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

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

Finite-dimensional pointed Hopf algebras with alternating groups are trivial

It is shown that Nichols algebras over alternating groups A_m, m>4, are infinite dimensional. This proves that any complex finite dimensional pointed Hopf algebra with group of group-likes isomorphic to A_m is isomorphic to the group algebra. In a similar fashion, it is shown that the Nichols algebras over the symmetric groups S_m are all infinite-dimensional, except maybe those related to the transpositions considered in [FK], and the class of type (2,3) in S_5. We also show that any simple rack X arising from a symmetric group, with the exception of a small list, collapse, in the sense that the Nichols algebra of (X,q) is infinite dimensional, for q an arbitrary cocycle. arXiv:0904.3978 is included here.Comment: Changes in version 7: We eliminate the Subsection 3.3 and references to type C throughout the paper. We remove Lemma 3.24, Proposition 3.28 and Example 3.29 (old numbering), since they are not needed in the present paper. Several minor mistakes are corrected. The proof of Step 2 in Theorem 4.1 is adjuste

Intermolecular interactions-photophysical properties relationships in phenanthrene-9,10-dicarbonitrile assemblies

Phenanthrene-9,10-dicarbonitriles show various luminescence behaviour in solution and in the solid state. Aggregation patterns of phenanthrene-9,10-dicarbonitriles govern their luminescent properties in the solid state. Single crystal structures of phenanthrene-9,10-dicarbonitriles showed head-to-tail intraplane (or quasi-intraplane) intermolecular interactions and π-stacking patterns with eclipsing of molecules when viewed orthogonal to the stacking plane. The π-stacking interactions were detected in the X-ray structures of phenanthrene-9,10-dicarbonitriles and studied by DFT calculations at the M06–2X/6–311++G(d,p) level of theory and topological analysis of the electron density distribution within the framework of QTAIM method. The estimated strength of the C⋯C contacts responsible for the π-stacking interactions is 0.6–1.1 kcal/mol. The orientation of molecules in crystals depends on the substituents in phenanthrene-9,10-dicarbonitriles. Distinct molecular orientation and packing arrangements in crystalline phenanthrene-9,10-dicarbonitriles ensured perturbed electronic communication among the nearest and non-nearest molecules through an interplay of excimer and dipole couplings. As a result, the intermolecular interactions govern the solid state luminescence of molecules

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

Quenched chiral logarithms in lattice QCD with exact chiral symmetry

We examine quenched chiral logarithms in lattice QCD with overlap Dirac quark. For 100 gauge configurations generated with the Wilson gauge action at $\beta = 5.8$ on the $8^3 \times 24$ lattice, we compute quenched quark propagators for 12 bare quark masses. The pion decay constant is extracted from the pion propagator, and from which the lattice spacing is determined to be 0.147 fm. The presence of quenched chiral logarithm in the pion mass is confirmed, and its coefficient is determined to be $\delta = 0.203 \pm 0.014$, in agreement with the theoretical estimate in quenched chiral perturbation theory. Further, we obtain the topological susceptibility of these 100 gauge configurations by measuring the index of the overlap Dirac operator. Using a formula due to exact chiral symmetry, we obtain the $\eta'$ mass in quenched chiral perturbation theory, $m_{\eta'} = (901 \pm 64)$ Mev, and an estimate of $\delta = 0.197 \pm 0.027$, which is in good agreement with that determined from the pion mass.Comment: 24 pages, 6 EPS figures; v2: some clarifications added, to appear in Physical Review

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