an approach to decision making.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46299172","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 study, we present the new concept of involute trajectory ruled surface in Minkowski 3-space. The involute trajectory timelike ruled surface is a surface generated by the motion of a timelike oriented line X along the spacelike involute curve γ(s) of a given timelike base curve r(s). The main purpose of this article is to present a new perspective on the generation of developable trajectory ruled surfaces in Minkowski 3-space. These surfaces are formed depending on the angle θ between the Darboux vector D and the binormal vector b of the evolute curve r(s). Also, some new results and theorems related to the developability of the involute trajectory timelike ruled surfaces are obtained. Finally, we illustrate these surfaces by presenting one example.
{"title":"A new method for designing involute trajectory timelike ruled surfaces in Minkowski 3-space","authors":"M. Bilici","doi":"10.5269/bspm.51594","DOIUrl":"https://doi.org/10.5269/bspm.51594","url":null,"abstract":"In this study, we present the new concept of involute trajectory ruled surface in Minkowski 3-space. The involute trajectory timelike ruled surface is a surface generated by the motion of a timelike oriented line X along the spacelike involute curve γ(s) of a given timelike base curve r(s). The main purpose of this article is to present a new perspective on the generation of developable trajectory ruled surfaces in Minkowski 3-space. These surfaces are formed depending on the angle θ between the Darboux vector D and the binormal vector b of the evolute curve r(s). Also, some new results and theorems related to the developability of the involute trajectory timelike ruled surfaces are obtained. Finally, we illustrate these surfaces by presenting one example.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46874577","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 study a harmonic evolute surface of quasi tangent surface associated with quasi frame. We construct quasi tangent surface with first and second fundamental forms. Moreover, we determine harmonic evolute surface of quasi tangent surface by using these fundamental forms. Finally, we obtain some new results about these new surfaces.
{"title":"A new construction for harmonic evolute surfaces of quasi tangent surfaces with quasi frame","authors":"T. Körpınar, Gül Uğur Kaymanlı","doi":"10.5269/bspm.51179","DOIUrl":"https://doi.org/10.5269/bspm.51179","url":null,"abstract":"In this paper, we study a harmonic evolute surface of quasi tangent surface associated with quasi frame. We construct quasi tangent surface with first and second fundamental forms. Moreover, we determine harmonic evolute surface of quasi tangent surface by using these fundamental forms. Finally, we obtain some new results about these new surfaces.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46172605","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}
Several authors have examined the solvability conditions for an infinite system of differential equations in different Banach spaces using the concept of measure of noncompactness. In all these studies, they have considered differential equations where the boundary conditions are defined on two points. In this paper, we have studied the solvability conditions for an infinite system of third-order three point boundary value problem in the sequence space of bounded variation $bv_0$ with the help of the theory of measure of noncompactness and have given a suitable example to illustrate the result.
{"title":"Consistency of an Infinite system of third order three-point boundary value problem in the $bv_0$ space by the theory of measure of noncompactness","authors":"Niraj Sapkota, Rituparna Das, Santonu Savapondit","doi":"10.5269/bspm.53112","DOIUrl":"https://doi.org/10.5269/bspm.53112","url":null,"abstract":"Several authors have examined the solvability conditions for an infinite system of differential equations in different Banach spaces using the concept of measure of noncompactness. In all these studies, they have considered differential equations where the boundary conditions are defined on two points. In this paper, we have studied the solvability conditions for an infinite system of third-order three point boundary value problem in the sequence space of bounded variation $bv_0$ with the help of the theory of measure of noncompactness and have given a suitable example to illustrate the result.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42178142","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 investigate the spectrum of the Seidel and Seidel Laplacian matrix of a graph. We generalized the concept of Seidel Laplacian matrix which denoted by Seidel matrix and obtained some results related to them. This can be intuitively understood as a consequence of the relationship between the Seidel and Seidel Laplacian matrix in the graph by Zagreb index. In closing, we mention some alternatives to and generalization of the Seidel and Seidel Laplacian matrices. Also, we obtain relation between Seidel and Seidel Laplacian energy, related to all graphs with order n.
{"title":"A note on the Seidel and Seidel Laplacian matrices","authors":"Jalal Askari","doi":"10.5269/bspm.51593","DOIUrl":"https://doi.org/10.5269/bspm.51593","url":null,"abstract":"In this paper we investigate the spectrum of the Seidel and Seidel Laplacian matrix of a graph. We generalized the concept of Seidel Laplacian matrix which denoted by Seidel matrix and obtained some results related to them. This can be intuitively understood as a consequence of the relationship between the Seidel and Seidel Laplacian matrix in the graph by Zagreb index. In closing, we mention some alternatives to and generalization of the Seidel and Seidel Laplacian matrices. Also, we obtain relation between Seidel and Seidel Laplacian energy, related to all graphs with order n.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45838291","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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