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The paper considers the process of filtration of water and oil phases, taking into account the deformation of the medium. A suitable mathematical model of the process is proposed. Using the proposed model, the influence of medium deformation on hydrodynamic parameters was analyzed. The problem was solved numerically by the large particle method. Based on the obtained results, the influence of environmental deformation on reservoir pressure, porosity, permeability, oil saturation and oil production was studied. [ABSTRACT FROM AUTHOR]

The paper examines optimization problems for underground structures based on algorithmic methods, develops mathematical models, and specifies algorithms for solving them. Solving these problems allowed us to achieve significant savings in materials and costs compared to existing projects. The possibility of designing vault structures with minimal consumption of materials is being explored. The results of calculations for the optimization of underground structures are presented. [ABSTRACT FROM AUTHOR]

It is difficult to deal with the uncertainty data issue which has incompleteness, impreciseness and incertitude. Normally, uncertain and vague information is confronted in form of data point. Various mathematical models were developed to resolve issues concerning uncertainty point. In this paper, Neutrosophic Bézier Curve model will be introduced. A mathematical model with a redefinition of the control points that is characterized by three important components of neutrosophic set is designed to solve this problem. These control points are blended with the Bézier basic functions to generate multiple models in the form of neutrosophic spline curve and surface. Then, the related data can be translated through the construction of those models with the neutrosophic concept and its relationships. [ABSTRACT FROM AUTHOR]

Problem-solving using mathematics in various aspects of daily life encourages the importance of mathematical modeling skills. Mathematical modeling holds a crucial role, particularly when solving real-world or contextual problems, as it bridges the extra-mathematical world and the mathematical world. This paper discusses a study on the mathematical modeling skills of eighth-graders in solving contextual problems. This study aimed to investigate the mathematical modeling competency level achievement of the students. This study used the qualitative research method with a case study approach, consisting of five major stages: design, preparation, data collection, data analysis, and reporting. In the design stage, we determined the research focus, and in the preparation stage, we developed research instruments. We collected data by giving tests to 24 participants. After we analyzed the data, we reviewed and rearranged all of the research stages. The results showed that, out of six levels of mathematical modeling competency, which includes level 0 to level 5, most students only achieved level 3. Therefore, we conclude that the students are not yet capable of carrying out all aspects of the mathematical modeling processes. [ABSTRACT FROM AUTHOR]

The paper deals with the study of a frictionless contact problem of pressing a rigid hollow cylinder into a deformable cylindrical body with a coating on the upper base. The coating consists of two materials with different characteristics. Geometry and mesh are built according to a simplified mathematical model. Particular attention is paid to solving the problem using the AsterStudy module of Salome-Meca software package. [ABSTRACT FROM AUTHOR]

The development of a unified approach to solving the problems of the dynamics and interaction of multiply connected structurally-inhomogeneous shell structures, which are an arbitrary composition of multilayer shells of revolution and rings, the creation and implementation of an appropriate software package with a high level of automation of all stages of calculations oriented to computer use significantly increase the design efficiency and are a major scientific problem of great economic importance. This paper is dedicated to solving this problem. The study and prediction of the deformation properties of the materials studied in the work are possible based on mathematical modeling of deformation and relaxation processes. In this article, we give an algorithm for solving a nonlinear functional equation with complex variables resulting from mathematical modeling of problems concerning the properties of a deformable solid. [ABSTRACT FROM AUTHOR]

The paper discusses an approach to the maintenance diagnostics and predictive evaluation of the operational health of electromechanical systems (EMS). It presents a mathematical model of an EMS, which is intended for problems of diagnosing an individual EMS and an EMS operation mode group, offers information on the EMS vector spaces, and describes the general methodology for vector space testing. To solve problems of the maintenance diagnostics and predictive evaluation of EMS health, it is proposed to use hybrid models based on a combination of the fuzzy cognitive approach and the fuzzy logic one. [ABSTRACT FROM AUTHOR]

Normally in engineering, conceptual models provide formal model of the system. Mathematical modeling gives the systematic representation in terms of properties. Modeling process is performed by using design space analysis and mathematical equations and this can be performed with different design alternatives. Conceptual analysis of natural convection is described. In this paper the modeling of heat and mass transfer is performed with the concepts of heat and mass transfer and properties of objects in the design space. Numerical solution has been conducted for energy equation with different boundary conditions. The present work analyses the heat and mass transfer modeling process with mathematical equations. [ABSTRACT FROM AUTHOR]

