Indian Journal of Pure and Applied Mathematics最新文献_第4页

Approximation of bivariate Lipschitz continuous functions by hidden variable fractal functions 用隐变分形函数逼近双变量利普齐兹连续函数

Indian Journal of Pure and Applied Mathematics Pub Date : 2024-07-11 DOI: 10.1007/s13226-024-00631-2

Vijender Nallapu

引用次数: 0

Robust numerical scheme for 2D fractional integro-differential equations of Volterra type Volterra 型二维分数积分微分方程的稳健数值方案

Indian Journal of Pure and Applied Mathematics Pub Date : 2024-07-11 DOI: 10.1007/s13226-024-00666-5

Bappa Ghosh, Jugal Mohapatra

{"title":"Robust numerical scheme for 2D fractional integro-differential equations of Volterra type","authors":"Bappa Ghosh, Jugal Mohapatra","doi":"10.1007/s13226-024-00666-5","DOIUrl":"https://doi.org/10.1007/s13226-024-00666-5","url":null,"abstract":"This article provides a numerical study of two-dimensional Volterra integro-differential equations involving fractional derivatives in the Caputo sense of order ( alpha ,gamma ) ( (0< alpha ,gamma <1). ) First, we establish a sufficient condition for the existence and uniqueness of the solution using the Banach fixed point theorem. Due to the limitation of finding the exact analytical solution, we derive and analyze an efficient numerical scheme to approximate the solution. The proposed scheme uses the L1 technique to discretize the differential components, whereas a composite trapezoidal rule is used to approximate the double integral. The convergence analysis and error estimation are carried out. It is shown that the proposed scheme converges with an optimal convergence rate of ( min {2-alpha ,2-gamma } ) for sufficiently smooth initial data. In addition, we apply the proposed difference scheme to solve the semilinear problem. The well-known Newton’s linearization technique is used to deal with semilinearity. Finally, a couple of numerical experiments are conducted to support our theoretical findings and validate the proposed scheme.","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141584958","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}

引用次数: 0

Nonexistence for Lane-Emden system involving Hardy potentials with singularities on the boundary 涉及边界上有奇点的哈代势的莱恩-埃姆登系统的不存在性

Indian Journal of Pure and Applied Mathematics Pub Date : 2024-07-11 DOI: 10.1007/s13226-024-00667-4

Ying Wang, Songqin Ye, Chunlan Li, Hongxing Chen

引用次数: 0

Probability inequalities for strongly left-invariant metric semigroups/monoids, including all lie groups 强左不变度量半群/单群（包括所有谎言群）的概率不等式

Indian Journal of Pure and Applied Mathematics Pub Date : 2024-07-09 DOI: 10.1007/s13226-024-00645-w

Apoorva Khare

{"title":"Probability inequalities for strongly left-invariant metric semigroups/monoids, including all lie groups","authors":"Apoorva Khare","doi":"10.1007/s13226-024-00645-w","DOIUrl":"https://doi.org/10.1007/s13226-024-00645-w","url":null,"abstract":"Recently, a general version of the Hoffmann-Jørgensen inequality was shown jointly with Rajaratnam [Ann. Probab. 2017], which (a) improved the result even for real-valued variables, but also (b) simultaneously unified and extended several versions in the Banach space literature, including that by Hitczenko–Montgomery-Smith [Ann. Probab. 2001], as well as special cases and variants of results by Johnson–Schechtman [Ann. Probab. 1989] and Klass–Nowicki [Ann. Probab. 2000], in addition to the original versions by Kahane and Hoffmann-Jørgensen. Moreover, our result with Rajaratnam was in a primitive framework: over all semigroups with a bi-invariant metric; this includes Banach spaces as well as compact and abelian Lie groups. In this note we show the result even more generally: over every semigroup ({mathscr {G}}) with a strongly left- (or right-)invariant metric. We also prove some applications of this inequality over such ({mathscr {G}}), extending Banach space-valued versions by Hitczenko and Montgomery-Smith [Ann. Probab. 2001] and by Hoffmann-Jørgensen [Studia Math. 1974]. Furthermore, we show several other stochastic inequalities – by Ottaviani–Skorohod, Mogul’skii, and Lévy–Ottaviani – as well as Lévy’s equivalence, again over ({mathscr {G}}) as above. This setting of generality for ({mathscr {G}}) subsumes not only semigroups with bi-invariant metric (thus extending the previously shown results), but it also means that these results now hold over all Lie groups (equipped with a left-invariant Riemannian metric). We also explain why this primitive setting of strongly left/right-invariant metric semigroups ({mathscr {G}}) is equivalent to that of left/right-invariant metric monoids ({mathscr {G}}_circ ): each such ({mathscr {G}}) embeds in some ({mathscr {G}}_circ ).\u0000","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141568789","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}

