Search results for: continuum approximation

Authors: Balachandra Kumaraswamy, P. G. Poonacha

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Automatic Music Information Retrieval has been one of the challenging topics of research for a few decades now with several interesting approaches reported in the literature. In this paper we have developed a pitch extraction method based on a finite Fourier series approximation to the given window of samples. We then estimate pitch as the fundamental period of the finite Fourier series approximation to the given window of samples. This method uses analysis of the strength of harmonics present in the signal to reduce octave as well as harmonic errors. The performance of our method is compared with three best known methods for pitch extraction, namely, Yin, Windowed Special Normalization of the Auto-Correlation Function and Harmonic Product Spectrum methods of pitch extraction. Our study with artificially created signals as well as music files show that Fourier Approximation method gives much better estimate of pitch with less octave and harmonic errors.

Keywords: pitch, fourier series, yin, normalization of the auto- correlation function, harmonic product, mean square error

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Authors: Diogo Silva, Fadul Rodor, Carlos Moraes

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This work compares the results of multidimensional function approximation using two algorithms: the classical Particle Swarm Optimization (PSO) and the Quantum Particle Swarm Optimization (QPSO). These algorithms were both tested on three functions - The Rosenbrock, the Rastrigin, and the sphere functions - with different characteristics by increasing their number of dimensions. As a result, this study shows that the higher the function space, i.e. the larger the function dimension, the more evident the advantages of using the QPSO method compared to the PSO method in terms of performance and number of necessary iterations to reach the stop criterion.

Keywords: PSO, QPSO, function approximation, AI, optimization, multidimensional functions

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Authors: Valeria Bondarenko

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We proposed algorithms for: estimation of parameters fBm (volatility and Hurst exponent) and for the approximation of random time series by functional of fBm. We proved the consistency of the estimators, which constitute the above algorithms, and proved the optimal forecast of approximated time series. The adequacy of estimation algorithms, approximation, and forecasting is proved by numerical experiment. During the process of creating software, the system has been created, which is displayed by the hierarchical structure. The comparative analysis of proposed algorithms with the other methods gives evidence of the advantage of approximation method. The results can be used to develop methods for the analysis and modeling of time series describing the economic, physical, biological and other processes.

Keywords: mathematical model, random process, Wiener process, fractional Brownian motion

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Authors: Sirapat Lookrak, Anol Paisal

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Space debris has numerous manifestations, including ferro-metalize and non-ferrous. The electric field will induce negative charges to split from positive charges inside the space debris. In this research, we focus only on conducting materials. The assumption is that the electric charge density of a conducting surface is proportional to the electric field on that surface due to Gauss's Law. We are trying to find the induced charge density from an external electric field perpendicular to a conducting spherical surface. An object is a sphere on which the external electric field is not uniform. The electric field is, therefore, considered locally. The localised spherical surface is a tangent plane, so the Gaussian surface is a very small cylinder, and every point on a spherical surface has its own cylinder. The electric field from a circular electrode has been calculated in near-field and far-field approximation and shown Explanation Touchless maneuvering space debris orbit properties. The electric charge density calculation from a near-field and far-field approximation is done.

Keywords: near-field approximation, far-field approximation, localized Gauss’s law, electric charge density

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Authors: Preeti Sharma

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This paper deals with the Stancu type generalization of Lupaş-Durrmeyer operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0, 1]. Also, Voronovskaja type theorem is studied.

Keywords: Lupas-Durrmeyer operators, polya distribution, weighted approximation, rate of convergence, modulus of continuity

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Authors: M. A. Ghebouli, H. Choutri, B. Ghebouli , M. Fatmi, L. Louail

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We employed the density-functional perturbation theory (DFPT) within the generalized gradient approximation (GGA), the local density approximation (LDA) and the virtual-crystal approximation (VCA) to study the effect of composition on the structure, stability, energy gaps, electron effective mass, the dynamic effective charge, optical and acoustical phonon frequencies and static and high dielectric constants of the rock-salt CaxMg1-xSe and CaxMg1-xTe alloys. The computed equilibrium lattice constant and bulk modulus show an important deviation from the linear concentration. From the Voigt-Reuss-Hill approximation, CaxMg1-xSe and CaxMg1-xTe present lower stiffness and lateral expansion. For Ca content ranging between 0.25-0.75, the elastic constants, energy gaps, electron effective mass and dynamic effective charge are predictions. The elastic constants and computed phonon dispersion curves indicate that these alloys are mechanically stable.

