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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]

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]

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 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]

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 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]

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]

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]

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]

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]

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]

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]

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 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]

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]

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]

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]

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]

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]

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]

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 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 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]

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]

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]

The present study examines the elastic displacements in plain strained condition of involute cylindrical gears with asymmetric profile. A modification has been implemented of the elastic half space by means of the initial conditions of Hertz and the Frenkel problem has been modified for approximation of the involutes to the sides with wedges. The integration constants were derived, allowing determination of the total elastic displacement of the tooth along the various lines of engagement by the method of superposition. [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]

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]

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 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]

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]

This article is deduction of the necessary and sufficient condition for geometric synthesis of involute cylindrical gears with asymmetric profile of the teeth by the classic approach. The necessary condition is presented for slack-free engagement of the corresponding involutes along the initial circles and the crossing of the lines of engagement along the inter-center straight line, which is a new interpretation of the Willis's basic law of the flat engagement. [ABSTRACT FROM AUTHOR]

Periodontal disease may lead to progressive loosen teeth and even to bone loss. Appropriate treatment is splinting the teeth in order to redistribute the loads. The aim of the study is to compare stress distribution between splinted and non-splinted teeth. A 3D model was made based on computed tomography of mandible and six anterior teeth. In order to make the 3D mesh the model was exported in CAD software and merged with the splint. The materials of the teeth and the splint were assigned according to CT density. The calculations were done in ANSYS using Finite Element Analysis where different directions of loads were applied. As engineers our role of the process is creating a 3D models from CT of a patient and a model of a splint. Then via ANSYS software to apply different loads on the teeth. The final pictures of von Mises stress distribution in all cases will give the dentists accurate results. The dentist as medical authorized people will make the decision about the treatment afterwards. [ABSTRACT FROM AUTHOR]

Innovations of the modern neurosurgery and tissue engineering also has led to development of methodology for designing, manufacturing and integration of spinal personalized implants. The purpose of these personalized implants is to perfectly match the needs and anatomical features of the particular patient and therefore it is a way to create better conditions for functional recovery, and overall improve treatment. In the whole process from MRI scanning to designing, developing and integrating the implant were involved a group of specialists-engineers and neurosurgeons. First step of the process is to make a 3D model from the CT file of the spine using MIMICS Medical software. The next step is to design a model of the personalized implant in 3D matching to the person's spine, which could be done in 3-Matic. Another step is adjusting the implant to the personal case. The development of the implant is the next step although every case is different and requires unique decisions about the size and the form of the implant. Various biocompatible materials and shapes of implants exist. The final step is the implementation of the implant by neurosurgeons. The aim of the innovations is to inculcate the methodology and moreover to make the process more precise. The innovations will find direct application in the field of modern neurosurgery and will achieve not only treatment of the disease but also improvement of the quality of life of the patient. Achieving this goal will provide access to this type of high-tech treatment for a broad group of patients. [ABSTRACT FROM AUTHOR]

This study is based on prior research and aims to improve stream wheel performance based on virtual prototyping. Examined stream wheel structure is developed in several vairants concerning its blades number, geometry and dimensions. Final result shows nearly 50% power output increase for some load cases. The research presents another advantage of virtual prototyping – for design variants evaluation without need for expensive physical prototyping and testing. [ABSTRACT FROM AUTHOR]

The increasing complexity of the cyber-physical products used nowadays along with the ever-expanding firmware and electronics and the connectivity aspects of the industrial environment, require thinking beyond the traditional engineering structures and related design stages. The development and evolution of today's virtual and physical prototypes to the digital twin approach requires high levels of accuracy of the simulation models, covering a wide range of multiphysical areas, as well as different levels of scale and reliability of the model - depending on life cycle applications. This high levels of accuracy in the use of engineering decision-making models can only be achieved in an integrated environment closely linked to the digital and physical worlds. The aim of this study is to define the Digital Twin concept based on Virtual Prototypes and create virtual prototypes for an existing uninterruptible power supply system with a kinetic battery accumulator. [ABSTRACT FROM AUTHOR]

The main purpose of this article is to present an approximation method for solving two-dimensional Hammerstein- Volterra fuzzy integral equations with partial integrals (2D-HVFIEPI). The proposed approach is based on homotopy analysis method (HAM). We transform this equation to Hammerstein-Volterra fuzzy integral equations with partial integrals to crisp case. The convergence analysis for the proposed methods is proved and error estimate between the exact and the approximate solution is find. We give numerical application to show efficiency and accuracy of the method. [ABSTRACT FROM AUTHOR]

The social sustainability is one of the three pillars of the sustainable development. In the article the respective domain ontology is developed as a part of the existing ontological metamodel of the sustainable development. A methodology for the ontology building is proposed including concept exploration, controlled vocabulary and thesaurus creating; ontology formalization, verification, querying and publication. The main concepts of the ontology are extracted from a text corpus covering well-established and authoritative sources, approved articles, standards and commonly accepted regulations of United Nations. For the purpose, manual selection and automatic text mining by the language processing toolkit GATE is performed. The ontology is formalized by OWL in Protégé environment and after verification its code in GitHub is published. [ABSTRACT FROM AUTHOR]

In the article the problems related to the analysis and measurement of competitiveness at the firm level are explored. An original methodology is proposed on the base of detailed literature review in the area including investigation of the known theoretical studies and the practical achievements. A special attention to the definitions and terminology is paid. The methodology is on the base of existing methods and own algorithms. It proposes an innovative information model of firm competitiveness using ontology engineering for creating metamodel, statistical methods for identifying firm competitiveness criteria and indicators and web technologies for prototype online information system building. A regression analysis is applied revealing the mutual dependency between the firm and the product competitiveness for identifying firm competitiveness criteria and indicators. Based on the methodology a prototype online information system is developed intended for firm competitiveness index calculation and analysis. The proposed information model and the prototype online system fill a gap in the firm competitiveness research and analysis tools. It is expected that their application in the practice would improve awareness of firm managers about positions of their organizations and increase the conclusion quality of the business analysts. [ABSTRACT FROM AUTHOR]

The purpose of this study is to determine analytically what and how acceleration from paralleling execution of a task depends. It is reasonable if level of parallelism is increased, the costs of synchronization will also be increased and upon reaching a certain degree of granulation acceleration of multi-program execution starts to decrease. It is shown that there is a limit to the possibilities for parallelization of activities, taking into account real restrictive conditions. [ABSTRACT FROM AUTHOR]

In this paper we introduce the notion of derivation in product (direct product) of additively idempotent semirings. These semirings are useful and important tools in diverse areas such as design of switching circuits, automata theory, information systems, dynamic programming and decision theory. We study hereditary derivations, inner derivations and obtain a representation of an arbitrary derivations which are zero on the multipliers. [ABSTRACT FROM AUTHOR]