In this paper, Crouzeix-Raveart type nonconforming rectangular element is applied to the Mumford-Shah functional for image segmentation subjected to Robin boundary conditions. Meanwhile, by using the special orthogona...In this paper, Crouzeix-Raveart type nonconforming rectangular element is applied to the Mumford-Shah functional for image segmentation subjected to Robin boundary conditions. Meanwhile, by using the special orthogonality of this element＇s basic functions, the convergence analysis for L2-norm and broken H1-norm with semi-implicit scheme is presented. And the error order is improved to the optimal, too.展开更多
In the present paper, the characterization of strong-type modular inequality ∫ 0 ∞φ(Sf (t))w(t)dt≤∫0∞ φ(Cf (t))w(t)dt, f↓ is given, where φ∈Δ' and S is a Hardy operator. Furthermore, the equivalent con...In the present paper, the characterization of strong-type modular inequality ∫ 0 ∞φ(Sf (t))w(t)dt≤∫0∞ φ(Cf (t))w(t)dt, f↓ is given, where φ∈Δ' and S is a Hardy operator. Furthermore, the equivalent conditions of modular inequalities and norm inequalities related to weak Orlicz-Lorentz spaces are researched. We also explore the conditions for Orlicz-Lorentz spaces and weak Orlicz-Lorentz spaces to be normable. Finally, the weak boundedness of certain Hardy-type operators on Orlicz-Lorentz spaces is studied.展开更多
After studying in a previous work the smoothness of the space where dr- measF0 〉 O, with p（.） E C（~） and p（x） 〉 1 for all x E , the authors study in this paper the strict and uniform convexity as well as some ...After studying in a previous work the smoothness of the space where dr- measF0 〉 O, with p（.） E C（~） and p（x） 〉 1 for all x E , the authors study in this paper the strict and uniform convexity as well as some special properties of duality mappings defined on the same space. The results obtained in this direction are used for proving existence results for operator equations having the form Ju = Niu, where J is a duality mapping on Uro corresponding to the gauge function ~, and Nf is the Nemytskij operator generated by a Caratheodory function f satisfying an appropriate growth condition ensuring that Nf may be viewed as acting from Ur0 into its dual.展开更多
This paper constructs several classes of new wavelet bases, which are unconditional bases for related operator spaces. Using these bases, the author analyzes non-homogeneous symbolic space OpSm1,1 and two related kern...This paper constructs several classes of new wavelet bases, which are unconditional bases for related operator spaces. Using these bases, the author analyzes non-homogeneous symbolic space OpSm1,1 and two related kernel-distribution spaces, and characterizes them in two wavelet coefficients spaces. Besides, some properties for singular integral operators are studied.展开更多
We give the classification of globally generated vector bundles of rank 2 on a smooth quadric surface with c1(2,2)in terms of the indices of the bundles,and extend the result to arbitrary higher rank case.We also inve...We give the classification of globally generated vector bundles of rank 2 on a smooth quadric surface with c1(2,2)in terms of the indices of the bundles,and extend the result to arbitrary higher rank case.We also investigate their indecomposability and give the sufficient and necessary condition on numeric data of vector bundles for indecomposability.展开更多
文摘In this paper, Crouzeix-Raveart type nonconforming rectangular element is applied to the Mumford-Shah functional for image segmentation subjected to Robin boundary conditions. Meanwhile, by using the special orthogonality of this element＇s basic functions, the convergence analysis for L2-norm and broken H1-norm with semi-implicit scheme is presented. And the error order is improved to the optimal, too.
基金supported by National Natural Science Foundation of China (Grant Nos.10931001, 10871173 and 11101372)
文摘In the present paper, the characterization of strong-type modular inequality ∫ 0 ∞φ(Sf (t))w(t)dt≤∫0∞ φ(Cf (t))w(t)dt, f↓ is given, where φ∈Δ' and S is a Hardy operator. Furthermore, the equivalent conditions of modular inequalities and norm inequalities related to weak Orlicz-Lorentz spaces are researched. We also explore the conditions for Orlicz-Lorentz spaces and weak Orlicz-Lorentz spaces to be normable. Finally, the weak boundedness of certain Hardy-type operators on Orlicz-Lorentz spaces is studied.
文摘After studying in a previous work the smoothness of the space where dr- measF0 〉 O, with p（.） E C（~） and p（x） 〉 1 for all x E , the authors study in this paper the strict and uniform convexity as well as some special properties of duality mappings defined on the same space. The results obtained in this direction are used for proving existence results for operator equations having the form Ju = Niu, where J is a duality mapping on Uro corresponding to the gauge function ~, and Nf is the Nemytskij operator generated by a Caratheodory function f satisfying an appropriate growth condition ensuring that Nf may be viewed as acting from Ur0 into its dual.
基金Project supported by the National Natural Science Foundation of China (No. 10001027).
文摘This paper constructs several classes of new wavelet bases, which are unconditional bases for related operator spaces. Using these bases, the author analyzes non-homogeneous symbolic space OpSm1,1 and two related kernel-distribution spaces, and characterizes them in two wavelet coefficients spaces. Besides, some properties for singular integral operators are studied.
基金supported by Ministero dell’Istruzione,dell’Universit`ae della Ricerca(Italy)and Gruppo Nazionale per le Strutture Algebrice,Geometriche e le loro Applicazioni of Istituto di Alta Matematica"F.Severi"(Italy),Basic Science Research Program through National Research Foundation of Korea funded by Ministry of Education and Science Technology(Grant No.2010-0009195)the framework of PRIN2010/11‘Geometria delle variet`a algebriche’,cofinanced by Ministero dell’Istruzione,dell’Universit`ae della Ricerca(Italy)
文摘We give the classification of globally generated vector bundles of rank 2 on a smooth quadric surface with c1(2,2)in terms of the indices of the bundles,and extend the result to arbitrary higher rank case.We also investigate their indecomposability and give the sufficient and necessary condition on numeric data of vector bundles for indecomposability.
