In this article we introduce some new type of summability methods for double sequences involving the ideas of de la Vallée-Poussin mean in probabilistic 2 -normed space and examine some important results.
本文介绍了在概率2赋范空间中，利用de la vall - poussin均值思想的几种新的二重序列可和性方法，并检验了一些重要结果。
{"title":"Some Results via De La Vallée-poussin Mean in Probabilistic 2-normed Spaces","authors":"U. Yamancı, M. Gürdal, S. Aytar","doi":"10.46300/91019.2022.9.1","DOIUrl":"https://doi.org/10.46300/91019.2022.9.1","url":null,"abstract":"In this article we introduce some new type of summability methods for double sequences involving the ideas of de la Vallée-Poussin mean in probabilistic 2 -normed space and examine some important results.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75669288","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 have proposed the second-derivative-free numerical method and determined the control parameters to converge cubically. In addition, we have developed the order of convergence and the asymptotic error constant. Applying this iterative scheme to a variety of examples, numerical results have shown a successful asymptotic error constants with cubic convergence.
{"title":"Derivation of a Numerical Method with Free Second-order Derivatives","authors":"Y. Geum","doi":"10.46300/91019.2022.9.2","DOIUrl":"https://doi.org/10.46300/91019.2022.9.2","url":null,"abstract":"We have proposed the second-derivative-free numerical method and determined the control parameters to converge cubically. In addition, we have developed the order of convergence and the asymptotic error constant. Applying this iterative scheme to a variety of examples, numerical results have shown a successful asymptotic error constants with cubic convergence.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"215 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86848589","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 establish a connection between the solvability of end-point BMO and Lp Dirichlet problems for a second order divergence form elliptic operator (not necessarily symmetric) with bounded measurable coefficients. In particular, we give a lower bound for the exponent p > 1 in terms of the BMO-constant of L (see Definition 8).
{"title":"Lp and BMO-solvability of the Dirichlet Problem for Elliptic Operators","authors":"Gabriella Zecca","doi":"10.46300/91019.2022.9.8","DOIUrl":"https://doi.org/10.46300/91019.2022.9.8","url":null,"abstract":"We establish a connection between the solvability of end-point BMO and Lp Dirichlet problems for a second order divergence form elliptic operator (not necessarily symmetric) with bounded measurable coefficients. In particular, we give a lower bound for the exponent p > 1 in terms of the BMO-constant of L (see Definition 8).","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84359529","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 some fundamental results of the elliptic curve over the quadratic field. After we create an elliptic curve over the quadratic field with an element of infinite order.[2,3,4].
{"title":"Elliptic Curves Over The Quadratic Field","authors":"S. Abdelalim, A. Chillali, S. Elhajji","doi":"10.46300/91019.2022.9.4","DOIUrl":"https://doi.org/10.46300/91019.2022.9.4","url":null,"abstract":"In this paper, we introduce some fundamental results of the elliptic curve over the quadratic field. After we create an elliptic curve over the quadratic field with an element of infinite order.[2,3,4].","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89964784","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}
Operator derivatives are determined as functors. Necessary optimality conditions with category interpretation are proved for abstract optimization control problems. Finite dimensional extremum problems and an optimization control problem for nonlinear parabolic equation with state constraints are considered as examples.
{"title":"Differentiation Functors and Category Interpretation of Optimality Conditions","authors":"S. Serovajsky, D. Diarova","doi":"10.46300/91019.2022.9.5","DOIUrl":"https://doi.org/10.46300/91019.2022.9.5","url":null,"abstract":"Operator derivatives are determined as functors. Necessary optimality conditions with category interpretation are proved for abstract optimization control problems. Finite dimensional extremum problems and an optimization control problem for nonlinear parabolic equation with state constraints are considered as examples.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84660045","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 prove the demiclosedness principle for k -strictly pseudo-contractive mappings and establish the Δ - convergence theorem of the cyclic algorithm for such mappings in CAT(0) spaces. Also, we give the strong convergence theorem of the modified Halpern iteration for k -strictly pseudo-contractive mappings in CAT(0) spaces. Our results extend and improve the corresponding recent results announced by many authors in the literature.
{"title":"On the Convergence of Two Iterative Methods for k-strictly Pseudo-contractive Mappings in Cat(0) Spaces","authors":"A. Şahin, M. Basarir","doi":"10.46300/91019.2022.9.7","DOIUrl":"https://doi.org/10.46300/91019.2022.9.7","url":null,"abstract":"In this paper, we prove the demiclosedness principle for k -strictly pseudo-contractive mappings and establish the Δ - convergence theorem of the cyclic algorithm for such mappings in CAT(0) spaces. Also, we give the strong convergence theorem of the modified Halpern iteration for k -strictly pseudo-contractive mappings in CAT(0) spaces. Our results extend and improve the corresponding recent results announced by many authors in the literature.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87729603","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}
A class of transcendental preferences is employed as an explicit representation of the luxurynecessity dichotomy which admits a smooth Cobb- Douglas limit. The analytical tractability of the model enables us to represent explicitly Marshallian demand and income elasticity of demand. The noncommutativity of scale and substitution effects, and measured by Lie brackets of the corresponding vector fields, is employed in order to define a measure of deviation from scale symmetry which is profoundly connected with Shephard’s distance.
