Approximations by Ideal Minimal Structure with Chemical Application

The theory of rough set represents a non-statistical methodology for analyzing ambiguity and imprecise information.It can be characterized by two crisp sets,named the upper and lower approximations that are used to determine the boundary region and accurate measure of any subset.This article endeavors to achieve the best approximation and the highest accuracy degree by using the minimal structure approximation space MSAS via ideal J.The novel approach(indicated by JMSAS)modifies the approximation space to diminish the bound-ary region and enhance the measure of accuracy.The suggested method is more accurate than Pawlak’s and EL-Sharkasy techniques.Via illustrated examples,several remarkable results using these notions are obtained and some of their properties are established.Several sorts of near open(resp.closed)sets based on JMSAS are studied.Furthermore,the connections between these assorted kinds of near-open sets in JMSAS are deduced.The advantages and disadvan-tages of the proposed approach compared to previous ones are examined.An algorithm using MATLAB and a framework for decision-making problems are verified.Finally,the chemical application for the classification of amino acids(AAs)is treated to highlight the significance of applying the suggested approximation.

A Class of Generalized Approximate Inverse Solvers for Unsymmetric Linear Systems of Irregular Structure Based on Adaptive Algorithmic Modelling for Solving Complex Computational Problems in Three Space Dimensions

A class of general inverse matrix techniques based on adaptive algorithmic modelling methodologies is derived yielding iterative methods for solving unsymmetric linear systems of irregular structure arising in complex computational problems in three space dimensions. The proposed class of approximate inverse is chosen as the basis to yield systems on which classic and preconditioned iterative methods are explicitly applied. Optimized versions of the proposed approximate inverse are presented using special storage (k-sweep) techniques leading to economical forms of the approximate inverses. Application of the adaptive algorithmic methodologies on a characteristic nonlinear boundary value problem is discussed and numerical results are given.

Approximation law for discrete-time variable structure control systems

Two approximation laws of sliding mode for discrete-time variable structure control systems are proposed to overcome the limitations of the exponential approximation law and the variable rate approximation law. By applying the proposed approximation laws of sliding mode to discrete-time variable structure control systems, the stability of origin can be guaranteed, and the chattering along the switching surface caused by discrete-time variable structure control can be restrained effectively. In designing of approximation laws, the problem that the system control input is restricted is also considered, which is very important in practical systems. Finally a simulation example shows the effectiveness of the two approximation laws proposed.

Assembly-oriented reliability analysis method for the top-connection structure of a nuclear fuel assembly

The nuclear fuel assembly is the core component of a nuclear reactor.In a pressurized water reactor fuel assembly,the top-connection structure connects the top nozzle to the guide thimble.Its performance reliability is essential for the stability of the nuclear fuel assembly.In this study,an assembly-oriented reliability analysis method for top-connection structures is presented by establishing an assembly-oriented top-connection structure parameter modeling method and a nonlinear contact gap and penetration correction method.A reliability model of the top-connection assembly structure,including multiple stochastic design variables,was constructed,and the overall reliability of the top-connection assembly structure was obtained via a Kriging model and Monte Carlo simulation.The acquired experimental data were consistent with real-world failure conditions,which verified the practicability and feasibility of the reliability analysis method proposed in this study.

THE STRUCTURE AND APPROXIMATION OF A.S. SELF-SIMILAR SET

The structure of any a.s. self-similar set K(w) generated by a class of random elements {gn,wσ} taking values in the space of contractive operators is given and the approximation of K(w) by the fixed points {Pn,wσ} of {gn,ow} is obtained. It is useful to generate the fractal in computer.

A Scheme for Calculating Atomic Structures beyond the Spherical Approximation

We present a scheme for calculating atomic single-particle wave functions and spectra with taking into ac-count the nonspherical effect explicitly. The actual calculation is also performed for the neutral carbon atom within the Hartree-Fock-Slater approximation. As compared with the conventional atomic structure of the spherical approximation, the degenerate energy levels are split partially. The ground state values of the total orbital and spin angular momenta are estimated to be both about unity, which corresponds to the term P3PP in the LS-multiplet theory. This means that the nonspherical effect may play an essential role on the description of the magnetization caused by the orbital polarization.

