Search

For the final outcomes of the combination scheme with their fixed probability distribution, an iterative process is developed for their complete repetition-free enumeration, which is represented by an inhomogeneous Markov chain. To this aim we determe the probabilities of its initial states and the transition probabilities (iterative transitions of the process). To calculate this process, we analyze the procedure for compiling a system of equations for them and a general method for solving it (for finding the probabilities of iterative transitions when listing the outcomes of any combinatorial schemes that lead to their desired final probability distribution) with an illustration on an example of a combination scheme with an equiprobable distribution on the set of its outcomes. Based on the process thus constructed, we propose methods for modeling the outcome of the combination scheme both from the result of solving the direct numbering problem and for sequential elementwise modeling of the outcome of the scheme, as the state of a Markov chain. [ABSTRACT FROM AUTHOR]

Text analytics and natural language processing become increasingly important in many business companies and the financial services world is no exception. The banking sector is struggling to find new ways of communicating with customers in order to answer to their needs in various innovative ways. The aim to ease customer communication through modern technologies has a central place in the digitalization roadmap of many banks and here comes the important role of text analytics. The goal of this paper is to derive new and useful insights on customer behavior, study the usefulness of a well-known topic modeling technique and propose a methodology for its application in the banking domain. The current empirical study is carried out on real chat data generated between operators in a call center and clients of a large bank. We capture the main topics of client interest, analyze their characteristics and trace their development over time. Several challenges are faced during the empirical study mainly stemming from the domain and noisiness of data - it is predominantly in Bulgarian but there are chats in other languages too; transliteration is extensively used; there are some specific structural characteristics inherent to chat data. Nevertheless, results are promising - the extracted topics are interpretable and meaningful which is confirmed by the application of different techniques for evaluation of results. As a major contribution of the current empirical study, we consider the valuable insights into customer behavior obtained from the analysis of real-world chat data in the banking domain. Furthermore, results can be used not only for tracking trends in customer behavior, but they can serve as guidance for the effective development of chatbot systems. Considering the challenges imposed by chat data in the banking domain, another contribution of the current paper is the development of a methodology for topic extraction from chats in this domain. The current research also suggests what text processing techniques should be applied on customer support chats in order to obtain more meaningful results. The last is applicable to data not only in the banking domain, but in any other text data domain too. Finally, results from the experiment are also evaluated through the lens of the COVID-19 crisis and the analysis of its impact on customer behavior. [ABSTRACT FROM AUTHOR]

In this paper a Non-central Pólya-Aeppli distribution is analyzed. It is a sum of two independent random variables, one that is a Poisson and another one, a Pólya-Aeppli distributed. Some basic properties of the distribution are given. A method of moments and a maximum likelihood estimation method for the Non-central Pólya-Aeppli distribution's parameters are derived. [ABSTRACT FROM AUTHOR]

This paper presents an interactive web based system with geolocation for the cultural and historic heritage in Bulgaria. The system uses a three-tier architecture with a presentation layer executed in a browser and the application is accessible over the Internet and allows the users to find cultural and historical content using three search strategies: by category, by keywords and by spatial search over an interactive map. We perform a case study on a real-world dataset from original research and provide some guidelines for future authors of such datasets. [ABSTRACT FROM AUTHOR]

In the present paper we study a Darboux-Goursat problem for a hyperbolic equation with a singular coefficient, where a third-type boundary condition on the non-characteristic segment is imposed. This problem is related to a four-dimensional Protter's problem for the wave equation and it has an unique generalized solution with possible singularity at a boundary point. We find an integral representation of this solution via Riemann-Hadamard function. The singularity of the generalized solution depends on orthogonality condition on the right-hand side of the equation in respect to nontrivial classical solutions of the corresponding adjoint homogeneous problem. Here we find an explicit formula for such nontrivial classical solutions. [ABSTRACT FROM AUTHOR]

We consider an exploited population distributed in a periodic environment. Its dynamics is described by the Kolmogorov - Piskunov - Petrovsky - Fisher equation, and exploitation is defined by the withdrawal of a distributed share of the population density. We prove the existence of a share that provides the maximum income from exploitation in long run. [ABSTRACT FROM AUTHOR]

In this article are considered a new type of subsemirings – the subsemirings of the endomorphism semiring of the interval [0, 1]. [ABSTRACT FROM AUTHOR]

