Authors:Jaroslav Mlýnek; Roman Knobloch Pages: 111 - 124 Abstract: This article focuses on heat radiation intensity optimization on the surface of a shell metal mould. Such moulds are used in the automotive industry in the artificial leather production (the artificial leather is used, e.g., on car dashboards). The mould is heated by infrared heaters. After the required temperature is attained, the inner mould surface is sprinkled with special PVC powder. The powder melts and after cooling down it forms the artificial leather. A homogeneous temperature field of the mould is a necessary prerequisite for obtaining a uniform colour shade and material structure of the artificial leather. The article includes a description of a mathematical model that allows to calculate the heat radiation intensity on the outer mould surface for each fixed positioning of the infrared heaters. Next, we use this mathematical model to optimize the locations of the heaters to provide approximately the same heat radiation intensity on the whole outer mould surface during the heating process. The heat radiation intensity optimization is a complex task, because the cost function may have many local minima. Therefore, using gradient methods to solve this problem is not suitable. A differential evolution algorithm is applied during the optimization process. Asymptotic convergence of the algorithm is shown. The article contains a practical example including graphical outputs. The calculations were performed by means of Matlab code written by the authors. PubDate: 2018-04-01 DOI: 10.21136/am.2018.0086-17 Issue No:Vol. 63, No. 2 (2018)

Authors:Mohsen Yousefnezhad; Seyyed Abbas Mohammadi; Farid Bozorgnia Pages: 125 - 147 Abstract: This paper deals with a reaction-diffusion system modeling a free boundary problem of the predator-prey type with prey-taxis over a one-dimensional habitat. The free boundary represents the spreading front of the predator species. The global existence and uniqueness of classical solutions to this system are established by the contraction mapping principle. With an eye on the biological interpretations, numerical simulations are provided which give a real insight into the behavior of the free boundary and the stability of the solutions. PubDate: 2018-04-01 DOI: 10.21136/am.2018.0227-17 Issue No:Vol. 63, No. 2 (2018)

Authors:Peng Gao; Heping Dong; Fuming Ma Pages: 149 - 165 Abstract: We consider the inverse scattering of time-harmonic plane waves to reconstruct the shape of a sound-soft crack from a knowledge of the given incident field and the phaseless data, and we check the invariance of far field data with respect to translation of the crack. We present a numerical method that is based on a system of nonlinear and ill-posed integral equations, and our scheme is easy and simple to implement. The numerical implementation is described and numerical examples are presented to illustrate the feasibility of the proposed method. PubDate: 2018-04-01 DOI: 10.21136/am.2018.0154-17 Issue No:Vol. 63, No. 2 (2018)

Authors:Amit Ghosh; Chanchal Kundu Pages: 167 - 193 Abstract: The notion of cumulative past inaccuracy (CPI) measure has recently been proposed in the literature as a generalization of cumulative past entropy (CPE) in univariate as well as bivariate setup. In this paper, we introduce the notion of CPI of order α and study the proposed measure for conditionally specified models of two components failed at different time instants, called generalized conditional CPI (GCCPI). Several properties, including the effect of monotone transformation and bounds of GCCPI are discussed. Furthermore, we characterize some bivariate distributions under the assumption of conditional proportional reversed hazard rate model. Finally, the role of GCCPI in reliability modeling has also been investigated for a real-life problem. PubDate: 2018-04-01 DOI: 10.21136/am.2018.0170-17 Issue No:Vol. 63, No. 2 (2018)

Authors:Ji-Chuan Liu Pages: 195 - 216 Abstract: In this paper, we consider a two-dimensional inverse medium problem from noisy observation data. We propose effective reconstruction algorithms to detect the num-ber, the location and the size of the piecewise constant medium within a body, and then we try to recover the unknown shape of inhomogeneous media. This problem is nonlinear and ill-posed, thus we should consider stable and elegant approaches in order to improve the corresponding approximation. We give several examples to show the viability of our proposed algorithms. PubDate: 2018-04-01 DOI: 10.21136/am.2018.0114-17 Issue No:Vol. 63, No. 2 (2018)

Authors:Bohdan Maslowski; Jana Šnupárková Pages: 7 - 35 Abstract: A stochastic affine evolution equation with bilinear noise term is studied, where the driving process is a real-valued fractional Brownian motion with Hurst parameter greater than 1/2. Stochastic integration is understood in the Skorokhod sense. The existence and uniqueness of weak solution is proved and some results on the large time dynamics are obtained. PubDate: 2018-01-08 DOI: 10.21136/am.2018.0036-17 Issue No:Vol. 63, No. 1 (2018)

