In this essay, extensions to the results of Lie symmetry classification of Reynolds equation are proposed. The infinitesimal technique is used to derive symmetry groups of the Reynolds equation. Onedimensional optimal system is constructed for symmetry sub-algebras gained through Lie point symmetry. At the end, the general symmetry group of the non-conservative generalized thin-film equation are determined.
{"title":"Symmetry classification and invariance of the Reynolds equation","authors":"Maryam Yourdkhany, Mehdi Nadjafikhah","doi":"10.30495/JME.V0I0.1855","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1855","url":null,"abstract":"In this essay, extensions to the results of Lie symmetry classification of Reynolds equation are proposed. The infinitesimal technique is used to derive symmetry groups of the Reynolds equation. Onedimensional optimal system is constructed for symmetry sub-algebras gained through Lie point symmetry. At the end, the general symmetry group of the non-conservative generalized thin-film equation are determined.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42053232","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 dynamics of a modied Nicholson-Baileymodel as a discrete dynamical system has been studied. Local dynamics in a neighborhood of boundary xed points are investigated. Itis also proved that the model has a unique positive xed point and a Neimark-Sacker bifurcation emerges at this xed point. Some numericalsimulations are presented to illustrate the analytical results.
{"title":"Dynamics and Neimark-Sacker Bifurcation of a Modified Nicholson-Bailey Model","authors":"M. H. Akrami, A. Atabaigi","doi":"10.30495/JME.V0I0.1695","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1695","url":null,"abstract":"In this paper, the dynamics of a modied Nicholson-Baileymodel as a discrete dynamical system has been studied. Local dynamics in a neighborhood of boundary xed points are investigated. Itis also proved that the model has a unique positive xed point and a Neimark-Sacker bifurcation emerges at this xed point. Some numericalsimulations are presented to illustrate the analytical results.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48790683","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}
By studying and using the quasi-pure part concept, we improve some statements and show that some assumptions in some articles are superfluous. We give some characterizations of Gelfand rings. For example: we prove that R is Gelfand if and only if m(sum_{ α in A} I_ α) = sum_{ α in A} m ( I_ α ), for each family { I_ α}_{ α in A} of ideals of R , in addition if R is semiprimitive and Max( R ) ⊆ Y ⊆ Spec( R ), we show that R is a Gelfand ring if and only if Y is normal. We prove that if R is reduced ring, then R is a von Neumann regular ring if and only if Spec( R ) is regular. It has been shown that if R is a Gelfand ring, then Max( R ) is a quotient of Spec( R ), and sometimes h M ( a )’s behave like the zerosets of the space of maximal ideal. Finally, it has been proven that Z Max( C ( X )) = { h_ M ( f ) : f in C ( X ) } if and only if { h_ M ( f ) : f in C ( X )} is closed under countable intersection if and only if X is pseudocompact.
通过对拟纯部分概念的研究和应用，我们改进了一些表述，证明了某些文章中的一些假设是多余的。给出了Gelfand环的一些特征。例如:证明R是格尔芬环当且仅当m(sum_{α in A} I_ α) = sum_{α in A} m(I_ α)，对于R的理想的每一个族{I_ α} {α in A}，当且仅当R是半原元且Max(R)，当Y是正态的，证明R是格尔芬环。证明了当R是约简环时，当且仅当Spec(R)是正则环时，R是von Neumann正则环。证明了如果R是一个Gelfand环，则Max(R)是Spec(R)的商，并且h M (a)有时表现为极大理想空间的零集。最后，证明了zmax (C (X)) = {h_ M (f): f in C (X)}当且仅当{h_ M (f): f in C (X)}是闭于可数交下的，当且仅当X是伪紧的。
{"title":"On commutative Gelfand rings","authors":"A. R. Aliabad, M. Badie, S. Nazari","doi":"10.30495/JME.V0I0.1866","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1866","url":null,"abstract":"By studying and using the quasi-pure part concept, we improve some statements and show that some assumptions in some articles are superfluous. We give some characterizations of Gelfand rings. For example: we prove that R is Gelfand if and only if m(sum_{ α in A} I_ α) = sum_{ α in A} m ( I_ α ), for each family { I_ α}_{ α in A} of ideals of R , in addition if R is semiprimitive and Max( R ) ⊆ Y ⊆ Spec( R ), we show that R is a Gelfand ring if and only if Y is normal. We prove that if R is reduced ring, then R is a von Neumann regular ring if and only if Spec( R ) is regular. It has been shown that if R is a Gelfand ring, then Max( R ) is a quotient of Spec( R ), and sometimes h M ( a )’s behave like the zerosets of the space of maximal ideal. Finally, it has been proven that Z Max( C ( X )) = { h_ M ( f ) : f in C ( X ) } if and only if { h_ M ( f ) : f in C ( X )} is closed under countable intersection if and only if X is pseudocompact.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45218175","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}
Fuzzy Integral equations is a mathematical tool for mod- eling the uncertain control system and economic. In this paper, we present numerical solution of nonlinear fuzzy Volterra integral equa- tions(NFVIEs) using successive approximations scheme and block-pulse functions. Additionally, the convergence analysis of the presented ap- proach is investigated involving Lipschitz and several conditions and error bound between the approximate and the exact solution is pro- vided. Finally, to approve the outcomes concerned with the theory a numerical experiment is considered.