Keywords: CaxMg1-xSe, CaxMg1-xTe, band structure, phonon

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Authors: Manoj K. Kumar, Deepthi Bathala

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Man has the need to know and feel as a part of the historical continuum and it is this continuum that reinforces his identity. Architecture and the built environment contribute to this identity as established by the various identity theories exploring the relationship between the two. Architecture which is organic has been successful in maintaining a continuum of identity until the advent of globalization when the world saw a drastic shift to architecture of ‘placelessness’. The answer to the perfect synthesis of ‘universalization’ and ‘regionalism’ is an ongoing quest. However, history has established a smooth transition from vernacular to colonial to modern unlike the architecture of today. The traditional Kerala architecture has evolved from the tropical climate, geography, local needs, materials, skills and foreign influences. It is unique in contrast to the architecture of the neighboring states as a result of the geographical barriers however influenced by the architecture of the Orient due to trade relations. Through 1805 to 1950, the European influence on the architecture of Kerala resulted in the emergence of the colonial style which managed to establish a continuum of the traditional architecture. The paper focuses on the identification of the components of architecture that established the continuity of place-identity in the architecture of Kerala and examines the transition from the traditional Kerala architecture to colonial architecture during the colonial period. Visual surveys based on the principles of urban design, cognitive mapping, typology analysis followed by the strong understanding of the morphological and built environment along with the matrix method are the research tools used. The understanding of these components of continuity can be useful in creating buildings which people can relate to in the present day. South-Asia shares the history of colonialism and the understanding of these components can pave the way for further research on how to establish a regional identity in the era of globalization.

Keywords: colonial, identity, place, regional

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Authors: Najrullah Khan, Athar Ali Khan

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The Topp-Leone distribution was introduced by Topp- Leone in 1955. In this paper, an attempt has been made to fit Topp-Leone Generalized exponential (TPGE) distribution. A real survival data set is used for illustrations. Implementation is done using R and JAGS and appropriate illustrations are made. R and JAGS codes have been provided to implement censoring mechanism using both optimization and simulation tools. The main aim of this paper is to describe and illustrate the Bayesian modelling approach to the analysis of survival data. Emphasis is placed on the modeling of data and the interpretation of the results. Crucial to this is an understanding of the nature of the incomplete or 'censored' data encountered. Analytic approximation and simulation tools are covered here, but most of the emphasis is on Markov chain based Monte Carlo method including independent Metropolis algorithm, which is currently the most popular technique. For analytic approximation, among various optimization algorithms and trust region method is found to be the best. In this paper, TPGE model is also used to analyze the lifetime data in Bayesian paradigm. Results are evaluated from the above mentioned real survival data set. The analytic approximation and simulation methods are implemented using some software packages. It is clear from our findings that simulation tools provide better results as compared to those obtained by asymptotic approximation.

Keywords: Bayesian Inference, JAGS, Laplace Approximation, LaplacesDemon, posterior, R Software, simulation

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Authors: Zaid Jamal Saeed Almahmoud

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Smart grid is emerging as the future power grid, with smart techniques to optimize power consumption and electricity generation. Minimizing peak power consumption under a fixed delay requirement is a significant problem in the smart grid.For this problem, all appliances must be scheduled within a given finite time duration. We consider the problem of minimizing the peak demand under appliances constraints by scheduling power jobs with uniform release dates and deadlines. As the problem is known to be NP-hard, we analyze the performance of a version of the natural greedy heuristic for solving this problem. Our theoretical analysis and experimental results show that the proposed heuristic outperforms existing methods by providing a better approximation to the optimal solution.

Keywords: peak demand scheduling, approximation algorithms, smart grid, heuristics

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Authors: Vikram Saini, Lillie Dewan

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This paper presents the iterative schemes based on Least square, Hierarchical Least Square and Stochastic Approximation Gradient method for the Identification of Wiener model with parametric structure. A gradient method is presented for the parameter estimation of wiener model with noise conditions based on the stochastic approximation. Simulation results are presented for the Wiener model structure with different static non-linear elements in the presence of colored noise to show the comparative analysis of the iterative methods. The stochastic gradient method shows improvement in the estimation performance and provides fast convergence of the parameters estimates.

