Estimation of diffusion coefficient of Ba++ ions in silica gel from periodic precipitation of BaMoO4

Formation of Liesegang rings on the growth of BaMoO₄ crystals in silica gel by single diffusion is discussed. The rhythmic precipitation is found to be influenced profoundly by (a) the molarity of inner and outerelectrolytes (b) the age of gel and (c) the pH of the gel medium. The time law, spacing law and the law relating diffusion depth and width are verified. A method to estimate the diffusion coefficient of the outer electrolyte in the gel medium is developed and calculated for Ba⁺⁺ions.     

Influence of the composition of perovskites based on SrMnO<Subscript>3</Subscript> on their catalytic properties in the oxidative coupling of methane

The oxidative coupling of methane (OCM) in a periodic regime over the SrMnO₃ and its derivatives has been investigated. It has been established that partial replacement of the strontium ion by alkali metal ions leads to an increase in both catalytic activity and in selectivity with respect to higher hydrocarbons. Comparison of the results obtained in the present work with those obtained earlier for catalysts based on SrCoO₃ led to the conclusion that the Co-containing catalysts were preferable to the Mn-containing catalysts for carrying out oxidative coupling of methane in a periodic regime.__________Translated from Teoreticheskaya i Éksperimentalnaya Khimiya, Vol. 41, No. 1, pp. 30–34, January–February, 2005.     

Operator Semigroup Compactifications

A weakly continuous, equicontinuous representation of a semitopological semigroup on a locally convex topological vector space gives rise to a family of operator semigroup compactifications of , one for each invariant subspace of . We consider those invariant subspaces which are maximal with respect to the associated compactification possessing a given property of semigroup compactifications and show that under suitable hypotheses this maximality is preserved under the formation of projective limits, strict inductive limits and tensor products.

     

Some nonlinear problems in servomechanisms

Summary A mathematical model for a hydraulic servomechanism is constructed. It is shown that the model, in general, reduces to a nonlinear third-order equation of the formxx+(₁+xx+–₂ x=p(t). Under certain conditions imposed on the constants involved, it is proved that above equation possesses a periodic solution.     

Bifurcation phenomena near homoclinic systems: A two-parameter analysis

The bifurcations of periodic orbits in a class of autonomous three-variable, nonlinear-differential-equation systems possessing a homoclinic orbit associated with a saddle focus with eigenvalues ( ±i,), where ¦/¦ < 1 (Sil'nikov's condition), are studied in a two-parameter space. The perturbed homoclinic systems undergo a countable set of tangent bifurcations followed by period-doubling bifurcations leading to periodic orbits which may be attractors if ¦/¦ < 1/2. The accumulation rate of the critical parameter values at the homoclinic system is exp(-2¦/¦). A global mechanism for the onset of homoclinicity in strongly contractive flows is analyzed. Cusp bifurcations with bistability and hysteresis phenomena exist locally near the onset of homoclinicity. A countable set of these cusp bifurcations with scaling properties related to the eigenvalues±i of the stationary state are shown to occur in infinitely contractive flows. In the two-parameter space, the periodic orbit attractor domain exhibits a spiral structure globally, around the set of homoclinic systems, in which all the different periodic orbits are continuously connected.     

Topological Space of the Chemical Elements and its Properties

We carried out a mathematical study of 72 chemical elements taking advantage of the chemotopological method. We selected 128 properties to define the elements (physico-chemical, geochemical and chemical properties). Then, we looked for correlated properties and we reduced the number of them to 90. In this way we defined each element as a 90-tuple. Afterwards, we applied principal component analysis and cluster analysis (4 similarity functions and 5 grouping methodologies). Then, we calculated a consensus tree for the 20 dendrograms generated by the CA. Afterwards, we extracted the similarity relationships from the consensus tree and built up a basis for a topology on the set of chemical elements. Finally, we calculated some topological properties (closures, derived sets, boundaries, interiors and exteriors) of several subsets of chemical elements. We found that alkali metals, alkaline earth metals and noble gases appear not related to the rest of the elements. Also, we found that the boundary of non-metals are the semimetals with a stair-shape on the periodic table     

Cobalt Ion Incorporation into Periodic Mesoporous Organosilica Materials Synthesized by Co-condensation of 1,2-Bistrimethoxysilylethane with 3-Glycidoxypropyltriethoxysilane

Bifunctional periodic mesoporous organosilica materials with and without cobalt ion incorporation were synthesized by co-condensation of 1,2-bistrimethoxysilylethane (BTME) with 3-glycidoxypropyltriethoxysilane (GPTS) in the presence of cetyltrimethylammonium bromide. Nitrogen gas adsorption on samples with varying ratios of BTME:GPTS revealed that increasing the amount of GPTS affects pore size, surface area and pore volume as well as shapes of the isotherms and hysteresis loops. The hysteresis loops of the Type IV isotherms obtained for GPTS-modified ethane silica materials (without cobalt ion) change from Type H3 to Type H4 with increasing GPTS content. There is a tendency for pore sizes to change from mesopore to micropore when the amount of GPTS is increased. Isotherms of cobalt ion incorporated GPTS-modified ethane silica materials change from Type IV to Type I with increasing GPTS content. The surface area, pore volume and pore diameter decrease with increasing loading of GPTS as well as after cobalt ion incorporation. Thermogravimetric analysis and differential thermal analysis show that the surfactant is removed by solvent extraction. Cobalt ion incorporation is confirmed by powder X-ray diffraction and Raman spectroscopy.     

基于双尺度渐近分析的有限元算法

1．引言正如文山所说，由于复合材料和周期结构的材料系数ail（x）在局部区域内间断且跳跃性很大，加上区域内含有周期性洞穴或裂缝，且周期长度很小．一般而言，直接采用有限元方法进行数值模拟，其计算量大得惊人，甚至难以实现．文山针对这种特征，提出了一种可计算的双尺度渐近分析模式，本文在此基础上给出了相应的有限元算法，它包括：1．周期解在一个基本构造上的有限元计算；2．边界层的有限元计算．同时，给出了相应的误差分析．2．周期解的有限元计算首先考虑下列形式的边值问题；其中把，代E尸（on叫，iii（0关于E—（EI，ZZ…     

Reflecting a single attosecond pulse by using periodic Mo/Si multilayer mirrors with different layers

The reflecting of a single attosecond pulse from a periodic Mo/Si multilayer was investigated. By changing the number of bi-layers, the periodic multilayer showed greatly different spectral and temporal responses of the attosecond pulse reflection, which has been discussed in detail in this paper. The capability of attosecond pulse reflection of the periodic multilayers with different bi-layer numbers has been evaluated using suitable temporal parameters. In addition, the condition for obtaining high-efficiency reflected pulses has been analyzed by comparing the pulse responses of the periodic multilayer with different layers. The transfer-matrix method together with the fast Fourier transform has been used in our simulation.     

On the construction of periodic solutions of kaplan-yorke type for some differential delay equations

In this paper we point out the main idea to yield periodic solutions of Kaplan-Yorke type of differential delay equations. Some new sufficient conditions for the existence of Kaplan-Yorke type periodic solutions have been given. Many interesting examples are also disscused.