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In this paper, the author first prove the theorem on bilateral generating relations for a certain two-variable generalised hypergeometric polynomials by the group theoretic technique introduced by Weisner. It is then shown how the main theorem can be applied to derive a large variety of bilateral generating functions for various special functions as well as for their various generalizations. Some results given by other researchers are thus observed to follow easily as special cases of the theorem proved in this paper. It is worth noting that special functions play role in the design of filters and approximation theory in communication engineering. [ABSTRACT FROM AUTHOR]

The paper deals with the problem of approximate construction of the reachable set on the plane for a bilinear control system with uncertainty. In the proposed approach of problem solving the uncertainty in the matrix of the system is considered as the control of the second player, that allows to apply solution methods similar to the approaches of the differential games theory. Unlike differential games here the second player acts in conjunction with the first thereby expanding the capabilities of the control system. This approach, with changes in the properties of the components of the system to diametrically opposite ones, fits within the framework of the concept of radical reimplementation. The paper proposes the solution algorithm that is based on operations with polygons and is intended for constructing reachable sets on the plane. On the basis of this algorithm a computer program was developed. This programm was used for a number of numerical experiments. [ABSTRACT FROM AUTHOR]

The paper is devoted approximation of real-valued functions defined on an unbounded interval by linear and non-linear operators. The publication pays special attention to defining class of operators and examining their certain approximation properties. The form of the class of operators given in the present paper makes the achieved results more helpful from the computational point of view. [ABSTRACT FROM AUTHOR]

The subject of this paper belongs to the theory of approximate metrics [23]. An approximate metric on X is a real application defined on X × X that satisfies only a part of the metric axioms. In a recent paper [23], we introduced a new type of approximate metric, named C-metric, that is an application which satisfies only two metric axioms: symmetry and triangular inequality. The remarkable fact in a C-metric space is that a topological structure induced by the C-metric can be defined. The innovative idea of this paper is that we obtain some convergence properties of a C-metric space in the absence of a metric. In this paper we investigate C-metric spaces. The paper is divided into four sections. Section 1 is for Introduction. In Section 2 we recall some concepts and preliminary results. In Section 3 we present some properties of C-metric spaces, such as convergence properties, a canonical decomposition and a C-fixed point theorem. Finally, in Section 4 some conclusions are highlighted. [ABSTRACT FROM AUTHOR]

In this paper, an attempt has been made to obtain generating functions for the Chebyshev polynomials Tn (x) (Special ultra spherical polynomials of first kind) using Weisner's group-theoretic method by interpreting 'n' suitably. It is possible to derive at least three generating relations for various special functions of mathematical physics using this method introduced by Louis Weisner. In approximation theory, the roots (nodes) of Tn(x) are used as matching-points for optimizing polynomial interpolation. Chebyshev polynomials are also used in many models to study them elegantly. [ABSTRACT FROM AUTHOR]

This paper attempts to obtain generating functions for the polynomials defined by Chebyshev denoted as Tn (x) (Special Ultra Spherical Polynomials of the first kind) using Weisner's group-theoretic method by interpreting 'n' suitably. It is possible to derive at least three generating relations for various special functions of mathematical physics using this method introduced by Louis Weisner. In approximation theory, the roots (nodes) of Tn (x) are used as matching points for optimizing polynomial interpolation. Chebyshev polynomials are also used in many models to study them elegantly, including filters in signal processing distributed networks. [ABSTRACT FROM AUTHOR]

The paper deals with suitability of use of the explicit and implicit method in heavily nonlinear seismic analysis and also deals with comparison of response of the Drucker-Prager plastic material model and the modified Mazars damage material model to strong seismic loading. Considering typical time of duration of earthquakes from several seconds to approximately twenty seconds, it would seem that use of the implicit method is definitely more suitable. The shape of accelerograms, however, requires quite short time steps. For the explicit method, on the other hand, very short time steps are required in order to obtain a stable solution. Both methods must be compared with respect to a heavily nonlinear response, typical for seismicity. Massive yielding or damage of the material structure is achieved. Behaviour of both models under the seismic loading is fundamentally different and the paper discusses the differences. Conclusions of the paper are made on the basis of detailed numerical study and may be very useful for practice. [ABSTRACT FROM AUTHOR]