Authors:Luca Sabatini Pages: 37 - 53 Abstract: The free motion of a thin elastic linear membrane is described, in a simply-fied model, by a second order linear homogeneous hyperbolic system of partial differential equations whose spatial part is the Laplace Beltrami operator acting on a Riemannian 2- dimensional manifold with boundary. We adapt the estimates of the spectrum of the Laplacian obtained in the last years by several authors for compact closed Riemannian manifolds. To make so, we use the standard technique of the doubled manifold to transform a Rie- mannian manifold with nonempty boundary (M, 'M, g) to a compact Riemannian manifold (M♯M, \(\tilde g\) ) without boundary. An easy numerical investigation on a concrete semi-ellipsoidic membrane with clamped boundary tests the sharpness of the method. PubDate: 2018-01-16 DOI: 10.21136/am.2018.0316-16 Issue No:Vol. 63, No. 1 (2018)

Authors:Lakshmi Kanta Patra; Suchandan Kayal; Phalguni Nanda Pages: 55 - 77 Abstract: We focus on stochastic comparisons of lifetimes of series and parallel systems consisting of independent and heterogeneous new Pareto type components. Sufficient con- ditions involving majorization type partial orders are provided to obtain stochastic compar- isons in terms of various magnitude and dispersive orderings which include usual stochastic order, hazard rate order, dispersive order and right spread order. The usual stochastic order of lifetimes of series systems with possibly different scale and shape parameters is studied when its matrix of parameters changes to another matrix in certain sense. PubDate: 2018-01-17 DOI: 10.21136/am.2018.0105-17 Issue No:Vol. 63, No. 1 (2018)

Authors:Hassan S. Bakouch; Mehrnaz Mohammadpour; Masumeh Shirozhan Pages: 79 - 105 Abstract: Many real-life count data are frequently characterized by overdispersion, excess zeros and autocorrelation. Zero-inflated count time series models can provide a powerful procedure to model this type of data. In this paper, we introduce a new stationary first-order integer-valued autoregressive process with random coefficient and zero-inflated geometric marginal distribution, named ZIGINARRC(1) process, which contains some sub-models as special cases. Several properties of the process are established. Estimators of the model parameters are obtained and their performance is checked by a small Monte Carlo simula- tion. Also, the behavior of the inflation parameter of the model is justified. We investigate an application of the process using a real count climate data set with excessive zeros for the number of tornados deaths and illustrate the best performance of the proposed process as compared with a set of competitive INAR(1) models via some goodness-of-fit statistics. Consequently, forecasting for the data is discussed with estimation of the transition prob- ability and expected run length at state zero. Moreover, for the considered data, a test of the random coefficient for the proposed process is investigated. PubDate: 2018-01-25 DOI: 10.21136/am.2018.0082-17 Issue No:Vol. 63, No. 1 (2018)

Authors:Jean-Philippe Lessard Pages: 1 - 17 Abstract: We introduce a method to compute rigorous component-wise enclosures of discrete convolutions using the fast Fourier transform, the properties of Banach algebras, and interval arithmetic. The purpose of this new approach is to improve the implementation and the applicability of computer-assisted proofs performed in weighed ℓ1 Banach algebras of Fourier/Chebyshev sequences, whose norms are known to be numerically unstable. We introduce some application examples, in particular a rigorous aposteriori error analysis for a steady state in the quintic Swift-Hohenberg PDE. PubDate: 2018-05-23 DOI: 10.21136/am.2018.0082-18

Authors:Hans-Goerg Roos Pages: 1 - 7 Abstract: Error estimates of finite element methods for reaction-diffusion problems are often realized in the related energy norm. In the singularly perturbed case, however, this norm is not adequate. A different scaling of the H1 seminorm leads to a balanced norm which reflects the layer behavior correctly. We discuss the difficulties which arise for systems of reaction-diffusion problems. PubDate: 2018-05-22 DOI: 10.21136/am.2018.0063-18

Authors:Kebaili Zahira; Benterki Djamel Pages: 1 - 16 Abstract: We propose a penalty approach for a box constrained variational inequality problem (BVIP). This problem is replaced by a sequence of nonlinear equations containing a penalty term. We show that if the penalty parameter tends to infinity, the solution of this sequence converges to that of BVIP when the function F involved is continuous and strongly monotone and the box C contains the origin. We develop the algorithmic aspect with theoretical arguments properly established. The numerical results tested on some examples are satisfactory and confirm the theoretical approach. PubDate: 2018-05-22 DOI: 10.21136/am.2018.0334-17