The paper presents the creation of a general mathematical model of a two-step optimization problem which finds the most-safer route of an electric-bicycle cyclist. The first step is a multi-criteria problem which finds the average risk in the different segments which forms the complete route. To solve the problem, a scalarization method is used (also known as weighted sum method). In the second step, the safer route is found by applying a network optimization model. To find the solution a method for dynamic optimization is applied (Bellman's Principle). The generation of data is based on the a priori known information as well as on information which is periodic and stochastic in the time and space. [ABSTRACT FROM AUTHOR]

The performed studies are aimed at the increase of the capacity of operating and prospective wheel shops by means of intensification of the use of existing equipment and creation of new specialized high-performance equipment for the repair and formation of wheelsets. To solve this problem, a technique is developed for the optimization of the parameters of equipment for wheel shops, including a mathematical model with a number of technical and technological limitations. The minimum value of the reduced costs is taken as the optimization criterion. As a result of the performed calculations, the optimal cutting conditions are obtained for the processing of carriage and locomotive axles from forgings and cross rolling products, taking into account the prospects for the development of cutting tools and the achievements of domestic and foreign machine tools. Based on the optimal ranges of changes in the rotation frequency of the principal movement and feed drive systems, and a number of other parameters of the tools, obtained as a result of calculations, the adjustments were made to the processing schemes and diagrammatic works of both existing and prospective machine tools of the enterprises wheel shops. A technical assignment is developed for the design and manufacture of a special multi-cutting semi-automatic lathe with two tool heads for axes. [ABSTRACT FROM AUTHOR]

Reflective thinking is an important component in the world of education, especially in professional education of teachers. In learning mathematics, reflective thinking is one way to solve mathematical problem because it can improve student's curiosity when student faces a mathematical problem. Reflective thinking is also a future competence that should be taught to students to face the challenges and to respond of demands of the 21st century. There are many factors which give impact toward the student's reflective thinking when student solves mathematical problem. One of them is cognitive style. For this reason, reflective thinking and cognitive style are important things in solving contextual mathematical problem. This research paper describes aspect of reflective thinking in solving contextual mathematical problem involved solution by using some mathematical concept, namely linear program, algebra arithmetic operation, and linear equations of two variables. The participant, in this research paper, is a male-prospective teacher who has Field Dependent. The purpose of this paper is to describe aspect of prospective teachers' reflective thinking in solving contextual mathematical problem. This research paper is a descriptive by using qualitative approach. To analyze the data, the researchers focus in four main categories which describe prospective teacher's activities using reflective thinking, namely; (a) formulation and synthesis of experience, (b) orderliness of experience, (c) evaluating the experience and (d) testing the selected solution based on the experience. [ABSTRACT FROM AUTHOR]

A thin orthotropic polygonal plate resting on the Winkler’s elastic foundation is considered in this paper. The method analysis of such plate named macroelement method has been suggested. According to this method, real plate is inscribed into rectangular contour and extended to rectangular area, which is called fundamental plate. It is union of real plate and additional part. Considered plate balanced in rectangular area and having specific links at the contour is called plate macroelement. First part of this definition is mathematical model and second is physical model of the macroelement. As examples trapeze and triangle plates were solved and results were compared with the similar results obtained by another methods. It is shown that they are in good agreement. [ABSTRACT FROM AUTHOR]

In this paper we consider a model case of stationary vibrations of a thin flat plate, one side of which is embedded, the opposite side is free, and the sides are freely leaned. In mathematical modeling there is a local boundary value problem for the biharmonic equation in a rectangular domain. Boundary conditions are given on all boundary of the domain. We show that the considered problem is self-adjoint. Herewith the problem is ill-posed. We show that the stability of solution to the problem is disturbed. Necessary and sufficient conditions of existence of the problem solution are found. Spaces of the ill-posedness of the considered problem are constructed. [ABSTRACT FROM AUTHOR]

In the paper Neumann type boundary value problems for inhomogeneous biharmonic equation are studied. Necessary and sufficient conditions on solvability of the considered problems are established. [ABSTRACT FROM AUTHOR]

The paper deals with the development of algorithms for solving nonlinear problems of heat conduction in bodies consisting of layered metal composites. The nonlinearity of the problems is governed by the temperature dependence of the heat conductivity coefficients of the composite layer materials. Mathematical models and solution algorithms based on the boundary element method have been constructed for one-dimensional cases of heat distribution. [ABSTRACT FROM AUTHOR]