Each university has different regulations in making lecture schedule according to the conditions of respective institution. In this study, regulation on lecture scheduling used the maximum limit of credits of lecturer in a day, in which if exceeds the maximum limit, then the schedule of course will be moved on another day. This study attempts to optimize the schedule preparation in each semester by considering the maximum limit of credits of a lecturer in a day. Lecture scheduling is a combination of space, time, and resources. It is categorized into combinatorial optimization group. There are two methods for solving the combinatorial optimization problems, i.e. exact and approximation method. The approximation method consists of two types, heuristics and metaheuristics. The algorithm metaheuristics categories include genetic algorithm (GA), particle swarm optimization (PSO), ant colony optimization (ACO), bee colony optimization (BCO), simulated annealing, and so on. This paper employed metaheuristics approach. Research on the preparation of lecture scheduling using ACO algorithm has been conducted and proven to be able to prepare the lecture scheduling. The ACO algorithm has numbers of parameters that in solving issues, one must manually set a number of parameters by using the Design of Experiments (DoE) tool, which takes time to solve the optimization problem. Hence, to solve the issue, an automated parameter optimization is required. PSO algorithm has fewer parameters compared to the ACO. Therefore, the purpose of this paper is a hybrid between PSO and ACO in preparing lecture scheduling. [ABSTRACT FROM AUTHOR]

The paper is a continuation of research undertaken in paper [22]. The considered problem consists in presenting some condition sufficient for approximation of the selective points in normed spaces by subseries of the given series. [ABSTRACT FROM AUTHOR]

Carl David Tolmé Runge was a German mathematician. In 1895 he brought about a revolution in the science of what has become numerical analysis. Numerical approximation to the solution of ordinary differential equations had been based on the method of Euler. but it suffered from a low convergence rate. Runge's discovery in his 1895 paper brought the so-called order from 1 up to 2. This development was followed within a few years by extensions of his techniques which brought the possible order up to 4. The analysis of order conditions for early work on Runge-Kutta methods was based on the use of a scalar test problem y' = f (x, y), but for high order method derivations and other applications, it is appropriate to use instead an autonomous high dimensional test problem y' = f (y). Because of the special requirements of stiff problems, implicit Runge-Kutta methods have an importance of their own and these developments are briefly surveyed. The intricate manipulations required to analyse the order of complicated methods has lead to an algebraic theory and its formulation as B-series. Finally, the special applications to structure-preserving algorithms are introduced. [ABSTRACT FROM AUTHOR]

A uniform quadratic approximation of degree 2 is created in explicit parametric form to represent elliptical arcs. The error function is identical to that of the Chebyshev polynomial of degree 4 and equioscillates five times with an approximation order of four. In this paper we provide the approximation method, show it is efficient, its error bound to be accurate and demonstrate that it satisfies properties of the best uniform approximation. [ABSTRACT FROM AUTHOR]

The probability distribution function of a weighted sum of non-identical lognormal random variables is required in various fields of science and engineering and specifically in finance for portfolio management as well as exotic options valuation. Unfortunately, it has no known closed form and therefore has to be approximated. Most of the approximations presented to date are complex as well as complicated for implementation. This paper presents a simple, and easy to implement, approximation method via modified moments matching and a polynomial asymptotic series expansion correction for a central limit theorem of a finite sum. The method results in an intuitively-appealing and computation-efficient approximation for a finite sum of lognormals of at least ten summands and naturally improves as the number of summands increases. The accuracy of the method is tested against the results of Monte Carlo simulationsand also compared against the standard central limit theorem andthe commonly practiced Markowitz' portfolio equations. [ABSTRACT FROM AUTHOR]