TWO－LEVEL MULTI－POINT APPROXIMATION METHOD FOR OPTIMUM DESIGN OF COMPLICATED STRUCTURES

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Wind Structure in an Intermediate Boundary Layer Model Based on Ekman Momentum Approximation

A quasi three–dimensional, intermediate planetary boundary layer (PBL) model is developed by including inertial acceleration with the Ekman momentum approximation, but a nonlinear eddy viscosity based on Blackadar’s scheme was included to improve the theoretical model proposed by Tan and Wu (1993). The model could keep the same complexity as the classical Ekman model in numerical, but extends the conventional Ekman model to include the horizontal accelerated flow with the Ekman momentum approximation. A comparison between this modified Ekman model and other simplified accelerating PBL models is made. Results show that the Ekman model overestimates (underestimates) the wind speed and pumping velocity in the cyclonic (anticyclonic) shear flow due to the neglect of the acceleration flow, however, the semi–geostrophic Ekman model overestimates the acceleration effects resulting from the underestimating (overestimating) of the wind speed and pumping velocity in the cyclonic (anticyclonic) shear flow. The Ekman momentum approximation boundary layer model could be applied to the baroclinic atmosphere. The baroclinic Ekman momentum approximation boundary layer solution has both features of classical baroclinic Ekman layer and the Ekman momentum approximate boundary lager.

ICM Method Combined with Meshfree Approximation for Continuum Structure

The independent continuous mapping（ICM） method is integrated into element free Galerkin method and a new implementation of topology optimization for continuum structure is presented.To facilitate the enforcement of the essential boundary condition and derivative of various sensitivities,a singular weight function in element free Galerkin method is introduced.Material point variable is defined to illustrate the condition of material point and its vicinity instead of element or node.The topological variables field is constructed by moving least square approximation which inherits the continuity and smoothness of the weight function.Due to reciprocal relationships between the topological variables and design variables,various structural responses sensitivities are derived according to the method for calculating the partial derivatives of compound functions.Numerical examples indicate that checkerboard pattern and mesh-dependence phenomena are overcome without additional restriction methods.

Computing Approximation GCD of Several Polynomials by Structured Total Least Norm

The task of determining the greatest common divisors (GCD) for several polynomials which arises in image compression, computer algebra and speech encoding can be formulated as a low rank approximation problem with Sylvester matrix. This paper demonstrates a method based on structured total least norm (STLN) algorithm for matrices with Sylvester structure. We demonstrate the algorithm to compute an approximate GCD. Both the theoretical analysis and the computational results show that the method is feasible.

MULTIVARIATE PROBABILISTIC APPROXIMATION IN WAVELET STRUCTURE

Let otherwise and F(x,y).be a continuous distribution function on R^2. Then there exist linear wavelet operators L_n(F,x,y)which are also distribution function and where the defining them mother wavelet is(x,y).These approximate F(x,y)in the supnorm.The degree of this approximation is estimated by establishing a Jackson type inequality.Furthermore we give generalizations for the case of a mother wavelet ≠,which is just any distribution function on R^2,also we extend these results in R^r,r>2.

APPROXIMATION TECHNIQUES FOR APPLICATION OF GENETIC ALGORITHMS TO STRUCTURAL OPTIMIZATION

Although the genetic algorithm (GA) has very powerful robustness and fitness, it needs a large size of population and a large number of iterations to reach the optimum result. Especially when GA is used in complex structural optimization problems, if the structural reanalysis technique is not adopted, the more the number of finite element analysis (FEA) is, the more the consuming time is. In the conventional structural optimization the number of FEA can be reduced by the structural reanalysis technique based on the approximation techniques and sensitivity analysis. With these techniques, this paper provides a new approximation model-segment approximation model, adopted for the GA application. This segment approximation model can decrease the number of FEA and increase the convergence rate of GA. So it can apparently decrease the computation time of GA. Two examples demonstrate the availability of the new segment approximation model.

ANALYSIS OF 2-D THIN STRUCTURES BY THE MESHLESS REGULAR HYBRID BOUNDARY NODE METHOD

Thin structures are generally solved by the Finite Element Method(FEM), using plate or shell finite elements which have manylimitations in applications, such as numerical locking, edge effects,length scaling and the cnvergence problem. Recently, by proposing anew approach to tranting the nearly- singular integrals, Liu et al.developed a BEM to successfully solve thin structures with thethickness-to- length ratios in the micro-or nano-scales. On the otherhand, the meshless Regular Hybrid Boundary Node Method (RHBNM), whichis proposed by the current authors and based on a modified functionaland the Moving Least-Square (MLS) approximation, has very promisingapplications for engineering problems owing To its meshless natureand dimension-reduction advantage, and not involving any singular ornearly-singular Integrals. Test examples show that the RHBNM can alsobe applied readily to thin structures with high accu- Racy withoutany modification.

