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.     

Asymptotic robustness of standard errors in multilevel structural equation models

Data in social and behavioral sciences are often hierarchically organized. Multilevel statistical methodology was developed to analyze such data. Most of the procedures for analyzing multilevel data are derived from maximum likelihood based on the normal distribution assumption. Standard errors for parameter estimates in these procedures are obtained from the corresponding information matrix. Because practical data typically contain heterogeneous marginal skewnesses and kurtoses, this paper studies how nonnormally distributed data affect the standard errors of parameter estimates in a two-level structural equation model. Specifically, we study how skewness and kurtosis in one level affect standard errors of parameter estimates within its level and outside its level. We also show that, parallel to asymptotic robustness theory in conventional factor analysis, conditions exist for asymptotic robustness of standard errors in a multilevel factor analysis model.     

Hyperbolic-parabolic singular perturbation for quasilinear equations of Kirchhoff type

We consider a hyperbolic-parabolic singular perturbation problem for a quasilinear equation of Kirchhoff type, and obtain parameter-dependent time decay estimates of the difference between the solutions of a quasilinear dissipative hyperbolic equation of Kirchhoff type and the corresponding quasilinear parabolic equation. For this purpose we show time decay estimates for hyperbolic-parabolic singular perturbation problem for linear equations with a time-dependent coefficient.     

A fiberwise analogue of the Borsuk-Ulam theorem for sphere bundles over a 2-cell complex II

We describe a finite complex B as I-trivial if there does not exist a Z₂-map from Si−1 to S(α) for any vector bundle α over B and any integer i with i>dimα. We prove that the m-fold suspension of projective plane FP² is I-trivial if and only if m≠0,2,4 for F=C, m≠0,4 for F=H. In the case where F is the Cayley algebra, the m-fold suspension is shown to be I-trivial for every m>0.     

Large-time behavior of perturbed diffusion markov processes with applications to the second eigenvalue problem for fokker-planck operators and simulated annealing

We study the large-time behavior and rate of convergence to the invariant measures of the processes dX (t)=b(X) (t)) dt + (X (t)) dB(t). A crucial constant appears naturally in our study. Heuristically, when the time is of the order exp( – )/² , the transition density has a good lower bound and when the process has run for about exp( – )/², it is very close to the invariant measure. LetL =(²/2) – U · be a second-order differential operator on ^d. Under suitable conditions,L ^z has the discrete spectrum

A strange pigeon-hole principle

Using Ramsey theory, we establish the following pigeon-hole type principle: From a large number of random variables (functions, vectors, etc.) one can always select two, X and Y, such that P(X < Y) 1/2. We apply the principle for a poset problem.     

软珊瑚Sinularia sp.中次生代谢产物的结构鉴定

细胞毒性;软珊瑚Sinularia sp.中次生代谢产物的结构鉴定     

碲氢化钠还原亚胺的方法

本文报道一种还原亚胺的新方法。取代的芳基和脂肪基亚胺可以在较温和的条件下被碲氢化钠顺利地还原为相应的仲胺。     

乙烯系单体自由基聚合的阻聚效应——Ⅸ.受阻胺-醌类电荷转移络合物对甲基丙烯酸甲酯自由基聚合的阻聚及历程

用膨胀计法研究了西氯苯醌(CA)、苯醌(BQ)与受阻胺二异丙胺(DIPA)、2,2,6,6-四甲基-4-羟基哌啶(TMP)形成的电荷转移络合物(CTC)对偶氮二异丁腈(AIBN)引发的甲基丙烯酸甲酯(MMA)自由基聚合阻聚效应。结果表明,CA-DIPA、CA-TMP、BQ-DIPA和BQ-TMP对MMA的自由基聚合均产生较单独的醌或胺更显著的阻聚能力。其中以CA-DIPA阻聚效果更佳。比较了MMA在苯或乙腈中的溶液聚合,得类似结果。初步讨论了受阻胺-醌电荷转移络合物对MMA自由基聚合的阻聚反应机理。