Search results for: density approximation

Authors: N. Lebga, Kh. Bouamama, K. Kassali

Abstract:

We report first-principles calculation results on the structural and elastic properties of ZnS x Se1−x alloy for which we employed the virtual crystal approximation provided with the ABINIT program. The calculations done using density functional theory within the local density approximation and employing the virtual-crystal approximation, we made a comparative study between the numerical results obtained from ab-initio calculation using ABINIT or Wien2k within the Density Functional Theory framework with either Local Density Approximation or Generalized Gradient approximation and the pseudo-potential plane-wave method with the Hartwigzen Goedecker Hutter scheme potentials. It is found that the lattice parameter, the phase transition pressure, and the elastic constants (and their derivative with respect to the pressure) follow a quadratic law in x. The variation of the elastic constants is also numerically studied and the phase transformations are discussed in relation to the mechanical stability criteria.

Keywords: density functional theory, elastic properties, ZnS, ZnSe,

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Authors: S. B. Provost, Susan Sheng

Abstract:

An alternative bivariate density estimation methodology is introduced in this presentation. The proposed approach involves estimating the density function associated with the marginal distribution of each of the two variables by means of the saddlepoint approximation technique and applying a bivariate polynomial adjustment to the product of these density estimates. Since the saddlepoint approximation is utilized in the context of density estimation, such estimates are determined from empirical cumulant-generating functions. In the univariate case, the saddlepoint density estimate is itself adjusted by a polynomial. Given a set of observations, the coefficients of the polynomial adjustments are obtained from the sample moments. Several illustrative applications of the proposed methodology shall be presented. Since this approach relies essentially on a determinate number of sample moments, it is particularly well suited for modeling massive data sets.

Keywords: density estimation, empirical cumulant-generating function, moments, saddlepoint approximation

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Authors: Serge B. Provost, Yishan Zhang

Abstract:

A moment-based adjustment to the saddlepoint approximation is introduced in the context of density estimation. First applied to univariate distributions, this methodology is extended to the bivariate case. It then entails estimating the density function associated with each marginal distribution by means of the saddlepoint approximation and applying a bivariate adjustment to the product of the resulting density estimates. The connection to the distribution of empirical copulas will be pointed out. As well, a novel approach is proposed for estimating the support of distribution. As these results solely rely on sample moments and empirical cumulant-generating functions, they are particularly well suited for modeling massive data sets. Several illustrative applications will be presented.

Keywords: empirical cumulant-generating function, endpoints identification, saddlepoint approximation, sample moments, density estimation

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Authors: Sirapat Lookrak, Anol Paisal

Abstract:

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: B. Bahloul, K. Babesse, A. Dkhira, Y. Bahloul, L. Amirouche

Abstract:

Structural and electronic properties of the rock-salt BaxSr1−xS are calculated using the first-principles calculations based on the density functional theory (DFT) within the generalized gradient approximation (GGA), the local density approximation (LDA) and the virtual-crystal approximation (VCA). The calculated lattice parameters at equilibrium volume for x=0 and x=1 are in good agreement with the literature data. The BaxSr1−xS alloys are found to be an indirect band gap semiconductor. Moreoever, for the composition (x) ranging between [0-1], we think that our results are well discussed and well predicted.

Keywords: semiconductor, Ab initio calculations, rocksalt, band structure, BaxSr1−xS

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Authors: Serge Provost, Yishan Zang

Abstract:

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: Kankeyanathan Kannan

Abstract:

On approximation properties of group C* algebras is everywhere; it is powerful, important, backbone of countless breakthroughs. For a discrete group G, let A(G) denote its Fourier algebra, and let M₀A(G) denote the space of completely bounded Fourier multipliers on G. An approximate identity on G is a sequence (Φn) of finitely supported functions such that (Φn) uniformly converge to constant function 1 In this paper we prove that approximation property pass to free product.

Keywords: approximation property, weakly amenable, strong invariant approximation property, invariant approximation property

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

Abstract:

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: S. B. Provost, Hossein Zareamoghaddam

Abstract:

A univariate density approximation technique whereby the derivative of the logarithm of a density function is assumed to be expressible as a rational function is introduced. This approach which extends Pearson’s curve system is solely based on the moments of a distribution up to a determinable order. Upon solving a system of linear equations, the coefficients of the polynomial ratio can readily be identified. An explicit solution to the integral representation of the resulting density approximant is then obtained. It will be explained that when utilised in conjunction with sample moments, this methodology lends itself to the modelling of ‘big data’. Applications to sets of univariate and bivariate observations will be presented.

