Calculation of the Slip Velocity of a Rarefied Gas on a Solid Spherical Surface with Allowance for Accommodation Coefficients

The slip velocity of a rarefied gas with inhomogeneous temperature and mass velocity on a solid spherical surface is calculated with the use of a twomoment boundary condition in the linear approximation in terms of the Knudsen number. The dependence of the slip velocity on accommodation coefficients of the two first moments of the distribution function is studied.     

A note on the fundamental solution for the Tricomi-type equation in the hyperbolic domain

Barros-Neto and Gelfand (Duke Math. J. 98 (3) (1999) 465; Duke Math. J. 117 (2) (2003) 561) constructed for the Tricomi operator on the plane the fundamental solutions with the supports in the regions related to the geometry of the characteristics of the Tricomi operator. We give for the Tricomi-type operator a fundamental solution relative to an arbitrary point of Rⁿ⁺¹ with the support in the region t?0, where the operator is hyperbolic. Our key observation is that the fundamental solution for the Tricomi-type operator can be written like an integral of the distributions generated by the fundamental solution of the Cauchy problem for the wave equation. The application of that fundamental solution to the L^p-L^q estimate for the forced Tricomi-type equation is given as well.     

Development of SnO2/Sb-based ceramic pigments

The color efficiency of ceramic glaze blue pigments obtained by the Pechini method was presented in this work. The fired pigments and enameled samples were characterized by thermogravimetry (TG) and differential thermal analysis (DTA), XRD, UV-VIS-NIR spectroscopy and CIE-L*a*b* color-measurements. The pigments obtained by the Pechini method present a better solubility in the molten glazes than the pigments obtained by the mechanical mixture of the precursor oxides. This revised version was published online in August 2006 with corrections to the Cover Date.     

Scattering matrix for Feshbach-Villars equation for spin 0 and 1/2: Woods-Saxon potential

The Feshbach-Villars equation for spin 0 and 1/2 in the presence of Woods-Saxon potential is solved using an unified approach. The good boundary conditions for jumping potential are found and Klein tunneling and Klein paradox are discussed. The scattering matrix is constructed and the phase shifts, the transmission and reflection coefficients are deduced.     

A Class of k-Quantum Nonlinear Coherent States and Some of Their Properties

A class of k-quantum nonlinear coherent states, i.e., the k eigenstates of the powers B ^k (k 3) of the annihilation operator of f-oscillators, is obtained and its completeness is investigated. An alternative method to construct them is proposed. We introduce a new kind of higher-order squeezing and sub-Poissonian distribution. The quantum statistical properties of the k states are studied. The result shows that all of the eigenstates can be generated by a linear superposition of k Roy-type nonlinear coherent states. These states may form a complete Hilbert space, and the M-th order [M = (n + 1/2)k; n = 0,1, ...] squeezing effects exist in all of the k states when k is even. There is the sub-Poissonian distribution in all of the states.     

Arbuzov rearrangement in the 1,3,2-oxazaphosphinane series

Reactions of 2-alkoxy-1,3,2-oxazaphosphinanes (including 3-alkyl derivatives) with methyl and ethyl bromoacetates give two types of Arbuzov rearrangement products (cyclic and acyclic ones). The ratio between their yields is virtually independent of the nature of the substituent in position 3 of the starting reagent, being mainly determined by the nature of the substituent in the phosphorus bound alkoxy group and varying from 96 : 4 to 2 : 98. Acyclic products can be converted into cyclic ones.Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1915–1918, September, 2004.     

The first example of direct heterylation of calixpyrrole

1,2,4-Triazine derivatives react with calixpyrrole to give stable nucleophilic addition products.     

Lipase-mediated deracemization of secondary 1-phenyl-substituted propargylic alcohols of different topology

Acetylation of (±)-1-phenylnon-2-yn-1-ol, (±)-1-phenylhept-1-yn-3-ol, and (±)-1-phenylundec-4-yn-3-ol ((±)-5) in the presence of lipase from Candida cylindracea (CCL) proceeds slowly to give products with ee 20%. The acetates of these alcohols are hydrolyzed in the presence of porcine pancreatic lipase (PPL) equally unsatisfactorily. The (⁶-arene)tricarbonylchromium complex of alcohol (±)-5 is acetylated in the presence of CCL up to 22% conversion to give (R)-acetate whose oxidative decomplexation followed by saponification results in alcohol (R)-(–)-5 with ee 95%. The configuration of alcohols (–)-5 and (+)-5 was determined by NMR spectroscopy of their esters with (R)- and (S)-Mosher"s acids.     

Synthesis of alkyl (α-phenylthioalkenyl) ketones containing a (Z)-trisubstituted olefinic fragment

Warren"s method, which has been proposed for the synthesis of -phenylthiodialkyl ketones, appeared to be inefficient for the preparation of their alkenyl alkyl analogs. The latter were prepared in good yields by alkenylation of alkyl phenylthiomethyl ketones with alkenyl bromides.     

A Negative Deviation from Stern–Volmer Equation in Fluorescence Quenching

A negative deviation from the normal Stern-Volmer equation shown in the fluorescence quenching of doxorubicin by adenosine 5' monophosphate is interpreted in terms of doxorubicin exists in two different conformers in the ground state. An estimate of the Stem-Volmer constant for the excited-state quenching is about 218 M(-1). The fluorescence decay of free doxorubicin is a bi-exponential in polar protic and polar aprotic solvents. In the presence of adenosine 5' monophosphate, doxorubicin shows a tri-exponential decay in water.