Geometric Properties of Generalized Hypergeometric Functions

Let denote the generalized hypergeometric function where no denominator parameter can be zero or a negative integer and (a,n) denotes the ascending factorial notation. Ponnusamy and Vuorinen raised the problem of finding conditions on the parameters a_j > 0, b_j > 0 so that the function is univalent in . The main aim of this paper is to discuss this problem in detail for the case q = 2.     

Properties of Some Families of Meromorphic Multivalent Functions Associated with Generalized Hypergeometric Functions

We introduce and study two subclasses ?_([α_1])(A, B, λ) and ?_([α_1])~+ (A, B, λ) of meromorphic p-valent functions defined by certain linear operator involving the generalized hypergeometric function. The main object is to investigate the various important properties and characteristics of these subclasses of meromorphically multivalent functions. We extend the familiar concept of neighborhoods of analytic functions to these subclasses. We also derive many interesting results for the Hadamard products of functions belonging to the class ?_([α_1])~+(α, β, γ, λ).     

Geometric Properties of the Shifted Hypergeometric Functions

We will provide sufficient conditions for the shifted hypergeometric function \(z_2F_1(a,b;c;z)\) to be a member of a specific subclass of starlike functions in terms of the complex parameters a, b and c. For example, we study starlikeness of order \(\alpha ,\) \(\lambda \)-spirallikeness of order \(\alpha \) and strong starlikeness of order \(\alpha .\) In particular, those properties lead to univalence of the shifted hypergeometric functions on the unit disk.     

p-adic超几何函数与Dwork超曲面上的有理点

p-adic超几何函数是经典的Gauss超几何函数在有限域上的模拟,与许多数论问题都有联系.设Fq是q元有限域,λ∈Fq,n为正整数.本文研究了Dwork超曲面Dλ^n:x1^n+x2^n+…+xn^n=nλx1x2…xn及其推广形式上的Fq-有理点,并在n与q(q-1)互素时给出了由p-adic超几何函数表示的各种Fq-有理点个数的公式,从而修正和改进了Barman与Goodson等人的结论.     

p-adic 超几何函数与 Dwork超曲面上的有理点

p-adic超几何函数是经典的Gauss超几何函数在有限域上的模拟,与许多数论问题都有联系.设F_q是q元有限域,λ∈F_q,n为正整数.本文研究了Dwork超曲面D_λⁿ：x₁ⁿ+x₂ⁿ+…+x_nⁿ=nλx₁x₂…x_n及其推广形式上的F_q-有理点,并在n与q（q-1）互素时给出了由p-adic超几何函数表示的各种F_q-有理点个数的公式,从而修正和改进了Barman与Goodson等人的结论.     

一致星象和凸象超几何函数的一些性质

介绍了(高斯)超几何函数属于一致星象函数和一致凸函数的某些子类的一些性质.还考虑了与超几何函数相关的算子.     

广义Cantor函数的不可微点集的维数

设K■R为由满足强分离条件的相似压缩映射族{h_k(x)=a_kx+b_k,k=1,…,N}所生成的自相似集,此处N≥2.对一个概率向量p=(p_1,…p_N),设γ_p为对应的支撑在K上的自相似测度.在单位线段上定义广义Cantor函数f(x)=γ_p([0,x]∩K),这里假设.设数ξ和q+β(q)分别由■和■,β'(q)=-1所确定.本文研究集合K中使得函数f(x)的导数不存在的点集,使得函数f(x)的导数为零的点集,及使得函数f(x)的导数为无穷的点集的维数,本文结果表明上述定义的两个数可以给出这些维数的一个很好的刻画.     

Weighted Norm Inequalities for Convolutions, Differential Operators, and Generalized Hypergeometric Functions

The recent work on discrete inequalities with the binomially made weights leads to a sharp weighted norm inequality for convolutions of complex-valued functions on a finite interval. This result and the Hadamard-type modifications of power series provide the basis for an integral approach to solution-kernel estimates for Volterra convolution equations and for various integro-differential and special function applications. The development of this approach and the new weighted norm inequalities for linear differential operators and generalized hypergeometric functions are presented in this paper.     

某些新广义函数类(英文)

给出由非标准离散函数及其差商所定义的新广义函数的某些类,它们密切联系于通常的直至某阶为连续可微的函数．周的一个深刻的定理被用来建立这些类与非标准Ｓｏｂｏｌｅｖ空间之间的关系．     

Non-Existence of Some Generalized Bent Functions

Several new results on the non-existence of some generalized bent functions are proved by using properties of the decomposition law of primes in cyclotomic fields and properties of the solutions of some special Diophantine equations.     

Some Generalized Problems for Polyharmonic Functions

In the first section of this paper, some non-local boundary value problem for the polyharmonic equation in the plane is considered. This problem consists in determining solution of the polyharmonic equation satisfying some special non-local-type boundary condition on two curves. The existence theorem is proved. In the second section, an example for the case of the biharmonic equation is considered. In the third section, some non-local, non-linear problem of Riquier type is examined. The Riquier-type problem consists in determining the polyharmonic function in the plane whose value together with its successive Laplacians are prescribed on the boundary. The existence theorem is proved and an example for the case of the biharmonic equation is considered.     

Some Functions of Points in Projective Spaces

Extending earlier results in the plane, we prove that every n-polygon in sufficiently general position in d-dimensional projective space, n d + 2, gives rise to a derived n-polygon, which preserves a few functions; these functions are the cyclial product of (actually affine) ratios of various points, obtained by proper projections on suitable lines.     

Generalized Transition Waves and Their Properties

In this paper, we generalize the usual notions of waves, fronts, and propagation speeds in a very general setting. These new notions, which cover all usual situations, involve uniform limits, with respect to the geodesic distance, to a family of hypersurfaces that are parametrized by time. We prove the existence of new such waves for some time‐dependent reaction‐diffusion equations, as well as general intrinsic properties, some monotonicity properties, and some uniqueness results for almost‐planar fronts. The classification results, which are obtained under some appropriate assumptions, show the robustness of our general definitions. © 2012 Wiley Periodicals, Inc.     

广义分数积分的复合与Gauss超几何函数积分的估计

In this paper, composition formulas for generalized fractional integral oper-ators involving Gauss hypergeometric function are applied to evaluating of de finite integrals involving two Gauss hypergeometric functions.     

Generalized Hypergeometric Solutions of the Heun Equation

Theoretical and Mathematical Physics - We present infinitely many solutions of the general Heun equation in terms of generalized hypergeometric functions. Each solution assumes that two...     

Some Properties of Bent Functions

First, this paper discusses and sums up some properties of a pair of functions p（x）, q（x） that makes （y ＋ 1）p（x） ＋ yq（x） into a bent function. Then it discusses the properties of bent functions. Also, the upper and lower bounds of the number of bent functions on GF（2）2k are discussed.     

The Lie Theory of Two-Variable Hypergeometric Functions

We develop a Lie-algebraic method that associates with each of the 34 distinct second-order hypergeometric functions in two variables a canonical system of partial differential equations. The special functions arise by partial separation of variables in these simple systems. Some consequences are a demonstration that all such functions appear as solutions of the 4-variable wave equation and a classification of the possible imbeddings. In each case the functions are characterized by first- and second-order operators in the enveloping algebra of the conformal symmetry algebra for the wave equation. In some cases the 3-variable wave and heat equations and the 2-variable Helmholtz equation also arise. This intimate relationship between Horn functions and some fundamental equations of mathematical physics shows that these functions are more interesting than was previously recognized and permits use of the powerful tools of Lie theory and separation of variables to obtain properties of the functions.