{"title":"Iterative approach for a class of fuzzy Volterra integral equations using block pulse functions","authors":"Kamran Akhavan Zakeri, M. A. Araghi, S. Ziari","doi":"10.30495/JME.V0I0.1816","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1816","url":null,"abstract":"Fuzzy Integral equations is a mathematical tool for mod- eling the uncertain control system and economic. In this paper, we present numerical solution of nonlinear fuzzy Volterra integral equa- tions(NFVIEs) using successive approximations scheme and block-pulse functions. Additionally, the convergence analysis of the presented ap- proach is investigated involving Lipschitz and several conditions and error bound between the approximate and the exact solution is pro- vided. Finally, to approve the outcomes concerned with the theory a numerical experiment is considered.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44137101","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}
It is known that even duals of a Banach algebra A with one of Arens products are Banach algebras, these products are natural multiplications extending the one on A. But the essence of A*is completely different. We investigate some algebraic and spectral properties of odd duals of A, by defning the products ⃝a, ⃝F as in [12]. We will show relations between these products and Arens products, weak or weak-starcontinuity, commutativity and unit elements of these algebras. Also we determine the spectrum and multiplier algebra for A*, and we calculate the quasi-inverses, spectrum and spectral radius for elements of these kinds of algebras.
{"title":"On Odd Duals of a Banach Algebra as a Banach Algebra","authors":"M. Ettefagh","doi":"10.30495/JME.V0I0.1676","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1676","url":null,"abstract":"It is known that even duals of a Banach algebra A with one of Arens products are Banach algebras, these products are natural multiplications extending the one on A. But the essence of A*is completely different. We investigate some algebraic and spectral properties of odd duals of A, by defning the products ⃝a, ⃝F as in [12]. We will show relations between these products and Arens products, weak or weak-starcontinuity, commutativity and unit elements of these algebras. Also we determine the spectrum and multiplier algebra for A*, and we calculate the quasi-inverses, spectrum and spectral radius for elements of these kinds of algebras.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42635128","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}
R. Prasad, M. Akyol, Punit Kumar Singh, Sushil Kumar
The paper deals with the notion of quasi bi-slant submersions from almostcontact metric manifolds onto Riemannian manifolds. These submersions aregeneralization of hemi-slant submersions and semi-slant submersions. Westudy such submersions from Kenmotsu manifolds onto Riemannian manifolds anddiscuss some examples of it. In this paper, we also study the geometry ofleaves of distributions which are involved in the definition of thesubmersion. Further, we obtain the conditions for such submersions to beintegrable and totally geodesic.
{"title":"On Quasi bi-slant submersions from Kenmotsu manifolds onto any Riemannian manifolds","authors":"R. Prasad, M. Akyol, Punit Kumar Singh, Sushil Kumar","doi":"10.30495/JME.V0I0.1588","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1588","url":null,"abstract":"The paper deals with the notion of quasi bi-slant submersions from almostcontact metric manifolds onto Riemannian manifolds. These submersions aregeneralization of hemi-slant submersions and semi-slant submersions. Westudy such submersions from Kenmotsu manifolds onto Riemannian manifolds anddiscuss some examples of it. In this paper, we also study the geometry ofleaves of distributions which are involved in the definition of thesubmersion. Further, we obtain the conditions for such submersions to beintegrable and totally geodesic.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47128010","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 perfect m-coloring with matrix A = [aij ]i,j∈{1,··· ,m} of a graph G = (V, E) with {1, · · · , m} color is a vertex coloring of G with m-color so that number of vertex in color j adjacent to a fixed vertex in color i is aij , independent from the choice of vertex in color i. The matrix A = [aij ]i,j∈{1,··· ,m} is called the parameter matrix. We study the perfect 4-coloring of the 3-regular graphs of order at Most 8, that is, we determine a list of all color parameter matrices corresponding to perfect coloring of 3-regular graphs of order 4, 6 and 8.
