Small deviation probability via chaining

We obtain several extensions of Talagrand’s lower bound for the small deviation probability using metric entropy. For Gaussian processes, our investigations are focused on processes with sub-polynomial and, respectively, exponential behaviour of covering numbers. The corresponding results are also proved for non-Gaussian symmetric stable processes, both for the cases of critically small and critically large entropy. The results extensively use the classical chaining technique; at the same time they are meant to explore the limits of this method.     

On strong and total Lagrange duality for convex optimization problems

We give some necessary and sufficient conditions which completely characterize the strong and total Lagrange duality, respectively, for convex optimization problems in separated locally convex spaces. We also prove similar statements for the problems obtained by perturbing the objective functions of the primal problems by arbitrary linear functionals. In the particular case when we deal with convex optimization problems having infinitely many convex inequalities as constraints the conditions we work with turn into the so-called Farkas-Minkowski and locally Farkas-Minkowski conditions for systems of convex inequalities, recently used in the literature. Moreover, we show that our new results extend some existing ones in the literature.     

The distribution of a generalized least squares estimator with covariance adjustment

The distribution theory is developed for a generalized least squares estimator of the growth curve model. A special case of the estimator is the maximum likelihood estimator which is weighted by the sample covariance matrix. The distribution of two conditional forms of the estimator are derived and from these its density is obtained. Two general pivots and their distributions are derived from the conditional forms and special cases of these are investigated. The results obtained are linked to carlier work.     

求条件极值的一种新方法

利用线性代数的理论方法，对多元函数求条件极值的拉格朗日乘数法加以改进，建立了求条件极值的一种新方法     

时标动力方程的稳定性分析

近来，一种称之为时标动力系统的新理论得到了蓬勃的发展. 该文给出并建立了时标动力系统的各种稳定性概念和Lyapunov稳定性准则(稳定, 一致稳定, 渐近稳定, 指数渐近稳定等等).     

The play operator on the rectifiable curves in a Hilbert space

The vector play operator is the solution operator of a class of evolution variational inequalities arising in continuum mechanics. For regular data, the existence of solutions is easily obtained from general results on maximal monotone operators. If the datum is a continuous function of bounded variation, then the existence of a weak solution is usually proved by means of a time discretization procedure. In this paper we give a short proof of the existence of the play operator on rectifiable curves making use of basic facts of measure theory. We also drop the separability assumptions usually made by other authors. Copyright © 2007 John Wiley & Sons, Ltd.     

Minimum Divergence Estimators,Maximum Likelihood and the Generalized Bootstrap

This paper states that most commonly used minimum divergence estimators are MLEs for suited generalized bootstrapped sampling schemes. Optimality in the sense of Bahadur for associated tests of fit under such sampling is considered.     

Scattering in Terms of Bohmian Conditional Wave Functions for Scenarios with Non-Commuting Energy and Momentum Operators

Without access to the full quantum state, modeling quantum transport in mesoscopic systems requires dealing with a limited number of degrees of freedom. In this work, we analyze the possibility of modeling the perturbation induced by non-simulated degrees of freedom on the simulated ones as a transition between single-particle pure states. First, we show that Bohmian conditional wave functions (BCWFs) allow for a rigorous discussion of the dynamics of electrons inside open quantum systems in terms of single-particle time-dependent pure states, either under Markovian or non-Markovian conditions. Second, we discuss the practical application of the method for modeling light–matter interaction phenomena in a resonant tunneling device, where a single photon interacts with a single electron. Third, we emphasize the importance of interpreting such a scattering mechanism as a transition between initial and final single-particle BCWF with well-defined central energies (rather than with well-defined central momenta).     

Triply bridged (1,3,5) cyclophanes from cystine and lanthionine linkers—a comparison

The condensation of benzene 1,3,5-tricarbonylchloride with cystine-di-Me [H₂N-CH(COOMe)-CH₂-S-S-CH₂-CH(COOMe)-NH₂] yielded triply bridged (1,3,5) cyclophane 1, which was shown by detailed spectral studies and molecular orbital calculations to have a D₃ symmetry with conformationally identical linkers and a spherical topology. In sharp contrast, the (1,3,5) cyclophane 2 from the rarely studied lanthionine di-Me [H₂N-CH(COOMe)-CH₂-S-CH₂-CH(COOMe)-NH₂], showed only a equatorial twofold symmetry. This work highlights the special properties of the -S-S- bridge in cystine, which makes it an exceptional synthon in nature and organic synthesis.     

An unexpected coupling reaction between isocyanides and carboxylic acids: a method for the synthesis of highly stable symmetrical and unsymmetrical alkylamidine and arylamidine carbocations

An unexpected coupling reaction between isocyanides and carboxylic acids which led to the synthesis of highly stable symmetrical and unsymmetrical alkylamidine and arylamidine carbocations under mild reaction conditions is described. The structures of these compounds were confirmed by IR, mass, ¹H NMR, ¹³C NMR, and single-crystal X-ray diffraction studies and a plausible mechanism is proposed.