Characterization of simple K 4-groups

In this paper, we prove that a group G is isomorphic to M, where M is a simple K ₄-group, if and only if the following hold: (1) |G| = |M|, (2) nse(G) = nse(M).      

Local Theory of Primitive Theta Functions

We study primitive theta functions, which were first introduced by Shintani, in a purely local setting. We investigate a metaplectic representation of U(1) acting on the space of local primitive theta functions and give its explicit irreducible decomposition. As a by-product, we give a new proof of epsilon dichotomy for (U(1),U(1)).     

TE011腔使用扁平样品管提高水溶液样品ESR波谱灵敏度的研究

实验表明,在TE₀₁₁模式园柱形腔中,不但可以使用扁平样品管测量水溶液样品的ESR波谱,而且获得好的腔品质因子Q和高品质的ESR信号。所观察到的信号高度,是使用最佳尺寸毛细管样品时最大信号高度的3.2倍;又是在具有波导尺寸的TE₁₀₂腔中使用扁平样品管时所获得信号高度的3倍。本文对此作了定性的理论分析。     

Racah operators for the group of motions

The author [5] introduced Racah operators for unitary representations of topological groups of type I. In the present paper, we indicate the explicit form of these operators for representations of the group of motions of three-dimensional Euclidean space.     

Geometries of functional group interactions in enzyme-ligand complexes: Guides for receptor modelling

Summary An approach is described which makes use of X-ray structural data from enzyme-ligand complexes in order to obtain information for application in receptor modelling. The atomic surroundings of five different ligand functional groups were determined for all complex structures recorded in the Brookhaven Protein Data Bank. These atomic surroundings were then superimposed with respect to the atoms of the functional groups of the ligands in order to obtain clouds of neighbouring atoms. General principles were sought to describe the orientiation or favoured position of groups or atoms around those functional groups when bound to a macromolecule. Some simple conclusions and leads for further modelling were thus derived.     

Integral models of representations of current groups

We suggest a new construction of nonlocal representations of the current group. Instead of the Fock space, which is usually used in this situation, we consider the direct integral of countable tensor products of representations over the trajectories of some stochastic process. The construction substantially uses the invariance of the so-called infinite-dimensional Lebesgue measure.     

Unsaturated Molecules Containing Main Group Metals

Molecules in which there are neighboring electrophilic and nucleophilic centers are unusually reactive. Oligomerization can be prevented only by bulky groups attached to the main group metal atom that would act as electron pair acceptor, or to the basic non-metal atom. The basic and the acid centers behave as a single unit in chemical reactions; the system is similar to a “double bond” whose π-electron density is largely concentrated at one atom. The unsaturated nature of these molecules can be seen in (for example) their addition reactions with hydrogen compounds of non-metals, or in reactions that are distantly related to cycloadditions at homopolar double bonds. The selection of suitable reaction partners leads to polycyclic, cage-like molecules containing metal atoms. If these atoms possess lone pairs (as is usual in the lower oxidation states of the third and fourth main groups), these can be utilized to form bonds to further (Lewis acid) metal centers. In some cases large assemblies can be built up from polycyclic systems in this way; a characteristic of these assemblies is a one-dimensional array of metal atoms. Commonly occurring structural features of the polycyclic species are tetrahedra, trigonal bipyramids and cubes.     

等效电流方法计算单模光纤的辐射损耗

本文将无源的不规则波导看作有源的理想波导,求等效极化电流电场,直接得到单一光波导模间耦合和辐射损耗问题的解。用这个方法计算了阶跃单模光纤折射率轴向不均匀变化的损耗。这种方法完全脱离了耦合波的概念,它不但物理意义明确,而且求解问题的方法简洁。最后以单模光纤弯曲和微弯损耗为例,说明等效电流方法还适用于广义耦合波理论才能求解的问题。     

Lehmer's problem for compact Abelian groups

We formulate Lehmer's Problem concerning the Mahler measure of polynomials for general compact abelian groups, introducing a Lehmer constant for each such group. We show that all nontrivial connected compact groups have the same Lehmer constant and conjecture the value of the Lehmer constant for finite cyclic groups. We also show that if a group has infinitely many connected components, then its Lehmer constant vanishes.