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:

Molecular structure and spectral properties of thionaphthalimides

The molecular structure and absorption spectra of monothio- and dithio-naphthalimides were compared to their naphthalimide analogues using AM1, PM3 and ZINDO/S semiempirical quantum chemical methods. The substitution of the 4R-naphthalimide oxygen atoms by sulphur atoms resulted in a red-shift of the absorption spectra by Δλ_max60-65 and 100-140 nm, respectively. The thionated naphthalimide derivatives do not show observable fluorescence due to intersystem crossing to the triplet -states localised at the CS groups. The -absorption bands of monothioimides are located at 525-580 nm (ε=60-80) and those for dithioimides at 535-560 nm (ε=140-390) and 628-686 nm (ε=34-68). None of these transitions are solvent sensitive. The -transitions of N-phenylthioimides have also a small contribution from -states due to a partial conjugation between CS group and π-electronic system of the N-phenyl ring. As a result, the bands of aromatic substituted N-phenylthioimides are red-shifted as compared to those of the aliphatic N-methyl-thioimides.     

Crystal structure and nontrivial magnetic properties of CuII binuclear complex based on 4-methyl-2,6-bis{[2-(4,6-dimethyl-pyrimidin-2-yl)hydrazono]methyl}phenol

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Spectroscopic Study of Azo- and Azoxycrowns Binding with Cations of Similar Ionic Radius

The complexation of 13- and 16-memberedazo- and azoxycrowns with metal cations of similarionic diameter (Na⁺ and Ca²⁺; and K⁺,Ba²⁺, Ag⁺ and Pb²⁺) was studied byuv/visible spectroscopic titration in acetonitrile andMeOH. In MeOH the 13-membered azo- and azoxycrowns 1 and 2 are weakly and non-selectively bound tohard cations of similar ionic diameter, but differentcharge (Na⁺ and Ca²⁺). At the same time thebinding to the soft cation Ag⁺ of larger sizethan the macrocycle cavity is considerably stronger.In contrast to solutions in acetonitrile no bindingwith the small Li⁺ cation was found.The 16-membered azocrowns 3 and 4 alsodiscriminate silver cation in MeOH withlog K = 3.65 ± 0.1 for both compounds.Unexpectedly low bindingwith the hard barium divalent cation of similar size(log K = 1.55 ± 0.4 and 1.95 ± 0.2, respectively)was found for these compounds. Similarly to13-membered compounds no binding with the smallLi⁺ cation was detected. A reverse order ofselectivity was observed for these crowns inacetonitrile with binding constant for association of3 with Ba²⁺ (log K 5.3) considerablyhigher than for other cations. The previously observedstrong binding with the smaller Li⁺ and Na⁺cations is confirmed.     

Synthesis and the Crystal Structure of a New Chiral 1D Metal–Organic Coordination Polymer Based on L-Prolineamide-Substituted Diarylacetylenedicarboxylic Acid Derivative

The new homochiral 1D metal–organic coordination polymer [Cu₂(EDPB)•H₂O]_n was synthesized starting from the original 3,3′-ethyne-1,2-diylbis[6-(L-prolylamino)benzoic acid] (H₄EDPB). The unique crystal structure of the new compound was established by powder X-ray diffraction. The [Cu₂(EDPB)•H₂O]_n system shows catalytic activity and enantioselectivity in a Henry reaction of p-nitrobenzaldehyde with nitromethane.     

Design and Synthesis of Nitrogen-Rich Azo-Bridged Furoxanylazoles as High-Performance Energetic Materials

A series of novel energetic materials comprising of azo-bridged furoxanylazoles enriched with energetic functionalities was designed and synthesized. These high-energy materials were thoroughly characterized by IR and multinuclear NMR (¹H, ¹³C, ¹⁴N) spectroscopy, high-resolution mass spectrometry, elemental analysis, and differential scanning calorimetry (DSC). The molecular structures of representative amino and azo oxadiazole assemblies were additionally confirmed by single-crystal X-ray diffraction and X-ray powder diffraction. A comparison of contributions of explosophoric moieties into the density of energetic materials revealed that furoxan and 1,2,4-oxadiazole rings are the densest motifs while the substitution of the azide and amino fragments on the nitro and azo ones leads to an increase of the density. Azo bridged energetic materials have high nitrogen-oxygen contents (68.8–76.9 %) and high thermal stability. The synthesized compounds exhibit good experimental densities (1.62–1.88 g cm⁻³), very high enthalpies of formation (846–1720 kJ mol⁻¹), and, as a result, excellent detonation performance (detonation velocities 7.66–9.09 km s⁻¹ and detonation pressures 25.0–37.7 GPa). From the application perspective, the detonation parameters of azo oxadiazole assemblies exceed those of the benchmark explosive RDX, while a combination of high detonation performance and acceptable friction sensitivity of azo(1,2,4-triazolylfuroxan) make it a promising potential alternative to PETN.     

Three-Dimensional Nonlinear Dynamics of Cold Atoms in an Optical Lattice and its Realizations

Journal of Russian Laser Research - We examine the coherent dynamics of cold atoms in a three-dimensional (3D) optical lattice (OL) without interference between counter-propagating laser beams. The...     

A remark on analytic Fredholm alternative

We apply a recent result of Borichev–Golinskii–Kupin on the Blaschke-type conditions for zeros of analytic functions on the complex plane with a cut along the positive semi-axis to the problem of the eigenvalues distribution of the Fredholm-type analytic operator-valued functions.