Two kinds of generalized gradient representations for holonomic mechanical systems

Two kinds of generalized gradient systems are proposed and the characteristics of the two systems are studied. The conditions under which a holonomic mechanical system can be considered as one of the two generalized gradient systems are obtained. The characteristics of the generalized gradient systems can be used to study the stability of the holonomic system. Some examples are given to illustrate the application of the results.

Electronic and Optical Properties of TiS2 Determined from Generalized Gradient Approximation Study

The electronic and optical properties of TiS2 are studied of density functional theory. A linearized and augmented by using an ab-initio calculation within the frame plane wave basis set with the generalized gradient approximation as proposed by Perdew et al. is used for the energy exchange-correlation determination. The results show a metallic character of TiS2, and the plots of total and partial densities of states of TiS2 show the metallic character of the bonds and a strong hybridization between the states d of Ti and p of S below the Fermi energy. The optical properties of the material such as real and imaginary parts of dielectric constant （ε（w） = ε1（w） ＋ iε2（w））, refractive index n（w）, optical reflectivity R（w）, for E / /x and E / /z are performed for the energy range of 0-.14 eV.

A MODIFIED ALGORITHM OF FINDING AN ELEMENT OF CLARKE GENERALIZED GRADIENT FOR A SMOOTH COMPOSITION OF MAX-TYPE FUNCTIONS A MODIFIED ALGORITHM OF FINDING AN ELEMENT OF CLARKE GENERALIZED GRADIENT FOR A SMOOTH COMPOSITION OF MAX-TYPE FUNCTIONS

This paper refers to Clarke generalized gradient for a smooth composition of max-type functions of the form: f(x) = g(x, maxj∈J1 f1j(x),''', maxj∈Jm fmj(x)), where x ∈Rn, Ji, i = 1,''',m are finite index sets, g and fij,j ∈ Ji, i = 1,... )m, are continuously differentiable on Rm+n and Rn, respectively. In a previous paper) we proposed an algorithm of finding an element of Clarke generalized gradient for f, at a point. In that paper, finding an element of Clarke generalized gradient for f, at a point, is implemented by determining the compatibilities of systems of linear inequalities many times. So its computational amount is very expensive. In this paper) we will modify the algorithm to reduce the times that the compatibilities of systems of linear inequalities have to be determined.

Application of the Generalized Reduced Gradient Method in Mechanical Optimization Design

This paper presents the generalized reduced gradient method （GRG） and its realization forms. The application example of GRG in the optimization design of a single-stage cylindrical gear reducer is introduced. The algo- rithm of the GRG method is realized in Vissim software. Based on the mathematical model of the single-stage cylin- drical gear reducer, the simulation structure of the optimization design was achieved. The experiment results show that the GRG method has fewer iterations and higher precision. The GRG method is very suitable for solving mechanical optimization design.

Density Functional Calculations of the Mechanical, Electronic and Dynamical Properties of Antiperovskite Ca3BO (B = Pb, Ge, Sn)

An analysis of mechanical, electronic and dynamical properties of antiperovskite Ca3BO (B = Pb, Ge, Sn) in cubic phase space group Pm-3m (221) has been studied using first principle density functional theory (DFT). Ground state energy computation was done using the Projector Augmented Wave (PAW) Pseudo Potentials and the Plane Wave (PW) basis set. The Generalized Gradient Approximation (GGA) was used for the exchange correlation. The open source code QUANTUM ESPRESSO (QE) was used in this study in which plane wave basis sets are applied for the expansion of the electronic structure wave function. Thermo_pw as a post-processing code was used for the computation of mechanical properties including bulk modulus and elastic constants with their derivatives. The lattice parameters are here calculated to be 4.87 Å, 4.86 Å and 4.84 Å for Ca3BO (B = Pb, Ge, Sn) respectively which compares well with other works. This also shows that the three crystals are similar in size and in most of their properties. In addition to this, projected density of states and band structure are also computed both showing that these materials are of semi-metallic nature and are stable in cubic phase. Phonon modes at gamma are also reported.

Electronic Structures of Wurtzite GaN with Ga and N Vacancies

The electronic band structures of wurtzite GaN with Ga and N vacancy defects are investigated by means of the first-principles total energy calculations in the neutral charge state. Our results show that the band structures can be significantly modified by the Ga and N vacancies in the GaN samples. Generally, the width of the valence band is reduced and the band gap is enlarged. The defect-induced bands can be introduced in the band gap of GMV due to the Ga and N vacancies. Moreover, the GaN with high density of N vacancies becomes an indirect gap semiconductor. Three defect bands due to Ga vacancy defects are created within the band gap and near the top of the valence band. In contrast, the N vacancies introduce four defect bands within the band gap. One is in the vicinity of the top of the valence band, and the others are near the bottom of the conduction band. The physical origin of the defect bands and modification of the band structures due to the Ga and N vacancies are analysed in depth.