Energy storage systems use electrical converters for charging and discharging. In order to obtain higher power of the converters, parallel operation of units is used. Often these converters are resonant converters operating on a common load and with dephased controls - multiphase systems. The processes in a multi-unit system are complex and model-based design can be used for the design. The paper presents basic steps for model-based design. A model of a multiphase converter is presented, suitable for model-based design. Simulation results of the operation of the model are shown. [ABSTRACT FROM AUTHOR]

The goal of this project is the development of a Simplified Simulator for Student Training for one of the nuclear power plant's main equipment, namely the steam generator. The TRIPLE S simulator is designed for basic understanding of undergraduate students in nuclear engineering educational programs. Scilab is used to implement a simulation model and to develop a graphical user interface and it run on a personal computer. [ABSTRACT FROM AUTHOR]

The problems of two types of dynamic optimization of flow around solids are described in general form. The features of these problems are analyzed from the point of view of the optimal control theory, the difficulties caused by such features, and ways to overcome them. The problem solving schemes developed for the applied engineer are briefly described, the idea of the mathematical justification of one of them is presented. [ABSTRACT FROM AUTHOR]

Traffic flows determine the hierarchy of transport network elements. More loaded arcs and vertices are more important for the entire network. It is obvious that the traffic flow on any element depends on the network design and the origin-destination matrix of network vertices. Therefore, any change in the origin-destination matrix changes to the hierarchy of network elements. In this study, we consider the origin–destination-based betweenness centrality with the origin-destination matrix obtained from the gravity model. We investigate the network elements hierarchy generated by the betweenness centrality. For such hierarchy we establish some features. In particular, we obtain conditions for the parameters of the gravity model under which the hierarchical ranks of the network element satisfy given properties. We also investigate the dependence of the element hierarchy on the the parameters of the origin-destination matrix for the highway network of a certain region. [ABSTRACT FROM AUTHOR]

Utilization of machine learning in electronics and in computer-aided design is in progress, giving an opportunity the electronic circuits to be studied in a new way that also contributes to automation of some engineering tasks. In this paper, a novel methodology for analysis and design of Gm-C filters is presented. It is based on applying classification machine learning algorithm Random Forest on theoretically gathered data sets and on published scientific results. The tree-based algorithm is chosen, because of its capability not only to identify the correct class for every training sample and to point out the decision, but also to give explanation related to this decision and to outline a set of rules. The proposed methodology is verified through creation of several data models. Gm-C filters are chosen for exploration because of their extensive usage in computer and communication systems, medical devices and sensors. [ABSTRACT FROM AUTHOR]

We deal in this paper with functions of the type f (t , x) = ∑ k = 0 ∞ a k (t) x k where t ∈ T, x ∈ X. In what follows we shall consider different types of spaces T it supposed to be a separable metric space of different kinds and X, which suppose to be some kind of a topological algebra. Next suppose that a k (t) k ∈ ℕ + is a partition of unity. More generally c α (t) α ∈ N + n we consider here a complex - valued (if necessary) partition of unity in ℝn with multi-indexes if n > 1. A partition of unity is locally finite hence the function f (t, x) is a polynomial concerning the variable x which should explain the name of this note. Note that x it may belong to various algebras, Banach one, operator algebras, functional algebras one etc. The aim of this note is to see how this point of view may help to solve some problems of mathematical physics in non-standard way. It may be Banach of different types, some Lie algebra etc. Here is our basic stock of examples: 1) Consider a topological space T and countable partition of unity {ak (t)}, (k ∈ N+) in it. Clearly that there is a locally finite open (or even point finite) cover U = {Uk} (k ∈ N+) for which supp (ak) ⊂ Uk. Because ordtU < ∞ we have ak ≡ 0 for almost all k and thus f (t , x) = ∑ k = 0 ∞ a k (t) x k is a polynomial of x ∈ X for every point t ∈ T. Note that we suppose here that X admits algebraic structure a field or a module or a ring, and it is not necessary to be loaded with some topology. 2) In addition, we can consider some structures on T or X. For example, if T = ℝn and ak(t) ∈ C∞(ℝn) then one may consider derivatives ∂tαf(t, x), so ∂ α f (t , x) = ∑ k = 0 ∞ ∂ t α a k (t) x k where α = (α 1 , α 2 , ... , α n) ∈ ℕ + n is a multi-index. Moreover, if X is an n-dimensional Euclidean space ℝn one can consider the function f (t , x) = ∑ | α | = 0 ∞ a α (t) x α where as usual x α = x 1 α 1 x 2 α 2 ⋯ x n α n follows next then for an arbitrary differential operator D we have D f (t , x) = ∑ | α | = 0 ∞ D (a α (t) x α) ; (1) note that we deal here with finite sums. In the following text we discuss some properties and examples of "analytical" functions of polynomial type. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new method for solving fuzzy partial differential equation (FPDE) using double fuzzy Natural transform (DFNT). We provide fundamental results of the double fuzzy Natural transform for fuzzy partial derivatives of the m-th order. By using them we construct the solution of fuzzy partial differential equation. We show that DFNT method is a simple and reliable approach for solving such equation analytically. Finally, we give illustrative example to show the ability of the proposed method. [ABSTRACT FROM AUTHOR]