In this paper, the meshless multi-point flux approximation (MMPFA) for general fluid flow in porous media is presented. The MMPFA is based on a gradient approximation commonly used in meshless method and can be extended to include higher-order terms in the appropriate Taylor series. The MMPFA is combined with the mixed corrections which ensure linear completeness. The mixed correction utilizes Shepard Functions in combination with a correction to derivative approximations. Incompleteness of the kernel support combined with the lack of consistency of the kernel interpolation in conventional meshless method results in fuzzy boundaries. In corrected meshless method, the domain boundaries and field variables at the boundaries are approximated with the default accuracy of the method. The resulting normalized and corrected MMPFA scheme not only ensures first order consistency O(h) but also alleviates the particle deficiency (kernel support incompleteness) problem. The MMPFA method can be used to model three-dimensional miscible flow in porous media with complex geometry and general anisotropic permeability distributions. To illustrate the performance of the MMPFA, a modelling of a single phase fluid flow in fully anisotropic porous media is presented. [ABSTRACT FROM AUTHOR]

Seismic tomography becomes important tool recently for imaging complex subsurface. It is well known that imaging complex rich fault zone is difficult. In this paper, The application of time domain inverse scattering wave tomography to image the complex fault zone would be shown on this paper, especially an efficient time domain inverse scattering tomography and their run in cluster parallel computer which has been developed. This algorithm is purely based on scattering theory through solving Lippmann Schwienger integral by using Born's approximation. In this paper, it is shown the robustness of this algorithm especially in avoiding the inversion trapped in local minimum to reach global minimum. A large data are solved by windowing and blocking technique of memory as well as computation. Parameter of windowing computation is based on shot gather's aperture. This windowing technique reduces memory as well as computation significantly. This parallel algorithm is done by means cluster system of 120 processors from 20 nodes of AMD Phenom II. Benchmarking of this algorithm is done by means Marmoussi model which can be representative of complex rich fault area. It is shown that the proposed method can image clearly the rich fault and complex zone in Marmoussi model even though the initial model is quite far from the true model. Therefore, this method can be as one of solution to image the very complex mode. [ABSTRACT FROM AUTHOR]

In this paper we prove the existence and uniqueness of a regular solution of the boundary-value problem for a linear nonclassical equatimethodon of odd order in time with changing time direction. The Faedo-Galerkin method is applied to the solution of the boundary value problem. For approximate solutions, an error estimate of the Faedo-Galerkin method is established via the regularization parameter and the eigenvalues of the Dirichlet spectral problem for the Laplace operator. [ABSTRACT FROM AUTHOR]

In 1958, Baranger published three papers in which he established a general theory of the broadening of spectral lines by perturbing particles which was based on several well-defined principles. Subsequently, many authors have carried out calculations using this theory, but which include extra subsidiary approximations. In this paper the original theory is reexamined and illustrative calculations performed in which subsidiary approximations are eliminated and thus enable a quantitative assessment of the accuracy of these approximations to be made. [ABSTRACT FROM AUTHOR]

This paper presents a conjugate gradient-based algorithm for feedback min-max optimal control of nonlinear systems. The algorithm has a backward-in-time recurrent structure similar to the back propagation through time (BPTT) algorithm. The control law is given as the output of the one-layer neural network. Main contribution of the paper includes the integration of BPTT techniques, conjugate gradient methods, Adams method for solving ODEs and automatic differentiation (AD), to provide an effective, novel algorithm for solving numerically optimally min-max control problems. The proposed algorithm is applied to the rotational/translational actuator (RTAC) nonlinear benchmark problem with control and state vector constraints. [ABSTRACT FROM AUTHOR]

