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In this paper, we present some double inequalities involving certain ratios of the Gamma function. These results are further generalizations of several previous results. The approach is based on the monotonicity properties of some functions…
We give a proof of Lipschitz continuity of p-harmonious functions, that are tug-of-war game analogies of ordinary p-harmonic functions. This result is used to obtain a new proof of Harnack's inequality for p-harmonic functions in the case…
We give the definition of uniform symmetric continuity for functions defined on a nonempty subset of the real line. Then we investigate the properties of uniformly symmetrically continuous functions and compare them with those of…
Motivated by the mean value property of harmonic functions, we introduce the local and global median value properties for continuous functions of two variables. We show that the Dirichlet problem associated with the local median value…
This is a survey of results about permanental processes, real valued positive processes which are a generalization of squares of Gaussian processes. In a certain sense the symmetric positive definite function that determines a Gaussian…
We study the generalized harmonic oscillator which has both the position-dependent mass and the potential depending on the form of mass function in a more general framework. The explicit expressions of the eigenvalue and eigenfunction for…
In this paper, generalizing the definition of G-convex functions defined by Peng [9] during the construction of G-expectations and related properties, we define a group of G-convex functions based on the Backward Stochastic Differential…
The connection between spherical harmonics and symmetric tensors is explored. For each spherical harmonic, a corresponding traceless symmetric tensor is constructed. These tensors are then extended to include nonzero traces, providing an…
In this article we study the existence and strong consistency of GEE estimators, when the generalized estimating functions are martingales with random coefficients. Furthermore, we characterize estimating functions which are asymptotically…
The maximum (or minimum) generalized eigenvalue of symmetric positive semidefinite matrices that depend on optimization variables often appears as objective or constraint functions in structural topology optimization when we consider…
We construct N-harmonic functions in a domain with one isolated singularity on the boundary of the domain. By using solutions of the spherical p-harmonic spectral problem, we give an inductive method to produce a large variety of separable…
We begin by shortly recalling a generalized mean value inequality for subharmonic functions, and two applications of it: first a weighted boundary behavior result (with some new references and remarks), and then a borderline case result to…
In this paper we investigate congruence relationships of particular finite generalized harmonic numbers sums. We suggest more transparent and simpler method to analyse these sums and present several additional results for certain special…
The main purpose of this paper is to study the concept of normal function in the context of harmonic mappings from the unit disk $\mathbb{D}$ to the complex plane. In particular, we obtain necessary conditions for that a function $f$ to be…
Several mean value identities for harmonic and panharmonic functions are reviewed along with the corresponding inverse properties. The latter characterize balls, annuli and strips analytically via these functions.
We define an analogue of the Baernstein star function for a meromorphic function f in several complex variables. This function is subharmonic on the upper half-plane and encodes some of the main functionals attached to f.We then…
We prove some basic properties of quasinearly subharmonic functions and quasinearly subharmonic functions in the narrow sense.
We derive new relationships expressing solid spherical harmonics as series of toroidal harmonics and vice versa. The expansions include regular and irregular spherical harmonics, ring and axial toroidal harmonics of even and odd parity…
For functions defined on the $n$-dimensional hypercube $I_n (r) = \{{\bm{x}} \in \mathbb{R}^n ~\vert~ \vert x_i \vert \le r,~ i = 1, 2, \ldots , n\}$ and harmonic therein, we establish certain analogues of Gauss surface and volume…
A method for time-frequency analysis is given. The approach utilizes properties of Gaussian distribution, properties of Hermite polynomials and Fourier analysis. We begin by the definitions of a set of functions called harmonic Gaussian…