Keywords: density estimation, log-density, moments, Pearson's curve system

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Authors: Sapan Mohan Saini

Abstract:

In this work, we report the calculations on the electronic and optical properties of YNi₄Si-type GdNi₅ compound. Calculations are performed using the full-potential augmented plane wave (FPLAPW) method in the framework of density functional theory (DFT). The Coulomb corrected local-spin density approximation (LSDA+U) in the self-interaction correction (SIC) has been used for exchange-correlation potential. Spin polarised calculations of band structure show that several bands cross the Fermi level (EF) reflect the metallic character. Analysis of density of states (DOS) demonstrates that spin up Gd-f states lie around 7.5 eV below EF and spin down Gd-f lie around 4.5 eV above EF. We found Ni-3d states mainly contribute to DOS from -5.0 eV to the EF. Our calculated results of optical conductivity agree well with the experimental data.

Keywords: electronic structure, optical properties, FPLAPW method, YNi₄Si-type GdNi₅

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Authors: Meriem Harmel, Houari Khachai

Abstract:

We have investigated the structural, electronic and optical properties of a compound perovskite CsSrF3 using the full-potential linearized augmented plane wave (FP-LAPW) method within density functional theory (DFT). In this approach, both the local density approximation (LDA) and the generalized gradient approximation (GGA) were used for exchange-correlation potential calculation. The ground state properties such as lattice parameter, bulk modulus and its pressure derivative were calculated and the results are compared whit experimental and theoretical data. Electronic and bonding properties are discussed from the calculations of band structure, density of states and electron charge density, where the fundamental energy gap is direct under ambient conditions. The contribution of the different bands was analyzed from the total and partial density of states curves. The optical properties (namely: the real and the imaginary parts of the dielectric function ε(ω), the refractive index n(ω) and the extinction coefficient k(ω)) were calculated for radiation up to 35.0 eV. This is the first quantitative theoretical prediction of the optical properties for the investigated compound and still awaits experimental confirmations.

Keywords: DFT, fluoroperovskite, electronic structure, optical properties

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Authors: Rekab Djabri Hamza, Daoud Salah

Abstract:

We report first-principles calculations of structural and magnetic properties of TmAs compound in zinc blende(B3) and CsCl(B2), structures employing the density functional theory (DFT) within the local density approximation (LDA). We use the full potential linear muffin-tin orbitals (FP-LMTO) as implemented in the LMTART-MINDLAB code (Calculation). Results are given for lattice parameters (a), bulk modulus (B), and its first derivatives(B’) in the different structures NaCl (B1) and CsCl (B2). The most important result in this work is the prediction of the possibility of transition; from cubic rocksalt (NaCl)→ CsCl (B2) (32.96GPa) for TmAs. These results use the LDA approximation.

Keywords: LDA, phase transition, properties, DFT

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Authors: D. K. Maurya, S. M. Saini

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We investigate theoretically the electronic and optical properties of YNi₄Si-type HoNi₄Si compound from first principle calculations. Calculations are performed using full-potential augmented plane wave (FPLAPW) method in the frame work of density functional theory (DFT). The Coulomb corrected local-spin density approximation (LSDA+U) in the self-interaction correction (SIC) has been used for exchange-correlation potential. Analysis of the calculated band structure of HoNi₄Si compound demonstrates their metallic character. We found Ni-3d states mainly contribute to density of states from -5.0 eV to the Fermi level while the Ho-f states peak stands tall in comparison to the small contributions made by the Ni-d and Ho-d states above Fermi level, which is consistent with experiment, in HoNi4Si compound. Our calculated optical conductivity compares well with the experimental data and the results are analyzed in the light of band to band transitions.

Keywords: electronic properties, density of states, optical properties, LSDA+U approximation, YNi₄Si-type HoNi4Si compound

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Authors: H. Krarcha

Abstract:

The structural, elastic, vibrational and thermal properties of AHfO3 compounds with the cubic perovskites structure have been investigated, by employing a first principles method, using the plane wave pseudo potential calculations (PP-PW), based on the density functional theory (DFT), within the local density approximation (LDA). The optimized lattice parameters, independent elastic constants (C11, C12 and C44), bulk modulus (B), compressibility (b), shear modulus (G), Young’s modulus (Y ), Poisson’s ratio (n), Lame´’s coefficients (m, l), as well as band structure, density of states and electron density distributions are obtained and analyzed in comparison with the available theoretical and experimental data. For the first time the numerical estimates of elastic parameters of the polycrystalline AHfO3 ceramics (in framework of the VoigteReusseHill approximation) are performed. The quasi-harmonic Debye model, by means of total energy versus volume calculations obtained with the FP-LAPW method, is applied to study the thermal and vibrational effects. Predicted temperature and pressure effects on the structural parameters, thermal expansions, heat capacities, and Debye temperatures are determined from the non-equilibrium Gibbs functions.