In the so called ‘causal’ interpretation of quantum mechanics, an electron is considered as a particle and such particle is influenced not only by a classical but also by a so called quantum potential. This idea was developed by Professor Bohm in an important paper. In this paper we use some of the basics of this interpretation in a financial option pricing environment. The causal interpretation allows for trajectories. Path breaking work by Professors Bohm and Hiley and Khrennikov and Choustova have made that the causal interpretation is a step closer to potential applications in social science. In this paper we consider the wave function as a wave of information. We consider the gradient of the phase of this wave function and show how the option price could be influenced by this gradient. © 2006 American Institute of Physics [ABSTRACT FROM AUTHOR]

A disk Bézier curve is a Bézier curve whose control points are disks. It can be considered as a parametric curve with error tolerances. In this paper, we propose method to find G2-multi degree reduction of disk Bézier curves based on two stages. The center and the radius curves are degree reduced using G2-continuity in the first stage and minimizing the error of approximating the radius curve in the second stage. We give some examples and figures to demonstrate the efficiency of the method. [ABSTRACT FROM AUTHOR]

The paper presents one important case of a canal surface called Dupin's cyclide. Non-degenerate forms of Dupin's cyclide are attractive for example for geometric design applications. In the paper, there is derived one possibility of a rational parameterization of the cyclide as a special case of a canal surface. An algorithm for that parameterization is also shown. The parameterization offers a good method how to approximate especially implicit blend canal surfaces. [ABSTRACT FROM AUTHOR]

In this paper, we give estimates of the distribution function for the approximation numbers of differential operators of mixed type. [ABSTRACT FROM AUTHOR]

Digital radiography has made its way into in-the-field girth weld testing. With recent generations of detectors and x-ray tubes it is possible to reach the image quality desired in standards as well as the speed of inspection desired to be competitive with film radiography and automated ultrasonic testing. This paper will show the application of these technologies in the RTD Rayscan system. The method for achieving an image quality that complies with or even exceeds prevailing industrial standards will be presented, as well as the application on pipeline girth welds with CRA layers. A next step in development will be to also achieve a measurement of weld flaw height to allow for performing an Engineering Critical Assessment on the weld. This will allow for similar acceptance limits as currently used with Automated Ultrasonic Testing of pipeline girth welds. Although a sufficient sizing accuracy was already demonstrated and qualified in the TomoCAR system, testing in some applications is restricted to time limits. The paper will present some experiments that were performed to achieve flaw height approximation within these time limits. [ABSTRACT FROM AUTHOR]

This paper presents a method to approximate discrete joint probability distributions using first-order dependence trees and the recent concept of cumulative residual entropy. A firstorder dependence tree is one where each variable is conditioned on at most one variable. The cumulative residual entropy measure is the entropy functional applied to the survival function instead of the probability measure. We formulate the cumulative residual Kullback-Leibler (KL)- divergence and the cumulative residual mutual information measures in terms of the survival function. We then show that the optimal first-order dependence tree approximation of the joint distribution using the cumulative Kullback-Leibler divergence is the one with the largest sum of cumulative residual mutual information pairs. The results parallel Chow-Liu's approximation of joint probability distributions using the traditional Kullback-Leibler divergence and mutual information but applied to survival functions. We compare the approximation results with those of Chow-Liu using the traditional entropy measure. Using a Monte Carlo simulation, we show that the two approximations perform almost equally but they are not same. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the possible use of control theory, particularly theory on optimal control to derive some numerical methods for unconstrained optimization problems. Based upon this control theory, we derive a Levenberg-Marquardt-like method that guarantees greatest descent in a particular search region. The implementation of this method in its original form requires inversion of a non-sparse matrix or equivalently solving a linear system in every iteration. Thus, an approximation of the proposed method via quasi-Newton update is constructed. Numerical results indicate that the new method is more effective and practical. [ABSTRACT FROM AUTHOR]

