Pub Date : 2014-06-21DOI: 10.2478/S11533-014-0428-8
A. Aubert, T. Przebinda
We describe a new approach to the Weil representation attached to a symplectic group over a finite or a local field. We dissect the representation into small pieces, study how they work, and put them back together. This way, we obtain a reversed construction of that of T. Thomas, skipping most of the literature on which the latter is based.
{"title":"A reverse engineering approach to the Weil representation","authors":"A. Aubert, T. Przebinda","doi":"10.2478/S11533-014-0428-8","DOIUrl":"https://doi.org/10.2478/S11533-014-0428-8","url":null,"abstract":"We describe a new approach to the Weil representation attached to a symplectic group over a finite or a local field. We dissect the representation into small pieces, study how they work, and put them back together. This way, we obtain a reversed construction of that of T. Thomas, skipping most of the literature on which the latter is based.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"63 1","pages":"1500-1585"},"PeriodicalIF":0.0,"publicationDate":"2014-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80122014","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/s11533-014-0424-z
Irina Căpraru, A. Lazu
We consider the nonlinear differential inclusion x′(t) ∈ Ax(t) + F(x(t)), where A is an m-dissipative operator on a separable Banach space X and F is a multi-function. We establish a viability result under Lipschitz hypothesis on F, that consists in proving the existence of solutions of the differential inclusion above, starting from a given set, which remain arbitrarily close to that set, if a tangency condition holds. To this end, we establish a kind of set-valued Gronwall’s lemma and a compactness theorem, which are extensions to the nonlinear case of similar results for semilinear differential inclusions. As an application, we give an approximate null controllability result.
{"title":"Near viability for fully nonlinear differential inclusions","authors":"Irina Căpraru, A. Lazu","doi":"10.2478/s11533-014-0424-z","DOIUrl":"https://doi.org/10.2478/s11533-014-0424-z","url":null,"abstract":"We consider the nonlinear differential inclusion x′(t) ∈ Ax(t) + F(x(t)), where A is an m-dissipative operator on a separable Banach space X and F is a multi-function. We establish a viability result under Lipschitz hypothesis on F, that consists in proving the existence of solutions of the differential inclusion above, starting from a given set, which remain arbitrarily close to that set, if a tangency condition holds. To this end, we establish a kind of set-valued Gronwall’s lemma and a compactness theorem, which are extensions to the nonlinear case of similar results for semilinear differential inclusions. As an application, we give an approximate null controllability result.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"56 1","pages":"1447-1459"},"PeriodicalIF":0.0,"publicationDate":"2014-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77298367","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/s11533-014-0431-0
Minh-Binh Tran
In this paper, we introduce a new approach for the convergence problem of optimized Schwarz methods by studying a generalization of these methods for a semilinear elliptic equation. We study the behavior of the algorithm when the overlapping length is large.
{"title":"The behavior of domain decomposition methods when the overlapping length is large","authors":"Minh-Binh Tran","doi":"10.2478/s11533-014-0431-0","DOIUrl":"https://doi.org/10.2478/s11533-014-0431-0","url":null,"abstract":"In this paper, we introduce a new approach for the convergence problem of optimized Schwarz methods by studying a generalization of these methods for a semilinear elliptic equation. We study the behavior of the algorithm when the overlapping length is large.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"23 1","pages":"1602-1614"},"PeriodicalIF":0.0,"publicationDate":"2014-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74000568","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 : 2014-06-01DOI: 10.2478/s11533-013-0382-x
Keiju Sono
In this paper, we give certain upper bounds for the 2k-th moments, k ≥ 1/2, of derivatives of Dirichlet L-functions at s = 1/2 under the assumption of the Generalized Riemann Hypothesis.
