According to the Ministry of Education, 22 Tsinghua University disciplines were evaluated as First Category National Key Disciplines, ranking first nationwide. It is the first time for China to establish First Categor...According to the Ministry of Education, 22 Tsinghua University disciplines were evaluated as First Category National Key Disciplines, ranking first nationwide. It is the first time for China to establish First Category Key Disciplines. Among the 22 First Category National Key Disciplines, 16 disciplines are in engineering, three in science, two in management, and one in medicine. In addition, fifteen Tsinghua disciplines were evaluated as Second Category National Key Disciplines, among which, two are in engineering, one in science, nine in medicine, and three in humanities and social sciences.展开更多
Let LSC(X) denote the set of all proper lower semicontinuous functions on X with the epi-topology. In this paper we give characterizations of the separation axioms. Baire properties and metrizability of LSC(X). We sho...Let LSC(X) denote the set of all proper lower semicontinuous functions on X with the epi-topology. In this paper we give characterizations of the separation axioms. Baire properties and metrizability of LSC(X). We show also that the continuous function space C(X) with the epi-topology is of first category when N is first countable.展开更多
We prove that for a given strictly increasing initial datum in Ck, the solution of the initial value problem is piecewise Ck smooth except for flux functions of nonconvex conservation laws in a certain subset of C^k＋...We prove that for a given strictly increasing initial datum in Ck, the solution of the initial value problem is piecewise Ck smooth except for flux functions of nonconvex conservation laws in a certain subset of C^k＋1 of first category, defined in the range of the initial datum.展开更多
In this article,we use some analytic and geometric characters of the smooth points in a sphere to study the isometric extension problem in the separable or reflexive real Banach spaces.We obtain that under some condit...In this article,we use some analytic and geometric characters of the smooth points in a sphere to study the isometric extension problem in the separable or reflexive real Banach spaces.We obtain that under some condition the answer to this problem is affirmative.展开更多
文摘According to the Ministry of Education, 22 Tsinghua University disciplines were evaluated as First Category National Key Disciplines, ranking first nationwide. It is the first time for China to establish First Category Key Disciplines. Among the 22 First Category National Key Disciplines, 16 disciplines are in engineering, three in science, two in management, and one in medicine. In addition, fifteen Tsinghua disciplines were evaluated as Second Category National Key Disciplines, among which, two are in engineering, one in science, nine in medicine, and three in humanities and social sciences.
文摘Let LSC(X) denote the set of all proper lower semicontinuous functions on X with the epi-topology. In this paper we give characterizations of the separation axioms. Baire properties and metrizability of LSC(X). We show also that the continuous function space C(X) with the epi-topology is of first category when N is first countable.
基金supported by National Natural Foundation of China(10671116 and 10871133)
文摘We prove that for a given strictly increasing initial datum in Ck, the solution of the initial value problem is piecewise Ck smooth except for flux functions of nonconvex conservation laws in a certain subset of C^k＋1 of first category, defined in the range of the initial datum.
基金Supported by National Natural Science Foundation of China(Grant No.11371201)
文摘In this article,we use some analytic and geometric characters of the smooth points in a sphere to study the isometric extension problem in the separable or reflexive real Banach spaces.We obtain that under some condition the answer to this problem is affirmative.
