Let M=S^(n)/Γand h be a nontrivial element of finite order p inπ_(1)(Μ),where the integers n,p≥2,Γis a finite abelian group which acts freely and isometrically on the n-sphere and therefore M is diffeomorphic to ...Let M=S^(n)/Γand h be a nontrivial element of finite order p inπ_(1)(Μ),where the integers n,p≥2,Γis a finite abelian group which acts freely and isometrically on the n-sphere and therefore M is diffeomorphic to a compact space form.In this paper,we prove that there are infinitely many non-contractible closed geodesics of class[h]on the compact space form with C^(r)-generic Finsler metrics,where 4≤r≤∞.The conclusion also holds for Cr-generic Riemannian metrics for 2≤r≤∞.The proof is based on the resonance identity of non-contractible closed geodesics on compact space forms.展开更多
Abstract The main purpose of this article is to prove a collection of new nxea point theorems for （ws）-compact and so-called 1-set weakly contractive operators under Leray- Schauder boundary condition. We also intro...Abstract The main purpose of this article is to prove a collection of new nxea point theorems for （ws）-compact and so-called 1-set weakly contractive operators under Leray- Schauder boundary condition. We also introduce the concept of semi-closed operator at the origin and obtain a series of new fixed point theorems for such class of operators. As consequences, we get new fixed point existence for （ws）-compact （in particular nonexpansive） self mappings unbounded closed convex subset of Banach spaces. The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness. Later on, we give an application to generalized Hammerstein type integral equations.展开更多
In this paper, let ∑ R2n be a symmetric compact convex hypersurface which is （r, R）-pinched with. Then Z carries at least two elliptic symmetric closed characteristics; moreover,∑ carries at least E[n-1/2] ＋ E[n-...In this paper, let ∑ R2n be a symmetric compact convex hypersurface which is （r, R）-pinched with. Then Z carries at least two elliptic symmetric closed characteristics; moreover,∑ carries at least E[n-1/2] ＋ E[n-1/3] non-hyperbolic symmetric closed characteristics.展开更多
Recently, Cristofaro-Gardiner and Hutchings proved that there exist at least two closed characteristics on every compact star-shaped hypersuface in R4. Then Ginzburg, Hein, Hryniewicz, and Macarini gave this result a ...Recently, Cristofaro-Gardiner and Hutchings proved that there exist at least two closed characteristics on every compact star-shaped hypersuface in R4. Then Ginzburg, Hein, Hryniewicz, and Macarini gave this result a second proof. In this paper, we give it a third proof by using index iteration theory, resonance identities of closed characteristics and a remarkable theorem of Ginzburg et at.展开更多
In this paper, let n ≥ 2 be an integer, P = diag（-In-k,In-k,Ik） for some integer κ∈[0, n）, and ∑∪→R^2n be a partially symmetric compact convex hypersurface, i.e., x ∈∑ implies Px∈∑. We prove that if ∑ is...In this paper, let n ≥ 2 be an integer, P = diag（-In-k,In-k,Ik） for some integer κ∈[0, n）, and ∑∪→R^2n be a partially symmetric compact convex hypersurface, i.e., x ∈∑ implies Px∈∑. We prove that if ∑ is （r, R）-pinched with R/r〈 √2, then there exist at least n -k geometrically distinct P-symmetric closed ∑ characteristics on ∑, as a consequence, Z carry at least n geometrically distinct P-invariant closed characteristics.展开更多
Let k≥2 be an integer and P be a 2n×2n symplectic orthogonal matrix satisfying P^(k)=I_(2n) and ker(P^(j)-I_(2n)=0,1≤j<k.For any compact convex hypersurface ∑■R^(2n) with n≥2 which is P-cyclic symmetric,i...Let k≥2 be an integer and P be a 2n×2n symplectic orthogonal matrix satisfying P^(k)=I_(2n) and ker(P^(j)-I_(2n)=0,1≤j<k.For any compact convex hypersurface ∑■R^(2n) with n≥2 which is P-cyclic symmetric,i.e.,x∈∑implies Px∈∑,we prove that if ∑ is(r,R)-pinched with R/r<√(2k+2)/k,then there exist at least n geometrically distince P-cyclic symmetric closed characteristics on ∑ for a broad class of matrices P.展开更多
Let ∑be a C^3 compact symmetric convex hypersurface in R^8.We prove that when ∑ carries exactly four geometrically distinct closed characteristics,then all of them must be symmetric.Due to the example of weakly non-...Let ∑be a C^3 compact symmetric convex hypersurface in R^8.We prove that when ∑ carries exactly four geometrically distinct closed characteristics,then all of them must be symmetric.Due to the example of weakly non-resonant ellipsoids,our result is sharp.展开更多
传统冲击电压发生装置采用塔式开放型结构,其体积和重量非常庞大,需拆装分级运输,现场试验时需专业人员配合,实施难度较大。为此,采用封闭式气体绝缘结构完成了3 000 kV/300 k J紧凑型一体式冲击电压发生器的设计研究,包括电阻、点火球...传统冲击电压发生装置采用塔式开放型结构,其体积和重量非常庞大,需拆装分级运输,现场试验时需专业人员配合,实施难度较大。为此,采用封闭式气体绝缘结构完成了3 000 kV/300 k J紧凑型一体式冲击电压发生器的设计研究,包括电阻、点火球隙等内部器件的优化设计、装置本体电场仿真计算分析等,整体本体的尺寸降低约37%,重量降低约25%。同时,该装置采用卧式运输、立式使用方案,无需现场拼装,极大地提高了现场工作效率。研制的气体绝缘冲击电压发生装置依照国家标准进行了各项性能测试,均满足要求,能够有效解决超、特高压GIS等变电设备现场试验困难的问题。展开更多
基金supported by NSFC(Grant Nos.12371195,12022111)the Fundamental Research Funds for the Central Universities(Grant No.2042023kf0207)+1 种基金the second author was partially supported by NSFC(Grant No.11831009)Fundings of Innovating Activities in Science and Technology of Hubei Province。
文摘Let M=S^(n)/Γand h be a nontrivial element of finite order p inπ_(1)(Μ),where the integers n,p≥2,Γis a finite abelian group which acts freely and isometrically on the n-sphere and therefore M is diffeomorphic to a compact space form.In this paper,we prove that there are infinitely many non-contractible closed geodesics of class[h]on the compact space form with C^(r)-generic Finsler metrics,where 4≤r≤∞.The conclusion also holds for Cr-generic Riemannian metrics for 2≤r≤∞.The proof is based on the resonance identity of non-contractible closed geodesics on compact space forms.