{"title":"Perfect 4-Colorings of the 3-Regular Graphs of Order at Most 8","authors":"M. Alaeiyan, Zeinab Vahedi, M. Maghasedi","doi":"10.30495/JME.V0I0.1501","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1501","url":null,"abstract":"The perfect m-coloring with matrix A = [aij ]i,j∈{1,··· ,m} of a graph G = (V, E) with {1, · · · , m} color is a vertex coloring of G with m-color so that number of vertex in color j adjacent to a fixed vertex in color i is aij , independent from the choice of vertex in color i. The matrix A = [aij ]i,j∈{1,··· ,m} is called the parameter matrix. We study the perfect 4-coloring of the 3-regular graphs of order at Most 8, that is, we determine a list of all color parameter matrices corresponding to perfect coloring of 3-regular graphs of order 4, 6 and 8.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42378520","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}
Fuzzy fractional heat equations (FFHEs) are utilized to analyse the behaviour of the certain phenomena in various mathematical and scientific models. The main goal of this paper is to construct the solution of fuzzy fractional heat equations by taking a reliable recipe of Sumudu transformation method and homotopy analysis method into account. This method allow us to remove the difficulties and restrictions confronted in other methods. The feasibility of this method is confirmed by given numerical examples. the result presented that the proposed method is suitable, powerful and liable for obtaining the solution of fuzzy fractional problems with FFHEs.
{"title":"Solutions of Fuzzy Time Fractional Heat Equation","authors":"Süleyman Çetinkaya, A. Demir","doi":"10.30495/JME.V0I0.1768","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1768","url":null,"abstract":"Fuzzy fractional heat equations (FFHEs) are utilized to analyse the behaviour of the certain phenomena in various mathematical and scientific models. The main goal of this paper is to construct the solution of fuzzy fractional heat equations by taking a reliable recipe of Sumudu transformation method and homotopy analysis method into account. This method allow us to remove the difficulties and restrictions confronted in other methods. The feasibility of this method is confirmed by given numerical examples. the result presented that the proposed method is suitable, powerful and liable for obtaining the solution of fuzzy fractional problems with FFHEs.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44912171","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}
S. Mirvakili, H. Naraghi, M. Shirvani, P. Ghiasvand
In this paper, first we produce a fuzzy multigroup from a fuzzy subgroup of a group $G$ and we show that there is a relationship between a fuzzy multigroup with underlying group $G$ and a fuzzy multigroup with underlying group $Aut(A)$. Moreover, we generate a code by using the defined special fuzzy multigroup automorphisms
{"title":"Some fuzzy multigroups obtained from fuzzy subgroups","authors":"S. Mirvakili, H. Naraghi, M. Shirvani, P. Ghiasvand","doi":"10.30495/JME.V0I0.1853","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1853","url":null,"abstract":"In this paper, first we produce a fuzzy multigroup from a fuzzy subgroup of a group $G$ and we show that there is a relationship between a fuzzy multigroup with underlying group $G$ and a fuzzy multigroup with underlying group $Aut(A)$. Moreover, we generate a code by using the defined special fuzzy multigroup automorphisms","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41812100","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}
Asha B. Nale, S. K. Panchal, V. L. Chinchane, Z. Dahmani
The main objective of this paper is to establish new fractional integral inequalities involving convex function by considering Marichev-Saigo-Maeda (MSM) fractional integral operator. Also we establish some fractional integral inequities for positive and continuous function usingMarichev-Saigo-Maeda fractional integral operator.
{"title":"Fractional integral inequalities involving convex functions via Marichev-Saigo-Maeda approach","authors":"Asha B. Nale, S. K. Panchal, V. L. Chinchane, Z. Dahmani","doi":"10.30495/JME.V15I0.2016","DOIUrl":"https://doi.org/10.30495/JME.V15I0.2016","url":null,"abstract":"The main objective of this paper is to establish new fractional integral inequalities involving convex function by considering Marichev-Saigo-Maeda (MSM) fractional integral operator. Also we establish some fractional integral inequities for positive and continuous function usingMarichev-Saigo-Maeda fractional integral operator.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48390248","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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