A necessary and sufficient condition for Hardy's operator in

The equivalent conditions are proved for the Hardy inequality to be fulfilled in the norms of a Lebesgue space with variable exponent . It is assumed that the function is monotone and positive on (0, 1).     

Kinetics of H2S destruction in the radiolysis of CH4−H2S gas mixtures

The kinetics of H₂S destruction in the radiolysis of CH₄–H₂S and CH₄–H₂S–O₂ mixtures has been studied. It has been shown that G(–H₂S) depends on amounts of hydrogen sulfide and the presence of oxygen in the starting mixture and is within the range of 5–13 mol/100 eV. G(H₂) decreases with the increases of O₂ content and amounts to the constant value of 2.     

The photolysis and radiolysis of H2S−CH4 gas-phase mixture

The purification of methane from hydrogen sulphide at room temperature as affected by U.V.-light and ionizing radiation has been studied. A probable reaction mechanisms is discussed.     

聚多巴胺功能化硅胶沉积单分散Pd纳米粒子的简易原位合成及用作醇需氧氧化反应的多相可循环使用的纳米催化剂（英文）

本文报道了一种不使用任何稳定剂或还原剂,原位合成硅胶/聚多巴胺复合物(SiO_2/PDA)负载的Pd纳米颗粒(Pd NPs)的简易方法.该方法先将PDA涂覆的SiO_2颗粒浸在Pd镀液中,然后利用PDA中含N基团的还原能力将Pd物种原位还原为纳米簇合物.并采用高分辨透射电镜、前场扫描电镜、能量散射谱、X射线衍射、X射线光电子能谱、诱导耦合等离子体和红外光谱等手段对所得纳米复合物的结构、形貌和物化性质进行了表征.被PDA基团锚合的Pd NPs具有显著的小颗粒(30–40 nm)特性.作为一个可循环使用的纳米催化剂,SiO_2/PDA/Pd NPs在醇的需氧氧化反应中表现出高活性.另外,催化剂经回收和多次重复使用时未出现明显的失活.     

Acid-catalyzed rearrangement of 3-(β-2-aminostyryl)quinoxalin-2(1H)ones—a new and efficient method for the synthesis of 2-benzimidazol-2-ylquinolines

A highly efficient, one-step, versatile method for the synthesis of 2-benzimidazol-2-ylquinolines has been developed on the basis of an acid-catalyzed rearrangement proceeding via a novel ring contraction of 3-(β-2-aminostyryl)quinoxalin-2(1H)ones.     

3-Indolizin-2-ylquinoxalines and the derived monopodands

The reactions of 3-acetylquinoxalin-2-one with methyl-and benzylpyridines in the presence of iodine produce the corresponding 3-(2-alkylpyridinioacetyl)quinoxalin-2(1H)-one iodides. Treatment of the latter with triethylamine affords the corresponding 3-indolizin-2-ylquinoxalin-2-ones. Due to the presence of the endocyclic carbamoyl group, the reactions of these compounds with bisalkylating reagents give quinoxaline-containing monopodands and monoalkylation products containing spacers with different lengths and of different nature. Dedicated to Professor Ya. A. Levin on the occasion of his 70th birthday. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2534–2542, November, 2005.     

Energy states of colored particle in a chromomagnetic field

The unitary transformation which diagonalizes the squared Dirac equation in a constant chromomagnetic field is found. Applying this transformation, we find the eigenfunctions of the diagonalized Hamiltonian, that describes the states with a definite value of energy, and we call them energy states. It is pointed out that the energy states are determined by the color interaction term of the particle with the background chromofield, and this term is responsible for the splitting of the energy spectrum. We construct supercharge operators for the diagonal Hamiltonian that ensure the superpartner property of the energy states. PACS 03.65.-w An erratum to this article can be found at     

The construction of reciprocity and integral representation formulas of the general solution for quasistatic and dynamic problems of uncoupled generalized thermoelasticity

Reciprocity formulas are constructed and representations of the Somigliani-type are obtained for quasistatic and dynamic problems of uncoupled generalized thermoelasticity in the Lord-Shulman formulation that is effective for applications. Moreover, representations are obtained for the stresses and heat flux. Unlike the existing approach (/1/, say) these formulas are derived on the basis of an examination of the system of differential equations of the above-mentioned problems of generalized thermoelasticity as a system with appropriate non-selfadjoint differential operators. Operators adjoint to the initial differential operators are introduced into consideration for the construction of the reciprocity formulas (second Green's formula), and a Laplace transformation is used.     

Vibrational distribution functions and relaxation rate in anharmonic-oscillator systems

Analytical expressions were derived for the vibrational distribution function in a system of anharmonic oscillators under conditions where the supply of vibrational energy considerably exceeded the equilibrium value. Distribution was found by considering the effect of vibrational-vibrational and vibrational-translational energy exchange, as well as spontaneous radiative transitions. Analytical expressions were also obtained for the relaxation rate of vibrational energy. It was shown that where there is a strong deviation from equilibrium this rate can significantly exceed the corresponding value for a model of harmonic oscillators and is determined by the probability of vibrational-vibrational exchange in the molecules.