In the paper for multidimensional parabolic equation we consider a problem of the right-hand side identification which is a product of two functions, one of which depends on time and the other one depends on space variables. For numerical solution of the posed inverse initial-boundary value problem, the conjugate gradient method is used in combination with the method of finite differences with a purely implicit time approximation. The results of the computational experiment for model problems with quasi-real solutions are discussed. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to approximate some matrix functions by using a family of high-order Newton-type iterative methods. We analyse the semilocal convergence and the speed of convergence of these methods. Concerning stability, it is well known that even the simplified Newton method can be unstable. Despite it, we present stable versions of our family of algorithms for several matrix functions. We test numerically the methods: we check the numerical robustness and stability by considering matrices that are close to be singular and badly conditioned. We find algorithms of the family with better numerical behavior than the Newton and the Halley methods. These two algorithms are basically the iterative methods proposed in the literature to solve many of this type of problems. [ABSTRACT FROM AUTHOR]

The paper focuses on numerical solution of a nonlinear aeroelastic problem. The classical approach of linearized aerodynamic forces is compared to the numerical approximation of the coupled fluid-structure problem. In the second case the finite element method is used for solution of the incompressible Navier-Stokes equations and coupled with the non-linear motion equations of a flexibly supported airfoil. The obtained results are compared to the linearized approach approximations. The influence of the nonlinear terms is discussed. [ABSTRACT FROM AUTHOR]

In this paper, the reliability of the two methods from the family of fourth-order implicit finite difference schemes, namely the fourth-order Crank-Nicolson approximation scheme and the fourth-order standard implicit approximation scheme in solving the diffusion equation has been studied. The corresponding system of linear approximation equations for both fourth-order schemes were derived and then solved iteratively. In addition, for the purpose of assessing the efficiency of both schemes, comparison was made by considering three parameters, which are the iteration numbers, the computation time and the maximum error. Based on the results of the numerical experiments, it shows that the performance of the fourth-order Crank-Nicolson scheme is more efficient compared to the fourth-order standard implicit scheme in solving one-dimensional (1D) diffusion equation. [ABSTRACT FROM AUTHOR]

In this paper, we used the modified Adomian Decomposition Method (LADM) joined Padé approximation to solve a system of delay differential equations (DDEs) with initial value problem (IVP). The main objective of the work to solve the Delay differential equations by approximate solutions method. The examples are solved using the presented method and compared the computed result with the exact solution to show the efficiency of the proposed technique. [ABSTRACT FROM AUTHOR]

The conjugate gradient (CG) and Davidon, Fletcher and Powell (DFP) method are both well known solvers for solving unconstrained optimization problems. In this paper, we proposed a new hybrid DFP-CG method and compared with the ordinary DFP method in terms of number of iteration and CPU times. Numerical results show that the new algorithm is more efficient compared to the ordinary DFP method and proven to posses both sufficient descent and global convergence properties. [ABSTRACT FROM AUTHOR]

In this paper we obtain estimation for the best approximation ... in the L-metric, where ... is the conjugate of the class ..., i.e. ... . Our results concern evaluations of the function ...(G;x), where ...(G;x) is the so-called .... representation of the function G, as defined in [2, p.144], and G(x) denotes the conjugate of the function G(x). After some preliminaries, we formulate three basic theorems (Theorems 2, 3, 4) from the first part of this work [9], necessary for the estimation of the functional... . Specially, in Theorem 4 we prove an inequality for this functional and show that the estimation is exact, i.e. the inequality becomes equality for some specific conjugate functions. Next, the new results in this paper are given as Theorems 5 and 6, with detailed proofs. Furthermore, in our work we prove the following estimation: [ABSTRACT FROM AUTHOR]

In this paper we discuss a fractional order predator-prey model with ratio-dependent functional response. The dynamical properties of this model is analyzed. Here we determine all equilibrium points of this model including their existence conditions and their stability properties. It is found that the model has two type of equilibria, namely the predator-free point and the co-existence point. If there is no co-existence equilibrium, i.e. when the coefficient of conversion from the functional response into the growth rate of predator is less than the death rate of predator, then the predator-free point is asymptotically stable. On the other hand, if the co-existence point exists then this equilibrium is conditionally stable. We also construct a nonstandard Grnwald-Letnikov (NSGL) numerical scheme for the propose model. This scheme is a combination of the Grnwald-Letnikov approximation and the nonstandard finite difference scheme. This scheme is implemented in MATLAB and used to perform some simulations. It is shown that our numerical solutions are consistent with the dynamical properties of our fractional predator-prey model. [ABSTRACT FROM AUTHOR]