Ab Initio Study of Structural and Electronic Properties of Sodium Bromide

The structural and electronic properties of sodium bromide （NaBr） are investigated by the density functional theory （DFT） within the generalized gradient approximation （GGA） for the exchange and correlation energy. The equilibrium lattice constant, bulk modulus and its pressure derivative are obtained by fitting the calculated total energy to the third-order Birch-Murnaghan equation of state. The band structure along the higher symmetry axes in the Brillouin zone, the density of states （DOS） and the partial density of states （PDOS） are presented. The results have been discussed and compared with the available experimental and theoretical data.

First principles study on electronic structure and optical properties of quaternary arsenide oxides YZnAsO and LaZnAsO

The electronic structure and optical properties of the tetragonal phase quaternary arsenide oxides YZnAsO and LaZnAsO were studied using density-functional theory(DFT) within generalized gradient approximation(GGA).The band structure along the higher symmetry axes in the Brillouin zone,the density of states(DOS) and the partial density of states(PDOS) were presented.The calculated energy band structures show that both YZnAsO and LaZnAsO are indirect gap semiconductors with band gap of 1.173 1 eV and 1.166 5 eV,respectively.The DOS and PDOS show the hybridization of Y-O/La-O atom orbits and Zn-As atom orbits.The dielectric function,reflectivity,absorption coefficient,refractive index,electron energy-loss function and optical conductivity were presented in an energy range from 0 to 25 eV for discussing the optical properties of YZnAsO and LaZnAsO.

Structural and thermodynamic properties of wurtzite-type aluminium nitride from first-principles calculations

The lattice parameter, bulk modulus and its pressure derivative of the wurtzite-type aluminium nitride （w-AlN） are investigated by using the Cambridge Serial Total Energy Package （CASTEP） program in the framework of Density Functional Theory （DFT）. The calculated results are in good agreement with the available experimental data and other theoretical results. Through the quasi-harmonic Debye model, the dependences of the normalized lattice parameters a/ao and c/c0, axial ratio c/a, normalized primitive-cell volume V/Vo, Debye temperature θD and heat capacity Cv on pressure P and temperature T are obtained. It is found that the interlayer covalent interactions （Al-N bonds） are more （even a little） sensitive to temperature and pressure than intralayer ones （N-N bonds）, which gives rise to a little lattice anisotropy in the w-AlN.

Be-composition effect on structure,electronic and optical properties of Be_xZn_(1-x)O alloys

This paper carries out first principles calculation of the structure, electronic and optical properties of BexZn1-xO alloys based on the density-functional theory for the compositions x = 0.0, 0.25, 0.5, 0.75, 1.0. The lattice constants deviations of alloys obey Vegard＇s law well. The BexZn1-xO alloys have the direct band gap （Г-Г） character, and the bowing coefficients axe less than the available theoretical values. Moreover, it investigates in detail the optical properties （dielectric functions, absorption spectrum and refractive index） of these ternary mixed crystals. The obtained results agree well with the available theoretical and experimental values.

First-principles study on the lattice stability of elemental Co,Rh,and Ir in the ⅧB group

Lattice constants, total energies, and densities of state of transition metals Co, Rh, and Ir in the VⅢB group with different crystalline structures were calculated via generalized gradient approximation （GGA） of the total energy plane wave pseudopotential method in first-principles. The lattice stabilities of Rh and Ir are ΔG^ bcc-hcp 〉 Δ G^fcc-hcp 〉 0, agreeing well with those of the projector augmented wave method in first-principles and the CALPHAD method in spite of elemental Co. Analyses of the electronic structures to lattice stability show that crystalline Rh and Ir with fcc structures have the obvious characteristic of a stable phase, agreeing with the results of total energy calculations. Analyses of atomic populations show that the transition rate of electrons from the s state to the p or d state for hcp, fcc, and bcc crystals of Co and Rh increases with the elemental period number to form a stronger cohesion, a higher cohesive energy, or a more stable lattice between atoms in heavier metals.

First-Principle Calculations for Transition Phase and Elastic Properties of SrS

The transition phase and elastic properties of SrS from NaCl structure （B1） to CsCl structure （B2） are investigated by ab initio plane-wave pseudopotential density functional theory method and by the quasi-harmonic Debye model. The transition pressure varies non-linearly with temperature, and the pressure of the mechanical instability increases linearly with increasing temperature. It is shown that the B1 structure SrS is a most elastically anisotropic minerat any pressure. The Debye temperature, the heat capacity, thermal expansion and Gruneisen parameter over a wide range of pressures and temperatures are also obtained.