Fabrication and characterization of rugate structures composed of SiO_(2) and Nb_(2)O_(5)

Gradient index layers and rugate structures were fabricated on a Leybold Syrus pro deposition system by plasma-assisted coevaporation of the low index material silica and the high index material niobium pentoxide.To obtain information about the compositional profiles of the produced layers,cross sectional transmission electron microscopy was used in assistance to deposition rate data recorded by two independent crystal monitors during the film preparation.The depth dependent concentration profiles were transformed to refractive index gradients by means of effective medium approximation.Based on the refractive index gradients the corresponding samples`transmission and reflection spectra could be calculated by utilizing matrix formalism.The relevance of the established refractive index profiles could be verified by comparison of the calculated spectra with the measured ones.

Relationship of quantitative structure and pharmacokinetics in fluoroquinolone antibacterials

AIM： To study the relationship between quantitative structure and pharmacokinetics （QSPkR） of fluorocluinolone antibacterials.METHODS： The pharmacokinetic （PK） parameters of oral fluoroquinolones were collected from the literature. These pharmacokinetic data were averaged, 19 compounds were used as the training set, and 3 served as the test set. Genetic function approximation （GFA） module of Cerius2 software was used in QSPkR analysis.RESULTS： A small volume and large polarizability and surface area of substituents at C-7 contribute to a large area under the curve （AUC） for fluoroquinolones. Large polarizability and small volume of substituents at N-1 contribute to a long half life elimination.CONCLUSION： QSPkR models can contribute to some fluoroquinolones antibacterials with excellent pharmacokinetic properties.

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.

Determination of Crystal Structure of Britholite-Y

Britholite-Y is milkwhite, rosy in colour. The measured specific gravity is 4.35, with Ng′ = 1.791, Np′ = 1.784. As determined by electron microprobe, its crystal formula is (Y2.82Ca1.58Ce0.27Dy0.21Er0.11)5 [(Si2.95P0.05)3O12](OH,F), space group = C22-P21, a = (0.9504±0.0005) nm, b = (0.9414±0.0004) nm, c = (0.6922±0.0002) nm, r = (119.71±0.04)°, V = (53.79±0.04) nm3, Z = 2. Least-squares refinements with 2272 independent reflection (F0>3σ|F0|) yielded R = 0.111. The change of symmetry group P63/m of apatite to P21 of britholite-Y results from the shifts of Y, Ca, Si, O and (OH) atoms (anions) from the pseudohexagonal P63/m equivalent positions (6h), (4f), (12i) and (2a) as produced by distortion of the polyhedra with 7-, 9-, and 4-corners. The substitution of Ca in apatite for Y and the order distribution of atoms Y and Ca on the equivalent positions (6h) and (4f) have contributed to the distortion of 7- and 9- cornered polyhedra. The substitutions of Si4+ for P5+ and OH- for F- may also be effected. The crystal chemistry of apatite-group minerals is also discussed.

UNIFORM NORMAL STRUCTURE AND SOLUTIONS OF REICH’S OPEN QUESTION

The open question raised by Reich is studied in a Banach space with uniform normal structure, whose norm is uniformly Gateaux differentiable. Under more suitable assumptions imposed on an asymptotically nonexpansive mapping, an affirmative answer to Reich＇ s open question is given. The results presented extend and improve Zhang Shisheng＇ s recent ones in the following aspects ： （i） Zhang＇ s stronger condition that the sequence of iterative parameters converges to zero is removed; （ii） Zhang＇ s stronger assumption that the asymptotically nonexpansive mapping has a fixed point is removed; （iii） Zhang＇ s stronger condition that the sequence generated by the Banach Contraction Principle is strongly convergent is also removed. Moreover, these also extend and improve the corresponding ones obtained previously by several authors including Reich, Shioji, Takahashi,Ueda and Wittmann.

Optical-Phonon Deformation Potentials in Diamond-Structure Crystals: ab initio LMTO-ASA Calculation

The optical-phonon deformation potentials of C,Si,Ge and Sn are calculated by LMTO-ASA approach within the frosen-phonon approximation.The comparisons between our results and those of geveral present theoretical calculations and experiments demonstrate that our calculation model is reasonable.

Electronic Structure and Optical Properties of SrBi_(2)A_(2)O_(9)(A=Nb,Ta)

The first-principles calculation is performed to investigate the energy band structures,density of states(DOS)and optical properties of SrBi_(2)A_(2)O_(9)(A=Nb,Ta),by using density functional theory(DFT)with the generalized gradient approximation(GGA).The results show that the band−gap of SrBi_(2)A_(2)O_(9) is smaller than that of SrBi_(2)A_(2)O_(9),and that there are strong hybridizations of A−O bands,which play very important roles in the electronic properties and optical responses of SrBi_(2)A_(2)O_(9).SrBi_(2)A_(2)O_(9) stimulates much higher photocatalytic activity than SrBi_(2)A_(2)O_(9),which is due to its suitable crystal structure.