Calculus of Generalized Quasi-differentiable Functions I: Some Results on the Space of Pairs of Convex-Set Collections

A Riesz space K1 whose elements are pairs of convex-set collections is presented for the study on the calculus of generalized quasi-differentiable functions. The space K1 is constructed by introducing a well-defined equivalence relation among pairs of collections of convex sets. Some important properties on the norm and operations in K1 are given.

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.

A Quasi-Interpolation Satisfying Quadratic Polynomial Reproduction with Radial Basis Functions

In this paper,a new quasi-interpolation with radial basis functions which satis- fies quadratic polynomial reproduction is constructed on the infinite set of equally spaced data.A new basis function is constructed by making convolution integral with a constructed spline and a given radial basis function.In particular,for twicely differ- entiable function the proposed method provides better approximation and also takes care of derivatives approximation.

Geometric Aspects of Quasi-Periodic Property of Dirichlet Functions

The concept of quasi-periodic property of a function has been introduced by Harald Bohr in 1921 and it roughly means that the function comes (quasi)-periodically as close as we want on every vertical line to the value taken by it at any point belonging to that line and a bounded domain Ω. He proved that the functions defined by ordinary Dirichlet series are quasi-periodic in their half plane of uniform convergence. We realized that the existence of the domain Ω is not necessary and that the quasi-periodicity is related to the denseness property of those functions which we have studied in a previous paper. Hence, the purpose of our research was to prove these two facts. We succeeded to fulfill this task and more. Namely, we dealt with the quasi-periodicity of general Dirichlet series by using geometric tools perfected by us in a series of previous projects. The concept has been applied to the whole complex plane (not only to the half plane of uniform convergence) for series which can be continued to meromorphic functions in that plane. The question arise: in what conditions such a continuation is possible? There are known examples of Dirichlet series which cannot be continued across the convergence line, yet there are no simple conditions under which such a continuation is possible. We succeeded to find a very natural one.

Gap Functions and Error Bounds for Set-Valued Vector Quasi Variational Inequality Problems

One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deriving the error bounds which provide an estimated distance between a specific point and the exact solution of variational inequality problem. In this paper, we follow a similar approach for set-valued vector quasi variational inequality problems and define the gap functions based on scalarization scheme as well as the one with no scalar parameter. The error bounds results are obtained under fixed point symmetric and locally α-Holder assumptions on the set-valued map describing the domain of solution space of a set-valued vector quasi variational inequality problem.

Common Fixed Point Results for Quasi-contractions Involving Altering Distance Functions in Ordered Cone Metric Spaces

Some common fixed point results for mappings satisfying a quasi-contractive condition which involves altering distance functions are obtained in partially ordered complete cone metric spaces. A sufficient condition for the uniqueness of common fixed point is proved. Also, an example is given to support our results.

Fekete-Szego Problem for Certain Subclass ofp-Valent Analytic Functions usingQuasi-Subordination

In this paper, a new certain class of р-valent analytic functions with quasisubordination is defined and the Fekete-Szeg? problems for functions belonging to the class are derived. The results presented here provide extensions of those given in some earlier works.

On the Equality of Weighted BajratarevićMeans to Quasi-Arithmetic Means

In this paper, we considered the equality problem of weighted Bajraktarević means with weighted quasi-arithmetic means. Using the method of substituting for functions, we first transform the equality problem into solving an equivalent functional equation. We obtain the necessary and sufficient conditions for the equality equation.

Fuzzy Henstock-Kurzweil Triple Integral on a Type 1 Quasi-Fuzzy Parallelepipedal Domain

In this article, we propose by using the Hausdorff distance Simpson’s rule for the triple integral of a fuzzy-valued function and the error bound of this method, one of the variables of which is fuzzy. In addition, thin δ-fine partitions are introduced. The integration domain is a quasi-fuzzy parallelipiped. A numerical example is presented in order to show the application and the significance of the method.

Assessment and Prediction of Thermodynamic Functions of Compounds in Sialon System

According to the quasi paraboloid rule, a computer program was developed and the Gibbs free energy functions of some compounds in Sialon system were assessed and predicted. It makes the theoretical design of the Sialon materials possible.

AN ASYMPTOTIC EXPANSION FORMULA OF KERNEL FUNCTION FOR QUASI FOURIER-LEGENDRE SERIES AND ITS APPLICATION

Is this paper we shall give cm asymptotic expansion formula of the kernel functim for the Quasi Faurier-Legendre series on an ellipse, whose error is 0(1/n2) and then applying it we shall sham an analogue of an exact result in trigonometric series.

QUASI-VARIATIONAL PRINCIPLE FOR THE VORTEX-POTENTIAL FUNCTION OF ROTATIONAL FLOW IN THREE-DIMENSION PIPE

The variational analysis of the Pseudo-potential function-vortex-potential function model, a new mathematical model, was developed and by which the flow field with transonic speed and curl was decided, and different sorts of the variational principle for vortex potential function were established by transforming the original equation for vortex-function, the boundary conditions for vortex-potential function was raised.

Value Distribution of the <i>k</i>th Derivatives of Meromorphic Functions

In the paper, we take up a new method to prove a result of value distribution of meromorphic functions: let f be a meromorphic function in , and let , where P is a polynomial. Suppose that all zeros of f have multiplicity at least , except possibly finite many, and as . Then has infinitely many zeros.

