Bulletin of Iranian Mathematical Society
Volume:38 Issue: 4, 2012

We reduce the two phase Stefan problem with kinetic to a system of nonlinear Volterra integral equations of second kind and apply Newton's method to linearize it. We found product integration solution of the linear form. Sufficient conditions for convergence of the numerical method are given and their applicability is illustrated with an example.

In this paper we will determine the multiple point manifolds of certain self-transverse immersions in Euclidean spaces. Following the triple points, these immersions have a double point self-intersection set which is the image of an immersion of a smooth 5-dimensional manifold, cobordant to Dold manifold $V^5$ or a boundary. We will show there is an immersion of $S^7times P^2$ in $mathbb{R}^{13}$ with double point manifold cobordant to Dold manifold $V^5$, and an immersion of $P^2times P^2times P^2times P^2times P^2$ in $mathbb{R}^{15}$ with double point manifold a boundary and the triple point set is odd number. These will be done by introducing the product technique and reading off the Stiefel-Whitney numbers of the self-intersection manifolds.

In this paper we introduce the concept of entropy operator for continuous systems of finite topological entropy. It is shown that it generates the Kolmogorov entropy as a special case. If $phi$ is invertible then the entropy operator is bounded with the topological entropy of $phi$ as its norm.

Let $R$ be a 2-torsion free ring and $U$ be a square closed Lie ideal of $R$. Suppose that $alpha, beta$ are automorphisms of $R$. An additive mapping $delta: R longrightarrow R$ is said to be a Jordan left $(alpha,beta)$-derivation of $R$ if $delta(x^2)=alpha(x)delta(x)+beta(x)delta(x)$ holds for all $xin R$. In this paper it is established that if $R$ admits an additive mapping $G: Rlongrightarrow R$ satisfying $G(u^2)=alpha(u)G(u)+alpha(u)delta(u)$ for all $uin U$ and a Jordan left $(alpha,alpha)$-derivation $delta$; and $U$ has a commutator which is not a left zero divisor, then $G(uv)=alpha(u)G(v)+alpha(v)delta(u)$ for all $u, vin U$. Finally, in the case of prime ring $R$ it is proved that if $G: R longrightarrow R$ is an additive mapping satisfying $G(xy)=alpha(x)G(y)+beta(y)delta(x)$ for all $x,y in R $ and a left $(alpha, beta)$-derivation $delta$ of $R$ such that $G$ also acts as a homomorphism or as an linebreak anti-homomorphism on a nonzero ideal $I$ of $R$, then either $R$ is commutative or $delta=0$ ~on $R$.

We introduce a two generated weakly branch contracting automaton group $G$ which is generated by a two state automaton on a three letter alphabet. Using its branch structure and the finiteness nature of a sequence of its factor groups we compute the order of some of these factors. Furthermore some algebraic properties of $G$ are detected.

A common fixed point result for weakly increasing mappings satisfying generalized contractive type of Zhang in ordered metric spaces are derived.

This paper uses the Tsuji’s characteristic to investigate the uniqueness of transcen- dental meromorphic function with shared values in an angular domain dealing with the multiple values which improve a result of J. Zheng.

Let R be a ring, M a right R-module and (S,≤) a strictly ordered monoid. In this paper we will show that if (S,≤) is a strictly ordered monoid satisfying the condition that 0 ≤ s for all s ∈ S, then the module [[MS,≤]] of generalized power series is a uniserial right [[RS,≤]]]]-module if and only if M is a simple right R-module and S is a chain monoid.

We characterize the natural diagonal almost product (locally product) structures on the tangent bundle of a Riemannian manifold. We obtain the conditions under which the tangent bundle endowed with the determined structure and with a metric of natural diagonal lift type is a Riemannian almost product (locally product) manifold, or an (almost) para-Hermitian manifold. We find the natural diagonal (almost) para-K"ahlerian structures on the tangent bundle, and we study the conditions under which they have constant para-holomorphic sectional curvature.

The probability that the commutator of two group elements is equal to a given element has been introduced in literature few years ago. Several authors have investigated this notion with methods of the representation theory and with combinatorial techniques. Here we illustrate that a wider context may be considered and show some structural restrictions on the group.

In this paper, the notion of fully idempotent modules is defined and it is shown that this notion inherits most of the essential properties of the usual notion of von Neumann's regular rings. Furthermore, we introduce the dual notion of fully idempotent modules (that is, fully coidempotent modules) and investigate some properties of this class of modules.

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 common value.

In this paper, we characterize multiresolution analysis(MRA) Parseval frame multiwavelets in L^2(R^d) with matrix dilations of the form (D f)(x) = sqrt{2}f (Ax), where A is an arbitrary expanding dtimes d matrix with integer coefficients, such that |detA| =2. We study a class of generalized low pass matrix filters that allow us to define (and construct) the subclass of MRA tight frame multiwavelets. This leads us to an associated class of generalized scaling functions that are not necessarily obtained from a multiresolution analysis. We also investigate several properties of these classes of generalized multiwavelets, scaling functions, matrix filters and give some characterizations about them. Finally, we describe the matrix multipliers classes associated with Parseval frame multiwavelets(PFMWs) in L^2(R^d) and give an example to prove our theory.

We prove a strong convergence result for a sequence generated by Halpern's type iteration for approximating a common fixed point of a countable family of quasi-Lipschitzian mappings in a real Hilbert space. Consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for continuous monotone mappings.

In this paper we define S algebras and show that every finite group can be found in some S algebra. We define and study the S degree of a finite group and determine the S degree of several classes of finite groups such as cyclic groups, elementary abelian $p$-groups, and dihedral groups $D_p$.