Search

The anomalous (fractional) diffusion has a wide application in modeling many physical processes including superconductivity phenomena, protein diffusion within cells, diffusion through porous media, etc. The Fractional Laplacian is a non-local operator. Thus, after the discretization we get a dense system of linear equations. Solving it with traditional Gaussian elimination results in computational complexity of O(n3). The hierarchical compression methods utilize the structure of the matrix A to compress it into a sparser approximation H. The Hierarchical Semi-Separable (HSS) compression is a derivative method that approximates the off-diagonal blocks as Ai j,i≠jUiBijVj. If the approximation of Aij,i≠j is low-rank, the generator matrices Ui, Bij and Vj are much smaller than the non-compressed block Aij,i≠j. The diagonal blocks Aii can be compressed in a similar way and so on recursively. The computational complexity is O(r2n), where r is the maximum off-diagonal rank and, ideally, r approaches O(log n). However, the performance heavily depends on the ordering of the unknowns. In this work we analyze and compare the use of Recursive Bisection and Nested Dissection on the initial mesh to produce a more suitable ordering. Recursive bisection uses a divide and conquer approach to recursively divide the mesh in two and then each halve in two again, and so on recursively. Nested Dissection also divides the mesh in two recursively, but it does so along a set of separator vortices, which form a third part in each level of dissection. We assess and compare the use of Recursive Bisection and Nested Dissection reorderings for improving the performance and accuracy of a parallel HSS solver from the STRUctured Matrix PACKage (STRUMPACK) for a fractional diffusion problem modeled with the Ritz potential. We also compare with results from the original and three other reorderings, as well as using a direct Gaussian elimination solver from Intel®'s Math Kernel Library (MKL). [ABSTRACT FROM AUTHOR]

For the studied average monthly values of the levels of the air pollutant PM10 in Silistra in the period 01.2015 – 12.2019, two modern methods for decomposition were used - X-13ARIMA-SEATS and STL. The trend-cycle and seasonal component of the series were estimated in a total of 24 different ways – 8 models with the X-13ARIMA-SEATS approach with two seasonal adjustment options each – X11 and SEATS and 8 with the STL method. A comparative analysis was made between them, both in terms of estimating the components of the decomposition and in terms of the quality of approximation of the predicted values for the first six months of 2020 to the actually observed ones. In 23 out of 24 assessments of the trend- cycle component, a decreasing trend is observed, followed by a slightly increasing trend in the last year and several months of the period 2015–2019. The STL method yielded better forecast results for the first six months of 2020, using the default settings in the corresponding functions of R programming language. The estimated trend-cycle component by STL method is significantly smoother than that by method X-13ARIMA-SEATS. [ABSTRACT FROM AUTHOR]

High levels of air pollutants PM10 are a problem of great importance for human health. During the months from April to September of the period 2010 - 2019 the levels in Ruse remain within the norm in 95% of the days. During the other, "cold" months of the year, only 58% of the days have values below the daily norm of 50µg/m3. When planning their activities, it is useful for people to have forecasts for PM10 levels in the coming days. Markov chains allow such predictions to be given in a tabular form, convenient to use, without the need for calculations. The data for the "cold" months are modelled using three Markov chains with different degrees of discretization of the original values, respectively with 12, 7 and 3 possible states. The latter, with states: {in the norm}, {slightly above the norm} and {a strong excess of the norm}, can be used without official data on the exact PM10 levels. Determining the condition of the PM10 pollutant today in this case can also be done on the basis of a personal assessment of the purity of the air over the city at the moment. The measured levels in the period 01.01.2020 - 31.03.2020 were used as test data. They show consistency of the measured levels in 2020 with all three Markov chains considered. The obtained tabular values can be used to predict PM10 levels in the following years, in the months from October to March. [ABSTRACT FROM AUTHOR]

A specific transportation problem is presented in the paper. A commonly used variant for the cost value determination is analysed. A Matlab code for solving this specific transportation problem by the heuristic algorithms is developed The optimization model used is related to solving a problem with nondeterministic polynomial-time (NP) hardness and large dimension. A comparison of different heuristic algorithms for solving this problem is made. Results are commented. [ABSTRACT FROM AUTHOR]