We present a novel double Ikeda map based source of pseudorandom numbers. Exact study has been presented on the novel generator using seed value calculation, linear complexity measurement, and statistical analysis with PractRand and ENT applications. The result proves that the generated bytes have excellent characteristics of pseudorandomness and resistance to different statistical attacks. [ABSTRACT FROM AUTHOR]

In the present work we obtain existence of positive solutions for a class of third order equations with parameter depen- dence. The exact expression of the related Green's function is given and some of its properties are proven. Although the Green's function is not positive, the obtained solutions are still positive. The results are based on the classical Krasosel'skii's fixed point theorem in cones. [ABSTRACT FROM AUTHOR]

Bessel functions and their generalizations with more indices are considered in this paper. Studying the properties of these Bessel type functions, some special cases of the fractional order Erdélyi–Kober integrals of them are calculated and interesting relations are proved. It turns out that usually these integrals are expressed in terms of the Bessel type functions with the same or more number of indices, up to a matching power function. [ABSTRACT FROM AUTHOR]

The collaborative approach has been applied for years in a number of distance learning courses, but they are relatively few in foreign language learning. The context of this research is an online distance learning course of French for specific purposes, delivered through the platform UNIV-Rст (Strasbourg University). Based on the online collaborative learning perspective, we have carried out a study analyzing 25 students' opinions in context of a distance learning French language course. By analyzing the students' perceptions of the online collaborative course in which they took part, we have tried to understand the processes that guide the development of a sense of belonging to an online learning community and see to what extent it contributes to reducing the sense of isolation in an online learning environment. [ABSTRACT FROM AUTHOR]

This study examines the student teachers' satisfaction with e-learning science courses "Ecological education" and "Didactics of natural sciences in primary school" in a public university in Bulgaria. Richard R. Aman's satisfaction questionnaire was used to obtain data, regarding quality factors of satisfaction. These factors were integrated in the Quality concept for development of student teachers' satisfaction, based on building of their professional competencies. The results of analysis reveal that professional-competent student teachers feel satisfy with science courses, because they are successful. However, some of students would feel more satisfied, if they could get additional technological help and support. [ABSTRACT FROM AUTHOR]

Machine learning proposes innovative methods for students' learning analysis and new ways for modeling the learning process and its realization. Learning analytics takes advantage of this fact and processes data according to accepted or emerging algorithms that leads to creation of analytical and predictive models. Learning performance is connected to a set of behavioral activities in educational environment concerning improvement of knowledge and skills. It is a very important criterion for students' progress and for the formation of the final students' outcomes. For achieving better learning performance, the activities should lead to the learning optimization in context of time duration, educational tasks organization, content presentation and management. Activities that support learning are oriented to self-dependent and self-regulated learning as well as socially-oriented and group-driven learning. The aim of the paper is to present an exploration focusing on the influence of self-dependent activities in the form of self- assessment on learning performance. An experiment is conducted with students who have had the possibility to direct and organize their self-assessment activities in the learning management system. Self-assessment activities are not graded and they are not included in the formation of the final course mark. The students' behavior is traced during one semester and machine learning algorithms are utilized to analyze the quality and quantity of the taken self-assessment activities. On this base analytical and predictive models regarding learning performance and the achieved academic results are created. The patterns and anomalies are outlined and they are used to point out the directions for learning performance and final outcomes improvement. [ABSTRACT FROM AUTHOR]

