On norm dependent positive definite functions

In the first part of the paper we prove a decomposition theorem for positive definite functions (Theorem 2.3) generalizing a result of de Leeuw and Glicksberg. Using this theorem, we then show (Theorem 3.1) that certain norm dependent positive definite functions are automatically continuous at every point different from zero.     

On toric h-vectors of centrally symmetric polytopes

We prove tight lower bounds for the coefficients of the toric h-vector of an arbitrary centrally symmetric polytope generalizing previous results due to R. Stanley and the author using toric varieties. Our proof here is based on the theory of combinatorial intersection cohomology for normal fans of polytopes developed by G. Barthel, J.-P. Brasselet, K. Fieseler and L. Kaup, and independently by P. Bressler and V. Lunts. This theory is also valid for nonrational polytopes when there is no standard correspondence with toric varieties. In this way we can establish our bounds for centrally symmetric polytopes even without requiring them to be rational. Received: 24 March 2004     

Some spectral synthesis results by the analytic semigroup method

In 1980, J. Esterle proved the Wiener theorem forL ¹ (—) by a completely new method using analytic semigroup techniques. We show here how to extend the method in two different ways. First, it is shown that spectral synthesis for points on the real line is also provided by analytic semigroup techniques. Second, Esterle's proof may also be adapted to provide Wiener theorem for some elementary hypergroups. Eine überarbeitete Fassung ging am 24. 4. 2001 ein     

Multiplication formulas and isomorphism theorem of ıSchur superalgebras

We introduce the notion of ?Schur superalgebra, which can be regarded as a type B/C counterpart of the q-Schur superalgebra (of type A) formulated as centralizer algebras of certain signed q-permutation modules over Hecke algebras. Some multiplication formulas for ?Schur superalgebra are obtained to construct their canonical bases. Furthermore, we established an isomorphism theorem between the ?Scuhr superalgebras and the q-Schur superalgebras of type A, which helps us derive semisimplicity criteria of the ?Schur superalgebras.     

TODGA/[C_2mim][NTf_2]萃取Th~(4+)

研究了N,N,N′,N′-四辛基-3-氧戊二酰胺(TODGA)溶于疏水性离子液体咪唑类离子液体1-乙基-3-甲基咪唑双三氟甲磺酰亚胺盐([C2mim][NTf2])中对硝酸水溶液体系中四价钍离子(Th4+)的萃取行为。详细考察了接触时间、酸度、Th4+浓度、TODGA浓度、温度对TODGA/[C2mim][NTf2]体系萃取性能的影响。作为对比,我们还考察了TODGA在传统有机溶剂异辛烷中对Th4+的萃取。结果表明:TODGA/[C2mim][NTf2]体系对Th4+的萃取是吸热反应,且在50℃下,能在5 min内达到平衡。萃取体系随着酸度对Th4+的萃取性能先降后增大;Th4+浓度的增大,TODGA浓度的降低,对Th4+的萃取性能下降。TODGA在离子液体萃取体系中比在有机体系中有更好的Th4+萃取效果,特别是在低酸条件下。通过萃取机理研究,推测出在低酸下萃取反应是离子交换且TODGA与Th4+配比为2∶1,在高酸下萃取是中性配位。     

一种应用于活细胞中检测Hg(Ⅱ)的苯并噻唑类荧光探针

合成和表征了一种苯并噻唑类的荧光探针(YH1),并用光谱法研究了它对不同金属离子的响应。结果表明:YH1对Hg2+显示出好的选择性和灵敏度,与Hg2+作用后,在紫外光的激发下它的溶液颜色由蓝色变为无色。在1.4~8.8μmol·L-1浓度的范围内,YH1的荧光强度与Hg2+浓度有线性关系,其对Hg2+的检出限为0.56μmol·L-1。此外,YH1可跨过细胞膜,细胞毒性低,还可应用于He La活细胞中对Hg2+进行荧光成像。     

A strict topology on Orlicz spaces

Let φ be a Young function, Ω be a locally compact space, and μ be a positive Radon measure on Ω. We consider a strict topology (in the sense of Sentilles‐Taylor) on the Orlicz function space and investigate various properties of this locally convex topology. We also study the Orlicz space of a locally compact group G with a left Haar measure under the strict topology and certain other natural locally convex topologies. Finally we present some results on various continuity properties of convolution operators on 435a-be17-e4b939522a04/mana201400100-math-0005.png"> under the topology and other natural ones.     

Quantum Schur algebras revisited

A geometric construction of quantum Schur algebras was given by Beilinson, Lusztig and MacPherson in terms of pairs of flags in a vector space. By viewing such pairs of flags as representations of a poset, we give a recursive formula for the structure constants of quantum Schur algebras which is related to certain Hall polynomials. As an application, we provide a direct proof of the fundamental multiplication formulas which play a key role in the Beilinson-Lusztig-MacPherson realization of quantum gl_n. In the appendix we show how to groupoidify quantum Schur algebras in the sense of Baez, Hoffnung and Walker.     

Generalized potentials in variable exponent Lebesgue spaces on homogeneous spaces

We consider generalized potential operators with the kernel on bounded quasimetric measure space (X, μ, d) with doubling measure μ satisfying the upper growth condition μB(x, r) ? Kr^N, N ∈ (0, ∞). Under some natural assumptions on a(r) in terms of almost monotonicity we prove that such potential operators are bounded from the variable exponent Lebesgue space L^p(?)(X, μ) into a certain Musielak‐Orlicz space L^p(X, μ) with the N‐function Φ(x, r) defined by the exponent p(x) and the function a(r). A reformulation of the obtained result in terms of the Matuszewska‐Orlicz indices of the function a(r) is also given. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim