Shenzhou Zheng

Green functions for a class of nonlinear degenerate operators with X-ellipticity

A maximum principle and some a priori estimates of a class of degenerate equations with X-ellipticity in the sense of distributions are established. A local comparison of the generalized Green function with its fundamental solutions is obtained. As an application, by means of the power of the Green function as a kernel function of a local integral, we also derive local Hölder continuity for nonlinear degenerate subelliptic equations.

Complex and Entropy of Fluctuations of Agent-Based Interacting Financial Dynamics with Random Jump

This paper investigates the complex behaviors and entropy properties for a novel random complex interacting stock price dynamics, which is established by the combination of stochastic contact process and compound Poisson process, concerning with stock return fluctuations caused by the spread of investors’ attitudes and random jump fluctuations caused by the macroeconomic environment, respectively. To better understand the fluctuation complex behaviors of the proposed price dynamics, the entropy analyses of random logarithmic price returns and corresponding absolute returns of simulation dataset with different parameter set are preformed, including permutation entropy, fractional permutation entropy, sample entropy and fractional sample entropy. We found that a larger λ or γ leads to more complex dynamics, and the absolute return series exhibit lower complex dynamics than the return series. To verify the rationality of the proposed compound price model, the corresponding analyses of actual market datasets are also comparatively preformed. The empirical results verify that the proposed price model can reproduce some important complex dynamics of actual stock markets to some extent.

Sharp inequalities for tangent function with applications

In the article, we present new bounds for the function etcot(t)−1

Complete monotonicity involving some ratios of gamma functions

e^{t\cot(t)-1}

Monotonicity of the ratio of modified Bessel functions of the first kind with applications

on the interval (0,π/2)

Sharp Smith’s bounds for the gamma function

(0, \pi/2)

Orlicz estimates for nondivergence linear elliptic equations with partially BMO coefficients

and find sharp estimations for the Sine integral and the Catalan constant based on a new monotonicity criterion for the quotient of power series, which refine the Redheffer and Becker-Stark type inequalities for tangent function.

Weighted Lorentz and Lorentz–Morrey estimates to viscosity solutions of fully nonlinear elliptic equations

In this paper, by using the properties of an auxiliary function, we mainly present the necessary and sufficient conditions for various ratios constructed by gamma functions to be respectively completely and logarithmically completely monotonic. As consequences, these not only unify and improve certain known results including Qi’s and Ismail’s conclusions, but also can generate some new inequalities.

Traveling Waves Connecting Equilibrium and Periodic Orbit for a Delayed Population Model on a Two-Dimensional Spatial Lattice

AbstractLet Wv(x)=xIv(x)/Iv+1(x)

THE COMPARISON OF GREEN FUNCTION FOR QUASI-LINEAR ELLIPTIC EQUATION

W_{v} ( x ) =xI_{v} ( x ) /I_{v+1} ( x )