{"title":"On the Geometry of Luxury","authors":"A. Mantovi","doi":"10.46300/91019.2022.9.3","DOIUrl":"https://doi.org/10.46300/91019.2022.9.3","url":null,"abstract":"A class of transcendental preferences is employed as an explicit representation of the luxurynecessity dichotomy which admits a smooth Cobb- Douglas limit. The analytical tractability of the model enables us to represent explicitly Marshallian demand and income elasticity of demand. The noncommutativity of scale and substitution effects, and measured by Lie brackets of the corresponding vector fields, is employed in order to define a measure of deviation from scale symmetry which is profoundly connected with Shephard’s distance.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"95 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82055012","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 article, we establish new characterizations of convex functions, prove some connected convex type integral inequality; consider the pair of convex functions as the dual semi-norms in functional space. The properties of the integral operators are considered in the scales of the convex semi-norm under the standard conditions on singular kernels.
{"title":"Convex Inequalities and Functional Space with the Convex Semi-Norm","authors":"M. Yaremenko","doi":"10.46300/91019.2021.8.9","DOIUrl":"https://doi.org/10.46300/91019.2021.8.9","url":null,"abstract":"In this article, we establish new characterizations of convex functions, prove some connected convex type integral inequality; consider the pair of convex functions as the dual semi-norms in functional space. The properties of the integral operators are considered in the scales of the convex semi-norm under the standard conditions on singular kernels.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74991742","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 Frobenius number of a set of relatively prime positive integers α1,α2,…,αn such that α1< α2< …< αn, is the largest integer that can not be written as a nonnegative integer linear combination of the given set. Finding the Frobenius number is known as the Frobenius problem, which is also named as the coin exchange problem or the postage stamp problem. This problem is closely related with the equality constrained integer knapsack problem. It is known that this problem is NP-hard. Extensive research has been conducted for finding the Frobenius number of a given set of positive integers. An exact formula exists for the case n=2 and various formulas have been derived for all special cases of n = 3. Many algorithms have been proposed for n≥4. As far as we are aware, there does not exist any integer programming approach for this problem which is the main motivation of this paper. We present four integer linear programming formulations about the Frobenius number of a given set of positive integers. Our first formulation is used to check if a given positive integer is the Frobenius number of a given set of positive integers. The second formulation aims at finding the Frobenius number directly. The third formulation involves the residue classes with respect to the least member of the given set of positive integers, where a residue table is computed comprising all values modulo that least member, and the Frobenius number is obtained from there. Based on the same approach underlying the third formulation, we propose our fourth formulation which produces the Frobenius number directly. We demonstrate how to use our formulations with several examples. For illustrative purposes, some computa-tional analysis is also presented.
{"title":"Integer Programming Formulations For The Frobenius Problem","authors":"Imdat Kara, H. I. Karakaş","doi":"10.46300/91019.2021.8.8","DOIUrl":"https://doi.org/10.46300/91019.2021.8.8","url":null,"abstract":"The Frobenius number of a set of relatively prime positive integers α1,α2,…,αn such that α1< α2< …< αn, is the largest integer that can not be written as a nonnegative integer linear combination of the given set. Finding the Frobenius number is known as the Frobenius problem, which is also named as the coin exchange problem or the postage stamp problem. This problem is closely related with the equality constrained integer knapsack problem. It is known that this problem is NP-hard. Extensive research has been conducted for finding the Frobenius number of a given set of positive integers. An exact formula exists for the case n=2 and various formulas have been derived for all special cases of n = 3. Many algorithms have been proposed for n≥4. As far as we are aware, there does not exist any integer programming approach for this problem which is the main motivation of this paper. We present four integer linear programming formulations about the Frobenius number of a given set of positive integers. Our first formulation is used to check if a given positive integer is the Frobenius number of a given set of positive integers. The second formulation aims at finding the Frobenius number directly. The third formulation involves the residue classes with respect to the least member of the given set of positive integers, where a residue table is computed comprising all values modulo that least member, and the Frobenius number is obtained from there. Based on the same approach underlying the third formulation, we propose our fourth formulation which produces the Frobenius number directly. We demonstrate how to use our formulations with several examples. For illustrative purposes, some computa-tional analysis is also presented.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85780976","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 the finite group G act transitively and non-regularly on a finite set whose cardinality |Ω| is greater than one. Use N to denote the full set of fixed-point-free elements of G acting on along with the identity element. Write H to denote the stabilizer of some α ∈ Ω in G. In the note, it is proved that the subset N is a subgroup of G if and only if G is a Frobenius group. It is also proved G = {N}H, where {N} is the subgroup of G generated by N.
{"title":"Remarks on Frobenius Groups","authors":"Liguo He, Yu Cao","doi":"10.46300/91019.2021.8.7","DOIUrl":"https://doi.org/10.46300/91019.2021.8.7","url":null,"abstract":"Let the finite group G act transitively and non-regularly on a finite set whose cardinality |Ω| is greater than one. Use N to denote the full set of fixed-point-free elements of G acting on along with the identity element. Write H to denote the stabilizer of some α ∈ Ω in G. In the note, it is proved that the subset N is a subgroup of G if and only if G is a Frobenius group. It is also proved G = {N}H, where {N} is the subgroup of G generated by N.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73573169","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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