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Central European Journal of Mathematics最新文献

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Some superconvergence results of high-degree finite element method for a second order elliptic equation with variable coefficients 二阶变系数椭圆型方程的高次有限元法的一些超收敛结果
Central European Journal of Mathematics Pub Date : 2014-06-29 DOI: 10.2478/s11533-014-0440-z
X. Guan, Mingxia Li, Wen‐ming He, Zheng-wu Jiang
{"title":"Some superconvergence results of high-degree finite element method for a second order elliptic equation with variable coefficients","authors":"X. Guan, Mingxia Li, Wen‐ming He, Zheng-wu Jiang","doi":"10.2478/s11533-014-0440-z","DOIUrl":"https://doi.org/10.2478/s11533-014-0440-z","url":null,"abstract":"In this paper, some superconvergence results of high-degree finite element method are obtained for solving a second order elliptic equation with variable coefficients on the inner locally symmetric mesh with respect to a point x0 for triangular meshes. By using of the weak estimates and local symmetric technique, we obtain improved discretization errors of O(hp+1 |ln h|2) and O(hp+2 |ln h|2) when p (≥ 3) is odd and p (≥ 4) is even, respectively. Meanwhile, the results show that the combination of the weak estimates and local symmetric technique is also effective for superconvergence analysis of the second order elliptic equation with variable coefficients.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"50 1","pages":"1733-1747"},"PeriodicalIF":0.0,"publicationDate":"2014-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91356110","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: 3
Secure sets and their expansion in cubic graphs 三次图中的安全集及其展开式
Central European Journal of Mathematics Pub Date : 2014-06-29 DOI: 10.2478/s11533-014-0411-4
Katarzyna Jesse-Józefczyk, E. Sidorowicz
{"title":"Secure sets and their expansion in cubic graphs","authors":"Katarzyna Jesse-Józefczyk, E. Sidorowicz","doi":"10.2478/s11533-014-0411-4","DOIUrl":"https://doi.org/10.2478/s11533-014-0411-4","url":null,"abstract":"Consider a graph whose vertices play the role of members of the opposing groups. The edge between two vertices means that these vertices may defend or attack each other. At one time, any attacker may attack only one vertex. Similarly, any defender fights for itself or helps exactly one of its neighbours. If we have a set of defenders that can repel any attack, then we say that the set is secure. Moreover, it is strong if it is also prepared for a raid of one additional foe who can strike anywhere. We show that almost any cubic graph of order n has a minimum strong secure set of cardinality less or equal to n/2 + 1. Moreover, we examine the possibility of an expansion of secure sets and strong secure sets.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"11 1","pages":"1664-1673"},"PeriodicalIF":0.0,"publicationDate":"2014-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85976509","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: 1
Fractional BVPs with strong time singularities and the limit properties of their solutions 具有强时间奇点的分数阶bvp及其解的极限性质
Central European Journal of Mathematics Pub Date : 2014-06-29 DOI: 10.2478/s11533-014-0435-9
S. Stanek
{"title":"Fractional BVPs with strong time singularities and the limit properties of their solutions","authors":"S. Stanek","doi":"10.2478/s11533-014-0435-9","DOIUrl":"https://doi.org/10.2478/s11533-014-0435-9","url":null,"abstract":"AbstractIn the first part, we investigate the singular BVP $$tfrac{d}\u0000{{dt}}^c D^alpha u + (a/t)^c D^alpha u = mathcal{H}u$$, u(0) = A, u(1) = B, cDαu(t)|t=0 = 0, where $$mathcal{H}$$ is a continuous operator, α ∈ (0, 1) and a < 0. Here, cD denotes the Caputo fractional derivative. The existence result is proved by the Leray-Schauder nonlinear alternative. The second part establishes the relations between solutions of the sequence of problems $$tfrac{d}\u0000{{dt}}^c D^{alpha _n } u + (a/t)^c D^{alpha _n } u = f(t,u,^c D^{beta _n } u)$$, u(0) = A, u(1) = B, $$left. {^c D^{alpha _n } u(t)} right|_{t = 0} = 0$$ where a < 0, 0 < βn ≤ αn < 1, limn→∞βn = 1, and solutions of u″+(a/t)u′ = f(t, u, u′) satisfying the boundary conditions u(0) = A, u(1) = B, u′(0) = 0.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"11 1","pages":"1638-1655"},"PeriodicalIF":0.0,"publicationDate":"2014-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85497649","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 frame of the unit ball of Banach spaces 巴拿赫空间单位球的框架
