Calculation of rate on the interphase surface in turbulent gas-liquid flows

Equations for the calculation of liquid rate on the interface in two-phase turbulent systems are derived on the base of momentum balance in boundary layer at the given law of turbulent pulsations damping in a liquid sublayer. The equations are tested for the cases of strigth-flow axial and twisted motion of dispersed-circular flows in cylindrical tubes as well as of gas(vapour)-liquid layer on mass exchange plates. The results of calculations are in a good agreement with experimental data

Lieb-Thirring inequalities for geometrically induced bound states

We prove new inequalities of the Lieb-Thirring type on the eigenvalues of Schr\"odinger operators in wave guides with local perturbations. The estimates are optimal in the weak-coupling case. To illustrate their applications, we consider, in particular, a straight strip and a straight circular tube with either mixed boundary conditions or boundary deformations.Comment: LaTeX2e, 14 page

Critical sound attenuation in a diluted Ising system

The field-theoretic description of dynamical critical effects of the influence of disorder on acoustic anomalies near the temperature of the second-order phase transition is considered for three-dimensional Ising-like systems. Calculations of the sound attenuation in pure and dilute Ising-like systems near the critical point are presented. The dynamical scaling function for the critical attenuation coefficient is calculated. The influence of quenched disorder on the asymptotic behaviour of the critical ultrasonic anomalies is discussed.Comment: 12 RevTeX pages, 4 figure

Eigenvalue bounds for Schr\"odinger operators with a homogeneous magnetic field

We prove Lieb-Thirring inequalities for Schr\"odinger operators with a homogeneous magnetic field in two and three space dimensions. The inequalities bound sums of eigenvalues by a semi-classical approximation which depends on the strength of the magnetic field, and hence quantifies the diamagnetic behavior of the system. For a harmonic oscillator in a homogenous magnetic field, we obtain the sharp constants in the inequalities.Comment: 12 page

Цифровая трансформация инструментов управления современными корпорациями: состояние и пути развития

The subject. Digital technologies have been integrated into all aspects of public life, including politics, law, finance, business, education, science, and society. Yet, digitalization exerts an even greater impact on the economy, which should prompt the State, represented by its legislative and executive bodies, to take timely action to ensure the legal regulation of diverse aspects of the digital economy. Digital transformation of the economy has redefined the approaches to the issues of legal capacity, corporate governance and management of business processes. Traditional management mechanisms are no longer competitive, unless used in conjunction with dynamically developing digital technologies.This article explores the issues related to digital legal personality of a corporation (online registration (e-residency) of corporations and the digital footprint that companies leave in public registers), digital corporate governance, and discuss the operation of digital corporations, including networked and decentralized autonomous organizations. The authors distinguish three types of digital corporate governance: remote management (exercised by human individuals), smart management (based on algorithms designed by human engineers), and artificial intelligence (AI) management (that does not require human involvement). Some tools of digital corporation management are illustrated, replacing traditional forms of management of the human cognitive system. Finally, we provide an overview of the operational characteristics of decentralized autonomous organizations.Purpose of the research. This article is devoted to the transformation of management tools for modern corporations in the digital economy. In order to comply with the Russian corporate legislation of the existing digital reality, it is necessary to develop a comprehensive scientific and legal concept of corporate governance, ensuring the balance and protection of the rights and legitimate interests of all participants in corporate relations and others related to corporate relations, as well as increasing the transparency and efficiency of corporations.Methodology. The methodology of this study was based on the following methods of scientific knowledge: general scientific empirical methods (observation (over the course of development of the use of digital technologies in corporate law), comparison (of the effectiveness of the use of digital technologies in corporate law of different countries)); methods of theoretical knowledge (analysis (of advantages and disadvantages of digitalization of individual institutions of corporate law), formal legal method (in the formulation and research of various concepts, determination of their characteristics and classification), theoretical modeling (of the prospects and areas of possible application of digital technologies in corporate law).The main results. Digitalization of corporate management is bound to increase business profitability and improve competitiveness on the market. We believe that in the coming years science will have to tackle the issues of assessing the implications of the introduction of digital technologies, determining technical, economic and legal prerequisites for their implementation, and identifying their limits. In addition, issues related to professional training / retraining of personnel capable of working with modern technologies are of importance.Conclusions. The authors came to the conclusion that the main direction of improving corporate legislation in the context of digitalization is currently the creation and provision of conditions for effective interaction between corporate actors and persons directly associated with them in the digital environment.Развитие и активное внедрение информационных технологий в современную экономику потребовало оценки трансформации сознания цифрового общества. Цифровая трансформация экономики изменила подходы к вопросу правоспособности, управления корпорациями и бизнес-процессами. Традиционные механизмы управления утрачивают свою конкурентоспособность при их использовании в отрыве от динамично развивающихся цифровых технологий.В статье исследуются вопросы, связанные с цифровой правосубъектностью корпорации (онлайн-регистрация корпораций (электронное (цифровое) резидентство корпораций), а также «цифровой отпечаток» компании в публичных реестрах), цифровым корпоративным управлением, а также деятельностью непосредственно цифровых (сетевых или децентрализованных автономных организаций) корпораций. Выделяются три типа цифрового корпоративного управления: дистанционное управление (с участием человека), смарт-управление (по алгоритмам, установленным человеком) и управление искусственным интеллектом (без участия человека). Иллюстрируются отдельные инструменты цифрового управления корпорацией, вытесняющие традиционные формы управления когнитивной системой человека. Раскрываются особенности функционирования децентрализованных автономных организаций