In this paper we will revisit the modification of the piecewise constant policy timestepping (PCPT) method for solving Hamilton-Jacobi-Bellman (HJB) equations. This modification is called piecewise predicted policy timestepping (PPPT) method and if properly used, it may be significantly faster. We will quickly recapitulate the algorithms of PCPT, PPPT methods and of the classical implicit method and apply them on a passport option pricing problem with non-standard payoff. We will present modifications needed to solve this problem effectively with the PPPT method and compare the performance with the PCPT method and the classical implicit method. [ABSTRACT FROM AUTHOR]

Whether there exists a computable universal numbering for a computable family is the key question in theory of numberings. In a very general setting, this problem was explored in [Yu. L. Ershov, Theory of Numberings, Handbook of Computability Theory, North-Holland; Amsterdam: Stud. Log. Found. Math., Vol. 140, pp. 473-503, 1999]. For sets A that are Turing jumps of the empty set, the problem was treated in [S. A. Badaev, S. S. Goncharov, and A. Sorbi, Computability and Models, 11-44 (2003)] and other papers. In this work, we investigate families of total functions computable relative to hyperimmune and hyperimmune-free oracles. [ABSTRACT FROM AUTHOR]

The solution of a problem that involves uncertainty data that is characterized by complex process in which the phenomenon of incomplete information obtained is difficult to handle. Various mathematical models have been developed to handle problems involving uncertainty data. This paper introduced new concept of geometric modeling with intuitionistic fuzzy called intuitionistic fuzzy Bezier model. This model is constructed through intuitionistic fuzzy set theory and based on intuitionistic fuzzy number and intuitionistic fuzzy relation. A new control point namely intuitionistic fuzzy control point is defined. Next, the new control point is blended with the spline basis function to developed intuitionistic fuzzy Bezier model and the curve is shaped. [ABSTRACT FROM AUTHOR]

A fuzzy evolutionary algorithm is an integration of an evolutionary algorithm and a fuzzy system. In this paper, we present an application of a genetic algorithm to a fuzzy evolutionary algorithm to detect and to solve chromosomes conflict. A chromosome conflict is identified by existence of any two genes in a chromosome that has the same values as two genes in another chromosome. Based on this approach, we construct an algorithm to solve a lecture scheduling problem. Time codes, lecture codes, lecturer codes, and room codes are defined as genes. They are collected to become chromosomes. As a result, the conflicted schedule turns into chromosomes conflict. Built in the Delphi program, results show that the conflicted lecture schedule problem is solvable by this algorithm. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm that is able to solve optimal control problems in which the modelling of the system contains variable parameters, with the added complication that, in certain cases, these parameters can lead to control problems governed by quasi-linear equations. Combining the techniques of Pontryagin's Maximum Principle and the shooting method, an algorithm has been developed that is not affected by the values of the parameters, being able to solve conventional problems as well as cases in which the optimal solution is shown to be bang-bang with singular arcs. [ABSTRACT FROM AUTHOR]

GeoGebra 5.0 is the dynamic geometric and mathematic software which dynamic tools allow the user to solve dynamic problems in a plane and as well as in the three-dimensional space. The contribution presents the dynamic applets constructed in GeoGebra 5.0 that show the origin as well as some properties of various kinds of canal surfaces. There are described the applets for constructing the canal surfaces in the paper. Some of the created canal surfaces are compared with the real life canal surface examples. [ABSTRACT FROM AUTHOR]

This paper investigates projective lag synchronization (PLS) behavior in drive-response dynamical networks (DRDNs) model with non-identical reference node. Based on Lyapunov stability theory and hybrid feedback control method the problem of PLS with mismatch terms is solved. Finally, analytical results show that the states of the dynamical network with non-delayed coupling can be asymptotically synchronized onto a desired scaling factor under the designed controller. Moreover, the numerical simulations results demonstrate the validity of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper we study numerically the behavior of worms transmission in a computer network. The model of worms transmission is derived by modifying a SIRS epidemic model. In this case, we consider that the transmission rate, recovery rate and rate of susceptible after recovery follows fuzzy membership functions, rather than constants. To study the transmission of worms in a computer network, we solve the model using the fourth order Runge-Kutta method. Our numerical results show that the fuzzy transmission rate and fuzzy recovery rate may lead to a changing of basic reproduction number which therefore also changes the stability properties of equilibrium points. [ABSTRACT FROM AUTHOR]

