Generalized KKM Type Theorems in FC-Spaces with Applications (I)

The class KKM(X,Y) (resp., s-KKM(X,Y,Z)) of set-valued mappings with KKM (resp., s-KKM) property is introduced in FC-spaces without any convexity structure. Some generalized KKM (resp., s-KKM) type theorems are proved in FC-spaces under much weak assumptions. As applications, some new section theorems and coincidence theorems are established in FC-spaces. These theorems generalize many known results in literature. The further applications of these results will be given in a follow-up paper.     

Molecular crystal structure and chemical properties of 4-phenyl-3,5-diethoxycarbonyl-1,2,6-trimethyl-1,2-dihydropyridine

The molecular crystal structure of 4-phenyl-3,5-diethoxycarbonyl-1,2,6-trimethyl-1,2-dihydropyridine has been investigated by x-ray structural analysis. The three-dimensional structural properties of the molecule have been compared against the large observed reactivity of the 3-ethoxycarbonyl group with respect to nucleophilic substitution reactions.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1236–1239, September, 1991.     

A family of skew Hadamard difference sets

In 1933 a family of skew Hadamard difference sets was described by Paley using matrix language and was called the Paley-Hadamard difference sets in the literature. During the last 70 years, no new skew Hadamard difference sets were found. It was conjectured that there are no further examples of skew Hadamard difference sets. This conjecture was proved to be true for the cyclic case in 1954, and further progress in favor of this conjecture was made in the past 50 years. However, the conjecture remains open until today. In this paper, we present a family of new perfect nonlinear (also called planar) functions, and construct a family of skew Hadamard difference sets using these perfect nonlinear functions. We show that some of the skew Hadamard difference sets presented in this paper are inequivalent to the Paley-Hadamard difference sets. These new examples of skew Hadamard difference sets discovered 70 years after the Paley construction disprove the longstanding conjecture on skew Hadamard difference sets. The class of new perfect nonlinear functions has applications in cryptography, coding theory, and combinatorics.     

1.54μmEr3+,Yb3+共掺玻璃激光器的速率方程及数值分析

LD抽运共掺Er,Yb玻璃激光器中的跃迁过程较复杂,针对双掺离子之间的能量传递和Er3+的多种跃迁过程,给出了详细的准三能级系统的速率方程,在合理简化后进行了数值分析,分析了Er3+掺杂浓度和介质长度、抽运光斑、输出镜透过率、谐振腔长、抽运光的椭圆度等因素对激光阈值及斜率效率的影响. 关键词： 1.54μm激光 Er3+玻璃 速率方程 数值分析     

Rank of quantized universal enveloping algebras and modular functions

We compute an intrinsic rank invariant for quasitriangular Hopf algebras in the case of general quantum groupsU _q (g). As a function ofq the rank has remarkable number theoretic properties connected with modular covariance and Galois theory. A number of examples are treated in detail, including rank (U _q (su(3))) and rank (U _q (e ₈)). We briefly indicate a physical interpretation as relating Chern-Simons theory with the theory of a quantum particle confined to an alcove ofg.     

Reaction of 2-formyl-1,3-cyclohexanediones with cyanoacetamide

Chemistry of Heterocyclic Compounds -     

Temporal characteristics of picosecond stimulated Raman scattering in oxide crystals

The temporal characteristics of stimulated Raman scattering (SRS) under 22-ps laser excitation were studied in eight oxide crystals with a T ₂ optical-phonon dephasing time variable by up to two orders of magnitude. The measured SRS pulse width was shortened from 13.8 ps for Ba(NO₃)₂ (T ₂ = 26.5 ps) to 4 ps for the LiNbO₃ (T ₂ = 0.38 ps) crystal. The dependence of SRS pulse width on the dephasing time was analyzed in the framework of the known SRS theory.