An inequality for the distance between densities of free convolutions

This paper contributes to the study of the free additive convolution of probability measures. It shows that under some conditions, if measures $\mu_i$ and $\nu_i, i=1,2$, are close to each other in terms of the L\'{e}vy metric and if the free convolution $\mu_1\boxplus\mu_2$ is sufficiently smooth, then $\nu_1\boxplus\nu_2$ is absolutely continuous, and the densities of measures $\nu_1\boxplus\nu_2$ and $\mu_1\boxplus\mu_2$ are close to each other. In particular, convergence in distribution $\mu_1^{(n)}\rightarrow \mu_1,$ $\mu_2^{(n)}\rightarrow\mu_2$ implies that the density of $\mu_1^{(n)}\boxplus\mu_2^{(n)}$ is defined for all sufficiently large $n$ and converges to the density of $\mu_1\boxplus\mu_2$. Some applications are provided, including: (i) a new proof of the local version of the free central limit theorem, and (ii) new local limit theorems for sums of free projections, for sums of $\boxplus$-stable random variables and for eigenvalues of a sum of two $N$-by-$N$ random matrices.Comment: Published in at http://dx.doi.org/10.1214/12-AOP756 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Curve forecasting by functional autoregression

Data in which each observation is a curve occur in many applied problems. This paper explores prediction in time series in which the data is generated by a curve-valued autoregression process. It develops a novel technique, the predictive factor decomposition, for estimation of the autoregression operator, which is designed to be better suited for prediction purposes than the principal components method. The technique is based on finding a reduced rank approximation to the autoregression operator that minimizes the norm of the expected prediction error. Implementing this idea, we relate the operator approximation problem to an eigenvalue problem for an operator pencil that is formed by the cross-covariance and covariance operators of the autoregressive process. We develop an estimation method based on regularization of the empirical counterpart of this eigenvalue problem, and prove that with a certain choice of parameters, the method consistently estimates the predictive factors. In addition, we show that forecasts based on the estimated predictive factors converge in probability to the optimal forecasts. The new method is illustrated by an analysis of the dynamics of the term structure of Eurodollar futures rates. We restrict the sample to the period of normal growth and find that in this subsample the predictive factor technique not only outperforms the principal components method but also performs on par with the best available prediction methods

Viscoelastic response of contractile filament bundles

The actin cytoskeleton of adherent tissue cells often condenses into filament bundles contracted by myosin motors, so-called stress fibers, which play a crucial role in the mechanical interaction of cells with their environment. Stress fibers are usually attached to their environment at the endpoints, but possibly also along their whole length. We introduce a theoretical model for such contractile filament bundles which combines passive viscoelasticity with active contractility. The model equations are solved analytically for two different types of boundary conditions. A free boundary corresponds to stress fiber contraction dynamics after laser surgery and results in good agreement with experimental data. Imposing cyclic varying boundary forces allows us to calculate the complex modulus of a single stress fiber.Comment: Revtex with 24 pages, 7 Postscript figures included, accepted for publication in Phys. Rev.

Method of Computer-aided Instruction in Situation Control Systems

The article considers the problem of computer-aided instruction in context-chain motivated situation control system of the complex technical system behavior. The conceptual and formal models of situation control with practical instruction are considered. Acquisition of new behavior knowledge is presented as structural changes in system memory in the form of situational agent set. Model and method of computer-aided instruction represent formalization, based on the nondistinct theories by physiologists and cognitive psychologists.The formal instruction model describes situation and reaction formation and dependence on different parameters, effecting education, such as the reinforcement value, time between the stimulus, action and the reinforcement. The change of the contextual link between situational elements when using is formalized.The examples and results of computer instruction experiments of the robot device “LEGO MINDSTORMS NXT”, equipped with ultrasonic distance, touch, light sensors

Research of Geopolymer Foam Concrete on the Base of the Wastes Produced By Kemerovo Heat and Power Enterprises

The article shows the results of the research on geopolymer foam concrete production on the base of the wastes of Kemerovo heat and power enterprises. Relationships between the compression strength and average density of geopolymer foam concrete and the alkaline activator amount, alkaline concentration, foaming agent amount and duration of the blend mechanical activation were determined. It was found out that being in its optimal composition the material obtained has strength 2.0-3.5 MPa under density from 350 up to 500 kg/m3. Infusion of the developed construction material on the basis of the industrial wastes will allow to change more expensive construction materials on the cement base and provide the utilization of the industrial wastes

Electrosynthesis of tetraethylsilane from elemental silicon

Electrolysis of alkylation reagents at silicon-containing electrodes results in alkylsilanes in both cathodic and anodic processes. A mechanism for the reaction is proposed. © 1995, Plenum Publishing Corporation. All rights reserved

Electrochemical Version of the Knorr Reaction

Electrochemical reduction of ethyl 2-hydroxyimino-3-oxobutanoate in acetic acid in the presence of sodium acetate requires four electrons per molecule and yields an intermediate amino derivative, whose condensation with ethyl acetoacetate affords diethyl 2,4-dimethylpyrrol-3,5-dicarboxylate. The substance-based yields of the pyrrol are 74% at a steel cathode, 72% at a nickel cathode, 68% at a platinum cathode, 67% at a lead cathode, and 63% at a copper cathode. Electrolysis conditions: current density 120 mA/cm2; amount of electricity 161 A h per mol of the initial compound; 95°C. With an amount of electricity of 107 A h per mol of the initial compound, the yield of diethyl 2,4-dimethylpyrrole-3,5-dicarboxylate at a steel cathode increases from 37 to 73% in the temperature range from 40 to 105°C. The process can be regarded as an electrochemical version of the Knorr synthesis

СИЛОВЫЕ УСЛОВИЯ ПРЕССОВАНИЯ ЛЕГКОСПЛАВНЫХ БУРИЛЬНЫХ ТРУБ СО СПИРАЛЬНЫМ ОРЕБРЕНИЕМ

Following I.L. Perlin’s technique based on active and reactive forces balance, the formula was suggested to calculate extrusion force for spiral-finned drill pipes. The spiral pipe cross section was regarded as a smooth tube with a screw arrangement of metal fibers and external spiral fins. A component introducing energy spent for the screw motion of metal was added to the formula. It was shown that the extrusion force obtained by the modified formula is 28 % higher than the same for a smooth pipe of equal area. It was discovered that the increase of fin helix angle leads to the increase of force compared to that of longitudinally finned pipes. На основе методики И.Л. Перлина, основанной на балансе активных и реактивных сил, предложено уравнение для расчета усилия прессования бурильных труб со спиральным оребрением. Поперечное сечение спиральной трубы представлено в виде гладкой трубы с винтовым расположением волокон металла и внешних спиральных ребер. В формулу добавлена составляющая, учитывающая энергию, затрачиваемую на винтовое движение металла. Показано, что усилие прессования, полученное по модернизированной формуле, на 28 % больше, чем для равновеликой по площади гладкой трубы. Выявлено, что увеличение угла подъема спирали ребер приводит к росту усилия по сравнению с таковым для продольно-оребренных труб.

РАСПРЕДЕЛЕНИЕ КОНТАКТНЫХ НАПРЯЖЕНИЙ В ПРОЦЕССЕ ВОЛОЧЕНИЯ КРУГЛЫХ ИЗДЕЛИЙ

The computer simulation of contact stresses in the course of round product drawing through conical draw dies has been carried out by the finite element method with the DEFORM-2D particularized bundled software.Приведены результаты компьютерного моделирования контактных напряжений при волочении круглых изделий в конические волоки с помощью метода конечных элементов в специализированном программном комплексе DEFORM-2D