Keywords: hard non-linearity, least square, parameter estimation, stochastic approximation gradient, Wiener model

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Authors: Masoud Safdari, Jacob Fish

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Despite vast amount of existing theoretical knowledge, the implementation of a universal multiscale modeling, analysis, and simulation software framework remains challenging. Existing multiscale software and solutions are often domain-specific, closed-source and mandate a high-level of experience and skills in both multiscale analysis and programming. Furthermore, tools currently existing for Atomistic-to-Continuum (AtC) multiscaling are developed with the assumptions such as accessibility of high-performance computing facilities to the users. These issues mentioned plus many other challenges have reduced the adoption of multiscale in academia and especially industry. In the current work, we introduce Multiscale Hub (MsHub), an effort towards making AtC more accessible through cloud services. As a joint effort between academia and industry, MsHub provides a universal web-enabled framework for practical multiscaling. Developed on top of universally acclaimed scientific programming language Python, the package currently provides an open-source, comprehensive, easy-to-use framework for AtC coupling. MsHub offers an easy to use interface to prominent molecular dynamics and multiphysics continuum mechanics packages such as LAMMPS and MFEM (a free, lightweight, scalable C++ library for finite element methods). In this work, we first report on the design philosophy of MsHub, challenges identified and issues faced regarding its implementation. MsHub takes the advantage of a comprehensive set of tools and algorithms developed for AtC that can be used for a variety of governing physics. We then briefly report key AtC algorithms implemented in MsHub. Finally, we conclude with a few examples illustrating the capabilities of the package and its future directions.

Keywords: atomistic, continuum, coupling, multiscale

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Authors: Eda Gök

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Peridynamics is a new modeling concept of non-local interactions for solid structures. The formulations of Peridynamic (PD) theory are based on integral equations rather than differential equations. Through, undefined equations of associated problems are avoided. PD theory might be defined as continuum version of molecular dynamics. The medium is usually modeled with mass particles bonded together. Particles interact with each other directly across finite distances through central forces named as bonds. The main assumption of this theory is that the body is composed of material points which interact with other material points within a finite distance. Although, PD theory developed for discontinuities, it gives good results for structures which have no discontinuities. In this paper, displacement control of the isotropic plate under the effect of tensile and bending loading has been investigated by means of PD theory. A MATLAB code is generated to create PD bonds and corresponding surface correction factors. Using generated MATLAB code the geometry of the specimen is generated, and the code is implemented in Finite Element Software. The results obtained from non-local continuum theory are compared with the Finite Element Analysis results and analytical solution. The results show good agreement.

Keywords: non-local continuum mechanics, peridynamic theory, solid structures, tensile loading, flexural loading

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Authors: Tarul Garg, P. N. Agrawal

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We propose to define the q-analogue of the α-Bernstein Kantorovich operators and then introduce the q-bivariate generalization of these operators to study the approximation of functions of two variables. We obtain the rate of convergence of these bivariate operators by means of the total modulus of continuity, partial modulus of continuity and the Peetre’s K-functional for continuous functions. Further, in order to study the approximation of functions of two variables in a space bigger than the space of continuous functions, i.e. Bögel space; the GBS (Generalized Boolean Sum) of the q-bivariate operators is considered and degree of approximation is discussed for the Bögel continuous and Bögel differentiable functions with the aid of the Lipschitz class and the mixed modulus of smoothness.

Keywords: Bögel continuous, Bögel differentiable, generalized Boolean sum, K-functional, mixed modulus of smoothness

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Authors: Guillaume Leduc

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In this paper, we describe a broad setting under which the error of the approximation can be quantified, controlled, and for which convergence occurs at a speed of n⁻¹ for European and American options. We describe how knowledge of the error allows for arbitrarily fast acceleration of the convergence.