Central European Journal of Mathematics Pub Date : 2014-06-29 DOI: 10.2478/s11533-014-0437-7
Ryotaro Tanaka
{"title":"On the frame of the unit ball of Banach spaces","authors":"Ryotaro Tanaka","doi":"10.2478/s11533-014-0437-7","DOIUrl":"https://doi.org/10.2478/s11533-014-0437-7","url":null,"abstract":"The notion of the frame of the unit ball of Banach spaces was introduced to construct a new calculation method for the Dunkl-Williams constant. In this paper, we characterize the frame of the unit ball by using k-extreme points and extreme points of the unit ball of two-dimensional subspaces. Furthermore, we show that the frame of the unit ball is always closed, and is connected if the dimension of the space is not less than three. As infinite dimensional examples, the frame of the unit balls of c0 and ℓp are determined.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"11 1","pages":"1700-1713"},"PeriodicalIF":0.0,"publicationDate":"2014-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78664816","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: 3
Commutator algebras arising from splicing operations 由拼接运算产生的对易子代数
Central European Journal of Mathematics Pub Date : 2014-06-29 DOI: 10.2478/s11533-014-0438-6
S. Sverchkov
{"title":"Commutator algebras arising from splicing operations","authors":"S. Sverchkov","doi":"10.2478/s11533-014-0438-6","DOIUrl":"https://doi.org/10.2478/s11533-014-0438-6","url":null,"abstract":"We prove that the variety of Lie algebras arising from splicing operation coincides with the variety CM of centreby-metabelian Lie algebras. Using these Lie algebras we find the minimal dimension algebras generated the variety CM and the variety of its associative envelope algebras. We study the splicing n-ary operation. We show that all n-ary (n > 2) commutator algebras arising from this operation are nilpotent of index 3. We investigate the generalization of the splicing n-ary operation, and we formulate a series of open problems.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"72 1","pages":"1687-1699"},"PeriodicalIF":0.0,"publicationDate":"2014-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74033353","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
Precise small deviations in L2 of some Gaussian processes appearing in the regression context 在回归环境中出现的一些高斯过程的L2精确的小偏差
Central European Journal of Mathematics Pub Date : 2014-06-29 DOI: 10.2478/s11533-014-0436-8
A. Kirichenko, Y. Nikitin
{"title":"Precise small deviations in L2 of some Gaussian processes appearing in the regression context","authors":"A. Kirichenko, Y. Nikitin","doi":"10.2478/s11533-014-0436-8","DOIUrl":"https://doi.org/10.2478/s11533-014-0436-8","url":null,"abstract":"We find precise small deviation asymptotics with respect to the Hilbert norm for some special Gaussian processes connected to two regression schemes studied by MacNeill and his coauthors. In addition, we also obtain precise small deviation asymptotics for the detrended Brownian motion and detrended Slepian process.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"12 1","pages":"1674-1686"},"PeriodicalIF":0.0,"publicationDate":"2014-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88717620","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: 5
Functions on adjacent vertex degrees of trees with given degree sequence 给定度序列的树的相邻顶点度函数
Central European Journal of Mathematics Pub Date : 2014-06-29 DOI: 10.2478/s11533-014-0439-5
Hua Wang