本文在广义黎曼假设的条件下，给出了Dirichlet l -函数在s = 1/2处导数的第2k阶矩k≥1/2的上界。
{"title":"Upper bounds for the moments of derivatives of Dirichlet L-functions","authors":"Keiju Sono","doi":"10.2478/s11533-013-0382-x","DOIUrl":"https://doi.org/10.2478/s11533-013-0382-x","url":null,"abstract":"In this paper, we give certain upper bounds for the 2k-th moments, k ≥ 1/2, of derivatives of Dirichlet L-functions at s = 1/2 under the assumption of the Generalized Riemann Hypothesis.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"13 1","pages":"848-860"},"PeriodicalIF":0.0,"publicationDate":"2014-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78181345","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 : 2014-05-10DOI: 10.2478/s11533-013-0390-x
K. Pióro
The aim of this paper is to characterize pairs (L, A), where L is a finite lattice and A a finite algebra, such that the subalgebra lattice of A is isomorphic to L. Next, necessary and sufficient conditions are found for pairs of finite algebras (of possibly distinct types) to have isomorphic subalgebra lattices. Both of these characterizations are particularly simple in the case of distributive subalgebra lattices. We do not restrict our attention to total algebras only, but we consider the more general case of partial algebras. Moreover, we use connections between algebras and hypergraphs to solve these problems.
{"title":"The subalgebra lattice of a finite algebra","authors":"K. Pióro","doi":"10.2478/s11533-013-0390-x","DOIUrl":"https://doi.org/10.2478/s11533-013-0390-x","url":null,"abstract":"The aim of this paper is to characterize pairs (L, A), where L is a finite lattice and A a finite algebra, such that the subalgebra lattice of A is isomorphic to L. Next, necessary and sufficient conditions are found for pairs of finite algebras (of possibly distinct types) to have isomorphic subalgebra lattices. Both of these characterizations are particularly simple in the case of distributive subalgebra lattices. We do not restrict our attention to total algebras only, but we consider the more general case of partial algebras. Moreover, we use connections between algebras and hypergraphs to solve these problems.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"8 1","pages":"1052-1108"},"PeriodicalIF":0.0,"publicationDate":"2014-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77943602","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 : 2014-05-10DOI: 10.2478/s11533-013-0394-6
P. Szczuka
In this paper we characterize the closures of arithmetic progressions in the topology T on the set of positive integers with the base consisting of arithmetic progressions {an + b} such that if the prime number p is a factor of a, then it is also a factor of b. The topology T is called the common division topology.
{"title":"The closures of arithmetic progressions in the common division topology on the set of positive integers","authors":"P. Szczuka","doi":"10.2478/s11533-013-0394-6","DOIUrl":"https://doi.org/10.2478/s11533-013-0394-6","url":null,"abstract":"In this paper we characterize the closures of arithmetic progressions in the topology T on the set of positive integers with the base consisting of arithmetic progressions {an + b} such that if the prime number p is a factor of a, then it is also a factor of b. The topology T is called the common division topology.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"31 1","pages":"1008-1014"},"PeriodicalIF":0.0,"publicationDate":"2014-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73436962","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 : 2014-05-10DOI: 10.2478/s11533-014-0404-3
Qingfeng Sun
Let F be the symmetric-square lift with Laplace eigenvalue λF (Δ) = 1+4µ2. Suppose that |µ| ≤ Λ. We show that F is uniquely determined by the central values of Rankin-Selberg L-functions L(s, F ⋇ h), where h runs over the set of holomorphic Hecke eigen cusp forms of weight κ ≡ 0 (mod 4) with κ≍ϱ+ɛ, t9 = max {4(1+4θ)/(1−18θ), 8(2−9θ)/3(1−18θ)} for any 0 ≤ θ < 1/18 and any ∈ > 0. Here θ is the exponent towards the Ramanujan conjecture for GL2 Maass forms.