First-principles calculations of structure and high pressure phase transition in gallium nitride

The phase transitions of semiconductor CaN from the Wurtzite （WZ） structure and the zinc-blende （ZB） structure to the rocksalt （R,S） structure are investigated by using the first-principles plane-wave pseudopotential density functional method combined with the ultrasoft pseudopotentied scheme in the generalized gradient approximation （GGA） correction. It is found that the phase transitions from the WZ structure and the ZB structure to the R,S structure occur at pressures of 46.1 GPa and 45.2 GPa, respectively. The lattice parameters, bulk moduli and their pressure derivatives of these structures of CaN are also calculated. Our results are consistent with available experimental and other theoretical results. The dependence of the normalized formula-unit volume V/V0 on pressure P is also successfully obtained.

Theoretical studies on the structural,electronic,and optical properties of Ag_2HgSnSe_4

We investigate the electronic structure of Ag2HgSnSe4 in a wurtzite-stannite structure with the first principles method. This crystal is a direct band-gap compound. In addition the dielectric function, absorption coefficient, reflectivity, and energy-loss function are studied using the density functional theory in the generalized gradient approximation. We discuss the optical transitions between the valence bands and the conduction bands in the spectrum of the imaginary part of the dielectric function at length. We also find a very high absorption coefficient and a wide absorption band for this material. The prominent structures in the spectra of reflectivity and the energy-loss function are discussed in detail.

Structural,electronic,and magnetic properties of Co-doped ZnO

Density functional theory based calculations have been carried out to study structural, electronic, and magnetic properties of Znl-xCoxO （x = 0, 0.25, 0.50, 0.75） in the zinc-blende phase, and the generalized gradient approximation proposed by Wu and Cohen has been used. Our calculated lattice constants decrease while the bulk moduli increase with the increase of Co2＋ concentration. The calculated spin polarized band structures show the metallic behavior of Co-doped ZnO for both the up and the down spin cases with various doping concentrations. Moreover, the electron population is found to shift from the Zn-O bond to the Co-O bond with the increase of Co2~ concentration. The total magnetic moment~ the interstitial magnetic moment, the valence and the conduction band edge spin splitting energies, and the exchange constants decrease, while the local magnetic moments of Zn, Co, O, the exchange spin splitting energies, and crystal field splitting energies increase with the increase of dopant concentration.

Convergence analysis on Browder-Tikhonov regularization for second-order evolution hemivariational inequality

This paper studies the Browder-Tikhonov regularization of a second-order evolution hemivariational inequality （SOEHVI） with non-coercive operators. With duality mapping, the regularized formulations and a derived first-order evolution hemivariational inequality （FOEHVI） for the problem considered are presented. By applying the Browder-Tikhonov regularization method to the derived FOEHVI, a sequence of regularized solutions to the regularized SOEHVI is constructed, and the strong convergence of the whole sequence of regularized solutions to a solution to the problem is proved.

Robust power amplifier predistorter by using memory polynomials

In memory polynomial predistorter design, the coefficient estimation algorithm based on normalized least mean square is sensitive to initialization parameters. A predistorter based on generalized normalized gradient descent algorithm is proposed. The merit of the GNGD algorithm is that its learning rate provides compensation for the independent assumptions in the derivation of NLMS, thus its stability is improved. Computer simulation shows that the proposed predistorter is very robust. It can overcome the sensitivity of initialization parameters and get a better linearization performance.

Existence of Weakly Efficient Solutions in Vector Optimization

In this paper, we present an existence result for weak efficient solution for the vector optimization problem. The result is stated for invex strongly compactly Lipschitz functions.

Global Optimization Approach to Non-convex Problems

A new approach to find the global optimal solution of the special non-convex problems is proposed in this paper. The non-convex objective problem is first decomposed into two convex sub-problems. Then a generalized gradient is introduced to determine a search direction and the evolution equation is built to obtain a global minimum point. By the approach, we can prevent the search process from some local minima and search a global minimum point. Two numerical examples are given to prove the approach to be effective.

OPTIMALITY CONDITIONS OF A CLASS OF SPECIAL NONSMOOTH PROGRAMMING

In this paper, we investigate the optimality conditions of a class of special nonsmoothprogramming min F(x) = which arises from Li-norm optimization,where ci ∈ R is constant and fi ∈ C1,i = 1,2, ...,m. These conditions can easily be tested by computer.