{"title":"Functions on adjacent vertex degrees of trees with given degree sequence","authors":"Hua Wang","doi":"10.2478/s11533-014-0439-5","DOIUrl":"https://doi.org/10.2478/s11533-014-0439-5","url":null,"abstract":"In this note we consider a discrete symmetric function f(x, y) where $$f(x,a) + f(y,b) geqslant f(y,a) + f(x,b) for any x geqslant y and a geqslant b,$$ associated with the degrees of adjacent vertices in a tree. The extremal trees with respect to the corresponding graph invariant, defined as $$sumlimits_{uv in E(T)} {f(deg(u),deg(v))} ,$$ are characterized by the “greedy tree” and “alternating greedy tree”. This is achieved through simple generalizations of previously used ideas on similar questions. As special cases, the already known extremal structures of the Randic index follow as corollaries. The extremal structures for the relatively new sum-connectivity index and harmonic index also follow immediately, some of these extremal structures have not been identified in previous studies.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"25 1","pages":"1656-1663"},"PeriodicalIF":0.0,"publicationDate":"2014-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73496415","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: 26
Ground states for asymptotically periodic Schrödinger-Poisson systems with critical growth 临界增长渐近周期Schrödinger-Poisson系统的基态
Central European Journal of Mathematics Pub Date : 2014-06-21 DOI: 10.2478/s11533-014-0426-x
Hui Zhang, Junxiang Xu, Fubao Zhang, Miao Du
{"title":"Ground states for asymptotically periodic Schrödinger-Poisson systems with critical growth","authors":"Hui Zhang, Junxiang Xu, Fubao Zhang, Miao Du","doi":"10.2478/s11533-014-0426-x","DOIUrl":"https://doi.org/10.2478/s11533-014-0426-x","url":null,"abstract":"For a class of asymptotically periodic Schrödinger-Poisson systems with critical growth, the existence of ground states is established. The proof is based on the method of Nehari manifold and concentration compactness principle.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"193 1","pages":"1484-1499"},"PeriodicalIF":0.0,"publicationDate":"2014-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86827944","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: 8
Partial regularity of solution to generalized Navier-Stokes problem 广义Navier-Stokes问题解的部分正则性
Central European Journal of Mathematics Pub Date : 2014-06-21 DOI: 10.2478/s11533-014-0427-9
V. Mácha
{"title":"Partial regularity of solution to generalized Navier-Stokes problem","authors":"V. Mácha","doi":"10.2478/s11533-014-0427-9","DOIUrl":"https://doi.org/10.2478/s11533-014-0427-9","url":null,"abstract":"In the presented work, we study the regularity of solutions to the generalized Navier-Stokes problem up to a C2 boundary in dimensions two and three. The point of our generalization is an assumption that a deviatoric part of a stress tensor depends on a shear rate and on a pressure. We focus on estimates of the Hausdorff measure of a singular set which is defined as a complement of a set where a solution is Hölder continuous. We use so-called indirect approach to show partial regularity, for dimension 2 we get even an empty set of singular points.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"61 3 1","pages":"1460-1483"},"PeriodicalIF":0.0,"publicationDate":"2014-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80527121","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: 2
Composition results for strongly summing and dominated multilinear operators 强和和控制多线性算子的复合结果
Central European Journal of Mathematics Pub Date : 2014-06-21 DOI: 10.2478/s11533-014-0423-0
Dumitru Popa
{"title":"Composition results for strongly summing and dominated multilinear operators","authors":"Dumitru Popa","doi":"10.2478/s11533-014-0423-0","DOIUrl":"https://doi.org/10.2478/s11533-014-0423-0","url":null,"abstract":"In this paper we prove some composition results for strongly summing and dominated operators. As an application we give necessary and sufficient conditions for a multilinear tensor product of multilinear operators to be strongly summing or dominated. Moreover, we show the failure of some possible n-linear versions of Grothendieck’s composition theorem in the case n ≥ 2 and give a new example of a 1-dominated, hence strongly 1-summing bilinear operator which is not weakly compact.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"1 1","pages":"1433-1446"},"PeriodicalIF":0.0,"publicationDate":"2014-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81020311","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: 15
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