Lower order terms in Szego type limit theorems on Zoll manifolds

This is a detailed version of the paper math.FA/0212273. The main motivation for this work was to find an explicit formula for a "Szego-regularized" determinant of a zeroth order pseudodifferential operator (PsDO) on a Zoll manifold. The idea of the Szego-regularization was suggested by V. Guillemin and K. Okikiolu. They have computed the second term in a Szego type expansion on a Zoll manifold of an arbitrary dimension. In the present work we compute the third asymptotic term in any dimension. In the case of dimension 2, our formula gives the above mentioned expression for the Szego-redularized determinant of a zeroth order PsDO. The proof uses a new combinatorial identity, which generalizes a formula due to G.A.Hunt and F.J.Dyson. This identity is related to the distribution of the maximum of a random walk with i.i.d. steps on the real line. The proof of this combinatorial identity together with historical remarks and a discussion of probabilistic and algebraic connections has been published separately.Comment: 39 pages, full version, submitte

Long-term glycemic control and factors, associated with response to pump insulin therapy in children

Background: In recent years, pump-based insulin therapy, also known as continuous subcutaneous insulin infusion (CSII), has become a common treatment for children with type 1 diabetes mellitus (T1DM). Despite the fact that, in general, children with type 1 diabetes achieve the best glycemic control indices during pump therapy, while there is a significant heterogeneity of metabolic outcomes among individual patients, many children with CSII do not reach the target level of HbA1c.Objective: To assess the level of glycemic control and factors associated by withdrawal of use, the response to treatment with prolonged use of CSII in children with type 1 diabetes.Materials and methods: The study included 458 children aged 1 to 18 years, treated to pump therapy at least 3 years before the study, the presence of the analyzed data in the register.Results: The level of HbA1c decreased by -0.7% compared with the primary endpoint, which was accompanied by an increase in the number of patients who reached the target level of HbA1c (<7.5%) from 17% to 36%. The best response was observed for patients under 6 years of age with HbA1c over 9% for pump insulin therapy, as well as in patients who regularly use additional bolus and basal functions and CGM. The main reason for stopping the use of the insulin pump is the inconvenience of using and wearing — 47.7%. Risk factors for pump abandonment: later age of start treatment on CSII and frequent episodes of severe hypoglycemia.Conclusion: According to the results of the study, it was shown that pump therapy is an effective method of insulin therapy, which allows to achieve a lower level of HbA1c compared to the initial values

Upper and lower limits on the number of bound states in a central potential

In a recent paper new upper and lower limits were given, in the context of the Schr\"{o}dinger or Klein-Gordon equations, for the number $N_{0}$ of S-wave bound states possessed by a monotonically nondecreasing central potential vanishing at infinity. In this paper these results are extended to the number $N_{\ell}$ of bound states for the $\ell$-th partial wave, and results are also obtained for potentials that are not monotonic and even somewhere positive. New results are also obtained for the case treated previously, including the remarkably neat \textit{lower} limit $N_{\ell}\geq \{\{[\sigma /(2\ell+1)+1]/2\}\}$ with $V(r)| ^{1/2}]$ (valid in the Schr\"{o}dinger case, for a class of potentials that includes the monotonically nondecreasing ones), entailing the following \textit{lower} limit for the total number $N$ of bound states possessed by a monotonically nondecreasing central potential vanishing at infinity: N\geq \{\{(\sigma+1)/2\}\} {(\sigma+3)/2\} \}/2 (here the double braces denote of course the integer part).Comment: 44 pages, 5 figure

Experimental study of direct photon emission in K- --> pi- pi0 gamma decay using ISTRA+ detector

The branching ratio in the charged-pion kinetic energy region of 55 to 90 MeV for the direct photon emission in the K- --> pi- pi0 gamma decay has been measured using in-flight decays detected with the ISTRA+ setup operating in the 25 GeV/c negative secondary beam of the U-70 PS. The value Br(DE)=[0.37+-0.39(stat)+-0.10(syst)]*10^(-5) obtained from the analysis of 930 completely reconstructed events is consistent with the average value of two stopped-kaon experiments, but it differs by 2.5 standard deviations from the average value of three in-flight-kaon experiments. The result is also compared with recent theoretical predictions.Comment: 13 pages, 8 figure