The coefficients of sine series which is monotone sequence (MS) have been generalized to General Monotone Sequences (GMS), Group Bounded Variation Sequences (GBVS), Mean Value Bounded Variation Sequences (MVBVS) and Supremum Bounded Variation Sequences of the first type (SBVS) and has been proven that MS ⊊ GMS ⊊ GBVS ⊊ MV BVS. Further it has also been shown that MBVS ⊊ S BVS. Furthermore, in this paper it will be discuss the application of the approximation theory of the sine sequence in the class of supremum Bounded Variation Sequences of the first type which is the generalization of the monotone sequences class. [ABSTRACT FROM AUTHOR]

This paper considered Rayleigh-Benard convection (natural convection). This is a flow, which is formed in a viscous medium when heated from below and cooled from above. As a result, are formed vortices (convective cells). This process is described by a system of nonlinear differential equations in Oberbeck-Boussinesq approximation. As the governing parameters characterizing convection states Rayleigh number, Prandtl number are picked. The problem is solved by using finite element method with computational package FEniCS. Numerical results for different Rayleigh numbers are obtained. Studied integral characteristic (Nusselt number) depending on the Rayleigh number. [ABSTRACT FROM AUTHOR]

In this paper, the systematization of numerical (implemented on a computer) randomized functional algorithms for approximation of a solution of Fredholm integral equation of the second kind is carried out. Wherein, three types of such algorithms are distinguished: the projection, the mesh and the projection-mesh methods. The possibilities for usage of these algorithms for solution of practically important problems is investigated in detail. The disadvantages of the mesh algorithms, related to the necessity of calculation values of the kernels of integral equations in fixed points, are identified. On practice, these kernels have integrated singularities, and calculation of their values is impossible. Thus, for applied problems, related to solving Fredholm integral equation of the second kind, it is expedient to use not mesh, but the projection and the projection-mesh randomized algorithms. [ABSTRACT FROM AUTHOR]

The multi-objective programming problem with fuzzy parameters can be solved by interval programming (IVP) approach which produces the optimal solutions in interval form. However, this paper presents new insights of solving the same problem by a defuzzification approach that is able to produce specific optimal solutions. In the proposed defuzzification approach, the linear programming model is used as an approximation technique to defuzzify fuzzy numbers in the objectives and constraints. In the model formulation, the interval of fuzzy numbers is employed to convert the problem into the standard goal programming problem. As a result, specific optimal solutions of the objective functions are obtained in the specified intervals instead of only in form of intervals as the final solutions. A numerical example is used to illustrate the proposed approach. [ABSTRACT FROM AUTHOR]

The paper deals with the problem of the 1D and 2D structures of detonation waves (DW) in the silane-air mixture within the framework of mathematical model of a nonequilibrium gas dynamics. Detailed kinetics scheme of silane oxidation as well as the newly developed reduced kinetic model of detonation combustion of silane are used. On its basis the DW structure in stoichiometric silane - air mixture and dependences of Chapman-Jouguet parameters of mixture on stoichiometric ratio between the fuel (silane) and an oxidizer (air) were obtained. It was revealed that in the reaction zone, in the structure of DW, the heat release in the model with detailed kinetics is non-monotonic. [ABSTRACT FROM AUTHOR]