Keywords: random walk approximation, European and American options, rate of convergence, option pricing

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Authors: Ladislav Écsi, Roland Jančo

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Contemporary multiplicative plasticity models assume that the body's intermediate configuration consists of an assembly of locally unloaded neighbourhoods of material particles that cannot be reassembled together to give the overall stress-free intermediate configuration since the neighbourhoods are not necessarily compatible with each other. As a result, the plastic deformation gradient, an inelastic component in the multiplicative split of the deformation gradient, cannot be integrated, and the material particle moves from the initial configuration to the intermediate configuration without a position vector and a plastic displacement field when plastic flow occurs. Such behaviour is incompatible with the continuum theory and the continuum physics of elastoplastic deformations, and the related material models can hardly be denoted as truly continuum-based. The paper presents a proper continuum-based reformulation of current problems in finite strain plasticity. It will be shown that the incompatible neighbourhoods in real material are modelled by the product of the plastic multiplier and the yield surface normal when the plastic flow is defined in the current configuration. The incompatible plastic factor can also model the neighbourhoods as the solution of the system of differential equations whose coefficient matrix is the above product when the plastic flow is defined in the intermediate configuration. The incompatible tensors replace the compatible spatial plastic velocity gradient in the former case or the compatible plastic deformation gradient in the latter case in the definition of the plastic flow rule. They act as local imperfections but have the same position vector as the compatible plastic velocity gradient or the compatible plastic deformation gradient in the definitions of the related plastic flow rules. The unstressed intermediate configuration, the unloaded configuration after the plastic flow, where the residual stresses have been removed, can always be calculated by integrating either the compatible plastic velocity gradient or the compatible plastic deformation gradient. However, the corresponding plastic displacement field becomes permanent with both elastic and plastic components. The residual strains and stresses originate from the difference between the compatible plastic/permanent displacement field gradient and the prescribed incompatible second-order tensor characterizing the plastic flow in the definition of the plastic flow rule, which becomes an assignment statement rather than an equilibrium equation. The above also means that the elastic and plastic factors in the multiplicative split of the deformation gradient are, in reality, gradients and that there is no problem with the continuum physics of elastoplastic deformations. The formulation is demonstrated in a numerical example using the regularized Mooney-Rivlin material model and modified equilibrium statements where the intermediate configuration is calculated, whose analysis results are compared with the identical material model using the current equilibrium statements. The advantages and disadvantages of each formulation, including their relationship with multiplicative plasticity, are also discussed.

Keywords: finite strain plasticity, continuum formulation, regularized Mooney-Rivlin material model, compatibility

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Authors: Zhao Wang, Hong Yan

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In this paper, a unified-gas kinetic scheme (UGKS) for the gas-particle flow is constructed. UGKS is a direct modeling method for both continuum and rarefied flow computations. The dynamics of particle and gas are described as rarefied and continuum flow, respectively. Therefore, we use the Bhatnagar-Gross-Krook (BGK) equation for the particle distribution function. For the gas phase, the gas kinetic scheme for Navier-Stokes equation is solved. The momentum transfer between gas and particle is achieved by the acceleration term added to the BGK equation. The new scheme is tested by a 2cm-in-thickness dense bed comprised of glass particles with 1.5mm in diameter, and reasonable agreement is achieved.

Keywords: gas-particle flow, unified gas-kinetic scheme, momentum transfer, shock-induced fluidization

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Authors: Eugene Kogan

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We analytically study the localized running waves in the discrete Josephson transmission lines (JTL), constructed from Josephson junctions (JJ) and capacitors. The quasi-continuum approximation reduces the calculation of the running wave properties to the problem of equilibrium of an elastic rod in the potential field. Making additional approximations, we reduce the problem to the motion of the fictitious Newtonian particle in the potential well. We show that there exist running waves in the form of supersonic kinks and solitons and calculate their velocities and profiles. We show that the nonstationary smooth waves, which are small perturbations on the homogeneous non-zero background, are described by Korteweg-de Vries equation, and those on zero background -by the modified Korteweg-de Vries equation. We also study the effect of dissipation on the running waves in JTL and find that in the presence of the resistors, shunting the JJ and/or in series with the ground capacitors, the only possible stationary running waves are the shock waves, whose profiles are also found.

Keywords: Josephson transmission line, shocks, solitary waves, nonlinear waves

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Authors: Sarisa Pinkham, Kanyarat Bussaban

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The research aims to approximate the amount of daily rainfall by using a pixel value data approach. The daily rainfall maps from the Thailand Meteorological Department in period of time from January to December 2013 were the data used in this study. The results showed that this approach can approximate the amount of daily rainfall with RMSE=3.343.