{"title":"On effective determination of symmetric-square lifts","authors":"Qingfeng Sun","doi":"10.2478/s11533-014-0404-3","DOIUrl":"https://doi.org/10.2478/s11533-014-0404-3","url":null,"abstract":"Let F be the symmetric-square lift with Laplace eigenvalue λF (Δ) = 1+4µ2. Suppose that |µ| ≤ Λ. We show that F is uniquely determined by the central values of Rankin-Selberg L-functions L(s, F ⋇ h), where h runs over the set of holomorphic Hecke eigen cusp forms of weight κ ≡ 0 (mod 4) with κ≍ϱ+ɛ, t9 = max {4(1+4θ)/(1−18θ), 8(2−9θ)/3(1−18θ)} for any 0 ≤ θ < 1/18 and any ∈ > 0. Here θ is the exponent towards the Ramanujan conjecture for GL2 Maass forms.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"106 1","pages":"976-990"},"PeriodicalIF":0.0,"publicationDate":"2014-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89819286","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 : 2014-05-10DOI: 10.2478/s11533-013-0397-3
R. F. Allen, Katherine C. Heller, Matthew A. Pons
Here we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces . Specifically we study differences of composition operators on the Dirichlet space and S2, the space of analytic functions whose first derivative is in H2, and then use Calderón’s complex interpolation to extend the results to the general weighted Dirichlet spaces. As a corollary we consider composition operators induced by linear fractional self-maps of the disk.
{"title":"Compact differences of composition operators on weighted Dirichlet spaces","authors":"R. F. Allen, Katherine C. Heller, Matthew A. Pons","doi":"10.2478/s11533-013-0397-3","DOIUrl":"https://doi.org/10.2478/s11533-013-0397-3","url":null,"abstract":"Here we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces . Specifically we study differences of composition operators on the Dirichlet space and S2, the space of analytic functions whose first derivative is in H2, and then use Calderón’s complex interpolation to extend the results to the general weighted Dirichlet spaces. As a corollary we consider composition operators induced by linear fractional self-maps of the disk.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"39 1","pages":"1040-1051"},"PeriodicalIF":0.0,"publicationDate":"2014-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76827408","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 : 2014-05-10DOI: 10.2478/s11533-013-0395-5
Stefano Bosia, M. Conti, V. Pata
The incompressible three-dimensional Navier-Stokes equations are considered. A new regularity criterion for weak solutions is established in terms of the pressure gradient.
研究了三维不可压缩Navier-Stokes方程。建立了基于压力梯度的弱解正则性判据。
{"title":"A regularity criterion for the Navier-Stokes equations in terms of the pressure gradient","authors":"Stefano Bosia, M. Conti, V. Pata","doi":"10.2478/s11533-013-0395-5","DOIUrl":"https://doi.org/10.2478/s11533-013-0395-5","url":null,"abstract":"The incompressible three-dimensional Navier-Stokes equations are considered. A new regularity criterion for weak solutions is established in terms of the pressure gradient.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"73 1","pages":"1015-1025"},"PeriodicalIF":0.0,"publicationDate":"2014-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82993702","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 : 2014-05-08DOI: 10.2478/s11533-014-0418-x
T. Cardinali
In this paper we prove some approximate fixed point theorems which extend, in a broad sense, analogous results obtained by Brânzei, Morgan, Scalzo and Tijs in 2003. By assuming also the weak demiclosedness property we state two fixed point theorems. Moreover, we study the existence of ɛ-Nash equilibria.
{"title":"On the existence of ɛ-fixed points","authors":"T. Cardinali","doi":"10.2478/s11533-014-0418-x","DOIUrl":"https://doi.org/10.2478/s11533-014-0418-x","url":null,"abstract":"In this paper we prove some approximate fixed point theorems which extend, in a broad sense, analogous results obtained by Brânzei, Morgan, Scalzo and Tijs in 2003. By assuming also the weak demiclosedness property we state two fixed point theorems. Moreover, we study the existence of ɛ-Nash equilibria.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"180 1","pages":"1320-1329"},"PeriodicalIF":0.0,"publicationDate":"2014-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73169733","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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