Keywords: Hafnium, elastic propreties, first principles calculation, perovskite

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Authors: N. Guruprasad

Abstract:

This paper presents a modification of approximation method for transportation problems. The initial basic feasible solution can be computed using either Russel's or Vogel's approximation methods. Russell’s approximation method provides another excellent criterion that is still quick to implement on a computer (not manually) In most cases Russel's method yields a better initial solution, though it takes longer than Vogel's method (finding the next entering variable in Russel's method is in O(n1*n2), and in O(n1+n2) for Vogel's method). However, Russel's method normally has a lesser total running time because less pivots are required to reach the optimum for all but small problem sizes (n1+n2=~20). With this motivation behind we have incorporated a variation of the same – what we have proposed it has TMC (Total Modified Cost) to obtain fast and efficient solutions.

Keywords: computation, efficiency, modified cost, Russell’s approximation method, transportation, Vogel’s approximation method

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Authors: Hamza Rekab Djabri, Salah Daoud

Abstract:

The present paper deals with the computational of structural and electronic properties of ThC and ThN compounds using density functional theory within generalized-gradient (GGA) apraximation and local density approximation (LDA). We employ the full potential linear muffin-tin orbitals (FP-LMTO) as implemented in the Lmtart code. We have used to examine structure parameter in eight different structures such as in NaCl (B1), CsCl (B2), ZB (B3), NiAs (B8), PbO (B10), Wurtzite (B4) , HCP (A3) βSn (A5) structures . The equilibrium lattice parameter, bulk modulus, and its pressure derivative were presented for all calculated phases. The calculated ground state properties are in good agreement with available experimental and theoretical results.

Keywords: DFT, GGA, LDA, properties structurales, ThC, ThN

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Authors: Dinesh Kumar Maurya, Sapan Mohan Saini

Abstract:

A theoretical formalism to calculate the structural, electronic and optical properties of orthorhombic crystals from first principle calculations is described. This is applied first time to new YNi4Si-type DyNi4Si compound. Calculations are performed using full-potential augmented plane wave (FPLAPW) method in the framework of density functional theory (DFT). The Coulomb corrected local-spin density approximation (LSDA+U) in the self-interaction correction (SIC) has been used for exchange-correlation potential. Our optimized results of lattice parameters show good agreement to the previously reported experimental study. Analysis of the calculated band structure of DyNi4Si compound demonstrates their metallic character. We found Ni-3d states mainly contribute to density of states from -5.0 eV to the Fermi level while the Dy-f states peak stands tall in comparison to the small contributions made by the Ni-d and R-d states above Fermi level, which is consistent with experiment, in DNi4Si compound. Our calculated optical conductivity compares well with the experimental data and the results are analyzed in the light of band-to-band transitions. We also report the frequency-dependent refractive index n(ω) and the extinction coefficient k(ω) of the compound.

Keywords: band structure, density of states, optical properties, LSDA+U approximation, YNi4Si- type DyNi4Si compound

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Authors: B. Bouadjemia, M. Houaria, S. Haida, Y. B. Idriss, A, Akham, M. Matouguia, A. Gasmia, T. Lantria, S. Bentataa

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It have investigated the structural, optoelectronic, elastic and thermodynamic properties of KGeX₃ (X = F, Cl and Br) using the density functional theory (DFT) with generalized gradient approximation (GGA) for potential exchange correlation. The modified Becke-Johnson (mBJ-GGA) potential approximation is also used for calculating the optoelectronic properties of the material.The results show that the band structure of the metalloid halide perovskites KGeX₃ (X = F, Cl and Br) have a semiconductor behavior with direct band gap at R-R direction, the gap energy values for each compound as following: 2.83, 1.27 and 0.79eV respectively. The optical properties, such as real and imaginary parts of the dielectric functions, refractive index, reflectivity and absorption coefficient, are investigated. As results, these compounds are competent candidates for optoelectronic and photovoltaic devices in this range of the energy spectrum.

