Non-catastrophicity in multidimensional convolutional coding

The property of non-catastrophicity of multidimensional convolutional codes is studied. In particular, an algebraic and system-theoretic characterization of non-catastrophicity is offered in the multidimensional setting, and the Massey–Sain classical criterion is extended to this setting.     

Past–future separation and normal forms in temporal predicate logic specifications

Temporal specifications are often used when phenomena are modelled where dynamics play a main role. If simulation is one of the aims of modelling, usually a restricted, executable modelling language format is used, based on some form of past to future implications. In this paper a detailed transformation procedure is described that takes any temporal predicate logic specification and generates a specification in a past-implies-future normal format. The procedure works for temporal specifications in which the atoms either express time ordering relations or are state-related, i.e., include only one time variable.     

A recursive algorithm for constructing complicated Dixon matrices

Whether the determinant of the Dixon matrix equals zero or not is used for determining if a system of n + 1 polynomial equations in n variables has a common root, and is a very efficient quantifier elimination approach too. But for a complicated polynomial system, it is not easy to construct the Dixon matrix. In this paper, a recursive algorithm to construct the Dixon matrix is proposed by which some problems that cannot be tackled by other methods can be solved on the same computer platform. A dynamic programming algorithm based on the recursive formula is developed and compared for speed and efficiency to the recursive algorithm.     

Reactivity of allenoates towards aziridines: synthesis of functionalized methylenepyrrolidines and pyrroles

The reactivity of buta-2,3-dienoates towards aziridines is reported. Typically, allenoates react as the 2π-component in the [3+2] cycloaddition with azomethine ylides generated from aziridines, affording 4-methylenepyrrolidines in a site-, regio- and stereoselective fashion. However, N-cyclohexyl- or N-tert-butyl-2-benzoyl-3-phenylaziridines showed a different reactivity in the reaction with buta-2,3-dienoates. Pyrrole derivatives were obtained as single or major products resulting from a formal [3+2] cycloaddition via C-N bond cleavage of the three-membered ring heterocycle leading to functionalized pyrroles. From the reaction with allenoates bearing bulkier C-4 substituents 4-methylenepyrrolidines were also formed as minor products.     

Morava K -theory rings for the modular groups in Chern classes

Morava K-theory rings of classifying spaces of the modular and quasi-dihedral groups are calculated in terms of Chern characteristic classes and the Honda formal group law. The author was supported by the INTAS 03-51-3251 and GRDF GEM1-3330-TB-03 grants.     

Uniqueness of Gibbs State for Nonideal Gas in ℝ d : The Case of Pair Potentials

We consider a classical gas of particles in ^d interacting via a pair potential. We prove that in a given region of the (, ) plane, where is the inverse temperature, and is the chemical potential, either the Gibbs state is unique or it does not exist. Our method uses a version of the well-known Dobrushin uniqueness theorem adapted for lattice systems with a noncompact spin space and proved by Dobrushin and Pechersky. The advantage of this version is that using it one needs to check Dobrushin's contraction condition not for all boundary configurations, but only for those that have spin values in some compact subset of the spin space.     

Preparation, thermal decomposition and lifetime of Eu(III)-phenanthroline complex doped xerogel

The main purpose of this work is proposing a new method of using non-isothermal formal kinetics analysis to predict the lifetime of luminescent complex materials. The Eu(III)-phenanthroline complex doped xerogel has been in situ synthesized by a catalyst-free sol-gel method. The photoluminescence spectra and TG curves of the xerogel verify the formation and decomposition of Eu(III)-phenanthroline complex in xerogel. The decomposition of the xerogel formally occurs in three steps. The Friedman and FWO isoconversional methods and multivariate non-linear regression method are used for formal kinetic analysis. The overall decomposition process below 800 °C is fitted by three-step consecutive reaction. The best fitted model for each step is F_n (n order reaction, the corresponding function f(α) is (1 − α)ⁿ). Correlation coefficient is 0.99956. The lifetime values of xerogel at different temperatures are predicted based on non-isothermal kinetic models by the 5% decomposition of europium organic complex.     

一类具有1:-4共振奇点的复三次Lotka-Volterra系统的可积性条件

对于一类具有1:-4共振奇点的复三次Lotka-Volterra系统,通过前12阶广义奇点量的计算,给出系统可积的充分条件.这些条件通过构造积分因子或形式积分得以证明.     

适合无限维实零点定理的序域之结构II

在本文的第二部分中,我们研究了适合无限维实零点定理的序域的结构。通过嵌入,我们证明了,一个序域适合无限维实零点定理,当且仅当它的实闭包同构于域Ｒ｛Γ｝的某个具有无限维逼近性质的子域。这里Γ是一个无裂缝的可除序群,Ｒ｛Γ｝是指数在Γ中,系数为实数的形式幂级数域。     

Asymptotic Normality of a Combined Regression Estimator

In this paper, we propose a combined regression estimator by using a parametric estimator and a nonparametric estimator of the regression function. The asymptotic distribution of this estimator is obtained for cases where the parametric regression model is correct, incorrect, and approximately correct. These distributional results imply that the combined estimator is superior to the kernel estimator in the sense that it can never do worse than the kernel estimator in terms of convergence rate and it has the same convergence rate as the parametric estimator in the case where the parametric model is correct. Unlike the parametric estimator, the combined estimator is robust to model misspecification. In addition, we also establish the asymptotic distribution of the estimator of the weight given to the parametric estimator in constructing the combined estimator. This can be used to construct consistent tests for the parametric regression model used to form the combined estimator.