Authors:Sahbi Boussandel Pages: 1 - 16 Abstract: We establish the existence of solutions for evolution equations in Hilbert spaces with antiperiodic boundary conditions. The energies associated to these evolution equations are quadratic forms. Our approach is based on application of the Schaefer fixed-point theorem combined with the continuity method. PubDate: 2018-05-20 DOI: 10.21136/am.2018.0233-17

Authors:Ali Khademi; Sergey Korotov; Jon Eivind Vatne Pages: 1 - 21 Abstract: We propose an analogue of the maximum angle condition (commonly used in finite element analysis for triangular and tetrahedral meshes) for the case of prismatic elements. Under this condition, prisms in the meshes may degenerate in certain ways, violating the so-called inscribed ball condition presented by P.G.Ciarlet (1978), but the interpolation error remains of the order O(h) in the H1-norm for sufficiently smooth functions. PubDate: 2018-04-17 DOI: 10.21136/am.2018.0357-17

Authors:Radim Blaheta; Tomáš Luber Pages: 561 - 577 Abstract: This paper deals with a nonlinear beam model which was published by D.Y.Gao in 1996. It is considered either pure bending or a unilateral contact with elastic foundation, where the normal compliance condition is employed. Under additional assumptions on data, higher regularity of solution is proved. It enables us to transform the problem into a control variational problem. For basic types of boundary conditions, suitable transformations of the problem are derived. The control variational problem contains a simple linear state problem and it is solved by the conditioned gradient method. Illustrative numerical examples are introduced in order to compare the Gao beam with the classical Euler-Bernoulli beam. PubDate: 2017-11-30 DOI: 10.21136/am.2017.0179-17 Issue No:Vol. 62, No. 6 (2017)

Authors:Petr Kurfürst; Jiří Krtička Pages: 633 - 659 Abstract: Bounds on the spectrum of the Schur complements of subdomain stiffness matrices with respect to the interior variables are key ingredients in the analysis of many domain decomposition methods. Here we are interested in the analysis of floating clusters, i.e. subdomains without prescribed Dirichlet conditions that are decomposed into still smaller subdomains glued on primal level in some nodes and/or by some averages. We give the estimates of the regular condition number of the Schur complements of the clusters arising in the discretization of problems governed by 2D Laplacian. The estimates depend on the decomposition and discretization parameters and gluing conditions. We also show how to plug the results into the analysis of H-TFETI methods and compare the estimates with numerical experiments. The results are useful for the analysis and implementation of powerful massively parallel scalable algorithms for the solution of variational inequalities. PubDate: 2017-12-13 DOI: 10.21136/am.2017.0135-17 Issue No:Vol. 62, No. 6 (2017)

Authors:Jitka Machalová; Horymír Netuka Pages: 661 - 677 Abstract: We calculate self-consistent time-dependent models of astrophysical processes. We have developed two types of our own (magneto) hydrodynamic codes, either the operator-split, finite volume Eulerian code on a staggered grid for smooth hydrodynamic flows, or the finite volume unsplit code based on the Roe’s method for explosive events with extremely large discontinuities and highly supersonic outbursts. Both the types of the codes use the second order Navier-Stokes viscosity to realistically model the viscous and dissipative effects. They are transformed to all basic orthogonal curvilinear coordinate systems as well as to a special non-orthogonal geometric system that fits to modeling of astrophysical disks. We describe mathematical background of our codes and their implementation for astrophysical simulations, including choice of initial and boundary conditions. We demonstrate some calculated models and compare the practical usage of numerically different types of codes. PubDate: 2017-11-23 DOI: 10.21136/am.2017.0168-17 Issue No:Vol. 62, No. 6 (2017)

Authors:Petr Vodstrčil; Jiří Bouchala; Marta Jarošová; Zdeněk Dostál Pages: 699 - 718 Abstract: The evaluation of option premium is a very delicate issue arising from the assumptions made under a financial market model, and pricing of a wide range of options is generally feasible only when numerical methods are involved. This paper is based on our recent research on numerical pricing of path-dependent multi-asset options and extends these results also to the case of Asian options with fixed strike. First, we recall the three-dimensional backward parabolic PDE describing the evolution of European-style Asian option contracts on two assets, whose payoff depends on the difference of the strike price and the average value of the basket of two underlying assets during the life of the option. Further, a suitable transformation of variables respecting this complex form of a payoff function reduces the problem to a two-dimensional equation belonging to the class of convection-diffusion problems and the discontinuous Galerkin (DG) method is applied to it in order to utilize its solving potentials. The whole procedure is accompanied with theoretical results and differences to the floating strike case are discussed. Finally, reference numerical experiments on real market data illustrate comprehensive empirical findings on Asian options. PubDate: 2017-12-11 DOI: 10.21136/am.2017.0193-17 Issue No:Vol. 62, No. 6 (2017)