In this paper a hybrid algorithm is proposed to find the optimal solution for any instance of the bin packing problem one-dimensional. The hybrid algorithm considers the use of a heuristic method and a mathematical model based on flow arcs technique to find the optimal solution for an instance of 1D-BPP. The hybrid algorithm makes use of the lower bound of an instance as an element that allows it to identify if it have found the optimum or starting from this value it must find the optimal solution. The experiments were performed using the instances of the hard28 set, finding it the optimal solutions for all instances. The results show that the developed algorithm, called AHR, used 75% less time than using the Valerio model. [ABSTRACT FROM AUTHOR]

A new embedded Runge-Kutta-Nyström method based on phase-lag properties is developed in this paper, for the numerical integration of periodic initial problems [ABSTRACT FROM AUTHOR]

The problem of Bin Packing is a problem that is still open. Different strategies have been proposed using heuristic algorithms and metaheuristics to solve it without any of them can get the optimal solutions for all instances of hard28 set. This paper presents a heuristic strategy that solves instances of the hard28 set in less time than that obtained by the best algorithm. This heuristic strategy uses two types of patterns that contain instances of the hard28; approximately one sixth of the values of the objects are prime numbers, and also, about a third of their values are greater than half the capacity of the container, these features allows to fill containers before applying First Fit Decreasing heuristic. The presented heuristic significantly reduces the time needed to obtain the optimal value of some instances. The 28 instances of the hard28 set are used to evaluate the heuristic and the optimal values were obtained five them. [ABSTRACT FROM AUTHOR]

In this paper, we concern at situations where we have to compare selected parameters from particular nonlinear models. A motivational examples of previously modelled data are given at the beginning. When comparing parameters from two models, it is possible to combine them into one model. But for three and more models, it is necessary to correct significance level at advance. Two approaches to solving this problem are stated, so-called Šidák correction and Bonferroni method. Results of these methods as well as results coming from the situation where significance level correction is omitted are compared based on simulated data. [ABSTRACT FROM AUTHOR]

In the past few decades, there is an increasing number of publications which show that solutions to complex mathematical problems can be found by applying unconventional computing methods. Among other examples, the plasmodium of Physarum Polycephalum has been intensively used for solving shortest path(s) problem, various graph problems, evaluation of transport networks, robotic control and many other engineering applications. In this paper we coupled the computing abilities of slime mould with one of the most powerful parallel computational models, namely Cellular Automata (CAs). CAs can capture the essential features of systems which global behavior emerges from the collective effect of simple components, which interact locally. Moreover, a Graphical Processing Unit (GPU) implementation will exploit the prominent feature of parallelism that CA structures inherently possess in contrast to the serial computers, thus accelerating the response of the proposed model. As a result, a slime mould CA based model in graphics processing unit (GPU) using CUDA programming model to describe and mimic the behavior of a plasmodium in a maze. In this way we are able to produce a virtual lab speeding up significantly the biological paradigm in GPU. [ABSTRACT FROM AUTHOR]

Over the years, nurse scheduling is a noticeable problem that is affected by the global nurse turnover crisis. The more nurses are unsatisfied with their working environment the more severe the condition or implication they tend to leave. Therefore, the current undesirable work schedule is partly due to that working condition. Basically, there is a lack of complimentary requirement between the head nurse's liability and the nurses' need. In particular, subject to highly nurse preferences issue, the sophisticated challenge of doing nurse scheduling is failure to stimulate tolerance behavior between both parties during shifts assignment in real working scenarios. Inevitably, the flexibility in shifts assignment is hard to achieve for the sake of satisfying nurse diverse requests with upholding imperative nurse ward coverage. Hence, Evolutionary Algorithm (EA) is proposed to cater for this complexity in a nurse scheduling problem (NSP). The restriction of EA is discussed and thus, enhancement on the EA operators is suggested so that the EA would have the characteristic of a flexible search. This paper consists of three types of constraints which are the hard, semi-hard and soft constraints that can be handled by the EA with enhanced parent selection and specialized mutation operators. These operators and EA as a whole contribute to the efficiency of constraint handling, fitness computation as well as flexibility in the search, which correspond to the employment of exploration and exploitation principles. [ABSTRACT FROM AUTHOR]