The double singular perturbation for boundary-value problem for system of ordinary differential equations in a critical case is considered. For a formal asymptotic solution, constructed by the method of boundary functions and generalized inverse matrices and projectors, we prove an asymptotic property of the formal series. [ABSTRACT FROM AUTHOR]

The paper below introduces a comparative analysis between two image classification technologies for the purposes of medical breast cancer. The first technology is based on the concept of convolutional neural networks, and the second one on the use of feature vectors generated by wavelet transform and the use of Euclidean distance to determine similarity. Experiments are performed using both technologies and a specialized test database. Based on the obtained results, the classification accuracy, precision and recall measures are determined. The obtained values are compared, analyzed and summarized, as the data show comparable values of classification in the technologies presented in the report. [ABSTRACT FROM AUTHOR]

In this paper we will explore the 2D system with Hamiltonian H = 1 2 (p r 2 + p z 2) + A r 2 + B z 2 + C z 3 + D r 2 z + E z 4 + F r 2 z 2 + G r 4 , describing trapped ionic system in the quadrapole field with a superposition of rationally symmetric hexapole and octopole fields for meromorphic integrability. We use the Lyapunov and Ziglin-Morales-Ruiz-Ramis's classical methods for the proofs. [ABSTRACT FROM AUTHOR]

The paper presents an overview and analysis of the workflow platforms used for solving problems in bioinformatics, biology, medicine. In the paper seven workflow frameworks are categorized in three groups: stand-alone platforms, web-based workflow systems, cloud-based workflow solutions. Chipster, Apache Taverna, Mobyle, Galaxy, NVIDIA Clara, Trident and Apache Spark are discussed in details and recommendations for their application are added. [ABSTRACT FROM AUTHOR]

The paper below presents an overview of big data integration techniques, methods and approaches. The report describes the data integration architecture and its components. Also, an overview of five big data integrators is included. Integrator.io, Oracle Data Integrator, Apache Spark, SQL Server Integration Service, Zapier are discussed in details. In addition, recommendations for their application are presented. [ABSTRACT FROM AUTHOR]

In recent years, survival rate after liver transplantation in children, especially in the early postoperative period, is very high. At the same time there are many complications that can lead to death in this period. Therefore, it is important to look for parameters that can predict a lethal outcome. The duration of mechanical ventilation after liver transplantation reflects many processes early after surgery. Some severe complications in the postoperative period are related to the time of mechanical ventilation and the latter can be used to predict the outcome for the recipients [1] - [4]. The aim of this paper is to model and estimate the probability function for this factor in order to prevent the mortality risk. Four mathematical models for this purpose are considered. [ABSTRACT FROM AUTHOR]

In a technology-rich business environment, accounting educators are challenged to develop the required skill set in accounting graduates and to prepare them for a successful career in a data-driven environment. As the deployment of AI and ML advances may substantially improve almost every area of accounting, future professionals have to be well equipped with the needed knowledge and competences to benefit from their capabilities. Universities are searching for innovative approaches and good practices for implementing AI and ML techniques into accounting curriculum. This paper introduces an AI-based case study for accounting students, supported by clear learning objectives, methods and detailed implementation guidance. By playing their assigned role as company management's consultants under the case hypothetical scenario, students have to complete several individual and group tasks that demonstrate how the quality of investment decisions might be improved by enhancing the usefulness of companies' financial statements. Students are also encouraged to develop their analytical thinking and interpretation skills as well as their communication and deliberation proficiencies complementing the targeted competences in AI and ML. [ABSTRACT FROM AUTHOR]

Depression is the most prevailing mental health problem nowadays and researchers expect it to deepen especially in most developed countries due to constantly aging population. This development would pose extreme financial burden on public finance. The SHARE project provides a huge variety of data sets including a mental health module used to form the 12-item EURO-D scale, which serves as a common metrics for depressions. However, in wave 7 this module includes respondents from only 12 countries. Consequently, this paper aims to construct data-driven indices reflecting the level of depression in Europe. We employ factor analysis and as a result, we derive two latent variables. High positive values of the first one indicate lack of depression, while high positive values of the second variable might be indicative for presence of serious depressive symptoms. We then inspect cross-national differences in terms of these two latent variables. Our major findings suggest that geographic location tends to have some effect on the presence of depressive symptoms among elderly people in Europe. [ABSTRACT FROM AUTHOR]

