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

Coulomb blockade and transport in a chain of one-dimensional quantum dots

A long one-dimensional wire with a finite density of strong random impurities is modelled as a chain of weakly coupled quantum dots. At low temperature T and applied voltage V its resistance is limited by "breaks": randomly occuring clusters of quantum dots with a special length distribution pattern that inhibits the transport. Due to the interplay of interaction and disorder effects the resistance can exhibit T and V dependences that can be approximated by power laws. The corresponding two exponents differ greatly from each other and depend not only on the intrinsic electronic parameters but also on the impurity distribution statistics.Comment: 4 pages, 1 figure. Changes from v2: Dropped discussion of the high-field regime. Added discussion of mesoscopic fluctuations and multiple channels in the quasi-1D case. Improved presentation styl

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

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

LAPAROSCOPIC RECONSTRUCTION OF THE URINARY TRACT IN PATIENTS WITH URETERAL STRICTURE AFTER KIDNEY TRANSPLANTATION

Aim. Ureteral obstruction secondary to ischemia is the most common urologic complication of kidney trans- plantation. Pyeloureteral anastomosis with recipient ureter has shown most satisfactory long-term results in its management. Existing urinary infection and immunosupression determine the high risk of wound complications. We have experience more than 50 reconstructive procedures of urinary tract after kidney transplantation by open surgery during 25 years. Till last time this procedure has been performed through open surgery. Method. We used pyeloureteral anastomosis with recipient ureter in two patients with ureteral stricture after kidney transplantation by laparoscopic approach. The operations lasted 215 and 275 min respectively. In both cases the surgery was per- formed after percutaneous nephrostomy because of deterioration of transplanted kidney function. Internal stent was indwelled laparoscopicaly. No drain tube was left. Results. The nephrostomy tubes were removed after 10 and 7 days respectively. The stents were removed after 27 and 20 days respectively. No complications were seen during the surgery and postoperative period. Now serum creatinine level is 0.12 mmol/l and 0.15 mmol/l after 15 and 12 months after surgery respectively. Conclusion. In spite of some difficulties related with topographic land- marks and severe tissues fibrosis after transplantation laparoscopic pyeloureterostomy in transplanted kidney is safe and feasible procedure. The main advantage is absence of risk of most serious complications related with wound infection in immune compromised patients. Moreover, early recovery to usual activity and diet facilita- tes to prevent pulmonary infections and to normalize intestinal absorbability of the immunosuppressive drugs

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

Hall Normalization Constants for the Bures Volumes of the n-State Quantum Systems

We report the results of certain integrations of quantum-theoretic interest, relying, in this regard, upon recently developed parameterizations of Boya et al of the n x n density matrices, in terms of squared components of the unit (n-1)-sphere and the n x n unitary matrices. Firstly, we express the normalized volume elements of the Bures (minimal monotone) metric for n = 2 and 3, obtaining thereby "Bures prior probability distributions" over the two- and three-state systems. Then, as an essential first step in extending these results to n > 3, we determine that the "Hall normalization constant" (C_{n}) for the marginal Bures prior probability distribution over the (n-1)-dimensional simplex of the n eigenvalues of the n x n density matrices is, for n = 4, equal to 71680/pi^2. Since we also find that C_{3} = 35/pi, it follows that C_{4} is simply equal to 2^{11} C_{3}/pi. (C_{2} itself is known to equal 2/pi.) The constant C_{5} is also found. It too is associated with a remarkably simple decompositon, involving the product of the eight consecutive prime numbers from 2 to 23. We also preliminarily investigate several cases, n > 5, with the use of quasi-Monte Carlo integration. We hope that the various analyses reported will prove useful in deriving a general formula (which evidence suggests will involve the Bernoulli numbers) for the Hall normalization constant for arbitrary n. This would have diverse applications, including quantum inference and universal quantum coding.Comment: 14 pages, LaTeX, 6 postscript figures. Revised version to appear in J. Phys. A. We make a few slight changes from the previous version, but also add a subsection (III G) in which several variations of the basic problem are newly studied. Rather strong evidence is adduced that the Hall constants are related to partial sums of denominators of the even-indexed Bernoulli numbers, although a general formula is still lackin