On the graded identities ofM 1,1(E)

We determine theS _n ×S _m -cocharacterX _n,m of the algebraM _1,1(E) and prove that theT ₂-ideal of its graded identities is generated by the polynomialsy ₁ y ₂−y ₂ y ₁ andz ₁ z ₂ z ₃+z ₃ z ₂ z ₁.     

Fourier Series Representation of Low-Lying Eigenfunctions for a Particle on the Torus

A Fourier series method for finding the low-lying eigenfunctions and eigenvalues of the Schrödinger equation for a particle on the surface of a torus is given.     

A Microoptic Network Unit Using Planar Microlens Array

We propose a new concept for an optical network unit using planar microlens array for fiber to the home networks. It is expected from this modeling that an optical coupling loss of 2.5 dB, a polarization dependent loss of 0.5 dB and an extinction ratio larger than 50 dB can be achieved. The structure design and its fabrication method are discussed.     

Commutative cancellative semigroups of finite rank

The rank of a commutative cancellative semigroup S is the cardinality of a maximal independent subset of S. Commutative cancellative semigroups of finite rank are subarchimedean and thus admit a Tamura-like representation. We characterize these semigroups in several ways and provide structure theorems in terms of a construction akin to the one devised by T. Tamura for N-semigroups.     

Effect of hemodialysis on left and right ventricular function--evaluation using electrocardiogram gated radionuclide ventriculography

Eighteen outpatients with chronic renal failure undergoing hemodialysis (HD) were studied. Immediately before and after HD, the left and right ventricular function measured by electrocardiogram gated radionuclide ventriculography (RNV). By HD, body weight changed 58.6 +/- 7.50 kg to 57.2 +/- 6.80 kg and BUN level changed 67.9 +/- 29.00 mg/dl to 37.1 +/- 18.96 mg/dl and creatinine level changed 11.3 +/- 3.90 mg/dl to 6.8 +/- 2.48 mg/dl. Before HD, cardiac output was 8.08 +/- 1.50 l/min and cardiac index was 5.00 +/- 0.87 l/(min m2). Left ventricular function improved (LVEF changed 60.4 +/- 6.85% to 64.2 +/- 8.7%, LVEF/LVET changed 0.237 +/- 0.048%/ms to 0.254 +/- 0.021%/ms) between before and after HD, but there was not significant difference. Right ventricular function improved (RVEF changed 41.2 +/- 8.00% to 50.0 +/- 11.96, RVEF/RVET changed 0.167 +/- 0.028%/ms to 0.209 +/- 0.059%/ms) between before and after HD, and there was significant difference (p less than 0.05).     

Configurational stabilization of mixed-valence states in the star-burst tetranuclear ruthenium complex bridged with acetylene links

A new tetranuclear ruthenium complex in which a metal was bridged radially to three identical metals with acetylene links showed a mixed-valence state in cyclic voltammograms. The peak potential difference for the mixed-valence state was twice the potential difference for a mixed-valence state of the corresponding binuclear complex. This fact suggests stabilization of the mixed-valence state twice by configurational modification of redox centers. However, this is inconsistent with the prediction from the additive pair model of the redox interaction. A quantum chemical model of the redox interaction was presented, in which the potential difference was expressed by the overlap integral S and the nearest neighbor interaction energy between the reduced center and the oxidized one. Application of the theory gave a negative value of S, which demonstrated reasonably the stabilization of the mixed-valence state from a quantum chemical viewpoint.     

Guaranteed approximation of Markov chains with applications to multiplexer engineering in ATM networks

Discrete Markov chains are applied widely for analysis and design of high speed ATM networks due to their essentially discrete nature. Unfortunately, their use is precluded for many important problems due to explosion of the state space cardinality. In this paper we propose a new method for approximation of a discrete Markov chain by a chain of considerably smaller dimension which is based on the duality theory of optimization. A novel feature of our approach is that it provides guaranteed upper and lower bounds for the performance indices defined on the steady state distribution of the original system. We apply our method to the problem of engineering multiplexers for ATM networks.     

A structural variability of copper(I) chloride-tetrahydrothiophene adducts crystallizing in polymeric forms and exhibiting polymorphism: The role of the solvent

The function of the solvent in the self-assembling mode of [CuCl] with tetrahydrothiophene is reported. Copper(l) chloride has been used in the form of [CuCOCl] _n , which is slightly soluble in the most common solvents, and to allow an homogeneous phase reaction. The reaction of [CuCOCl] _n with THT gave [(CuCl)₂(THT)₃] _x ,1, in CH₃OH, [(CuCl)(THT)₂] _x ,2 in THF [(CuCl)(THT)] _x ,3, in CH₂Cl₂, and [(CuCl)₃(THT)₂] _x ,4, in DME. Compound1 consists of polymeric chains of centrosymmetric Cu₂Cl₂ dinuclear units bridged by THIT molecules running parallel to the [101] axis. In the structure of2 we found polymeric layers generated from the [(CuCl)(THT)] asymmetric unit by the center of symmetry and by the twofold axis. In compound3 the structure consists of layers generated through the center of symmetry by the [(Cu₂Cl₂)(THT)₂] asymmetric unit, while4 consists of layers generated through the center of symmetry by the [(Cu₃Cl₃)(THT)₂] asymmetric unit. Crystallographic details are as [ollows:2 is monoclinic, space group P2₁/c.a=9.657(3) A,b=6.441(2) A,c=11.459(3) A,\=111.96(2)°,V=661.0(4) A³. andR=0.075;3 is monoclinic, space group P2₁/n,a=19.327(7) A,b=6.703(2) A,c=10.116(3) A,ß=103.04(3)°,V=1276.7(7) A³ andR=0.043:4 is triclinic, space group Pl,a=12.513(2) A,b=6.698(1) A,c=9.651(1) A,=91.98(1)°,\=107.86(1)°,=74.59(1)°,V=741.2(2) A³, andR=0.044.