On the conductance of order Markov chains

Let Q be a convex solid in ⁿ , partitioned into two volumes u and v by an area s. We show that s>min(u,v)/diam Q, and use this inequality to obtain the lower bound n ^-5/2 on the conductance of order Markov chains, which describe nearly uniform generators of linear extensions for posets of size n. We also discuss an application of the above results to the problem of sorting of posets.Computing Center of the USSR Academy of Sciences USSR     

Three-dimensional absolute and convective instabilities,and spatially amplifying waves in parallel shear flows

A formalism for absolute and convective instabilities in parallel shear flows is extended to the three-dimensional case. Assuming that the dispersion relation function is given byD(k, l, ), wherek andl are wave numbers, and is a frequency, the analytic criterion is formulated by which a point (k ₀,l ₀, ₀) with Im ₀>0 contributes to the absolute instability if and only if one of the two equivalent conditions is satisfied:

Geometries and NMR properties of cisplatin and transplatin revisited at the four-component relativistic level

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A comparison of numerical and analytical radiative-transfer solutions for plane albedo of natural waters

Several numerical and analytical solutions of the radiative transfer equation (RTE) were compared for plane albedo in a problem of solar light reflection by sea water. The study incorporated the simplest case—a semi-infinite one-dimensional plane—parallel absorbing and scattering homogeneous layer illuminated by a monodirectional light beam. Inelastic processes (such as Raman scattering and fluorescence), polarization and air-water surface refraction-reflection effects, were not considered. Algorithms were based on the invariant imbedding method and two different variants of the discrete ordinate method (DOM). Calculations were performed using parameters across all possible ranges (single-scattering albedo ω₀ and refracted solar zenith angle θ₁), but with a special emphasis on natural waters. All computations were made for two scattering phase functions, which included an almost isotropic Rayleigh phase function and strongly anisotropic double-peaked Fournier-Forand-Mobley phase function. Models were validated using quasi-single-scattering (QSSA) and exponential approximations, which represent the extreme cases of ω₀→0 and ω₀→1, respectively. All methods yielded relative differences within 1.8% for modeled natural waters. An analysis of plane albedo behavior resulted in the development of a new extended QSSA approximation, which when applied in conjunction with the extended Hapke approximation developed earlier, resulted in a maximum relative error of 2.7%. The study results demonstrated that for practical applications, the estimation of inherent optical properties from observed reflectance can best be achieved using an extended Hapke approximation.     

Synthesis and Crystal Structure of LiY(CN2)2, Having a Structure Related to That of NiAs

The new ternary carbodiimide LiY(CN₂)₂ was synthesized by solid state metathesis reaction between YF₃ and Li₂(CN₂) in a silica tube at 550 °C. The X‐ray single‐crystal structure determination yielded an orthorhombic crystal system (Pbcn, Z = 4, a = 982.0(3), b = 698.5(2), c = 613.4(2) pm). The crystal structure can be considered related to the NiAs structure. The carbodiimide ions are arranged in layers following the motif of a hexagonal closest packing of sticks. Lithium and yttrium cations occupy all octahedral voids in an ordered fashion, alternating on top of each other along the hcp stacking direction.     

Nitrous Oxide Adsorption and Decomposition on Zeolites and Zeolite-like Materials

Decomposition of N₂O on modified zeolites, crystalline titanosilicalites, and related amorphous systems is studied by the catalytic and spectroscopic methods. Zinc-containing HZSM-5 zeolites and titanosilicalites with moderate Ti/Si ratios are shown to exhibit a better catalytic performance in N₂O decomposition as compared with conventionally used Cu/HZSM-5 zeolites and amorphous Cu-containing catalysts. Dehydroxylation of the HZSM-5 zeolite by calcination at 1120 K results in an enhancement of the N₂O conversion. The mechanism of the reaction and the role of coordinatively unsaturated cations and Lewis acid sites in N₂O decomposition are discussed on the basis of the spectroscopic data.