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We study scattering properties in non-isotropic Sobolev fractional spaces for small data solutions to the following system of N ≥ 2, nonlinear Schrödinger equations (NLS) having mass-supercritical power-type nonlinearity and posed on product spaces ℝd × ℳk, for d, k ≥ 1 and ℳk any k-dimensional compact Riemaniann manifold. [ABSTRACT FROM AUTHOR]

We study scattering properties in non-isotropic Sobolev fractional spaces for small data solutions to the following system of N ≥ 2, nonlinear Schrödinger equations (NLS) having mass-supercritical power-type nonlinearity and posed on product spaces ℝd × ℳk, for d, k ≥ 1 and ℳk any k-dimensional compact Riemaniann manifold. [ABSTRACT FROM AUTHOR]

We perform a new inequality regarding the operator L+ = - Δ + 1- β(Q²) - 2β′(Q²) concerning the ground states Q associated to the nonlinear Schrödinger equations (NLS), ... with d ≥ 1. We present also some results straightforward consequence of an application of such an inequality. [ABSTRACT FROM AUTHOR]

We perform new Morawetz identities, interaction Morawetz identities and their corresponding inequalities for the system of N nonlinear defocusing Schrodinger equations (NLS), with N ≥ 2, ... Here, for all ... and .... are coupling parameters, moreover we require that the nonlinearity parameter p is both L²(Rd × T)-supercritical and H¹(Rd × T)-subcritical (or at most H¹(Rd × T)-critical). [ABSTRACT FROM AUTHOR]

We perform new Morawetz identities, interaction Morawetz identities and their corresponding inequalities for the system of N nonlinear defocusing Schrodinger equations (NLS), with N ≥ 2, ... Here, for all ... are coupling parameters, moreover we require that the nonlinearity parameter p is both L²(Rd × T)-supercritical and H¹(Rd × T)-subcritical (or at most H¹(Rd × T)-critical). [ABSTRACT FROM AUTHOR]

In this article we define the Coulomb energy space and study its fundamental properties as a function space. [ABSTRACT FROM AUTHOR]

In this work we are concerned with the minimization problem associated to the best constant Cn,α in the following interpolation inequality ∫∫|u(x)|α|u(y)|α|x-y|n-2dxdy≤Cn,α|∇ψ|L2nα-(n+2)|ψ|L2(n+2)-(n-2)α, u∈H1(Rn) for 2≤α<1+4/(n-2) and n≥3. The corresponding variational problem is equivalent to the problem of existence of a ground state solution to the nonlinear non-local elliptic equation -Δu+ωu-(|x|-(n-2)*|u|α)|u|α-2u = 0. We show that the ground state solution is unique and its mass |u|L22 determines the best constant Cn,α. As a consequence of the above results, we obtain sharp sufficient condition for global existence for the L2-critical Hartree equation. [ABSTRACT FROM AUTHOR]

In this work we prove the existence of solitary wave solutions and give conditions for formation of singularities for the focusing time-dependent Schrödinger-Hartree equation in Rn. [ABSTRACT FROM AUTHOR]

We study the Cauchy problem for the Schrödinger equation with a mixed type nonlinear term. We analyze the local and global properties of solutions in dependence of the nonlinear power, the repulsive or attractive character of nonlinear interaction and the size of the initial data. [ABSTRACT FROM AUTHOR]

We present new Strichartz estimates in Lorentz spaces for the solutions to the heat equation with inhomogeneous nonlinearity in the mass subcritical framework and space dimension d ≥ 1. As an application we prove local and global well-posedness in the Strichartz-Lorentz space Lq((0, T); Lr,2(ℝd)), both in the focusing and the defocusing case, assuming the initial data are in the L2(ℝd) space. [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 present new extended Strichartz estimates for the solutions to the heat equation with inhomogeneous nonlinearity in the mass-energy intercritical framework in space dimension d ≥ 1. As an application we show local and global well-posedness in the Strichartz space Lq((0,T); Lr(ℝd)), both in the focusing and the defocusing case, assuming the initial data are in the Sobolev space Hσ(ℝd)), with σ ∈ (0, 1]. [ABSTRACT FROM AUTHOR]

In the present paper we show that the ground state standing waves eiωt u(x) for the generalized Klein–Gordon–Hartree equation ψtt−Δψ+ψ−(|x|−(n−α)*|ψ|p)|ψ|p−2ψ=0,α∈(0,n),n≥3 in ℝn, are orbitally unstable in the domain of all frequencies 0 ≤ ω < 1 for the supercritical case and for frequencies, strictly less than a critical frequency ωc=√p−1/n+α+1−p(n−1), in the subcritical case. [ABSTRACT FROM AUTHOR]

We display new extended Strichartz estimates for the solutions to the heat equation with pure power mass-energy inter-critical nonlinearity. As an application, local well-posedness in some Lebesgue spaces assuming initial data with fractional Sobolev regularity. [ABSTRACT FROM AUTHOR]

We prove unconditional well-posedness in the energy space for the solution to the heat equation with pure power mass-energy intercritical nonlinearity, both in focusing and defocusing cases. The main tools used are new nonlinear extended Strichartz estimates. [ABSTRACT FROM AUTHOR]

We prove new type of conservation laws and unconditional well-posedness in the energy space for the solution to the Ginzburg-Landau equation with complex pure power nonlinearity. The main tools used are an approach unfolding the conservation of mass and energy as basically independent from the regularity of the solution in combination with classical Strichartz estimates and a new extended Strichartz estimates. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses various reports presented during the 39th International conference "Applications of Mathematics in Engineering and Economics" held in Sozopol, Bulgaria on June 8-13, 2013 and printed within the issue on topics including differential equations, probability theory, and operations research.

In this paper, by variational methods and the profile decomposition of bounded sequences in H¹, we study the existence of solitary waves for the Schrödinger–Choquard equation with an L²-critical nonlinearity. [ABSTRACT FROM AUTHOR]

In this paper, by variational methods and the profile decomposition of bounded sequences in H¹, we study the existence of solitary waves for the Schrödinger–Choquard equation with an L²-critical nonlinearity. [ABSTRACT FROM AUTHOR]

In the present paper we consider the minimization problem associated with the best constant CGN of Gagliardo-Nirenberg interpolation inequality ... [ABSTRACT FROM AUTHOR]

Due to the unprecedented COVID-19 pandemic, and the resultant recommendations of the public health officials and local governments, the Organizing committee decided to use remote technologies to hold the AMEE'20 conference as a virtual meeting in place of the usual in-person conference. The present volume of proceedings consists of the papers presented during the 46 th International Conference "Applications of Mathematics in Engineering and Economics" (AMEE'20), 7- 13 June 2020. The Conference is organized every year by the Faculty of Applied Mathematics and Informatics at the Technical University of Sofia and the Faculty of Mathematics and Informatics at Sofia University "St. Kliment Ohridski". [Extracted from the article]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]