Keywords: daily rainfall, image processing, approximation, pixel value data

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Authors: Kyu Chul Lee, Sung Hyun Yoo, Choon Ki Ahn, Myo Taeg Lim

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Recent experimental evidences have shown that because of a fast convergence and a nice accuracy, neural networks training via extended Kalman filter (EKF) method is widely applied. However, as to an uncertainty of the system dynamics or modeling error, the performance of the method is unreliable. In order to overcome this problem in this paper, a new finite impulse response (FIR) filter based learning algorithm is proposed to train radial basis function neural networks (RBFN) for nonlinear function approximation. Compared to the EKF training method, the proposed FIR filter training method is more robust to those environmental conditions. Furthermore, the number of centers will be considered since it affects the performance of approximation.

Keywords: extended Kalman filter, classification problem, radial basis function networks (RBFN), finite impulse response (FIR) filter

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Authors: Smriti, Ajeet Kumar

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We present a variant of the Irving-Kirkwood procedure to obtain the microscopic expressions of the cross-section averaged continuum fields such as internal force and moment in one-dimensional nanostructures in the non-equilibrium setting. In one-dimensional continuum theories for slender bodies, we deal with quantities such as mass, linear momentum, angular momentum, and strain energy densities, all defined per unit length. These quantities are obtained by integrating the corresponding pointwise (per unit volume) quantities over the cross-section of the slender body. However, no well-defined cross-section exists for these nanostructures at finite temperature. We thus define the cross-section of a nanorod to be an infinite plane which is fixed in space even when time progresses and defines the above continuum quantities by integrating the pointwise microscopic quantities over this infinite plane. The method yields explicit expressions of both the potential and kinetic parts of the above quantities. We further specialize in these expressions for helically repeating one-dimensional nanostructures in order to use them in molecular dynamics study of extension, torsion, and bending of such nanostructures. As, the Irving-Kirkwood procedure does not yield expressions of stiffnesses, we resort to a thermodynamic equilibrium approach to obtain the expressions of axial force, twisting moment, bending moment, and the associated stiffnesses by taking the first and second derivatives of the Helmholtz free energy with respect to conjugate strain measures. The equilibrium approach yields expressions independent of kinetic terms. We then establish the equivalence of the expressions obtained using the two approaches. The derived expressions are used to understand the extension, torsion, and bending of single-walled carbon nanotubes at non-zero temperatures.

Keywords: thermoelasticity, molecular dynamics, one dimensional nanostructures, nanotube buckling

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Authors: Iva Hereitova, Miroslav Svatek, Vit Novacek

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Background and Aim: Autonomic imbalance is one of the complications for immobilized patients in the acute stage after a stroke. The predominance of sympathetic activity significantly increases cardiac activity. The technique of glenohumeral joint approximation may contribute in a non-pharmacological way to the regulation of blood pressure and heart rate in patients in this risk group. The aim of the study was to evaluate the effect of glenohumeral joint approximation on the change in heart rate and blood pressure in immobilized patients in the acute phase after a stroke. Methods: The experimental study bilaterally evaluated heart rate, systolic and diastolic pressure values before and after glenohumeral joint approximation in 40 immobilized participants (72.6 ± 10.2 years) in the acute phase after stroke. The experimental group was compared with 40 healthy participants in the control group (68.6 ± 14.2 years). An SpO2 vital signs monitor and a validated Microlife WatchBP Office blood pressure monitor were used for evaluation. Statistical processing and evaluation were performed in MATLAB R2019 (The Math Works®, Inc., Natick, MA, USA). Results: Approximation of the glenohumeral joint resulted in a statistically significant decrease in systolic and diastolic pressure. An average decrease in systolic pressure for individual groups ranged from 8.2 to 11.3 mmHg (p <0.001). For diastolic pressure, the average decrease ranged from 5.0 - 14.2 mmHg (p <0.001). There was a statistically significant reduction in heart rate (p <0.01) only in patients after ischemic stroke in the inferior cerebral artery. There was the average decrease in heart rate of 3.9 beats per minute (median 4 beats per minute). Conclusion: Approximation of the glenohumeral joint leads to a statistically significant decrease in systolic and diastolic pressure in immobilized patients in the acute phase after stroke.

