Guaranteed-accuracy approximation of reachable sets for a linear dynamic system subject to impulse actions

A method is proposed for approximating the reachable set of a dynamic system with a state space dimension no higher than six-eight considered on a finite time interval. The system is governed by linear differential equations with piecewise constant coefficients and impulse actions specified at prescribed times. The method is based on guaranteed-accuracy polyhedral approximations of reachable sets at researcher-specified times. Every approximation is constructed using the preceding one. A procedure is described for choosing parameters of the method that ensure the required accuracy with close-to-minimal time costs.     

一类具无穷时滞泛函微分方程的周期解

讨论具有无穷时滞中立型泛函微分方程$ \frac{\rm d}{{\rm d}t}\left(x(t)-\int_{-\infty}^{0}g(s,x(t+s)){\rm d}s\right) =A(t,x(t))x(t)+f(t,x_t)$的周期解问题,利用重合度理论中的延拓定理得到了周期解的存在性和唯一性条件;特别地,当$g(s,x)\equiv 0, A(t,x)=A(t)$时, 给出了存在唯一稳定周期解的条件.     

Szász型算子线性组合的同时逼近

本文利用ω^2r_φλ(f,t)代替ω^r_φλ(f,t)给出了Szász-Kantorovich算子线性组合同时逼近的估计。     

Response to high acidity and basicity at a platinum electrode in chronopotentiometry

A simple and rapid method is developed to determine the high acidity and the basicity of solutions by chronopotentiometry with a platinum working electrode. The acidity range from 5.0 mol/l H⁺ to 1.0 mol/l OH⁻ can be measured by the adjustment of deposition potential and time. The response mechanism to acidity and basicity has been explored. The transition potential plateau in chronopotentiograms is caused from the oxidation of hydrogen adsorbed on electrode surface.     

傅里叶变换红外光谱固体制样技术

通过对溴化钾与纳米固体超强酸样品的比例进行了探讨 ,得出制样时溴化钾与样品比例范围为1∶ 0 .0 0 1— 1∶ 0 .0 2 9,其最佳比例范围为 1∶ 0 .0 0 98— 1∶ 0 .0 1 5 ,并且应用于其他固体样品的测定 ,结果基本一致。同时得出 ,固体样品的最少检测量为 2 .0× 1 0 -5g     

Deconvolving compactly supported densities

This paper addresses the statistical problem of density deconvolution under the condition that the density to be estimated has compact support. We introduce a new estimation procedure, which establishes faster rates of convergence for smooth densities as compared to the optimal rates for smooth densities with unbounded support. This framework also allows us to relax the usual condition of known error density with non-vanishing Fourier transform, so that a nonparametric class of densities is valid; therefore, even the shape of the noise density need not be assumed. These results can also be generalized for fast decaying densities with unbounded support. We prove optimality of the rates in the underlying experiment and study the practical performance of our estimator by numerical simulations.      

Torsors and Stacks

It is shown that the groupoid of G-torsors, suitably defined, can be used to construct a model for the stack associated to G, for arbitrary sheaves of groupoids G. This research was supported by the Natural Sciences and Engineering Research Council of Canada.     

慢速饮酒血液中酒精含量的数学模型

描述的是在一定时间内慢慢地匀速喝完一定数量酒的问题,并建立了相应的数学模型.同时也建立了快速饮酒的数学模型,以及证明了在各次饮酒后的某时刻酒精含量的可叠加性.     

Activity of TiO2 deposited by the CVD method on ammoxidized surface of a carbonaceous material in hydrogenation of styrene

Hydrogenation of styrene has been applied as a test reaction to study the catalytic activity of TiO₂ deposited by the CVD (chemical vapour deposition) method on the surface of a carbonaceous material enriched in nitrogen (C_N).     

Spectra of computable models for Ehrenfeucht theories

We construct an example of a theory with a finite (greater than one) number of isomorphism types of countable models such that its prime and saturated models have computable presentations and there exists a model which lacks in such. Supported by the Council for Grants (under RF President) and State Aid of Fundamental Science Schools via project NSh-4413.2006.1. __________ Translated from Algebra i Logika, Vol. 46, No. 3, pp. 275–289, May–June, 2007.