The paper deals with a nonlinear second-order parabolic equation with partial derivatives, which is usually called 'the porous medium equation'. It describes the processes of heat and mass transfer as well as ...
The paper deals with a nonlinear second-order parabolic equation with partial derivatives, which is usually called 'the porous medium equation'. It describes the processes of heat and mass transfer as well as filtration of liquids and gases in porous media. In addition, it is used for mathematical modeling of growth and migration of population. Usually this equation is studied numerically like most other nonlinear equations of mathematical physics. So, the construction of exact solution in an explicit form is important to verify the numerical algorithms. The authors deal with a special solutions which are usually called 'heat waves'. A new class of heat-wave type solutions of one-dimensional (plane-symmetric) porous medium equation is proposed and analyzed. A logarithmic heat wave front is studied in details. Considered equation has a singularity at the heat wave front, because the factor of the highest (second) derivative vanishes. The construction of these exact solutions reduces to the integration of a nonlinear second-order ordinary differential equation (ODE). Moreover, the Cauchy conditions lead us to the fact that this equation has a singularity at the initial point. In other words, the ODE inherits the singularity of the original problem. The qualitative analysis of the solutions of the ODE is carried out. The obtained results are interpreted from the point of view of the corresponding heat waves' behavior. The most interesting is a damped solitary wave, the length of which is constant, and the amplitude decreases.
The conditional gradient idea proposed by Marguerite Frank and Philip Wolfe in 1956 was so well received by the community that new algorithms (also called Frank-Wolfe type algorithms) are still being actively created....
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We address an important problem of automation in simulation modeling of logistics warehouses. An effective solution for such a large-scale problem is difficult to obtain without high-performance computing. To this end...
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We address an important problem of automation in simulation modeling of logistics warehouses. An effective solution for such a large-scale problem is difficult to obtain without high-performance computing. To this end, we propose a new approach for adjusting management system parameters of the warehouse in its production use. It is based on the integration of conceptual, wireframe, and service-oriented programming used to develop parameter sweep applications and data analysis in simulation modeling in heterogeneous distributed computing environments. We design a toolkit to support modeling of warehouse logistics. Using this toolkit, we develop a parameter sweep application and solve three optimization tasks for adjusting parameters of a warehouse management system. The practical experiments are focused on the refrigerated warehouse. The developed applications demonstrate high efficiency and scalability capabilities to optimize nine criteria to cope with different production demands.
In this paper, we address the development of efficient global search methods for a sum of ratios (i.e. a fractional programming) problem. This is, in general, a nonconvex problem (with numerous local extremum) which b...
In this paper, we address the development of efficient global search methods for a sum of ratios (i.e. a fractional programming) problem. This is, in general, a nonconvex problem (with numerous local extremum) which belongs to a class of global optimization problems. We proved the reduction theorem for the fractional programming problem with the d.c. functions and one equation with the vector parameter that satisfy the nonnegativity assumption. This theorem allows a justified use of the Dinkelbach’s approach to solving fractional programming problems with the goal function given by d.c. functions.
The article demonstrates the application of the Return-Risk model to develop a synthesized investment strategy. The following parameters of the model are determined as the main sought-for parameters: the size of the t...
The article demonstrates the application of the Return-Risk model to develop a synthesized investment strategy. The following parameters of the model are determined as the main sought-for parameters: the size of the time interval, the frequency of portfolio structure revision and the optimal length of the training set. On the example of indices of real estate investment trusts, computational experiments were carried out. Most databases on prices and dividends of financial instruments are updated monthly, so 1 month is chosen as the time interval. The sliding verification method was used to calculate the optimal frequency of revising the portfolio structure in terms of profitability – twice a year. With this frequency, the average portfolio returns increased by 1.5 times. More frequent restructuring reduces the profitability and stability of the portfolio. The search for the optimal length of the training sample was made by the method of coordinate descent and amounted to 5 years. The average monthly expected return on one instrument with this parameter was 0.4%. The evaluation of the resulting synthesized portfolio showed its superiority in terms of profitability over the S&P 500 stock index by almost 2 times.
The Baikal Natural Territory includes Lake Baikal, its water protection zone, the basin within the territory of the Russian Federation, adjacent specially protected natural areas, and also the territory adjacent to th...
The Baikal Natural Territory includes Lake Baikal, its water protection zone, the basin within the territory of the Russian Federation, adjacent specially protected natural areas, and also the territory adjacent to the lake up to 200 kilometers wide to the west and northwest of it. The development of decisions to solve environmental problems of Baikal Natural Territory should be based on a comprehensive analysis of the monitoring data. The monitoring data and analysis methods are distributed among participants (organizations and departments). But data and analysis methods exchange is very low. An approach is proposed for the introduction of digitalization in the environmental monitoring of the Baikal natural territory, based on the integrated implementation of cyber-physical systems, the digital method of data transmission, as well as the use of digital ecosystems and platforms using the service-oriented paradigm, OGC standards, end-to-end and WEB technologies, cloud and distributed computing, large amounts of spatio-temporal data. Based on service-oriented paradigm digital resources and processing services implementing REST or WPS standard should be created by the monitoring participants. Requirements for digital resources have been defined. Infrastructure components have been developed to simplify development of digital resources, processing services and to organize interaction among participants.
In the paper we address the d.c. optimization problem with inequality constraints. Further we use the Exact Penalization Approach to develop new global optimality conditions (GOC) for a penalized problem. In addition,...
In the paper we address the d.c. optimization problem with inequality constraints. Further we use the Exact Penalization Approach to develop new global optimality conditions (GOC) for a penalized problem. In addition, we study the properties of GOC and its relations to classical optimization theory. Finally, we demonstrate the effectiveness of GOC in comparison with the classical tools on an example.
The contribution from the axial-vector meson exchange to the potential of the muon-proton interaction in muonic hydrogen induced by anomalous axial-vector meson coupling to two photon state is calculated. It is shown ...
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The paper describes a method and tools for prototyping components of intelligent systems. These means are the parts of the PESoT technology based on generative and visual programming as well as the model transformatio...
The paper describes a method and tools for prototyping components of intelligent systems. These means are the parts of the PESoT technology based on generative and visual programming as well as the model transformations. The proposed method redefines the main stages and models of the standardized model-driven approach, in particular, Model Driven Architecture in the context of developing knowledge bases and expert systems that use the logical rules formalism. The description of the method is presented. Proposed tools include languages and software. Specifically, the Rule Visual Modeling Language and Personal Knowledge Base Designer are used for knowledge bases engineering including modeling and codification; the Transformation Model Representation Language and Knowledge Base Development system support model transformations and the rapid creation of computation-independent models. Described tools were applied to solve problems in the field of reliability and safety of technical systems.
The paper presents a method for Ontology Design Patterns (ODP) engineering based on the transformation of conceptual models serialized in the XML-like formats. In this paper, we use UML class diagrams as the source of...
The paper presents a method for Ontology Design Patterns (ODP) engineering based on the transformation of conceptual models serialized in the XML-like formats. In this paper, we use UML class diagrams as the source of conceptual models. The method includes the following activities: design and serialization of a source conceptual domain model; analysis and transformation of an XML structure of a source conceptual model to an ontological schema model; transformation of an ontological schema model to a content ODP code in the OWL 2 DL format; verification and modification of obtained content ODPs by domain experts. All transformations are implemented with the use of original domain-specific language, namely, Transformation Model Representation Language (TMRL). The proposed method is used for ODPs engineering in tasks of industrial safety inspection of technical systems. Obtained ODPs can be used for knowledge bases and intelligent systems engineering.
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