ON α-CONVEX FUNCTIONS WITH MISSING COEFFICIENTS

Let Jn(α,A,B),α≥0,-1≤B<A≤1,n≥1,denote the class of functions f(z)=z+∑k=n+1^∞αkZ^k which are analytic in E={z:|z|<1} and satisfy the conditions f(z)f′(z)/z≠0 and (1-α)zf′(z)/f(z)+α(1+zf″(z)/f′(z))-<1+Az/1+Bz for z∈E.In this paper we obtain incluion relations,distortion properties and estimates of |αn+2-λα^2n+1| for the class Jn(α,A,B),where λ is complex.

ON THE COEFFICIENTS OF SEVERAL CLASSES OF BI-UNIVALENT FUNCTIONS

In this paper, we investigate the bounds of the coefficients of several classes of bi-univalent functions. The results presented in this paper improve of generalize the recent works of other authors.

THE NORMALITY OF ALGEBROID MULTIFUNCTIONS AND THEIR COEFFICIENT FUNCTIONS

In this paper, we investigate the normality relationship between algebroid multifunctions and their coefficient functions. We prove that the normality of a k-valued entire algebroid multifunctions family is equivalent to their coefficient functions in some conditions. Furthermore, we obtain some new normality criteria for algebroid multifunctions families based on these results. We also provide some examples to expound that some restricted conditions of our main results are necessary.

On the Coefficients of Several Classes of Bi-univalent Functions Defined by Convolution

In this paper, we introduce several new subclasses of the function class Σ of bi-univalent functions analytic in the open unit disc defined by convolution.Furthermore, we investigate the bounds of the coefficients |a2| and |a3| for functions in these new subclasses. The results presented in this paper improve or generalize the recent works of other authors.

HARMONIC FUNCTION WITH CORRELATED COEFFICIENTS

In the paper we introduce an idea of harmonic functions with correlated coefficients which generalize the ideas of harmonic functions with negative coefficients introduced by Silverman and harmonic functions with varying coefficients defined by Jahangiri and Silverman. Next we define classes of harmonic functions with correlated coefficients in terms of generalized Dziok-Srivastava operator. By using extreme points theory, we obtain estimations of classical convex functionals on the defined classes of functions. Some applications of the main results are also considered.

THE BOREL DIRECTIONS OF ALGEBROIDAL FUNCTION AND ITS COEFFICIENT FUNCTIONS

In this article, the relationship between the Borel direction of algebroidal function and its coefficient functions is studied for the first time. To begin with, several theorems of algebroidal functions in unit disk are proved. By these theorems, some interesting conclusions are obtained.

Decoupling coefficients of dilatational wave for Biot's dynamic equation and its Green's functions in frequency domain

Green＇s functions for Blot＇s dynamic equation in the frequency domain can be a highly useful tool for the investigation of dynamic responses of a saturated porous medium. Its applications are found in soil dynamics, seismology, earthquake engineering, rock mechanics, geophysics, and acoustics. However, the mathematical work for deriving it can be daunting. Green＇s functions have been presented utilizing an analogy between the dynamic thermoelasticity and the dynamic poroelasticity in the frequency domain using the u-p formulation. In this work, a special term ＂decoupling coefficient＂ for the decomposition of the fast and slow dilatational waves is proposed and expressed to present a new methodology for deriving the poroelastodynamic Green＇s functions. The correct- ness of the solution is demonstrated by numerically comparing the current solution with Cheng＇s previous solution. The separation of the two waves in the present methodology allows the more accurate evaluation of Green＇s functions, particularly the solution of the slow dilatational wave. This can be advantageous for the numerical implementation of the boundary element method （BEM） and other applications.

Coefficient Estimates for a Subclass of Bi-univalent Strongly Quasi-starlike Functions

The aim of this paper is to establish the Fekete-Szego inequality for a subclass of bi-univalent strongly quasi-starlike functions which is defined in the open unit disk. Furthermore, the coefficients a2 and a3 for functions in this new subclass are estimated.

Coefficient Estimates for a Class of m-fold Symmetric Bi-univalent Function Defined by Subordination

In this paper, we investigate the coefficient estimates of a class of m-fold bi-univalent function de?ned by subordination. The results presented in this paper improve or generalize the recent works of other authors.

Correlation Degree and Correlation Coefficient of Multi-Output Functions

We present definitions of the correlation degree and correlation coefficient of multi-output functions. Two relationships about the correlation degree of multi-output functions are proved. One is between the correlation degree and independency, the other is between the correlation degree and balance. Especially the paper discusses the correlation degree of affine multioutput functions. We demonstrate properties of the correlation coefficient of multi-output functions. One is the value range of the correlation coefficient, one is the relationship between the correlation coefficient and independency, and another is the sufficient and necessary condition that two multi-output functions are equivalent to each other.