引用次数: 0

Numerical solution of nonlinear fractional delay integro-differential equations with convergence analysis 非线性分数延迟积分微分方程的数值解法及收敛性分析

Indian Journal of Pure and Applied Mathematics Pub Date : 2024-07-09 DOI: 10.1007/s13226-024-00620-5

N. Peykrayegan, M. Ghovatmand, M. H. Noori Skandari, S. Shateyi

引用次数: 0

An approximate equivalence for the GNS representation of the Haar state of $$SU_{q}(2)$$ $$SU_{q}(2)$$哈尔态的 GNS 表示的近似等价性

Indian Journal of Pure and Applied Mathematics Pub Date : 2024-07-08 DOI: 10.1007/s13226-024-00633-0

Partha Sarathi Chakraborty, Arup Kumar Pal

引用次数: 0

Mackey imprimitivity and commuting tuples of homogeneous normal operators 同质正则算子的麦基隐含性和共通元组

Indian Journal of Pure and Applied Mathematics Pub Date : 2024-07-08 DOI: 10.1007/s13226-024-00644-x

Gadadhar Misra, E. K. Narayanan, Cherian Varughese

{"title":"Mackey imprimitivity and commuting tuples of homogeneous normal operators","authors":"Gadadhar Misra, E. K. Narayanan, Cherian Varughese","doi":"10.1007/s13226-024-00644-x","DOIUrl":"https://doi.org/10.1007/s13226-024-00644-x","url":null,"abstract":"In this semi-expository article, we investigate the relationship between the imprimitivity introduced by Mackey several decades ago and commuting d- tuples of homogeneous normal operators. The Hahn–Hellinger theorem gives a canonical decomposition of a (*)- algebra representation (rho ) of (C_0({mathbb {S}})) (where ({mathbb {S}}) is a locally compact Hausdorff space) into a direct sum. If there is a group G acting transitively on ({mathbb {S}}) and is adapted to the (*)- representation (rho ) via a unitary representation U of the group G, in other words, if there is an imprimitivity, then the Hahn–Hellinger decomposition reduces to just one component, and the group representation U becomes an induced representation, which is Mackey’s imprimitivity theorem. We consider the case where a compact topological space (Ssubset {mathbb {C}}^d) decomposes into finitely many G- orbits. In such cases, the imprimitivity based on S admits a decomposition as a direct sum of imprimitivities based on these orbits. This decomposition leads to a correspondence with homogeneous normal tuples whose joint spectrum is precisely the closure of G- orbits.","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141577539","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}

引用次数: 0

On the asymptotic risk of ridge regression with many predictors 关于多预测因子脊回归的渐近风险

Indian Journal of Pure and Applied Mathematics Pub Date : 2024-07-08 DOI: 10.1007/s13226-024-00646-9

Krishnakumar Balasubramanian, Prabir Burman, Debashis Paul

引用次数: 0

Sequences of operator algebras converging to odd spheres in the quantum Gromov–Hausdorff distance 在量子格罗莫夫-豪斯多夫距离中收敛于奇数球的算子代数序列

Indian Journal of Pure and Applied Mathematics Pub Date : 2024-07-06 DOI: 10.1007/s13226-024-00635-y

Tirthankar Bhattacharyya, Sushil Singla

引用次数: 0

Divisibility of integer laurent polynomials, homoclinic points, and lacunary independence 整数月桂多项式的可分性、同偶点和裂隙独立性

Indian Journal of Pure and Applied Mathematics Pub Date : 2024-07-06 DOI: 10.1007/s13226-024-00650-z

Douglas Lind, Klaus Schmidt

引用次数: 0