High levels of air pollutants PM10 are a problem of great importance for human health. During the months from April to September of the period 2010 - 2019 the levels in Ruse remain within the norm in 95% of the days. During the other, "cold" months of the year, only 58% of the days have values below the daily norm of 50µg/m3. When planning their activities, it is useful for people to have forecasts for PM10 levels in the coming days. Markov chains allow such predictions to be given in a tabular form, convenient to use, without the need for calculations. The data for the "cold" months are modelled using three Markov chains with different degrees of discretization of the original values, respectively with 12, 7 and 3 possible states. The latter, with states: {in the norm}, {slightly above the norm} and {a strong excess of the norm}, can be used without official data on the exact PM10 levels. Determining the condition of the PM10 pollutant today in this case can also be done on the basis of a personal assessment of the purity of the air over the city at the moment. The measured levels in the period 01.01.2020 - 31.03.2020 were used as test data. They show consistency of the measured levels in 2020 with all three Markov chains considered. The obtained tabular values can be used to predict PM10 levels in the following years, in the months from October to March. [ABSTRACT FROM AUTHOR]

End-of-Life tires (EOLT) are ones of the most dangerous waste in the world. They do not practically decompose in nature. Because of this their sound treatment is needed for the environment protection. One of the possible methods for such a treatment is pyrolysis process. It is well known [3, 4] that globally around 23% of all EOLT are processed through pyrolysis, whereas in the Republic of Bulgaria only 5% are processed by this method. Thus for Bulgaria it becomes clear that the pyrolysis method for EOLT treatment still has a good potential for usage, development and further research. This method is very complicated for modeling and studying, because it is 3D and non-stationary. In our previous work [1] we created an adequate mathematical model and numerical algorithm in MATLAB for numerical solving the mathematical initial and boundary value problems for model equations which describe pyrolysis process used for the treatment of the End-of-Life tires (EOLT). Some results for the temperature field for several characteristic periods of operation of pyrolysis station are presented and commented in the papers [1, 2, 5]. This paper deals with studying the influence of two-burner heating upon the heat transfer during EOLT treatment by pyrolysis process. The results for temperature fields, temperature isolines and gradients at some specific moments of time and for two different initial heating functions are graphically presented and commented. Results from this modeling can be used in the real pyrolysis stations for more precise displacement of heathers and measurement devices and for designing of automated management of the process. [ABSTRACT FROM AUTHOR]

Nowadays, the stocks trading is very popular. That is why the problem of forecasting assets’ prices is of a special scientific interest. ARIMA (Autoregressive Integrated Moving Average) models for forecasting the stock prices are presented in this paper. For every model the expected return of the shares is calculated and the variance of the rate of returns is analyzed based on a given historical data. Quarterly data on stock prices of the four biggest banks in the United States, that are classified by total assets, are examined for the period 01.01.2014 – 01.04.2019. An optimization problem is formulated, that is based on Harry Markowitz’s model. The solution of this problem leads to finding an optimal risk portfolio for one period ahead and gives an estimate value of the expected rate of return. Depending on the coefficient of risk aversion, a comparative analysis of the structure of a complete portfolio of a risky and a risk-free asset is made. A Matlab programming code is developed, giving the results for an optimal risk portfolio with n assets. [ABSTRACT FROM AUTHOR]

One of the most dangerous waste in the world are the End-of-Life tires (EOLT). They are waste that does not practically decompose in nature. Because of this their sound treatment is needed for environment protection. Pyrolysis process is one of the possible methods for such a treatment. Globally, around 23% of all EOLT are processed through pyrolysis, whereas in the Republic of Bulgaria only 5% are processed by pyrolysis. It is clear that for Bulgaria this method still has a good potential for usage, development and further research. The pyrolysis process, used for EOLT treatment, usually is 3D and non-stationary. Thus it is very complicated for modeling and studying. Following [3] an adequate mathematical model of the heat transfer during the pyrolysis process used for the treatment of the End-of-Life tires (EOLT) has been presented in our previous paper [1].There a numerical algorithm in MATLAB for solving the respective mathematical initial and boundary value problems has been also developed. Some results for the temperature field for several characteristic periods of operation of pyrolysis station are presented and commented in this paper [1]. In our next paper [2] we have examined the influence of the heating upon the heat transfer during the pyrolysis process used for EOLT treatment. This paper deals with studying the influence of the heater position upon the heat transfer during EOLT treatment by pyrolysis process. The results for temperature fields, temperature isolines and gradients at some specific moments of time and for two different initial heating functions are graphically presented and commented. Results from this modeling can be used in the real pyrolysis stations for more precise displacement of heathers and measurement devices and for designing of automated management of the process. [ABSTRACT FROM AUTHOR]

