An improvement of the Berry--Esseen inequality with applications to Poisson and mixed Poisson random sums

By a modification of the method that was applied in (Korolev and Shevtsova, 2009), here the inequalities $$\rho(F_n,\Phi)\le\frac{0.335789(\beta^3+0.425)}{\sqrt{n}}$$ and $$\rho(F_n,\Phi)\le \frac{0.3051(\beta^3+1)}{\sqrt{n}}$$ are proved for the uniform distance $\rho(F_n,\Phi)$ between the standard normal distribution function $\Phi$ and the distribution function $F_n$ of the normalized sum of an arbitrary number $n\ge1$ of independent identically distributed random variables with zero mean, unit variance and finite third absolute moment $\beta^3$. The first of these inequalities sharpens the best known version of the classical Berry--Esseen inequality since $0.335789(\beta^3+0.425)\le0.335789(1+0.425)\beta^3<0.4785\beta^3$ by virtue of the condition $\beta^3\ge1$, and 0.4785 is the best known upper estimate of the absolute constant in the classical Berry--Esseen inequality. The second inequality is applied to lowering the upper estimate of the absolute constant in the analog of the Berry--Esseen inequality for Poisson random sums to 0.3051 which is strictly less than the least possible value of the absolute constant in the classical Berry--Esseen inequality. As a corollary, the estimates of the rate of convergence in limit theorems for compound mixed Poisson distributions are refined.Comment: 33 page

Beam propagation in a Randomly Inhomogeneous Medium

An integro-differential equation describing the angular distribution of beams is analyzed for a medium with random inhomogeneities. Beams are trapped because inhomogeneities give rise to wave localization at random locations and random times. The expressions obtained for the mean square deviation from the initial direction of beam propagation generalize the "3/2 law".Comment: 4 page

LABOR PRODUCTIVITY AS A PRODUCTION EFFICIENCY FACTOR

El objetivo de esta investigación es estudiar el factor de eficiencia y la productividad laboral. En gran medida, el nivel de productividad laboral creció debido a la intensificación de la producción. Al mismo tiempo, según Rosstat, en agricultura, silvicultura y pesca solo hay un 8% de empleos altamente eficientes. Por lo tanto, el factor de intensificación de la producción se utiliza de manera insignificante. Es obvio que hay una necesidad de un componente innovador del crecimiento de la productividad laboral, por un lado, y la creación de nuevos empleos en las zonas rurales para los recursos laborales liberados, por otro lado. Aquí es necesario determinar los principales factores que afectan la productividad en las condiciones modernas, y justificar las propuestas para mejorarla.Of the goal of this investigation is to study the efficiency factor and labor productivity. To a large extent, the level of labor productivity grew due to the intensification of production. At the same time, according to Rosstat, in agriculture, forestry and fisheries there are only 8% of high-efficient jobs. Thus, the factor of production intensification is used insignificantly. It is obvious that there is a need for an innovative component of labor productivity growth on the one hand, and the creation of new jobs in rural areas for the released labor resources, on the other hand. Here it is necessary to determine the main factors affecting productivity in modern conditions, and to justify proposals to improve it.O objetivo desta investigação é estudar o fator de eficiência e a produtividade do trabalho. Em grande medida, o nível de produtividade do trabalho aumentou devido à intensificação da produção. Ao mesmo tempo, segundo Rosstat, na agricultura, silvicultura e pesca, existem apenas 8% dos empregos de alta eficiência. Assim, o fator de intensificação da produção é usado de forma insignificante. É óbvio que é necessário um componente inovador do crescimento da produtividade do trabalho, por um lado, e a criação de novos empregos nas áreas rurais para os recursos liberados, por outro. Aqui é necessário determinar os principais fatores que afetam a produtividade nas condições modernas e justificar propostas para melhorá- la

Итерационная томография труб в процессе эксплуатации

The pipe wall thickness was estimated based on three-dimensional images of the pipe recovered from several X-ray projections, which were made in a limited angle of view. Since the effects of scattered radiation and beam hardening are up to 50 % of the main radiation, ignoring them leads to blur of the image and inaccuracy in determining dimensions. To restore pipe images from projections, a volume and/or shell representation of the pipe is used, as well as iterative Bayesian methods. Using these methods, the error in estimating the pipe wall thickness from the projection data can be equal to or less than 300 μm. It has been shown that standard X-ray projections on the film or imaging plates used to obtain data can be used to restore pipe wall thickness profiles in factory conditions.Проведена оценка толщины стенки трубы, исходя из трехмерных изображений трубы, восстановленных из нескольких рентгеновских проекций, которые были выполнены в ограниченном угле обзора. Поскольку эффекты рассеянного излучения и ужесточения лучей составляют до 50 % от основного излучения, их игнорирование приводит к размытию изображения и неточности при определении размеров. Для восстановления изображений труб из проекций применяются объемное и/или оболочечное представление трубы, а также итеративные байесовские методы. При использовании этих методов ошибка оценки толщины стенки трубы из проекционных данных может быть равной или меньше 300 мкм. Показано, что полученные рентгеновским излучением стандартные проекции на пленке или визуализирующих пластинах, применяемых для получения данных, могут использоваться для восстановления профилей толщин стенок труб в заводских условиях