Aging population across developed countries is a problem that no nation has faced before. It puts severe financial burden on every public budget. Non-financial burdens are also common. Depression turns out to be the most common mental disease. Studying the features, that could boost the exhibition of depressive symptoms, and those, that could protect individuals from them, would have significant effect on the precision of public health policies. That is the aim of the paper. We base our research on wave 7 data of the Survey of Health, Aging, and Retirement in Europe that for the first time summarizes information about 27 European countries and Israel. As a preliminary step in our analysis, we construct two latent variables used to quantify the level of depression. On the basis of extensive literature review, we identify a long list of potential features and apply lasso regression so as to select those of them that contribute most in explaining the variance of each of the latent variables. Delivered results indicate that among the most common features, leading to poor mental health, are working conditions, self-perceived health and the presence of functional limitations. On the other hand, educational attendance, lack of chronic diseases and sport activities are among the factors that protect from exhibiting depression symptoms. [ABSTRACT FROM AUTHOR]

This paper represents the usability strategy for web portal development of Bulgarian Cultural and Historical Heritage and exhibits all the necessary guidelines for accessibility that needs to be comprehended. The output of that strategy should be a fully-fledged plan supporting the needs of all potential users, whether they are physically disabled (e.g., color-blind users) or users they are encountering situational difficulties. The backbone of this strategy will be based on Web Content Accessibility Guidelines (WCAG) 2.0 and usability studies with people using assistive technologies by Kara Pernitz and Jakob Nielsen. This will provide coherence by considering the defined guidelines and real-life case scenarios. [ABSTRACT FROM AUTHOR]

Gross Regional Product (GRP) is the main indicator of the effectiveness of any given region. However, it is usually not possible to predict and analyze its change. The article considers the main indicators that potentially affect the GRP of the Kurgan region, assesses the impact of these factors on the GRP, and compares the correlation matrix and pleiade. The results of the study allow us to evaluate the real impact of various factors and determine the vector of actions for the development of the region. [ABSTRACT FROM AUTHOR]

Many recent papers conclude on short-term profitable patterns based on trading strategies relying on the belief that best (worst) performing securities over the past short-term period tend to continue to perform well (poorly) over the subsequent period of up to 12 months. Along with exploiting past price patterns, ever since the early 1980s the researchers' attention is drawn on the usefulness of company financial statements in predicting stock market returns. We argue on the necessity to develop a framework that would enable investors to support their everyday decisions by taking into account information retrieved from financial statements in an automated manner. We propose an ML-based AI system that inputs historic price information as well as information on a number of balance sheet items, profit and loss items, and cash flow items for the company of interest and predicts the probability of its stock price going down in the next period. The prediction relies on a dynamic automated selection of significant accounting and historic features. Tracking the dynamics in the structure of significant features could shed additional light on company specific issues that might be taken into account by investors when making their decisions. [ABSTRACT FROM AUTHOR]

In this article, the author considers various strategies for the development of the Kurgan region. However, in order to follow the presented strategies, the region needs the support of the state. The results of the study allow us to assess the real level of development of the Kurgan region and choose a suitable vector for improving the economic condition. [ABSTRACT FROM AUTHOR]

Liver transplantation is treatment of choice for patients with end stage liver disease (ESLD). However, due to high surgical risk and risk of complications from the immunosuppressive agents pose significant challenges in transplanting setting. The aim of our study was to evaluate survival after liver transplantation. In this paper survival analysis is used to determine the prognostic significance of age of the recipient at the time of transplantation, sex, Model for End-Stage Liver Disease (MELD) score, complications after transplantation and treatment of complications, and to model the time it takes for death. The data is obtained from 41 patients, who have been transplanted at the University Hospital "Lozenetz", Sofia, Bulgaria in the period 2006-2019. For estimating event (death) free survival rate the Kaplan–Meier method is used. Time to event is calculated as the time from study entry to first event or date of last contact. Multivariate analysis is conducted by using Cox proportional hazards regression. [ABSTRACT FROM AUTHOR]