Keywords: Aproximation technique, Cardiovaskular system, Glenohumeral joint, Stroke

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Authors: Somaye Zare

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The critical beam radius is a significant factor that predicts the behavior of the laser beam in the plasma, so if the laser beam radius is adequately greater in comparison to it, the beam will experience stable focusing on the plasma; otherwise, the beam will diverge after entering into the plasma. In this work, considering the paraxial approximation and moment theories, the localization of a relativistic laser beam in thermal quantum plasma is investigated. Using the dielectric function obtained in the quantum hydrodynamic model, the mathematical equation for the laser beam width parameter is attained and solved numerically by the fourth-order Runge-Kutta method. The results demonstrate that the stouter focusing effect is occurred in the moment theory compared to the paraxial approximation. Besides, similar to the two theories, with increasing Fermi temperature, plasma density, and laser intensity, the oscillation rate of the beam width parameter growths and focusing length reduces which means improving the focusing effect. Furthermore, it is understood that behaviors of the critical laser radius are different in the two theories, in the paraxial approximation, the critical radius after a minimum value is enhanced with increasing laser intensity, but in the moment theory, with increasing laser intensity, the critical radius decreases until it becomes independent of the laser intensity.

Keywords: laser localization, quantum plasma, paraxial approximation, moment theory, quantum hydrodynamic model

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Authors: Mourad Ben Bennani

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Views of language and language learning have undergone a tremendous change over the last decades. Language is no longer seen as a set of structured rules. It is rather viewed as a tool of interaction and communication. This shift in views has resulted in change in viewing language learning, which gave birth to various approaches and methodologies of language teaching. Two of these approaches are content-based instruction and content and language integrated learning (CLIL). These are similar approaches which integrate content and foreign/second language learning through various methodologies and models as a result of different implementations around the world. This presentation deals with sociocultural view of CBI and CLIL. It also defines language and content as vital components of CBI and CLIL. Next it reviews the origins of CBI and the continuum perspectives and CLIL definitions and models featured in the literature. Finally it summarizes current aspects around research in program evaluation with a focus on the benefits and challenges of these innovative approaches for second language teaching.

Keywords: CBI, CLIL, CBI continuum, CLIL models

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Authors: Serge Provost, Yishan Zang

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Copulas are currently utilized in finance, reliability theory, machine learning, signal processing, geodesy, hydrology and biostatistics, among several other fields of scientific investigation. It follows from Sklar's theorem that the joint distribution function of a multidimensional random vector can be expressed in terms of its associated copula and marginals. Since marginal distributions can easily be determined by making use of a variety of techniques, we address the problem of securing the distribution of the copula. This will be done by using several approaches. For example, we will obtain bivariate least-squares approximations of the empirical copulas, modify the kernel density estimation technique and propose a criterion for selecting appropriate bandwidths, differentiate linearized empirical copulas, secure Bernstein polynomial approximations of suitable degrees, and apply a corollary to Sklar's result. Illustrative examples involving actual observations will be presented. The proposed methodologies will as well be applied to a sample generated from a known copula distribution in order to validate their effectiveness.

Keywords: copulas, Bernstein polynomial approximation, least-squares polynomial approximation, kernel density estimation, density approximation

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Authors: Marwane Ben Hcine, Ridha Bouallegue

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The aim of this work is to provide an original analytical framework for downlink effective SINR evaluation in LTE networks. The classical single carrier SINR performance evaluation is extended to multi-carrier systems operating over frequency selective channels. Extension is achieved by expressing the link outage probability in terms of the statistics of the effective SINR. For effective SINR computation, the exponential effective SINR mapping (EESM) method is used on this work. Closed-form expression for the link outage probability is achieved assuming a log skew normal approximation for single carrier case. Then we rely on the lognormal approximation to express the exponential effective SINR distribution as a function of the mean and standard deviation of the SINR of a generic subcarrier. Achieved formulas is easily computable and can be obtained for a user equipment (UE) located at any distance from its serving eNodeB. Simulations show that the proposed framework provides results with accuracy within 0.5 dB.