Keywords: density functional theory (DFT), semiconductor behavior, metalloid halide perovskites, optical propertie and photovoltaic devices

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Authors: I. Benkaddour, Y. Benkaddour, A. Benk Addour

Abstract:

The structural, elastic, Thermal, electronic, and magnetic properties of intermetallic RMn₂Ge₂ (R= Ca, Y, Nd) are investigated by density functional theory (DFT), using the full potential –linearised augmented plane wave method (FP-LAPW). In this approach, the local-density approximation (LDA) is used for the exchange-correlation (XC) potential. The equilibrium lattice constant and magnetic moment agree well with the experiment. The density of states shows that these phases are conductors, with contribution predominantly from the R and Mn d states. We have determined the elastic constants C₁₁, C₁₂, C₁₃, C₄₄, C₃₃, andC₆₆ at ambient conditions in, which have not been established neither experimentally nor theoretically. Thermal properties, including the relative expansion coefficients and the heat capacity, have been estimated using a quasi-harmonic Debye model.

Keywords: RMn₂Ge₂, intermetallic, first-principles, density of states, mechanical properties

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Authors: H. A. Bentounes, A. Abbad, W. Benstaali

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Using first principles calculations based on the density functional theory and local spin density approximation, we investigate optical properties of GaFeMnN quaternary compound. Results show that optical properties confirm that GaFeMnN can be a good candidate in the design of thin film solar cells in the visible and ultraviolet parts of the spectrum, and a good sensor in the infrared

Keywords: GaN, optical absorption, semi-metallic, dielectric function

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Authors: Chaghoub Soraya, Zhang Xiaoyan

Abstract:

This research presents the first constant approximation algorithm to the p-median network design problem with multiple cable types. This problem was addressed with a single cable type and there is a bifactor approximation algorithm for the problem. To the best of our knowledge, the algorithm proposed in this paper is the first constant approximation algorithm for the p-median network design with multiple cable types. The addressed problem is a combination of two well studied problems which are p-median problem and network design problem. The introduced algorithm is a random sampling approximation algorithm of constant factor which is conceived by using some random sampling techniques form the literature. It is based on a redistribution Lemma from the literature and a steiner tree problem as a subproblem. This algorithm is simple, and it relies on the notions of random sampling and probability. The proposed approach gives an approximation solution with one constant ratio without violating any of the constraints, in contrast to the one proposed in the literature. This paper provides a (21 + 2)-approximation algorithm for the p-median network design problem with multiple cable types using random sampling techniques.

Keywords: approximation algorithms, buy-at-bulk, combinatorial optimization, network design, p-median

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Authors: Valeria Bondarenko

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In this paper, we propose two problems related to fractal Brownian motion. First problem is simultaneous estimation of two parameters, Hurst exponent and the volatility, that describe this random process. Numerical tests for the simulated fBm provided an efficient method. Second problem is approximation of the increments of the observed time series by a power function by increments from the fractional Brownian motion. Approximation and estimation are shown on the example of real data, daily deposit interest rates.

Keywords: fractional Brownian motion, Gausssian processes, approximation, time series, estimation of properties of the model

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Authors: Smita Sonker, Uaday Singh

Abstract:

Various investigators have determined the degree of approximation of functions belonging to the classes W(L r , ξ(t)), Lip(ξ(t), r), Lip(α, r), and Lipα using different summability methods with monotonocity conditions. Recently, Lal has determined the degree of approximation of the functions belonging to Lipα and W(L r , ξ(t)) classes by using Ces`aro-N¨orlund (C 1 .Np)- summability with non-increasing weights {pn}. In this paper, we shall determine the degree of approximation of 2π - periodic functions f belonging to the function classes Lipα and W(L r , ξ(t)) by C 1 .T - means of Fourier series of f. Our theorems generalize the results of Lal and we also improve these results in the light off. From our results, we also derive some corollaries.

Keywords: Lipschitz classes, product matrix operator, signals, trigonometric Fourier approximation

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Authors: M. Saadi, S. E. H. Abaidia, M. Y. Mokeddem.