The liability limitation clause is a required element of any insurance policy. Determining such a limit requires an interruption (one or more) in the distribution of the claim process used for estimating the financial balance. These distributions are found in the literature as truncated distributions. This in turn leads to the question how to proceed with such mixed continuous/discrete distributions if one needs comprehensive analysis, including derivatives, mass functions, accurate simulations random variables with such distributions etc. In the present work the process of claiming as a stochastic process is defined by the important properties of the Poisson process. The question about defining models of the claim process, which arise in practice when imposing a limitation on liability for the individual payment of claims by the insurer is considered. There are different approaches for approximating the distribution functions for solving these issues. The focus in this paper is placed on an algorithmic method for approximation of functions of distribution with a trigonometric Fourier series, giving analytical form of these functions and allowing simulations to be made in the area of interruption of the obtained particular distribution. Results for one of the basically used distribution in the insurance practice - Gamma distribution are presented. The results are compared with normal approximation. Any approximation leads to errors. For estimating and forecasting some of the most often used errors in the analysis are considered two methods - minimax estimation and the least square method. Considered regression models to predict the error, depending on the distribution parameters, provides an opportunity for comparative analysis when using generators of random variables. The achieved algorithmic method could be applied for estimating and forecasting the process of claiming and classical risk models. [ABSTRACT FROM AUTHOR]

Mathematical modeling of the heat transfer during the pyrolysis process used for the treatment of the Endof-Lifetires (EOLT) is presented in this paper. The pyrolysis process is 3D and non-stationary and because of this it is very complicated for modeling and studying. To simplify the modeling here a hierarchy of 2D models for the temperature which describe the non-stationary heat transfer in such a pyrolysis station is created. An algorithm for solving the model equations, based on MATLAB software is developed. The results for the temperature for some characteristic periods of operation of pyrolysis station are presented and commented in the paper. The results from this modeling can be used in the real pyrolysis station for more precise displacement of measurement devices and for designing of automated management of the process. [ABSTRACT FROM AUTHOR]

Current developments on modeling of groundwater flow and contaminant transport and removal in the porous media of Horizontal Subsurface Flow Constructed Wetlands (HSF CWs) are first reviewed in a short way. The two usual environmental engineering approaches, the black-box and the process-based one, are briefly presented. Next, recent research results obtained by using these two approaches are briefly discussed as application examples, where emphasis is given to the evaluation of the optimal design and operation parameters concerning HSF CWs. For the black-box approach, the use of Artificial Neural Networks is discussed for the formulation of models, which predict the removal performance of HSF CWs. A novel mathematical prove is presented, which concerns the dependence of the first-order removal coefficient on the Temperature and the Hydraulic Residence Time. For the process-based approach, an application example is first discussed which concerns procedures to evaluate the optimal range of values for the removal coefficient, dependent on either the Temperature or the Hydraulic Residence Time. This evaluation is based on simulating available experimental results of pilot-scale units operated in Democritus University of Thrace, Xanthi, Greece. Further, in a second example, a novel enlargement of the system of Partial Differential Equations is presented, in order to include geothermal effects. Finally, in a third example, the case of parameters uncertainty concerning biodegradation procedures is considered and the use of upper and a novel approach is presented, which concerns the upper and the lower solution bound for the practical draft design of HSF CWs. [ABSTRACT FROM AUTHOR]

In this paper we propose an iterative steepest-descent-type algorithm that is observed to converge towards the exact solution of the l0 discrete optimization problem, related to graph-Laplacian based image segmentation. Such an algorithm allows for significant additional improvements on the segmentation quality once the minimizer of the associated relaxed lt continuous optimization problem is computed, unlike the standard strategy of simply hard-thresholding the latter. Convergence analysis of the algorithm is not a subject of this work. Instead, various numerical experiments, confirming the practical value of the algorithm, are documented. [ABSTRACT FROM AUTHOR]