Keywords: LTE, OFDMA, effective SINR, log skew normal approximation

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Authors: M. Khalfa, H. Khachai, F. Chiker, K. Bougherara, R. Khenata, G. Murtaza, M. Harmel

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A theoretical study of structural, elastic, electronic and thermodynamic properties of Fe2VX, (with X = Al and Ga), were studied by means of the full-relativistic version of the full-potential augmented plane wave plus local orbitals method. For exchange and correlation potential we used both generalized-gradient approximation (GGA) and local-density approximation (LDA). Our calculated ground state properties like as lattice constants, bulk modulus and elastic constants appear more accurate when we employed the GGA rather than the LDA approximation, and these results agree very well with the available experimental and theoretical data. Further, prediction of the thermal effects on some macroscopic properties of Fe2VAl and Fe2VGa are given in this paper using the quasi-harmonic Debye model in which the lattice vibrations are taken into account. We have obtained successfully the variations of the primitive cell volume, volume expansion coefficient, heat capacities and Debye temperature with pressure and temperature in the ranges of 0–40 GPa and 0–1500 K.

Keywords: full Heusler, FP-LAPW, electronic properties, thermal properties

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Authors: Takuro Kida, Yuichi Kida

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In this paper, it is shown a base of the new trend of algorithm mathematically that treats a historical reason of continuous discrimination in the world as well as its solution by introducing new concepts of parallel world that includes an invisible set of errors as its companion. With respect to a matrix operator-filter bank that the matrix operator-analysis-filter bank H and the matrix operator-sampling-filter bank S are given, firstly, we introduce the detail algorithm to derive the optimum matrix operator-synthesis-filter bank Z that minimizes all the worst-case measures of the matrix operator-error-signals E(ω) = F(ω) − Y(ω) between the matrix operator-input-signals F(ω) and the matrix operator-output-signals Y(ω) of the matrix operator-filter bank at the same time. Further, feedback is introduced to the above approximation theory, and it is indicated that introducing conversations with feedback do not superior automatically to the accumulation of existing knowledge of signal prediction. Secondly, the concept of category in the field of mathematics is applied to the above optimum signal approximation and is indicated that the category-based approximation theory is applied to the set-theoretic consideration of the recognition of humans. Based on this discussion, it is shown naturally why the narrow perception that tends to create isolation shows an apparent advantage in the short term and, often, why such narrow thinking becomes intimate with discriminatory action in a human group. Throughout these considerations, it is presented that, in order to abolish easy and intimate discriminatory behavior, it is important to create a parallel world of conception where we share the set of invisible error signals, including the words and the consciousness of both worlds.

Keywords: matrix filterbank, optimum signal approximation, category theory, simultaneous minimization

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Authors: Hassan Al Salman

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We consider a nonlinear parabolic cross diffusion model arising in applied mathematics. A fully practical piecewise linear finite element approximation of the model is studied. By using entropy-type inequalities and compactness arguments, existence of a global weak solution is proved. Providing further regularity of the solution of the model, some uniqueness results and error estimates are established. Finally, some numerical experiments are performed.

Keywords: cross diffusion model, entropy-type inequality, finite element approximation, numerical analysis

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Authors: Ratna Sen

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As due to very high temperature of Plasma it is very difficult to confine it for sufficient time so that nuclear fusion reactions to take place, As we know Plasma escapes faster than the binary collision rates. We studied the ball analogy and the ‘energy principle’ and calculated the total potential energy for the whole Plasma. If δ ⃗w is negative, that is decrease in potential energy then the plasma will be unstable. We also discussed different approaches of stability analysis such as Nyquist Method, MHD approximation and Vlasov approach of plasma stability. So that by using magnetic field configurations we can able to create a stable Plasma in Tokamak for generating energy for future generations.

Keywords: jello, magnetic field configuration, MHD approximation, energy principle

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Authors: Alicia C. Sanchez

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This paper investigates the implementation of RAFU functions (radical functions) in robotics and automation. Specifically, the main goal is to show how these functions may be useful in lane-keeping control and the lateral control of autonomous machines, vehicles, robots or the like. From the knowledge of several points of a certain route, the RAFU functions are used to achieve the lateral control purpose and maintain the lane-keeping errors within the fixed limits. The stability that these functions provide, their ease of approaching any continuous trajectory and the control of the possible error made on the approximation may be useful in practice.

Keywords: automatic navigation control, lateral control, lane-keeping control, RAFU approximation

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