The solution of a singularly perturbed problem corresponds to a function with large gradients. Therefore the question of interpolation and numerical differentiation of such functions is relevant. The interpolation based on Lagrange polynomials on uniform mesh is widely applied. However, it is known that the use of such interpolation for the function with large gradients leads to estimates that are not uniform with respect to the perturbation parameter and therefore leads to errors of order O(1). To obtain the estimates that are uniform with respect to the perturbation parameter, we can use the polynomial interpolation on a fitted mesh like the piecewise-uniform Shishkin mesh or we can construct on uniform mesh the interpolation formula that is exact on the boundary layer components. In this paper the numerical differentiation formulas for functions with large gradients based on the interpolation formulas on the uniform mesh, which were proposed by A.I. Zadorin, are investigated. The formulas for the first and the second derivatives of the function with two or three interpolation nodes are considered. Error estimates that are uniform with respect to the perturbation parameter are obtained in the particular cases. The numerical results validating the theoretical estimates are discussed. [ABSTRACT FROM AUTHOR]

Coastal erosion is one of the global problems which also one of the national's environmental major concerns. The coastal erosion can be easily happened if the sea level rises along with the frequent and huge storms. There are various risk factors that can be related with coastal erosion such as tidal range, storm surge, wave height and etc. However, the relative weights for these risk factors are still inconclusive. Thus, this paper aims to determine the relative global weights of risk factors that contribute to coastal erosion using the Analytic Hierarchy Process (AHP) method. Three decision makers were invited to provide judgments for pair-wise comparison matrices of the method. The global weights were obtained using the concept of group decision making environment. The result shows that the most influencing risk factor is shoreline evolution with the highest weightage (20.74%) compared to the other factors. [ABSTRACT FROM AUTHOR]

The paper presents the approach to modelling of the transport delay using several approximation formulas. The selected approximation of the transport delay is then used in the simple control system model to demonstrate its operation. The aim of the approach is to create the homogeneous system, therefore, hardware representation is discussed. [ABSTRACT FROM AUTHOR]

Some interesting identities of Sheffer polynomials was given by Roman [11], [12]. In this paper, we study a q-analogue of Laguerre polynomials which are also q-Sheffer polynomials. Furthermore, we give some new properties and formulas of these q-Laguerre polynomials of higher order by using the theory of the umbral algebra and umbral calculus. [ABSTRACT FROM AUTHOR]

In this paper, a quadratic spline is presented. The boundary conditions are adjusted to get new parameters that are used to get better approximation. Some numerical results are given to demonstrate the advantages and efficiency of the method. The proposed method is more accurate than the traditional quadratic method. [ABSTRACT FROM AUTHOR]

Usually, numerical simulation is used to predict the acoustic filed and temperature distribution of high intensity focused ultrasound (HIFU). In this paper, the simulated lesion volumes obtained by temperature threshold (TRT) 60 °C and equivalent thermal dose (ETD) 240 min were compared with the experimental results which were obtained by animal tissue experiment in vitro. In the simulation, the calculated model was established according to the vitro tissue experiment, and the Finite Difference Time Domain (FDTD) method was used to calculate the acoustic field and temperature distribution in bovine liver by the Westervelt formula and Pennes bio-heat transfer equation, and the nonlinear characteristics of the ultrasound was considered. In the experiment, the fresh bovine liver was exposed for 8s, 10s, 12s under different power conditions (150W, 170W, 190W, 210W), and the exposure was repeated 6 times under the same dose. After the exposures, the liver was sliced and photographed every 0.2mm, and the area of the lesion region in every photo was calculated. Then, every value of the areas was multiplied by 0.2mm, and summed to get the approximation volume of the lesion region. The comparison result shows that the lesion volume of the region calculated by TRT 60 °C in simulation was much closer to the lesion volume obtained in experiment, and the volume of the region above 60 °C was larger than the experimental results, but the volume deviation was not exceed 10%. The volume of the lesion region calculated by ETD 240 min was larger than that calculated by TRT 60 °C in simulation, and the volume deviations were ranged from 4.9% to 23.7%. [ABSTRACT FROM AUTHOR]