The U.S.-Russia Joint Threat Assessment of Nuclear Terrorism

Nuclear terrorism is a real and urgent threat. Given the potentially catastrophic consequences, even a small probability of terrorists getting and detonating a nuclear bomb is enough to justify urgent action to reduce the risk. Al-Qaeda and North Caucasus terrorist groups have both made statements indicating that they seek nuclear weapons and have attempted to acquire them; these groups are presented together as a case study to assess nuclear terrorism as a present and future threat. (The only other terrorist group known to have systematically sought to get nuclear weapons was the Japanese cult group Aum Shinrikyo.) This study makes the case that it is plausible that a technically sophisticated group could make, deliver, and detonate a crude nuclear bomb if it could obtain sufficient fissile material. The study offers recommendations for actions to reduce this danger

Investigation of new modification strategies for PVA membranes to improve their dehydration properties by pervaporation

International audienceNovel supported membranes based on polyvinyl alcohol (PVA) were developed using two strategies: first, by the modification of the PVA network, via so-called bulk modification, with the formation of the selective layer accomplished through the introduction of fullerenol and/or poly(allylamine hydrochloride), and second, by the functionalization of the surface with successive depositions of multilayered films of polyelectrolytes, such as poly(allylamine hydrochloride) and poly(sodium 4-styrenesulfonate) on the PVA surface. The membrane surface modifications were characterized by scanning electron microscopy and contact angle measurements. The modified PVA membranes were examined for their dehydration transport properties by the perva-poration of isopropyl alcohol-water (80/20% w/w), which was chosen as a model mixture. Compared with the pristine PVA membrane, the main improvement was a marked increase in permeance. It was found that the surface modifications mainly gave rise to a higher global flux but with a strong reduction in selectivity. Only the combination of both bulk and surface modifications with PEL could significantly increase the flux with a high water content in the permeate (over 98%). Lastly, it should be noted that this study developed a green procedure to prepare innovative membrane layers for dehydration, making use of only water as a working medium

Steady-State L\'evy Flights in a Confined Domain

We derive the generalized Fokker-Planck equation associated with a Langevin equation driven by arbitrary additive white noise. We apply our result to study the distribution of symmetric and asymmetric L\'{e}vy flights in an infinitely deep potential well. The fractional Fokker-Planck equation for L\'{e}vy flights is derived and solved analytically in the steady state. It is shown that L\'{e}vy flights are distributed according to the beta distribution, whose probability density becomes singular at the boundaries of the well. The origin of the preferred concentration of flying objects near the boundaries in nonequilibrium systems is clarified.Comment: 10 pages, 1 figur

Parameters of the fractional Fokker-Planck equation

We study the connection between the parameters of the fractional Fokker-Planck equation, which is associated with the overdamped Langevin equation driven by noise with heavy-tailed increments, and the transition probability density of the noise generating process. Explicit expressions for these parameters are derived both for finite and infinite variance of the rescaled transition probability density.Comment: 5 page

Structural data of phenanthrene-9,10-dicarbonitriles

In this data article, we present the single-crystal XRD data of phenanthrene-9,10-dicarbonitriles. Detailed structure analysis and photophysical properties were discussed in our previous study, "Intermolecular interactions-photophysical properties relationships in phenanthrene-9,10-dicarbonitrile assemblies" (Afanasenko et al., 2020). The data include the intra- and intermolecular bond lengths and angles. (c) 2019 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)

Linear Relaxation Processes Governed by Fractional Symmetric Kinetic Equations

We get fractional symmetric Fokker - Planck and Einstein - Smoluchowski kinetic equations, which describe evolution of the systems influenced by stochastic forces distributed with stable probability laws. These equations generalize known kinetic equations of the Brownian motion theory and contain symmetric fractional derivatives over velocity and space, respectively. With the help of these equations we study analytically the processes of linear relaxation in a force - free case and for linear oscillator. For a weakly damped oscillator we also get kinetic equation for the distribution in slow variables. Linear relaxation processes are also studied numerically by solving corresponding Langevin equations with the source which is a discrete - time approximation to a white Levy noise. Numerical and analytical results agree quantitatively.Comment: 30 pages, LaTeX, 13 figures PostScrip