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Code generation approaches for parallel geometric multigrid solvers 并行几何多网格求解器的代码生成方法
IF 0.6 4区 数学
Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica Pub Date : 2020-12-01 DOI: 10.2478/auom-2020-0038
H. Köstler, M. Heisig, N. Kohl, S. Kuckuk, Martin Bauer, U. Rüde
{"title":"Code generation approaches for parallel geometric multigrid solvers","authors":"H. Köstler, M. Heisig, N. Kohl, S. Kuckuk, Martin Bauer, U. Rüde","doi":"10.2478/auom-2020-0038","DOIUrl":"https://doi.org/10.2478/auom-2020-0038","url":null,"abstract":"Abstract Software development for applications in computational science and engineering has become complex in recent years. This is mainly due to the increasing parallelism and heterogeneity in modern computer architectures and to the more realistic physical and mathematical models that have to be processed. One idea to address this issue is to use code generation techniques. In contrast to manual implementations in a general-purpose computing language, they allow to integrate automatic code transforms to produce efficient code for different models and platforms. As an example the numerical solution of an elliptic partial differential equation via generated geometric multigrid solvers is considered. We present three code generation approaches for it and discuss their advantages and disadvantages with respect to performance, portability, and productivity.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82935482","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Jacobsons Lemma fails for nil-clean 2 × 2 integral matrices 零清洁2 × 2积分矩阵的Jacobsons引理失效
IF 0.6 4区 数学
Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica Pub Date : 2020-12-01 DOI: 10.2478/auom-2020-0035
G. Călugăreanu, Horia F. Pop
{"title":"Jacobsons Lemma fails for nil-clean 2 × 2 integral matrices","authors":"G. Călugăreanu, Horia F. Pop","doi":"10.2478/auom-2020-0035","DOIUrl":"https://doi.org/10.2478/auom-2020-0035","url":null,"abstract":"Abstract We show that for two 2 × 2 integral matrices A, B, if the product AB is nil-clean then BA may not be nil-clean. Despite the fact that for many special cases, BA is also nil-clean, we finally found three counterexamples. All the way, the computer aid was decisive.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76393586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New aspects in polygroup theory 多群理论的新进展
IF 0.6 4区 数学
Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica Pub Date : 2020-12-01 DOI: 10.2478/auom-2020-0044
A. Sonea
{"title":"New aspects in polygroup theory","authors":"A. Sonea","doi":"10.2478/auom-2020-0044","DOIUrl":"https://doi.org/10.2478/auom-2020-0044","url":null,"abstract":"Abstract The aim of this paper is to compute the commutativity degree in polygroup’s theory, more exactly for the polygroup PG and for extension of polygroups by polygroups, obtaining boundaries for them. Also, we have analyzed the nilpotencitiy of 𝒜[𝒝], meaning the extension of polygroups 𝒜 and 𝒝.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73318662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Approximation of functions with linear positive operators which fix {1, φ} and {1, φ2} 具有固定{1，φ}和{1，φ2}的线性正算子的函数逼近
IF 0.6 4区 数学
Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica Pub Date : 2020-12-01 DOI: 10.2478/auom-2020-0045
F. Usta
{"title":"Approximation of functions with linear positive operators which fix {1, φ} and {1, φ2}","authors":"F. Usta","doi":"10.2478/auom-2020-0045","DOIUrl":"https://doi.org/10.2478/auom-2020-0045","url":null,"abstract":"Abstract In this manuscript, linear and positive operators described on bounded and unbounded intervals that fix the function sets {1, φ} and {1, φ2} such that φ ∈ C[0, 1] are presented. Then we present different types of operators by choosing different functions and values. Finally, Voronovskaya type theorems are given for this newly defined sequences of linear and positive operators.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81537509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Edge metric dimension of some classes of circulant graphs 几类循环图的边度量维数
IF 0.6 4区 数学
Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica Pub Date : 2020-12-01 DOI: 10.2478/auom-2020-0032
M. Ahsan, Z. Zahid, Sohail Zafar
{"title":"Edge metric dimension of some classes of circulant graphs","authors":"M. Ahsan, Z. Zahid, Sohail Zafar","doi":"10.2478/auom-2020-0032","DOIUrl":"https://doi.org/10.2478/auom-2020-0032","url":null,"abstract":"Abstract Let G = (V (G), E(G)) be a connected graph and x, y ∈ V (G), d(x, y) = min{ length of x − y path } and for e ∈ E(G), d(x, e) = min{d(x, a), d(x, b)}, where e = ab. A vertex x distinguishes two edges e1 and e2, if d(e1, x) ≠ d(e2, x). Let WE = {w1, w2, . . ., wk} be an ordered set in V (G) and let e ∈ E(G). The representation r(e | WE) of e with respect to WE is the k-tuple (d(e, w1), d(e, w2), . . ., d(e, wk)). If distinct edges of G have distinct representation with respect to WE, then WE is called an edge metric generator for G. An edge metric generator of minimum cardinality is an edge metric basis for G, and its cardinality is called edge metric dimension of G, denoted by edim(G). The circulant graph Cn(1, m) has vertex set {v1, v2, . . ., vn} and edge set {vivi+1 : 1 ≤ i ≤ n−1}∪{vnv1}∪{vivi+m : 1 ≤ i ≤ n−m}∪{vn−m+ivi : 1 ≤ i ≤ m}. In this paper, it is shown that the edge metric dimension of circulant graphs Cn(1, 2) and Cn(1, 3) is constant.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91047558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Nonlinearities on particular elliptic curves subspaces and applications 特定椭圆曲线子空间上的非线性及其应用