The purpose of this article is to introdused the inference techniques for the mean vector μ, the correlation matrix π and the covariance matrix Σ of the multivariate normal sample and to apply these techniques using the software package STATISTICA 13.0 (StatSoft Inc, USA). The sample contains 50 weekly return observations (in percent) on each of ten stock portfolios constructed from stocks on the Toronto Stock Exchanges. Since the data are obtained as a random sample of multivariate normal distribution the Wishart distribution can be used to make inference about covariance matrix. [ABSTRACT FROM AUTHOR]

In 2003 Nadarajah and Kotz investigated Exponentiated-Fréchet distribution. They showed that its cumulative distribu- tion function has regularly varying right tail. An interesting fact about this distribution is that its index of regular variation depends on two parameters. In 2019 Jordanova defined and investigated the main properties of p-outside values and showed that they do not depend on the center and the scale parameter of the considered distribution. Therefore, they are appropriate for estimation of the parameters which govern the tail-behavior of the c.d.f. IPO and MN-IPO estimators were introduced by Jordanova and Stehlik in 2019 in the general case. Here we compute probabilities for right p-outside values in Exponentiated-Fréchet case. Then, we express the unknown parameters via the empirical relative frequencies of these p-outside values. We observe that the corresponding system of equations has no explicit solution, therefore, we solve it by using new appropriate numerical methods. The last solutions are the so called IPO-NM estimators. If we use, as an auxiliary characteristic the empirical p-fences, we show that the corresponding system of equations has an easier solution and these are the IPO estimators. The properties of IPO and IPO-NM estimator are discussed. The rates of convergences of the last are visualized via a simulation study. The corresponding distribution sensitive estimators of the quantiles outside the range of the data are obtained. The paper finishes with some conclusive remarks where new open problems are posed. [ABSTRACT FROM AUTHOR]

In this article, using a computer program - electronic spreadsheet, a transport task is solved. One of the advantages of algorithmic tasks is that it can be solved by software that significantly extends their practical application related to data processing and execution of numerous computational operations. [ABSTRACT FROM AUTHOR]

The Hausdorff, Hamburger and Stieltjes moment problem and the sequence of maximum entropy (MaxEnt) approx- imates with given moments are considered. Thanks to MaxEnt formalism it is proved, through a unified procedure, MaxEnt approximate converges in entropy to the unknown distribution when the Hausdorff, Hamburger or Stieltjes moment problem are determinate and the underlying distribution has finite or (minus) infinite entropy. [ABSTRACT FROM AUTHOR]

The Virtual Reality (VR) experiences are great for an engaging presentation creating wide public awareness of cultural heritage, especially if the experience is built on a web-based technology. One of the still posing challenges is that once an application has been developed, for example for a virtual museum or a virtual tour, it usually remains fixed to an embedded in the application model. Adding new functionalities or interaction paradigms needs additional development and new deployment. In this paper, we propose a framework, which achieves the decoupling of an experience from the used models and interaction paradigms through scene and input templates and configuration files. This allows an easy way for generation of a variety of experiences even by people with no or limited programming skills. [ABSTRACT FROM AUTHOR]

Range finder sensors are widely used in the obstacle detection and collision avoidance applications. In this research, we propose rotating range finder sensor that provides economic and efficient solution for mobile robot applications. Rotating approach is achieved by coupling the range sensors with servomotor. In this article, rotating approach model design, main parameters, equations and limitation are described. In addition, an algorithm is developed to control the rotation angle of the range sensor, extract data from the approach and analyze it. A case study of the rotating approach by implementing ultrasonic sensor is simulated and the results are obtained. Simulation platform Gazebo and ROS are used to simulate the rotating approach. [ABSTRACT FROM AUTHOR]

Technology is transforming how we interact with the world around us. We rely more and more on mobile applications to plan our daily routines. Mobile applications are used for many areas of our life and how we travel is one of them. This article provides an overview of the development process and main architectural decisions of one such application which main purpose is to showcase the cultural and historical heritage of Bulgaria. [ABSTRACT FROM AUTHOR]

We present new extended Strichartz estimates for the solutions to the heat equation, perturbed with a time dependent potential V : ℝ+ ℝd → ℝ, satisfying appropriate space and time integrability conditions (i.e. bounded with respect to some La(I, Lb(ℝd)) norms). We focus ourselves to the case with initial datum in Hσ, σ ∈ (0, 1] and d ≥ 1. Some applications of these new estimates are also displayed. [ABSTRACT FROM AUTHOR]

