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...

in this work we develop a new optimal without memory class for approximating a simple root of a nonlinear equation. this class includes three parameters. therefore, we try to derive some with memory methods so that the convergence order increases as high as possible. some numerical examples are also ‎presented.‎‎

‎An  oriented perfect path double cover (OPPDC) of a‎ ‎graph $G$ is a collection of directed paths in the symmetric‎ ‎orientation $G_s$ of‎ ‎$G$ such that‎ ‎each arc‎ ‎of $G_s$ lies in exactly one of the paths and each‎ ‎vertex of $G$ appears just once as a beginning and just once as an‎ ‎end of a path‎. ‎Maxov{'a} and Ne{v{s}}et{v{r}}il (Discrete‎ ‎Math‎. ‎276 (2004) 287-294) conjectured that ...

This paper establishes the Manin conjecture for a certain non-split singular del Pezzo surface of degree four X ⊂ P 4. In fact, if U ⊂ X is the open subset formed by deleting the lines from X, and H is the usual projective height function on P 4 (Q), then the height zeta function P x∈U (Q) H(x) −s is analytically continued to the half-plane ℜe(s) > 17/20.

(2) ‖Hα(f1, f2)‖p ≤ Cα,p1,p2‖f1‖p1‖f2‖p2 with constants Cα,p1,p2 depending only on α, p1, p2 and p := p1p2 p1+p2 hold. The first result of this type is proved in [4], and the purpose of the current paper is to extend the range of exponents p1 and p2 for which (2) is known. In particular, the case p1 = 2, p2 = ∞ is solved to the affirmative. This was originally considered to be the most natural ...

This is the first of a series of two papers in which we solve the Clemens conjecture: there are only finitely many smooth rational curves of each degree in a generic quintic threefold. In this paper, we deal with a family of smooth Calabi-Yau threefolds fǫ for a small complex number ǫ. If fǫ contains a smooth rational curve cǫ, then its normal bundle is Ncǫ (fǫ) = Ocǫ (k) ⊕ Ocǫ (−2− k) for k ≥ ...

in the present paper we give a partially negative answer to a conjecture of ghahramani, runde and willis. we also discuss the derivation problem for both foundation semigroup algebras and clifford semigroup algebras. in particular, we prove that if s is a topological clifford semigroup for which es is finite, then h1(m(s),m(s))={0}.

x0 h and S Cobordism Theorems-review-In this article the author would like to propose a natural generalization of celebrated h and S coboridism theorems to loop space. We will explain some part of the idea of the proof of an (easier) half of it, and also a nite dimensional analogue of the conjecture which can be proved under some additional assumptions. The detailed proof of them will appear el...

We show that K1(E) of an exact category E agrees with K1(DE) of the associated triangulated derivator DE. More generally we show that K1(W) of a Waldhausen category W with cylinders and a saturated class of weak equivalences agrees with K1(DW) of the associated right pointed derivator DW. Introduction For a long time there was an interest in defining a nice K-theory for triangulated categories ...

In the present paper, among other results, a decomposition formula is given for the w-bounded continuous negative definite functions of a topological *-semigroup S with a weight function w into a proper H*-algebra A in terms of w-bounded continuous positive definite A-valued functions on S. A generalization of a well-known result of K. Harzallah is obtained. An earlier conjecture of the author ...