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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...

1. Notation. Let Z and N be the sets of integers and positive integers respectively. For b, c ∈ Z the Lucas sequences {U n (b, c)} and {V n (b, c)} are defined by (1.1) U 0 (b, c) = 0, U 1 (b, c) = 1, U n+1 (b, c) = bU n (b, c) − cU n−1 (b, c) (n ≥ 1) and (1.2) V 0 (b, c) = 2, V 1 (b, c) = b, V n+1 (b, c) = bV n (b, c) − cV n−1 (b, c) (n ≥ 1). Let d = b 2 − 4c. It is well known that for n ∈ N, ...

We consider the linear complementarity problem (LCP): Mz + q ≥ 0, z ≥ 0, z′(Mz + q) = 0 as an absolute value equation (AVE): (M + I)z + q = |(M − I)z + q|, where M is an n× n square matrix and I is the identity matrix. We propose a concave minimization algorithm for solving (AVE) that consists of solving a few linear programs, typically two. The algorithm was tested on 500 consecutively generat...

In the title compound, {[Cu(C(9)H(15)N(13))(2)](ClO(4))(2)}(n), the Cu(2+) cation lies on an inversion center and is coordinated by the tetra-zole N(4) atoms of six symmetry-equivalent tris-[2-(1H-tetra-zol-1-yl)eth-yl]amine ligands (t(3)z) in the form of a Jahn-Teller-distorted octa-hedron with Cu-N bond distances of 2.0210 (8), 2.0259 (8) and 2.4098 (8) Å. The tertiary amine N atom is stereoc...

Let D be a 2-strong digraph of order n ≥ 8 such that for every vertex x ∈ V(D)\{z}, d(x) and d(z) − 4, where z is in V(D). We prove that: If contains cycle passing through length equal to 2, then Hamiltonian. also give new sufficient condition Hamiltonian-connected.

We consider various aspects of the Segre variety S := S1,1,1(2) in PG(7, 2), whose stabilizer group GS < GL(8, 2) has the structure N o Sym(3), where N := GL(2, 2) × GL(2, 2) × GL(2, 2). In particular we prove that S determines a distinguished Z3-subgroup Z < GL(8, 2) such that AZA−1 = Z, for all A ∈ GS , and in consequence S determines a GS invariant spread of 85 lines in PG(7, 2). Furthermore...