文摘Abstract The main purpose of this article is to prove a collection of new nxea point theorems for （ws）-compact and so-called 1-set weakly contractive operators under Leray- Schauder boundary condition. We also introduce the concept of semi-closed operator at the origin and obtain a series of new fixed point theorems for such class of operators. As consequences, we get new fixed point existence for （ws）-compact （in particular nonexpansive） self mappings unbounded closed convex subset of Banach spaces. The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness. Later on, we give an application to generalized Hammerstein type integral equations.
基金Partially supported by NNSF, RFDP of MOE of China
文摘In this paper, let ∑ R2n be a symmetric compact convex hypersurface which is （r, R）-pinched with. Then Z carries at least two elliptic symmetric closed characteristics; moreover,∑ carries at least E[n-1/2] ＋ E[n-1/3] non-hyperbolic symmetric closed characteristics.
基金partially supported by China Postdoctoral Science Foundation(Grant No.2013M540512)partially supported by NSFC(Grant No.11131004),MCME,LPMC of MOE of China,Nankai University and BCMIIS of Capital Normal University
文摘Recently, Cristofaro-Gardiner and Hutchings proved that there exist at least two closed characteristics on every compact star-shaped hypersuface in R4. Then Ginzburg, Hein, Hryniewicz, and Macarini gave this result a second proof. In this paper, we give it a third proof by using index iteration theory, resonance identities of closed characteristics and a remarkable theorem of Ginzburg et at.
基金supported by China Postdoctoral Science Foundation(Grant No.2013M540512)National Natural Science Foundation of China(Grant Nos.10801078,11171341 and 11271200)Lab of Pure Mathematics and Combinatorics of Nankai University
文摘In this paper, let n ≥ 2 be an integer, P = diag（-In-k,In-k,Ik） for some integer κ∈[0, n）, and ∑∪→R^2n be a partially symmetric compact convex hypersurface, i.e., x ∈∑ implies Px∈∑. We prove that if ∑ is （r, R）-pinched with R/r〈 √2, then there exist at least n -k geometrically distinct P-symmetric closed ∑ characteristics on ∑, as a consequence, Z carry at least n geometrically distinct P-invariant closed characteristics.
基金supported by the National Natural Science Foundation of China(Grant Nos.11771341,12022111).
文摘Let k≥2 be an integer and P be a 2n×2n symplectic orthogonal matrix satisfying P^(k)=I_(2n) and ker(P^(j)-I_(2n)=0,1≤j<k.For any compact convex hypersurface ∑■R^(2n) with n≥2 which is P-cyclic symmetric,i.e.,x∈∑implies Px∈∑,we prove that if ∑ is(r,R)-pinched with R/r<√(2k+2)/k,then there exist at least n geometrically distince P-cyclic symmetric closed characteristics on ∑ for a broad class of matrices P.
基金Hui Liu Partially supported by NSFC(No.11401555)China Postdoctoral Science Foundation No.2014T70589,CUSF(No.WK0010000037)Yiming Long Partially supported by NSFC。
文摘Let ∑be a C^3 compact symmetric convex hypersurface in R^8.We prove that when ∑ carries exactly four geometrically distinct closed characteristics,then all of them must be symmetric.Due to the example of weakly non-resonant ellipsoids,our result is sharp.
文摘传统冲击电压发生装置采用塔式开放型结构,其体积和重量非常庞大,需拆装分级运输,现场试验时需专业人员配合,实施难度较大。为此,采用封闭式气体绝缘结构完成了3 000 kV/300 k J紧凑型一体式冲击电压发生器的设计研究,包括电阻、点火球隙等内部器件的优化设计、装置本体电场仿真计算分析等,整体本体的尺寸降低约37%,重量降低约25%。同时,该装置采用卧式运输、立式使用方案,无需现场拼装,极大地提高了现场工作效率。研制的气体绝缘冲击电压发生装置依照国家标准进行了各项性能测试,均满足要求,能够有效解决超、特高压GIS等变电设备现场试验困难的问题。
