ON DIRICHLET TYPE SPACES AND α-BLOCH SPACES IN THE UNIT BALL OF Cn

In this paper, the authors study the inclusion relations between Dirichlet type spaces DT and α-Bloch spacesβα by means of higher radial derivative. The strictness and the best possibility of the inclusion relations are shown with constructive methods.Furthermore, they sharpen one of the results when T = n, which proves that a conjecture in [7] is true.     

Relations among eigenvalues of Sturm-Liouville problems with different types of leading coefficient functions

For any Sturm-Liouville problem with a separable boundary condition and whose leading coefficient function changes sign (exactly once), we first give a geometric characterization of its eigenvalues λn using the eigenvalues of some corresponding problems with a definite leading coefficient function. Consequences of this characterization include simple proofs of the existence of the λn's, their Prüfer angle characterization, and a way for determining their indices from the zeros of their eigenfunctions. Then, interlacing relations among the λn's and the eigenvalues of the corresponding problems are obtained. Using these relations, a simple proof of asymptotic formulas for the λn's is given.     

Perturbed recurrence relations II the general case

In this paper, we give some new explicit relations between two families of polynomials defined by recurrence relations of all order. These relations allow us to analyze, even in the Sobolev case, how some properties of a family of orthogonal polynomials are affected when the coefficients of the recurrence relation and the order are perturbed. In a paper we have already given a method which allows us to study the polynomials defined by a three-term recurrence relation. Also here some generalizations are given.     

Representations, convolution square roots and spherical vectors

We extend results on square integrable representations of a locally compact group to subrepresentations of a representations induced from a character of a closed subgroup. We do so working in the framework of quotient representations of ∗-algebras.     

Fuzzy集的基数

关于Fuzzy集的基数，[1]中曾对有限支集的Fuzzy集以及极苛刻条件下的无限Fuzzy集给出过一种定义。但是，正如本文将要指出的那样，该定义是不合理的。本文将从研究Fuzzy映射入手，给出Fuzzy集基数的一般性定义。基于这一定义，不但得到有关基数的大部分结论，而且有其自身的特殊性。     

RECONSTRUCTION OF BINARY RELATIONS FROM THEIR RESTRICTIONS OF CARDINALITY 2, 3, 4 and (n - 1) II

We shall prove here that any binary relation on a base E with cardinality n > 6 is reconstructible from its restrictions of cardinality 2, 3, 4 and (n - 1). This proof needs results of part I of this paper where we characterize any pair of relations R, R' which are 2-, 3- and 4-hypomorphic. As a corollary we obtain that any binary relation is (n - 4)-reconstructible (when n > 9).     

Mössbauer Studies and Magnetic Properties of Y3−x Ce x Fe5O12

It is shown that in-situ ^166mHo (I = 7) in a spherical single crystal of HoF₃ can be used as sensitive internal thermometer to thermally detect NMR (NMR-TDNO) from the 100% abundant stable ¹⁶⁵Ho (I = 7/2) nuclei. In addition, new ^166mHo NMRON results are reported. Both the ^166mHo NMRON and ¹⁶⁵Ho NMR-TDNO spectra show three distinct quadrupolar split sub-resonances, in zero applied field. The data is used to make estimates of the Ho magnetic moments and quadrupole parameters for the ^166mHo and ^166mHo sites.     

Synthesis and orientation study of a magnetically aligned liquid‐crystalline chitin/poly(acrylic acid) composite

A high magnetic field of 5 T was used to fabricate a magnetically aligned, optically anisotropic, liquid‐crystalline chitin/poly(acrylic acid) composite. The aligned mesophase was fixed by photoinitiated free‐radical polymerization. From an examination of polarized optical micrographs and an X‐ray diffraction study, a high degree of orientation of 0.70 was observed for the composite with a higher liquid‐crystalline chitin concentration (10.70 wt %); the orientation was reduced with a decreased chitin concentration at a given acrylic acid concentration. The X‐ray data for the developed composite showed a uniplanar orientation for the chitin crystallites, with its molecular long axes perpendicular to the direction of the magnetic field. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 711–714, 2003     

Influence of the network chain orientation on the fracture toughness of a mesogenic epoxy resin modified with CTBN

A biphenol‐type epoxy resin, which had a mesogenic group in the backbone moiety, was modified with carboxy‐terminated butadiene acrylonitrile copolymer (CTBN) as a reactive elastomer, and its fracture toughness was measured. With the addition of CTBN, the fracture toughness of the biphenol‐type epoxy resin significantly increased and became significantly higher than that of a bisphenol A‐type epoxy resin modified with CTBN. The network chain orientation in the cured biphenol‐type epoxy resin system was clearly observed during the fracture process with polarized microscopy Fourier transform infrared measurements, although such a phenomenon was not observed in the bisphenol A‐type epoxy resin system. The high toughness of the cured biphenol‐type system was clearly due to the consumption of the mechanical energy by a large deformation of the matrix resin due to the orientation of the network chains during the fracture process. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1198–1209, 2003