Quasi-distribution Appraisal about Finite Element Analysis of Multi-functional Structure Made of Honeycomb Sandwich Materials

A new appraisal method（QDA, quasi-distribution appraisal） which could be used to evaluate the finite element analysis of multi-functional structure made of honeycomb sandwich materials is developed based on sub-section Bezier curve. It is established by simulating the distribution histogram data obtained from the numerical finite element analysis values of a satellite component with sub-section Bezier curve. Being dealt with area normalization method, the simulation curve could be regarded as a kind of probability density function（PDF）, its mathematical expectation and the variance could be used to evaluate the result of finite element analysis. Numerical experiments have indicated that the QDA method demonstrates the intrinsic characteristics of the finite element analysis of multi-functional structure made of honeycomb sandwich materials, as an appraisal method, it is effective and feasible.

THE DISPLACEMENT FUNCTION OF QUASI-CONFORMING ELEMENT AND ITS NODE ERROR

Based on the strain formulation of the quasi-conforming finite element, displacement functions are constructed which have definite physical meaning, and a conclusion can be obtained that the coefficients of the constant and the linear strain are uniquely determined, and the quasi-conforming finite element method is convergent to constant strain. There are different methods for constructing the rigid displacement items, and different methods correspond to different order node errors, and this is different from ordinary displacement method finite element.

Maximally Holomorphic Functions of a Bounded Linear Operator

The maximally holomorphic functions of a bounded linear operator is introduced and applied to representthe spectrum and characterize the single--valued extension property. The well known results of quasi--nilpo-tent equivalent operators follow easily from the relation of their maximally holomorphie functions.

Approximate derivative-dependent functional variable separation for quasi-linear diffusion equations with a weak source

By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = （A（u）Ux）x ＋ eB（u, Ux）. A complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is listed. As a consequence, some approxi- mate solutions to the resulting perturbed equations are constructed via examples.

General Solution and Stability of Quattuordecic Functional Equation in Quasi β-Normed Spaces

In this paper, we introduce the following quattuordecic functional equation f(x+7y)-14f(x+6y)+91f(x+5y)-364f(x+4y)+1001f(x+3y)-2002f(x+2y)+3003f(x+y)-3432f(x)+3003f(x-y)-2002f(x-2y)+1001f(x-3y)-364f(x-4y)+91f(x-5y)-14f(x-6y)+f(x-7y)=14!f(y), investigate the general solution and prove the stability of this quattuordecic functional equation in quasi &beta;-normed spaces by using the fixed point method.

AN INTEGRATION METHOD WITH FITTING CUBIC SPLINE FUNCTIONS TO A NUMERICAL MODEL OF 2ND-ORDER SPACE-TIME DIFFERENTIAL REMAINDER——FOR AN IDEAL GLOBAL SIMULATION CASE WITH PRIMITIVE ATMOSPHERIC EQUATIONS

In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubic spline numerical model(Spline Model for short),which is with a quasi-Lagrangian time-split integration scheme of fitting cubic spline/bicubic surface to all physical variable fields in the atmospheric equations on spherical discrete latitude-longitude mesh.A new algorithm of"fitting cubic spline—time step integration—fitting cubic spline—……"is developed to determine their first-and2nd-order derivatives and their upstream points for time discrete integral to the governing equations in Spline Model.And the cubic spline function and its mathematical polarities are also discussed to understand the Spline Model’s mathematical foundation of numerical analysis.It is pointed out that the Spline Model has mathematical laws of"convergence"of the cubic spline functions contracting to the original functions as well as its 1st-order and 2nd-order derivatives.The"optimality"of the 2nd-order derivative of the cubic spline functions is optimal approximation to that of the original functions.In addition,a Hermite bicubic patch is equivalent to operate on a grid for a 2nd-order derivative variable field.Besides,the slopes and curvatures of a central difference are identified respectively,with a smoothing coefficient of 1/3,three-point smoothing of that of a cubic spline.Then the slopes and curvatures of a central difference are calculated from the smoothing coefficient 1/3 and three-point smoothing of that of a cubic spline,respectively.Furthermore,a global simulation case of adiabatic,non-frictional and"incompressible"model atmosphere is shown with the quasi-Lagrangian time integration by using a global Spline Model,whose initial condition comes from the NCEP reanalysis data,along with quasi-uniform latitude-longitude grids and the so-called"shallow atmosphere"Navier-Stokes primitive equations in the spherical coordinates.The Spline Model,which adopted the Navier-Stokes primitive equations and quasi-Lagrangian time-split integration scheme,provides an initial ideal case of global atmospheric circulation.In addition,considering the essentially non-linear atmospheric motions,the Spline Model could judge reasonably well simple points of any smoothed variable field according to its fitting spline curvatures that must conform to its physical interpretation.

Local Radial Basis Function Methods: Comparison, Improvements, and Implementation

Radial Basis Function methods for scattered data interpolation and for the numerical solution of PDEs were originally implemented in a global manner. Subsequently, it was realized that the methods could be implemented more efficiently in a local manner and that the local approaches could match or even surpass the accuracy of the global implementations. In this work, three localization approaches are compared: a local RBF method, a partition of unity method, and a recently introduced modified partition of unity method. A simple shape parameter selection method is introduced and the application of artificial viscosity to stabilize each of the local methods when approximating time-dependent PDEs is reviewed. Additionally, a new type of quasi-random center is introduced which may be better choices than other quasi-random points that are commonly used with RBF methods. All the results within the manuscript are reproducible as they are included as examples in the freely available Python Radial Basis Function Toolbox.