COMPENSATION OF THE EFFECTS OF SOUND PROPAGATION CHANNEL IN UNDERWATER ACOUSTIC SYSTEMS

Состояние гидроакустического канала распространения звука зависит от множества случайных факторов среды. Для учета влияния такого канала на передаваемый сигнал может использоваться метод линейной фильтрации, в рамках которого канал представляется в виде линейной инвариантной системы с аддитивным гауссовским шумом, где связь между сигналами на входе и выходе описывается импульсной характеристикой. Необходимыми условиями эффективности применения данного метода являются выбор входного сигнала и оценка весовых коэффициентов используемой системы, что в работе выполнено на основе теоремы Гаусса–Маркова. При решении задачи получены несмещенные оценки с минимальной дисперсией, в том числе для случая применения в качестве входного сигнала псевдослучайной последовательности. Предложен метод компенсации влияния канала с учетом знания его импульсной характеристики, позволяющий уменьшать уровень шумовой составляющей. The state of the underwater acoustic channel depends on a variety of random factors of the media. Estimation of the influence of such channel on the transmitting signal can be performed by the method of linear filtration. It considers channel as a linear non-variant system with additive Gaussian noise, where the relation between input and output signals is described by impulse response. The necessary condition of efficient implementation of this method is the selection of valid input signals and estimation of the weight coefficient of the implemented system, which was performed using Gauss–Markov theorem in the present work. Following the results of solving the problem, the minimum variance unbiased estimates were obtained, including the case of using the pseudorandom sequence as an input signal. At long last, the paper presents the method of channel influence compensation with consideration of known impulse response, which allows reducing the level of the noise component.

Falsifcation of Financial Statements: Concept and Tools of Identifcation

To succeed in a market economy an economic entity should attract investments. The quality of accounting and analytical information about a company’s activities is an important factor in the decisions potential investors make. Accounting (fnancial) reporting is a signifcant part of the informational support of the company’s activity. The problem of reliability of the accounting (fnancial) statements has always been relevant. According to the modern concept of business audit, audit is primarily understood as an activity aimed at reducing business risks. Nowadays the main task of an auditor is to provide assurance that the accounting (fnancial) reporting does not contain signifcant misstatements because of its falsifcation, or mistakes made by employees of the auditee. Assessing the risk of fnancial statements falsifcation is an urgent and diffcult task. Though the term “falsifcation of fnancial statements” is widely used and seems clear in terms of common sense, the scientifc understanding and normative defnition of this concept is not so defnite. This article analyzes the concept of “falsifcation of fnancial statements” and approaches to its defnition in foreign and domestic practice; reviews modern tools to identify risks of fnancial statements falsifcation; discusses issues related to the use of mathematical models to identify the risk of fnancial statements falsifcation. To do this the authors analyze the index model of the American scientist M. Benish, carry out econometric tests within the assumptions of the Gauss-Markov theorem and propose a variant of developing an index model to detect accounting (fnancial) statements falsifcation. An attempt was made to create a model to identify the risk of reporting information falsifcation with a certain degree of probability that could be applied in Russia. To create such a model, called NARM, there were selected 75 reports of Russian organizations, of which 1/3 were falsifed. This model makes it possible to identify the probability of fnancial statements falsifcation to within 76%.

Regression Analysis

This chapter teaches how to use R to conduct regression analysis to answer the question: Does trade promote economic growth? It demonstrates how to specify a statistical model from a theoretical argument, prepare data, estimate and interpret the statistical model, and use the estimated results to make inferences and answer the question of interest. More specifically, it discusses the logic of regression analysis, the relationship between population and sample regression models, how to estimate a regression model in theory and practice, the estimation of sample regression model using OLS (ordinary least squares), the interpretation of estimation results, the statistical inference in regression analysis using hypothesis testing and confidence interval, the types of sum of squares and overall model fit, and how to report the model results. The validity of regression analysis is contingent upon the assumptions of the Gauss-Markov theorem being met.

The Markov theorems for spatial graphs and handlebody-knots with Y-orientations

We establish the Markov theorems for spatial graphs and handlebody-knots. We introduce an IH-labeled spatial trivalent graph and develop a theory on it, since both a spatial graph and a handlebody-knot can be realized as the IH-equivalence classes of IH-labeled spatial trivalent graphs. We show that any two orientations of a graph without sources and sinks are related by finite sequence of local orientation changes preserving the condition that the graph has no sources and no sinks. This leads us to define two kinds of orientations for IH-labeled spatial trivalent graphs, which fit a closed braid, and is used for the proof of the Markov theorem. We give an enhanced Alexander theorem for orientated tangles, which is also used for the proof.