Pub Date : 2014-06-29DOI: 10.2478/s11533-014-0440-z
X. Guan, Mingxia Li, Wen‐ming He, Zheng-wu Jiang
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.
{"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}
Pub Date : 2014-06-29DOI: 10.2478/s11533-014-0411-4
Katarzyna Jesse-Józefczyk, E. Sidorowicz
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.
{"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}
Pub Date : 2014-06-29DOI: 10.2478/s11533-014-0435-9
S. Stanek
AbstractIn the first part, we investigate the singular BVP $$tfrac{d} {{dt}}^c D^alpha u + (a/t)^c D^alpha u = mathcal{H}u$$, 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 $$tfrac{d} {{dt}}^c D^{alpha _n } u + (a/t)^c D^{alpha _n } u = f(t,u,^c D^{beta _n } u)$$, 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.
在第一部分中，我们研究了奇异BVP $$tfrac{d}{{dt}}^c D^alpha u + (a/t)^c D^alpha u = mathcal{H}u$$, u(0) = A, u(1) = B, cDαu(t)|t=0 =0，其中$$mathcal{H}$$是一个连续算子，α∈(0,1)且A < 0。这里，cD表示卡普托分数阶导数。用Leray-Schauder非线性替代证明了存在性结果。第二部分建立了问题序列$$tfrac{d}{{dt}}^c D^{alpha _n } u + (a/t)^c D^{alpha _n } u = f(t,u,^c D^{beta _n } u)$$, u(0) = A, u(1) = B, $$left. {^c D^{alpha _n } u(t)} right|_{t = 0} = 0$$其中A < 0, 0 < βn≤αn < 1, limn→∞βn = 1的解与满足边界条件u(0) = A, u(1) = B, u '(0) = 0的u″+(A /t)u ' = f(t, u, u ')的解之间的关系。
{"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}
Pub Date : 2014-06-29DOI: 10.2478/s11533-014-0437-7
Ryotaro Tanaka
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.
{"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}
Pub Date : 2014-06-29DOI: 10.2478/s11533-014-0438-6
S. Sverchkov
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.
{"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}
Pub Date : 2014-06-29DOI: 10.2478/s11533-014-0436-8
A. Kirichenko, Y. Nikitin
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.
{"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}
Pub Date : 2014-06-29DOI: 10.2478/s11533-014-0439-5
Hua Wang
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.
在本文中，我们考虑一个离散对称函数f(x, y)，其中$$f(x,a) + f(y,b) geqslant f(y,a) + f(x,b) for any x geqslant y and a geqslant b,$$与树中相邻顶点的度相关。对应图不变量的极值树定义为$$sumlimits_{uv in E(T)} {f(deg(u),deg(v))} ,$$，其特征为“贪心树”和“交替贪心树”。这是通过简单概括以前在类似问题上使用的想法来实现的。作为特殊情况，已知的兰迪奇指数的极值结构作为推论遵循。相对较新的和连通性指数和调和指数的极值结构也紧随其后，其中一些极值结构在以前的研究中没有被确定。
{"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}
Pub Date : 2014-06-21DOI: 10.2478/s11533-014-0426-x
Hui Zhang, Junxiang Xu, Fubao Zhang, Miao Du
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.
{"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}
Pub Date : 2014-06-21DOI: 10.2478/s11533-014-0427-9
V. Mácha
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.
{"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}
Pub Date : 2014-06-21DOI: 10.2478/s11533-014-0423-0
Dumitru Popa
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.
{"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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：