IF 0.6 4区 数学
Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica Pub Date : 2020-12-01 DOI: 10.2478/auom-2020-0033
R. Alsaedi, A. Dhifli, A. Ghanmi
{"title":"Nonlinearities on particular elliptic curves subspaces and applications","authors":"R. Alsaedi, A. Dhifli, A. Ghanmi","doi":"10.2478/auom-2020-0033","DOIUrl":"https://doi.org/10.2478/auom-2020-0033","url":null,"abstract":"Abstract Researching on mathematical models for cryptography means to, primary, define the optimal spaces and rules for which we can archive the maximum time to find the involved parameters of the keys and, in the same time, to optimise the time for key generation. In the present work, we treat a particular case of some subspaces from elliptic curves which respect the announced principles.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76910786","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Matrix Manipulations for Properties of Pell p-Numbers and their Generalizations Pell p-数性质的矩阵处理及其推广
IF 0.6 4区 数学
Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica Pub Date : 2020-12-01 DOI: 10.2478/auom-2020-0036
Özgür Erdağ, Ö. Deveci, A. Shannon
{"title":"Matrix Manipulations for Properties of Pell p-Numbers and their Generalizations","authors":"Özgür Erdağ, Ö. Deveci, A. Shannon","doi":"10.2478/auom-2020-0036","DOIUrl":"https://doi.org/10.2478/auom-2020-0036","url":null,"abstract":"Abstract In this paper, we define the Pell-Pell p-sequence and then we discuss the connection of the Pell-Pell p-sequence with Pell and Pell p-sequences. Also, we provide a new Binet formula and a new combinatorial representation of the Pell-Pell p-numbers by the aid of the nth power of the generating matrix the Pell-Pell p-sequence. Furthermore, we obtain an exponential representation of the Pell-Pell p-numbers and we develop relationships between the Pell-Pell p-numbers and their permanent, determinant and sums of certain matrices.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88005840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The modified Ishikawa iteration process with errors in CAT(0) spaces 在CAT(0)空格中存在误差的改进Ishikawa迭代过程
IF 0.6 4区 数学
Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica Pub Date : 2020-12-01 DOI: 10.2478/auom-2020-0042
S. Ranjbar
{"title":"The modified Ishikawa iteration process with errors in CAT(0) spaces","authors":"S. Ranjbar","doi":"10.2478/auom-2020-0042","DOIUrl":"https://doi.org/10.2478/auom-2020-0042","url":null,"abstract":"Abstract In this article, Δ-convergence and strong convergence of the modified Ishikawa iteration process with errors are established for continuous mappings of asymptotically nonexpansive type in CAT(0) spaces. Our results extend and improve the previous results given by many authors.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75721082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A generalization of Kruskal–Katona’s theorem Kruskal-Katona定理的推广
IF 0.6 4区 数学
Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica Pub Date : 2020-07-01 DOI: 10.2478/auom-2020-0018
Luca Amata, M. Crupi
{"title":"A generalization of Kruskal–Katona’s theorem","authors":"Luca Amata, M. Crupi","doi":"10.2478/auom-2020-0018","DOIUrl":"https://doi.org/10.2478/auom-2020-0018","url":null,"abstract":"Abstract Let K be a field, E the exterior algebra of a finite dimensional K-vector space, and F a finitely generated graded free E-module with homogeneous basis g1, . . ., gr such that deg g1 ≤ deg g2 ≤ · · · ≤ deg gr. We characterize the Hilbert functions of graded E–modules of the type F/M, with M graded submodule of F. The existence of a unique lexicographic submodule of F with the same Hilbert function as M plays a crucial role.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78641583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Fitzpatrick transform of monotone relations in Hadamard spaces Hadamard空间单调关系的Fitzpatrick变换
IF 0.6 4区 数学
Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica Pub Date : 2020-07-01 DOI: 10.2478/auom-2020-0026
A. Moslemipour, M. Roohi, M. Mardanbeigi, Mahdi Azhini
{"title":"Fitzpatrick transform of monotone relations in Hadamard spaces","authors":"A. Moslemipour, M. Roohi, M. Mardanbeigi, Mahdi Azhini","doi":"10.2478/auom-2020-0026","DOIUrl":"https://doi.org/10.2478/auom-2020-0026","url":null,"abstract":"Abstract In the present paper, monotone relations and maximal monotone relations from an Hadamard space to its linear dual space are investigated. Fitzpatrick transform of monotone relations in Hadamard spaces is introduced. It is shown that Fitzpatrick transform of a special class of monotone relations is proper, convex and lower semi-continuous. Finally, a representation result for monotone relations is given.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90665658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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