Almost maximal spaces

A topological space X is called almost maximal if it is without isolated points and for every x∈X, there are only finitely many ultrafilters on X converging to x. We associate with every countable regular homogeneous almost maximal space X a finite semigroup Ult(X) so that if X and Y are homeomorphic, Ult(X) and Ult(Y) are isomorphic. Semigroups Ult(X) are projectives in the category F of finite semigroups. These are bands decomposing into a certain chain of rectangular components. Under MA, for each projective S in F, there is a countable almost maximal topological group G with Ult(G) isomorphic to S. The existence of a countable almost maximal topological group cannot be established in ZFC. However, there are in ZFC countable regular homogeneous almost maximal spaces X with Ult(X) being a chain of idempotents.     

Conjugate points and Maslov index in locally symmetric semi-Riemannian manifolds

We study the singularities of the exponential map in semi Riemannian locally symmetric manifolds. Conjugate points along geodesics depend only on real negative eigenvalues of the curvature tensor, and their contribution to the Maslov index of the geodesic is computed explicitly. We prove that degeneracy of conjugate points, which is a phenomenon that can only occur in semi-Riemannian geometry, is caused in the locally symmetric case by the lack of diagonalizability of the curvature tensor. The case of Lie groups endowed with a bi-invariant metric is studied in some detail, and conditions are given for the lack of local injectivity of the exponential map around its singularities.     

The twisted SU(N) group. On the C *-algebra C(S μ U(N))

It is proved that C(S U(N)) is a type I C ^*-algebra.     

A shape-optimization technique for the capillary surface problem

Summary The problem of the construction of an equilibrium surface taking the surface tension into account leads to Laplace-Young equation which is a nonlinear elliptic free-boundary problem. In contrast to Orr et al. where an iterative technique is used for direct solution of the equation for problems with simple geometry, we propose here an alternative approach based on shape optimization techniques. The shape of the domain of the liquid is varied to attain the optimality condition. Using optimal control theory to derive expressions for the gradient, a numerical scheme is proposed and simple model problems are solved to validate the scheme.     

Building of mathematical models of continuum media on the basis of the invariance principle

The system of differential equations which describes the motion of continuum media of gas, liquid, Reiner-Rievling-type liquid, etc., is considered.% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacqaHbp% GCdaWgaaWcbaGaamiDaaqabaGccqGHRaWkcaqGKbGaaeyAaiaabAha% caqGOaGaeqyWdiNaaeyDaiaabMcacaqG9aGaaeimaiaabUdaaeaacq% aHbpGCcaGGBbGaaeyDamaaBaaaleaacaqG0baabeaakiabgUcaRiaa% cIcacaqG1bGaeyyXICTaey4bIeTaaiykaiaabwhacaGGDbGaeyOeI0% IaamizaiaadMgacaWG2bGaey4dIuTaaiikaiabgEGirlaabwhacaGG% PaGaey4kaSIaey4bIeTaamiCaiaacUdaaeaacaWGWbWaaSbaaSqaai% aadshaaeqaaOGaey4kaSIaaeyDaiabgwSixlabgEGirlaadchacqGH% RaWkcaWGhbGaaeizaiaabMgacaqG2bGaaeiiaiaabwhacqGHRaWkca% WGibGaeqOXdyMaeyypa0JaaGimaiaac6caaaaa!7268!\[\begin{gathered} \rho _t + {\text{div(}}\rho {\text{u) = 0;}} \hfill \\ \rho [{\text{u}}_{\text{t}} + ({\text{u}} \cdot \nabla ){\text{u}}] - div\prod (\nabla {\text{u}}) + \nabla p; \hfill \\ p_t + {\text{u}} \cdot \nabla p + G{\text{div u}} + H\phi = 0. \hfill \\ \end{gathered} \]Solving the problem of its group classification, we obtained all the state equations which lead to the expansion of the main group assumed by the initial equations under the arbitrary elements , G, H.     

Normal subgroups and elementary theories of lattice-ordered groups

We show that any lattice-ordered group (l-group) G can be l-embedded into continuously many l-groups H _i which are pairwise elementarily inequivalent both as groups and as lattices with constant e. Our groups H _i can be distinguished by group-theoretical first-order properties which are induced by lattice-theoretically nice properties of their normal subgroup lattices. Moreover, they can be taken to be 2-transitive automorphism groups A(S _i ) of infinite linearly ordered sets (S _i , ) such that each group A(S _i ) has only inner automorphisms. We also show that any countable l-group G can be l-embedded into a countable l-group H whose normal subgroup lattice is isomorphic to the lattice of all ideals of the countable dense Boolean algebra B.     

Fluorescence quenching of anthropogenic fulvic acids by Cu(II), Fe(III) and UO(2)(2+)

The quenching of the fluorescence of three anthropogenic fulvic acids (FA) provoked by Cu(II) (pH 6.0), Fe(III) (pH 4.0) and UO₂²⁺ (pH 3.5), was analyzed by a non-linear method and by Stern-Volmer plots. The FA samples were extracted from composted sewage sludges (csFA), composted municipal wastes (mwFA) and composted livestock wastes (lsFA). Synchronous-scan fluorescence (SyF) spectra were collected as a function of metal ion concentration. Spectral data were treated by a self-modeling mixture analysis method (SIMPLISMA) to detect the SyF spectral band with the strongest quenching and to calculate the corresponding quenching profile. The analysis of these profiles by a non-linear method allowed the estimation of conditional stability constants (K) and of the percentage of non-complexing fluorophores. The same quantitative information was obtained by the modified Stern-Volmer equation taking into account the existence of fluorophores that do not participate in the complexation. Good agreement was found between the results of the two procedures. The log K calculated by the non-linear method were (standard deviation in parenthesis): csFA, Cu(II), 4.22 (5); Fe(III), 5.0 (1); UO₂²⁺, 5.2 (2); mwFA, Cu(II), 4.21 (3); Fe(III), 5.6 (2); UO₂²⁺, 4.7 (3); lsFA, Cu(II), 4.51 (8); Fe(III), 5.5 (2); UO₂²⁺, 3.6 (2).     

Simultaneous hydrogen and peroxide production by photocatalytic water splitting

Photocatalytic oxidation of water is a promising method to realize large-scale H₂O₂ production without a hazardous and energy-intensive process. In this study, we introduce a Pt/TiO₂(anatase) photocatalyst to construct a simple and environmentally friendly system to achieve simultaneous H₂ and H₂O₂ production. Both H₂ and H₂O₂ are high-value chemicals, and their separation is automatic. Even without the assistance of a sacrificial agent, the system can reach an efficiency of 7410 and 5096 μmol g^–1 h^–1 (first 1 h) for H₂ and H₂O₂, respectively, which is much higher than that of a commercial Pt/TiO₂(anatase) system that has a similar morphology. This exceptional activity is attributed to the more favorable two-electron oxidation of water to H₂O₂, compared with the four-electron oxidation of water to O₂.     

Ge—132对小鼠H22肝癌移植瘤的影响

Ｇｅ－１３２对小鼠Ｈ２２肝癌移植瘤的实验研究证明：１．Ｇｅ－１３２对Ｈ２２肝癌移植瘤有一定的抑制作用，３００ｍｇ／ｋｇ体重剂量抑瘤率达到３６．１９％；２．增强机体的抗氧化作用，抑制脂质的过氧化物水平；３．促进免疫功能，当Ｇｅ－１３２和环磷酰胺联合使用时，可抵抗环磷酰胺的免疫抑制作用，而且并不减弱其抑制瘤作用。