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We present the results of a systematic and comparative study of the bulk, the structural properties, and phonon calculations of aluminum alloys using several exchange–correlations functional theory (DFT) with different plane-wave basis pseudo potential techniques. Density functional theory implemented by the Vienna Ab Initio Simulation Package (VASP) technique is applied to calculate the bulk and the structural properties of several structures. The calculations were performed for within several exchange–correlation functional and pseudo pententials available in this code (local density approximation (LDA), generalized gradient approximation (GGA), projector augmented wave (PAW)). The lattice dynamic code “PHON” developed by Dario Alfè was used to calculate some thermodynamics properties and phonon dispersion relation frequency distribution of Aluminium alloys using the VASP LDA PAW and GGA PAW results. The bulk and structural properties of the calculated structures were compared to different experimental and calculated works.

Keywords: DFT, exchange-correlation functional, LDA, GGA, pseudopotential, PAW, VASP, PHON, phonon dispersion

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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: Y. Benmalem , A. Abbad, W. Benstaali, T. Lantri

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Density functional theory is used to investigate the.the structural, electronic, and magnetic properties of the cubic anti-perovskites InNNi3 and ZnNNi3. The structure of antiperovskite also called (perovskite-inverse) identical to the perovskite structure of the general formula ABX3, where A is a main group (III–V) element or a metallic element, B is carbon or nitrogen, and X is a transition metal, displays a wide range of interesting physical properties, such as giant magnetoresistance. Elastic and electronic properties were determined using generalized gradient approximation (GGA), and local spin density approximation (LSDA) approaches, ), as implemented in the Wien2k computer package. The results show that the two compounds are strong ductile and satisfy the Born-Huang criteria, so they are mechanically stable at normal conditions. Electronic properties show that the two compounds studied are metallic and non-magnetic. The studies of these compounds have confirmed the effectiveness of the two approximations and the ground-state properties are in good agreement with experimental data and theoretical results available.

Keywords: anti-perovskites, elastic anisotropy, electronic band structure, first-principles calculations

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Authors: Anusuya Ghosh, Vishnu Narayanan

Abstract:

The approximation of convex set by semidefinite representable set plays an important role in semidefinite programming, especially in modern convex optimization. To optimize a linear function over a convex set is a hard problem. But optimizing the linear function over the semidefinite representable set which approximates the convex set is easy to solve as there exists numerous efficient algorithms to solve semidefinite programming problems. So, our approximation technique is significant in optimization. We develop a technique to approximate any closed convex set, say K by compactly semidefinite representable set. Further we prove that there exists a sequence of compactly semidefinite representable sets which give tighter approximation of the closed convex set, K gradually. We discuss about the convergence of the sequence of compactly semidefinite representable sets to closed convex set K. The recession cone of K and the recession cone of the compactly semidefinite representable set are equal. So, we say that the sequence of compactly semidefinite representable sets converge strongly to the closed convex set. Thus, this approximation technique is very useful development in semidefinite programming.

Keywords: semidefinite programming, semidefinite representable set, compactly semidefinite representable set, approximation

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Authors: Somaye Zare

Abstract:

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: B. Gueridi, T. Chihi, M. Fatmi, A. Faci

Abstract:

Some fundamental physical properties of BiGaO₃ were investigated under pressure and temperature effect using generalized gradient approximation and local density approximation approaches. The effect of orientation on Debye temperature and sound waves velocities were estimated from elastic constants. The value of the bulk modulus of BiGaO₃ is a sign of its high hardness because it is linked to an isotropic deformation. BiGaO₃ is a semiconductor and ductile material with covalent bonding (Ga–O), and the Bi-O bonding is ionic. The optical transitions were observed when electrons pass from the top of the valence band (O-2p) to the bottom of the conduction band (Ga-4p or Bi-6p). The thermodynamic parameters are determined in temperature and pressure ranging from 0 to 1800 K and 0 to 50 GPa.

Keywords: BiGaO₃ perovskite, optical absorption, first principle, band structure

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Authors: Tulin Coskun

Abstract:

We investigate the approximation of analytic functions of several variables in polydisc by the sequences of linear k-positive operators in Gadjiev sence. The approximation of analytic functions of complex variable by linear k-positive operators was tackled, and k-positive operators and formulated theorems of Korovkin's type for these operators in the space of analytic functions on the unit disc were introduced in the past. Recently, very general results on convergence of the sequences of linear k-positive operators on a simply connected bounded domain within the space of analytic functions were proved. In this presentation, we extend some of these results to the approximation of analytic functions of several complex variables by sequences of linear k-positive operators.

Keywords: analytic functions, approximation of analytic functions, Linear k-positive operators, Korovkin type theorems

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