Studies of n-Octanol/water Partition Coefficients (lgK_(ow)) for Organophosphate Compounds by Density Functional Theory

Optimized calculation of 35 dialkyl phenyl phosphate compounds （OPs） was carded out at the B3LYP/6-31G^＊ level in Gaussian 98 program. Based on the theoretical linear solvation energy relationship （TLSER） model, the obtained parameters were taken as theoretical descriptors to establish the novel QSPR model for predicting n-octanol/water partition coefficients （lgKow） of OPs. The new model achieved in this work contains three variables, i.e., molecular volume （Vm）, dipole moment of the molecules （μ） and enthalpy （H^0）. For this model, R^2 = 0.9167 and SD = 0.31 at large t values. In addition, the variation inflation factors （VIF） of variables are all close to 1.0, suggesting high accuracy of the predicting model. And the results of cross-validation test （q^2 = 0.8993） and method validation also showed the model of this study exhibited optimum stability and better predictive power than that from semi-empirical method. The model achieved can be used to predict IgKow of congeneric compounds.

A numerical method based on boundary integral equations and radial basis functions for plane anisotropic thermoelastostatic equations with general variable coefficients

A boundary integral method with radial basis function approximation is proposed for numerically solving an important class of boundary value problems governed by a system of thermoelastostatic equations with variable coe?cients. The equations describe the thermoelastic behaviors of nonhomogeneous anisotropic materials with properties that vary smoothly from point to point in space. No restriction is imposed on the spatial variations of the thermoelastic coe?cients as long as all the requirements of the laws of physics are satis?ed. To check the validity and accuracy of the proposed numerical method, some speci?c test problems with known solutions are solved.

STARLIKENESS ASSOCIATED WITH THE SINE HYPERBOLIC FUNCTION

Let q_(λ)(z)=1+λsinh(ζ),0<λ<1/sinh(1)be a non-vanishing analytic function in the open unit disk.We introduce a subclass S^(*)(q_(λ))of starlike functions which contains the functions f such that zf'/f is subordinated by q_(λ).We establish inclusion and radii results for the class S^(*)(q_(λ))for several known classes of starlike functions.Furthermore,we obtain sharp coefficient bounds and sharp Hankel determinants of order two for the class S^(*)(q_(λ)).We also find a sharp bound for the third Hankel determinant for the caseλ=1/2.

FUNCTIONAL-COEFFICIENT REGRESSION MODEL AND ITS ESTIMATION

In this paper,a class of functional-coefficient regression models is proposed and an estimation procedure based on the locally weighted least equares is suggested.This class of models,with the proposed estimation method,is a powerful means for exploratory data analysis.

ON CERTAIN CLASS OF MEROMORPHIC FUNCTIONS WITH POSITIVE COEFFICIENTS

In the present investigation we define a new class of meromorphic functions on the punctured unit disk A△^＊ ：= {z ∈ C ： 0 〈 ｜z｜ 〈 1} by making use of the generalized Dziok-Srivastava operator Hm^l [α1]. Coefficient inequalities, growth and distortion inequalities, as well as closure results are obtained. We also establish some results concerning the partial sums of meromorphic functions and neighborhood results for functions in new class.

Coefficient Inequalities for p-Valent Functions

In the present paper, the authors introduce a new subclass of p-valent analytic functions with complex order defined on the open unit disk U={z:z∈C and |z|<1} and obtain coefficient inequalities for the functions in these class. Application of these results for the functions defined by the convolution are also obtained.

MEROMORPHIC p-VALENT FUNCTION WITH FIXED SECOND NEGATIVE COEFFICIENTS

In this paper we consider the class ∑^＊（p,α,β,k,c） consisting of analytic functions with negativecoefficients and fixed second coefficient. The object of the present paper is to give coefficient estimates, convex linear combinations, some distortion theorems and radii of starlikeness and convexity for f（z） in the class ∑^＊（p,α,β,k,c） .

Improvement of a new rotation function for molecular replacement by designing new scoring functions and dynamic correlation coefficient

A previously published new rotation function has been improved by using a dynamic correlation coefficient as well as two new scoring functions of relative entropy and mean-square-residues to make the rotation function more robust and independent of a specific set of weights for scoring and ranking. The previously described new rotation function calculates the rotation function of molecular replacement by matching the search model directly with the Patterson vector map. The signal-to-noise ratio for the correct match was increased by averaging all the matching peaks. Several matching scores were employed to evaluate the goodness of matching. These matching scores were then combined into a single total score by optimizing a set of weights using the linear regression method. It was found that there exists an optimal set of weights that can be applied to the global rotation search and the correct solution can be ranked in the top 100 or less. However, this set of optimal weights in general is dependent on the search models and the crystal structures with different space groups and cell parameters. In this work, we try to solve this problem by designing a dynamic correlation coefficient. It is shown that the dynamic correlation coefficient works for a variety of space groups and cell parameters in the global search of rotation function. We also introduce two new matching scores： relative entropy and mean-square-residues. Last but not least, we discussed a valid method for the optimization of the adjustable parameters for matching vectors.

Some Properties of Analytic Functions with the Fixed Second Coefficients

In this paper, we investigate some argument properties for analytic functions with fixed second coefficient and positive real part. And we apply the argument properties to the functions that are analytic and normalized. In particular, the order of strongly starlikeness of strongly convex functions with fixed second coefficients is given.

The Jacobi elliptic function-like exact solutions to two kinds of KdV equations with variable coefficients and KdV equation with forcible term

By use of an auxiliary equation and through a function transformation, the Jacobi elliptic function wave-like solutions, the degenerated soliton-like solutions and the triangle function wave solutions to two kinds of Korteweg de Vries （KdV） equations with variable coefficients and a KdV equation with a forcible term are constructed with the help of symbolic computation system Mathematica, where the new solutions are also constructed.