One method of efficiently modelling of ultrasonic array data is based on a combination of a ray-tracing approach and far-field scattering amplitude of a scatterer. This technique uses two main assumptions: all scatterers are located in the far-field from each array element and the size of each scatterer is small relative to its distance to array elements. The key part of the model is the so-called scattering matrix, which provides the amplitude and phase of scattered waves in the far-field of the scatterer. However, the far-field approximation fails when the size of the scatterer becomes comparable to its distance to array elements. In this paper a near-field model of ultrasonic array data is developed. In particular, it is shown that the near-field scattering behavior can be extracted from the scattering matrix. The applications of the model are discussed and supported with modelling examples. [ABSTRACT FROM AUTHOR]

In the ring of quaternionic polynomials there is no easy solution to the problem of finding a suitable definition of multiplicity of a zero. In this paper we discuss different notions of multiple zeros available in the literature and add a computational point of view to this problem, by taking into account the behavior of the well known Newton's method in the presence of such roots. [ABSTRACT FROM AUTHOR]

After Black-Scholes proposed a model for pricing European Options in 1973, Cox, Ross and Rubinstein in 1979, and Heston in 1993, showed that the constant volatility assumption made by Black-Scholes was one of the main reasons for the model to be unable to capture some market details. Instead of constant volatilities, they introduced stochastic volatilities to the asset dynamic modeling. In 2009, Christo ersen empirically showed "why multifactor stochastic volatility models work so well". Four years later, Chiarella and Ziveyi solved the model proposed by Christo ersen. They considered an underlying asset whose price is governed by two factor stochastic volatilities of mean reversion type. Applying Fourier transforms, Laplace transforms and the method of characteristics they presented a semi-analytical formula to compute an approximate price for American options. The huge calculation involved in the Chiarella and Ziveyi approach motivated the authors of this paper in 2014 to investigate another methodology to compute European Option prices on a Christo ersen type model. Using the first and second order asymptotic expansion method we presented a closed form solution for European option, and provided experimental and numerical studies on investigating the accuracy of the approximation formulae given by the first order asymptotic expansion. In the present paper we will perform experimental and numerical studies for the second order asymptotic expansion and compare the obtained results with results presented by Chiarella and Ziveyi. [ABSTRACT FROM AUTHOR]

A multi-peaked analytically extended function (AEF), previously applied by the authors to modeling of lightning discharge currents, is used in this paper for representation of the electrostatic discharge (ESD) currents. In order to estimate its non-linear parameters, the Marquardt least-squares method (MLSM) is used. ESD currents' modelling is illustrated through an essential example corresponding to approximation of the IEC Standard 61000-4-2 waveshape. [ABSTRACT FROM AUTHOR]

The paper presents two different approaches to reduce the time of computer calculation of reachability sets. First of these two approaches use different data structures for storing the reachability sets in the computer memory for calculation in single-threaded mode. Second approach is based on using parallel algorithms with reference to the data structures from the first approach. Within the framework of this paper parallel algorithm of approximate reachability set calculation on computer with SMP-architecture is proposed. The results of numerical modelling are presented in the form of tables which demonstrate high efficiency of parallel computing technology and also show how computing time depends on the used data structure. [ABSTRACT FROM AUTHOR]

We consider the problem of Bayesian inference for parameters in non-linear regression models whereby the underlying unknown response functions are formed by a set of differential equations. Bayesian methods of inference for unknown parameters rely primarily on the posterior obtained by Bayes rule. For differential equation models, analytic and closed forms for the posterior are not available and one has to resort to approximations. We propose a two-stage Laplace expansion to approximate the marginal likelihood, and hence, the posterior, to obtain an approximate closed form solution. For large sample sizes, the method of inference borrows from non-linear regression theory for maximum likelihood estimates, and is therefore, consistent. Our approach is exact in the limit and does not need the specification of an additional penalty parameter. Examples in this paper include the exponential model and SIR (Susceptible-Infected-Recovered) disease spread model. [ABSTRACT FROM AUTHOR]