in this paper, we show that for any finite order entire function $f(z)$, the function of the form $f(z)^{n}[f(z+c)-f(z)]^{s}$ has no nonzero finite picard exceptional value for all nonnegative integers $n, s$ satisfying $ngeq 3$, which can be viewed as a different result on hayman conjecture. we also obtain some uniqueness theorems for difference polynomials of entire functions sharing one comm...

We prove a geometric logarithmic derivative lemma for rigid analytic mappings to algebraic varieties in characteristic zero. We use the lemma to give a new and simpler proof (at least in characteristic zero) of Berkovich’s little Picard theorem [Ber, Theorem 4.5.1], which says there are no nonconstant rigid analytic maps from the affine line to non-singular projective curves of positive genus, ...

We present a modified Picard-like method to solve absolute value equations by equivalently expressing the implicit fixed-point equation form of as two-by-two block nonlinear equation. This unifies some existing matrix splitting algorithms and improves efficiency algorithm introducing parameter ω. For choice ω in new method, we give way determine quasi-optimal values. Numerical examples are give...

Newton’s iteration is modified for the computation of the group inverses of singular Toeplitz matrices. At each iteration, the iteration matrix is approximated by a matrix with a low displacement rank. Because of the displacement structure of the iteration matrix, the matrix-vector multiplication involved in Newton’s iteration can be done efficiently. We show that the convergence of the modifie...

Given M ∈ <n×n and q ∈ <, the linear complementarity problem (LCP) is to find (x, s) ∈ < × < such that (x, s) ≥ 0, s = Mx + q, x s = 0. By using the ChenHarker-Kanzow-Smale (CHKS) smoothing function, the LCP is reformulated as a system of parameterized smooth-nonsmooth equations. As a result, a smoothing Newton algorithm, which is a modified version of the Qi-Sun-Zhou algorithm [Mathematical Pr...

We prove a geometric logarithmic derivative lemma for rigid analytic mappings to algebraic varieties in characteristic zero. We use the lemma to give a new and simpler proof (at least in characteristic zero) of Berkovich’s little Picard theorem, which says there are no nonconstant rigid analytic maps from the affine line to nonsingular projective curves of positive genus, and of Cherry’s result...

Using the Modified Picard Method of Parker and Sochacki [1, 2], we derive a hybrid scheme using the analytical Picard method with approximations to the differential operators. This new method, called Discretized Picard’s Method, uses approximations in the space dimensions to compute derivatives but utilizes a continuous approximation in the time dimension. We illustrate the method using finite ...

Abstract This paper develops an efficient and robust solution technique for the steady Boussinesq model of non-isothermal flow using Anderson acceleration applied to a Picard iteration. After analyzing fixed point operator associated with nonlinear iteration prove that certain stability regularity properties hold, we apply authors’ recently constructed theory acceleration, which yields converge...

A question arising out of the late 80’s about computation systems was could machines be intelligent without emotions ([Minsky 1988]). It seems that the machines of today are not only inhuman but also behave stupidly. Studies by psychologists have shown that humans who lack the emotional features usually used by many aspects of human reasoning do not behave intelligently [Damasio 1994]. This the...