Group classification of the Sachs equations for a radiating axisymmetric, non-rotating, vacuum space-time

We carry out a Lie group analysis of the Sachs equations for a time-dependent axisymmetric non-rotating space-time in which the Ricci tensor vanishes. These equations, which are the first two members of the set of Newman-Penrose equations, define the characteristic initial-value problem for the space-time. We find a particular form for the initial data such that these equations admit a Lie symmetry, and so defines a geometrically special class of such spacetimes. These should additionally be of particular physical interest because of this special geometric feature.Comment: 18 Pages. Submitted to Classical and Quantum Gravit

Group Analysis of the Novikov Equation

We find the Lie point symmetries of the Novikov equation and demonstrate that it is strictly self-adjoint. Using the self-adjointness and the recent technique for constructing conserved vectors associated with symmetries of differential equations, we find the conservation law corresponding to the dilations symmetry and show that other symmetries do not provide nontrivial conservation laws. Then we investigat the invariant solutions

Reconstruction of Structured Quadratic Pencils from Eigenvalues on Ellipses and Parabolas

In the present paper we study the reconstruction of a structured quadratic pencil from eigenvalues distributed on ellipses or parabolas. A quadratic pencil is a square matrix polynomial QP(λ) = M λ2+Cλ +K, where M, C, and K are real square matrices. The approach developed in the paper is based on the theory of orthogonal polynomials on the real line. The results can be applied to more general distribution of eigenvalues. The problem with added single eigenvector is also briefly discussed. As an illustration of the reconstruction method, the eigenvalue problem on linearized stability of certain class of stationary exact solution of the Navier-Stokes equations describing atmospheric flows on a spherical surface is reformulated as a simple mass-spring system by means of this method

Heavy tails and upper-tail inequality: The case of Russia

© 2017 The Author(s)Motivated, in part, by the recent surge of interest in robust inequality measurement, cross-country inequality comparisons, applications of heavy-tailed distributions and the study of global and upper-tail inequality, this paper focuses on robust analysis of heavy-tailedness properties and inequality in the upper tails of income distribution in Russia, as measured, mainly, by its tail indices. The study is based on recently developed approaches to robust inference on the degree of heavy-tailedness and their implications for the analysis of upper-tail inequality discussed in the paper. Among other results, the paper provides robust estimates of heavy-tailedness parameters and tail indices for Russian income distribution and their comparisons with the benchmark values in developed economies reported in the previous literature. The estimates point out to important similarity between heavy-tailedness properties of income distribution and their implications for the analysis of upper-tail income inequality in Russia and those in developed markets

A symmetry classification for a class of (2+1)-nonlinear wave equation

In this paper, a symmetry classification of a $(2+1)$-nonlinear wave equation $u_{tt}-f(u)(u_{xx}+u_{yy})=0$ where $f(u)$ is a smooth function on $u$, using Lie group method, is given. The basic infinitesimal method for calculating symmetry groups is presented, and used to determine the general symmetry group of this $(2+1)$-nonlinear wave equation

Избыточная созданная ценность как метрика результативности и ее определение посредством показателя TEVA

The paper explores the excess value created (EVC) metric, which is an aggregated measure of the financial performance of a company over a multi-period measurement interval. The relevance of the study is due to the demand for practical solutions in the field of financial performance monitoring and incentive compensation, which makes it possible to achieve congruence between the interests of shareholders and the decisions of managers. The aim of the study is to build and justify a periodic financial measure that takes into account not only the current result but also the long-term consequences of management decisions. The scientific novelty of the study lies in the determination of the EVC metric via the TEVA indicator and providing the rationale for the new design of the performance measure. The result of the study is the derivation of formulas for calculating the EVC measure on multi-period and one-period intervals, which are free from restrictions on changes in the capital structure and the cost of capital, allow for a time-varying systematic risk of operating activities and possess the advantage of computational simplicity important for practical applications. The study concludes that the measurement of value created using the EVC indicator determined via TEVA makes it possible to achieve close conformity of the metric constructed to the real-world conditions with the unification of calculations in its retrospective and forecast components based on data available from historical and Pro Forma financial statements and information from the capital market.Автор исследует показатель избыточной созданной ценности (EVC), являющейся агрегированной мерой финансовой результативности деятельности компании на многопериодном интервале измерения. Актуальность исследования обусловлена востребованностью практических решений в сфере контроля результативности и материального стимулирования, позволяющих достичь согласованности между интересами акционеров и решениями менеджеров. Целью исследования является построение и обоснование периодического финансового измерителя, учитывающего не только текущий результат, но и долгосрочные последствия решений менеджмента. Научная новизна исследования состоит в определении показателя EVC посредством показателя TEVA и обосновании новой конструкции измерителя результативности. Результатом исследования является вывод формул для расчета показателя EVC на многопериодном и однопериодном интервалах, свободных от ограничений на изменение структуры и стоимости капитала, допускающих изменяющийся во времени систематический риск операционной деятельности и имеющих преимущество вычислительной простоты, важное для практических применений. Сделан вывод, что измерение созданной ценности с помощью показателя EVС, определенного посредством TEVA, позволяет достичь близкого соответствия построенной метрической конструкции условиям реального мира с унификацией расчетов в ее ретроспективной и прогнозной составляющих на основе данных, доступных из исторической и Pro Forma финансовой отчетности, и информации рынка капитала