Incorporation in concrete composition of steel macro- and micro - fiber reinforcement with structural function increases the degree of ductility of typically brittle cement-containing composites, which in some cases can replace completely or partially conventional steel reinforcement in the form of rods and meshes. Thus, that can reduce manufacturing, detailing and placement of conventional reinforcement, which enhances productivity and economic efficiency of the building process. In this paper, six fiber-reinforced with different amounts of steel fiber cement-containing self-compacting compositions are investigated. The results of some of their main strength-deformation characteristics are presented. Advance approach for the study of structural and material properties of these type composites is proposed by using the methods of industrial computed tomography. The obtained original tomography results about the microstructure and characteristics of individual structural components make it possible to analyze the effective macro-characteristics of the studied composites. The resulting analytical data are relevant for the purposes of multi-dimensional modeling of these systems. Multifactor structure-mechanical analysis of the obtained with different methods original scientific results is proposed. It is presented a conclusion of the capabilities and effectiveness of complex analysis in the studies to characterize the properties of self-compacting fiber-reinforced concrete. [ABSTRACT FROM AUTHOR]

Incorporation in concrete composition of steel macro- and micro - fiber reinforcement with structural function increases the degree of ductility of typically brittle cement-containing composites, which in some cases can replace completely or partially conventional steel reinforcement in the form of rods and meshes. Thus, that can reduce manufacturing, detailing and placement of conventional reinforcement, which enhances productivity and economic efficiency of the building process. In this paper, six fiber-reinforced with different amounts of steel fiber cement-containing self-compacting compositions are investigated. The results of some of their main strength-deformation characteristics are presented. Advance approach for the study of structural and material properties of these type composites is proposed by using the methods of industrial computed tomography. The obtained original tomography results about the microstructure and characteristics of individual structural components make it possible to analyze the effective macro-characteristics of the studied composites. The resulting analytical data are relevant for the purposes of multi-dimensional modeling of these systems. Multifactor structure-mechanical analysis of the obtained with different methods original scientific results is proposed. It is presented a conclusion of the capabilities and effectiveness of complex analysis in the studies to characterize the properties of self-compacting fiber-reinforced concrete. [ABSTRACT FROM AUTHOR]

A numerical approach for a problem arising in Civil and Environmental Engineering is presented. This problem concerns the dynamic soil-pipeline interaction, when unilateral contact conditions due to tensionless and elastoplastic softening/fracturing behaviour of the soil as well as due to gapping caused by earthquake excitations are taken into account. Moreover, soil-capacity degradation due to environmental effects are taken into account. The mathematical formulation of this dynamic elastoplasticity problem leads to a system of partial differential equations with equality domain and inequality boundary conditions. The proposed numerical approach is based on a double discretization, in space and time, and on mathematical programming methods. First, in space the finite element method (FEM) is used for the simulation of the pipeline and the unilateral contact interface, in combination with the boundary element method (BEM) for the soil simulation. Concepts of the non-convex analysis are used. Next, with the aid of Laplace transform, the equality problem conditions are transformed to convolutional ones involving as unknowns the unilateral quantities only. So the number of unknowns is significantly reduced. Then a marching-time approach is applied and a non-convex linear complementarity problem is solved in each time-step. [ABSTRACT FROM AUTHOR]

In this paper we present a new construction of generalized hierarchical bases for symmetric positive definite matrices arising from discontinuous Galerkin discretization of second-order partial differential equations (PDE) with highly varying coefficients. In the well-established theory of hierarchical basis multilevel methods one basic assumption is that the PDE coefficients are smooth functions on the elements of the coarsest mesh partition. It is shown numerically that the developed hierarchical bases yields a robust splitting with respect to jump discontinuities of the PDE coefficient at arbitrary element interfaces on the finest mesh. [ABSTRACT FROM AUTHOR]

In this paper we study the problem of a load, traveling along elastic structures, such as strings, beams or plates. The case of semi-active viscous dampers is also considered. The numerical method, based on the Immersed Interface Finite Element Method is developed. The presence of Dirac-delta function terms in the mathematical model leads to using of a special basis functions near the interfaces. Many numerical experiments are presented for different practical cases. [ABSTRACT FROM AUTHOR]

FEM for a linear and nonlinear elliptic interface problems with discontinuous coefficients is presented. The standard basis functions are modified near the interface in such a way that they satisfy the jump conditions on the interface. Convergence of the method is discussed and numerical experiments, confirming second order of accuracy are shown. [ABSTRACT FROM AUTHOR]