Properties of the Coxeter transformations for the affine Dynkin cycle

We study spectral properties of the Coxeter transformations for the affine Dynkin cycle and find the Jordan form of the Coxeter transformation and the Coxeter numbers.     

Temperature hysteresis phenomena in heterogeneous catalysis

Temperature hysteresis is observed only in exothermic heterogeneous catalytic reactions (viz., oxidation and methanation of CO or propene hydrogenation) and is absent in the case of endothermic reactions (dehydrogenation of isobutane) or reactions with heat close to zero (viz., 2-butene isomerization). Temperature hysteresis in hydrogenation reactions was discovered for the first time. The concept of local overheating of catalyst active sites caused by poor removal of the reaction heat is proposed to provide a noncontradictory interpretation of the appearance of hysteresis loops. Published inIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1379–1385, August, 2000.     

Electrohydrodynamics of a Cone–Jet Flow at a High Relative Permittivity

We have proposed a new solution of the electrohydrodynamic equations describing a novel cone–jet flow structure formed at a conductive liquid meniscus in an electric field. Focusing on the liquids characterized by a high relative permittivity and using the slender body approximation, the cone–jet transition profiles and their characteristic radii are predicted in relation to the material parameters. The stable value of the cone angle is obtained using the Onsager’s principle of maximum entropy production. Three different regimes of the cone–jet flow behavior are identified depending on the relative importance of capillary, viscous and inertial stress contributions. The presented complete analytical solutions for the cone–jet transition zone and the far jet region yield several different laws of algebraic decrease for the radius, surface charge, and electric field of the jet.     

Modular,Homochiral, Porous Coordination Polymers: Rational Design,Enantioselective Guest Exchange Sorption and Ab Initio Calculations of Host–Guest Interactions

Two new, homochiral, porous metal–organic coordination polymers [Zn₂(ndc){(R)‐man}(dmf)]?3DMF and [Zn₂(bpdc){(R)‐man}(dmf)]?2DMF (ndc=2,6‐naphthalenedicarboxylate; bpdc=4,4′‐biphenyldicarboxylate; man=mandelate; dmf=N,N′‐dimethylformamide) have been synthesized by heating Zn^II nitrate, H₂ndc or H₂bpdc and chiral (R)‐mandelic acid (H₂man) in DMF. The colorless crystals were obtained and their structures were established by single‐crystal X‐ray diffraction. These isoreticular structures share the same topological features as the previously reported zinc(II) terephthalate lactate [Zn₂(bdc){(S)‐lac}(dmf)]?DMF framework, but have larger pores and opposite absolute configuration of the chiral centers. The enhanced pores size results in differing stereoselective sorption properties: the new metal–organic frameworks effectively and stereoselectively (ee up to 62 %) accommodate bulkier guest molecules (alkyl aryl sulfoxides) than the parent [Zn₂(bdc){(S)‐lac}(dmf)]?DMF, while the latter demonstrates decent enantioselectivity toward precursor of chiral anticancer drug sulforaphane, CH₃SO(CH₂)₄OH. The new homochiral porous metal–organic coordination polymers are capable of catalyzing a highly selective oxidation of bulkier sulfides (2‐NaphSMe (2‐C₁₀H₇SMe) and PhSCH₂Ph) that could not be achieved by the smaller‐pore [Zn₂(bdc){(S)‐lac}(dmf)]?DMF. The sorption of different guest molecules (both R and S isomers) into the chiral pores of [Zn₂(bdc){(S)‐lac}(dmf)]?DMF was modeled by using ab initio calculations that provided a qualitative explanation for the observed sorption enantioselectivity. The high stereo‐preference is accounted for by the presence of coordinated inner‐pore DMF molecule that forms a weak C? H???O bond between the DMF methyl group and the (S)‐PhSOCH₃ sulfinyl group.     

Motion of a planar domain wall in the ferroelectric-ferroelastic gadolinium molybdate

The lateral motion of a planar domain wall (PDW) in an electric field and the spontaneous rotation of the wall in the initial position after the field is switched off were investigated in the improper ferroelectric-ferroelastic gadolinium molybdate Gd₂(MoO₄)₃, using optical visualization and measurement of the switching currents. The characteristic behavior found for the PDW is attributed to the delay of the volume screening of the depolarizing fields. It is shown that the dependence of the motion of the PDW on the switching duration in an ac field is due to the redistribution of the screening charges. Fiz. Tverd. Tela (St. Petersburg) 41, 126–129 (January 1999)     

Exact values of relative widths of classes of differentialbe functions

We study relative widths in the spacesC andL of classes of periodic differentiable functionsW ^r,r=1,2,…, when in contrast to the Kolmogorov widths it is additionally required that the approximating functions belong to the classMW ^r with a given majorantM of the norm of the derivative of orderr. It is proved that ifM satisfies the estimate

Barkhausen effect in stepped motion of a plane domain boundary in gadolinium molybdate

Barkhausen pulses generated in stepped motion of a single plane domain boundary (PDB) are investigated experimentally in single-crystalline wafers of the extrinsic ferroelastic ferroelectric gadolinium molybdate containing artificial pinning centers of the “field inhomogeneity” type near the edges of the sample. Two scenarios of the evolution of a PDB in interaction with “defects” are proposed on the basis of analyzing the shape of the pulses in a linearly increasing field: small changes of the pulse shape in a weak field and the generation of wedge domains in a strong field. The proposed mechanism of PDB motion due to the generation of steps near the edge of the sample and their longitudinal motion provides a means for explaining the experimentally observed linear field dependence of the PDB velocity and for determining the velocity of the steps. Fiz. Tverd. Tela (St. Petersburg) 41, 301–305 (February 1999)     

Cascades of atomic displacements in solids: The ballistic stage

The evolution of cascades of atomic displacements in solids is analyzed. The charge-exchange, ionization, and elastic scattering cross sections are calculated for the atoms and ions involved in cascade evolution. The effects due to the material density are taken into account. These results are used to perform the first Monte Carlo computations of cascades based on the knowledge of microscopic processes without invoking phenomenological potentials. The proposed approach is unique in that detailed characteristics of atomic processes are obtained by ab initio calculation and applied to analyze cascades of atomic displacements. Subcascade development is described, and a relation between the number of Frenkel pairs and the energy of the primary knock-on atom is found for a wide energy range. This provides a basis for characterizing the dose dependence of the hardening of reactor pressure vessel steel and for comparing the effects of primary radiation damage for fission and fusion reactors.     

Approximation by splines and smooth bases in C(0, 2π)

An estimate of the deviation of the splines interpolating on a uniform net a function continuous on the whole axis by means of the k^th module of continuity. These results are applied for the construction of smooth bases in C(0, 2).Translated from Matematicheskie Zametki, Vol. 12, No. 1, pp. 43–51, July, 1972.