We apply Pohozhaev type identity to establish nonexistence of nontrivial regular solution of a problem of mixed type. The result is obtained in both supercritical and critical case with brief discussion on the derivation of Sobolev embedding constant. Since boundary conditions are imposed on elliptic boundary and part of hyperbolic boundaries we apply Hardy-Sobolev inequality to ensure that integrals on the boundaries where no boundary conditions are imposed have appropriate sign. [ABSTRACT FROM AUTHOR]

This work is the continuation of the article [7], in which we are interested in the mathematical study of a system of nonstationary Navier-Stokes equations coupled to the energy equation in a bounded domain of R3. The considered system could model the flow of a fluid in a solar collector. We establish the existence and uniqueness of the weak solution of the variational problem in an appropriate Sobolev space under certain conditions on the parameters of the problem. [ABSTRACT FROM AUTHOR]

The mathematical models of the mechanical systems "pipeline – pressure sensor" are considered. These systems are designed to measure the pressure in gas-liquid media, for example, to control the pressure of the working medium in the combustion chambers of engines. Based on the proposed models described by systems of differential equations, the joint dynamics of the sensitive element of the pressure sensor and the working medium in the pipeline is investigated. To describe the dynamics, both linear and nonlinear models of the mechanics of a solid deformable body and the mechanics of fluid and gas are used under various assumptions about the physical model of the working medium: incompressible ideal, compressible ideal. Analytical and numerical methods for solving the indicated initial-boundary value problems are developed. [ABSTRACT FROM AUTHOR]

The derivation of asymptotic equations describing the processes of heat and mass transfer in axisymmetric swirling laminar flows of a viscous incompressible fluid. Self-similar solutions of these equations are obtained, on the basis of which steady hydrodynamic fields (velocities, pressures) and a temperature field in swirling jets are constructed. The plane and axisymmetric heat and mass transfer problems for unsteady laminar layered flows of a viscous incompressible fluid in channels are also considered. [ABSTRACT FROM AUTHOR]

In the paper we discuss conformable derivative behavior in arbitrary Banach spaces and clear the connection between two conformable derivatives of different order. As a consequence we obtain the important result that an abstract function has a conformable derivative at a point (which does not coincide with the lower terminal of the conformable derivative) if and only if it has a first order derivative at the same point. As an application of the obtained results we prove that the existence of a weak solution of a mixed (initial/boundary) problem for a parabolic partial differential equation with conformable derivative on time is equivalent to the existence of a weak solution of the same mixed problem for an appropriate considered parabolic equation with integer order derivative. [ABSTRACT FROM AUTHOR]

For one class of nonlinear wave equations with a small parameter, an initial-boundary value problem with zero boundary conditions is considered. The solution of such a problem is constructed with using series with recurrently calculated coefficients in two ways. In the first case, the method of special series is considered, which is based on the choice of some functions (basic functions), by the powers of these functions the solution of the original problem is presented into a series with recurrently calculated coefficients. In the other case to represent solutions of the problem a combination of Fourier and small parameter methods is used. It is shown that both proposed constructions of series with recurrently calculated coefficients converge to the solution of the initial- boundary value problem on a finite time interval. [ABSTRACT FROM AUTHOR]

The aim of this study is to investigate weighted time-varying causal graphs based on daily log-return and realized volatility time series of the S&P500 stocks. In order to construct causal graphs for each quarter between Q1 2005 and Q2 2020, we compute cross-correlations between series and conduct pairwise Granger Causality tests for lead-lag relationships. We take individual stocks as nodes and significant causal relationships as weighted edges. Our analysis is based on a comparison of network topology and properties for different periods, including the 2007-2010 subprime crisis, the European sovereign debt crisis, and the coronavirus pandemic, as well as tranquil periods. In addition to edge weights, our study also takes into account the estimated lag of the causal interactions and uses network level measures to identify meaningful patterns over time. We also conduct an analysis of the industrial sectors interconnectedness via smaller graphs derived from the stock-level causality graphs. The results of the work reveal that network topology changes during periods of market stress and crisis and this can be captured by using convenient network construction methods and measures. Our results also show that the patterns of network topology transformation and magnitude of spillovers transmission during the coronavirus crisis and accompanying events differs from previous crisis periods. [ABSTRACT FROM AUTHOR]