Existence of Pseudo-Almost Automorphic Solutions for Nonlinear Differential Equations

In this paper, we discuss the existence of pseudo-almost automorphic solutions to linear differential equation which has an exponential trichotomy~ and the results also hold for some nonlinear equations with the form x＇（t） = f（t,x（t）） ＋ λg（t,x（t））, where f,g are pseudo-almost automorphic functions. We prove our main result by the application of Leray-Schauder fixed point theorem.

A Set of Almost Automorphic Functions and Applications

For a set S of real numbers, we introduce the concept of S-almost automorphic functions valued in a Banach space. It generalizes in particular the space of Z-almost automorphic functions. Considering the space of S-almost automorphic functions, we give sufficient conditions of the existence and uniqueness of almost automorphic solutions of a differential equation with a piecewise constant argument of generalized type. This is done using the Banach fixed point theorem.

EXISTENCE AND ATTRACTIVITY OF k-ALMOST AUTOMORPHIC SEQUENCE SOLUTION OF A MODEL OF CELLULAR NEURAL NETWORKS WITH DELAY

In this paper we discuss the existence and global attractivity of k-almost automorphic sequence solution of a model of cellular neural networks. We consider the corresponding difference equation analogue of the model system using suitable discretization method and obtain certain conditions for the existence of solution. Almost automorphic function is a good generalization of almost periodic function. This is the first paper considering such solutions of the neural networks.

The Khuri-Jones Threshold Factor as an Automorphic Function

The Khuri-Jones correction to the partial wave scattering amplitude at threshold is an automorphic function for a dihedron. An expression for the partial wave amplitude is obtained at the pole which the upper half-plane maps on to the interior of semi-infinite strip. The Lehmann ellipse exists below threshold for bound states. As the system goes from below to above threshold, the discrete dihedral (elliptic) group of Type 1 transforms into a Type 3 group, whose loxodromic elements leave the fixed points 0 and ∞ invariant. The transformation of the indifferent fixed points from -1 and +1 to the source-sink fixed points 0 and ∞ is the result of a finite resonance width in the imaginary component of the angular momentum. The change in symmetry of the groups, and consequently their tessellations, can be used to distinguish bound states from resonances.

MULTIPLICATIVE GROUP AUTOMORPHISMS OF INVERTIBLE UPPER TRIANGULAR MATRICES OVER FIELDS

Suppose F is a field of characteristic not 2 and F* its multiplicative group. Let T*n(F) be the multiplicative group of invertible upper triangular n x n matrices over F and STn(F) its subgroup {(aij) E T*n(F)aii = 1, i}. This paper proves that f: T*n(F) → T*n(F) is a group automorphism if and only if there exist a matrix Q in T*n(F) and a field automorphism rs of F such that either where A = ((aij)), A-T is the transpose inverse of A, J = Ei n+1-i, and : i= 1T*n(F) → F* is a homomorphism which satisfies {(xIn)(x)x F*} = F* and {x F*(xIn)(x) = 1} = {1}. Simultaneously, they also determine the automorphisms of STn(F).

Finitely Generated Torsion-free Nilpotent Groups Admitting an Automorphism of Prime Order

Let G be a finitely generated torsion-free nilpotent group and a an automorphism of prime order p of G. If the map ψ ： G → G defined by g^φ = [g, α] is surjective, then the nilpotent class of G is at most h（p）, where h（p） is a function depending only on p. In particular, if α^3 = 1, then the nilpotent class of G is at most 2.

The Orders of Automorphism Group of p^6 Rank Groups

In this paper, we determine the order of automorphism group of p-groups in the third family ( Φ 3) and the fourth family ( Φ 4) in [1], whose order is p^6(p≥3). Here p denotes an odd prime.

The Orders of the Automorphism Groups of all Groups of Order p^5

In this paper by techniques of group we give some formulae for solving the general quadratic equations of two variables over a finite field,completely calculate and uniformly deal with the orders of automorphism groups of all p-groups of orders less than p6 under the P Hall's concept of isoclinism,also make a number of corrections for orders of automorphism groups offered for a mistake or fault before.

THE BANACH-LIE GROUP OF LIE TRIPLE AUTOMORPHISMS OF AN H^＊-ALGEBRA^＊

We study the Banach-Lie group Ltaut（A） of Lie triple automorphisms of a complex associative H^＊-algebra A. Some consequences about its Lie algebra, the algebra of Lie triple derivations of A, Ltder（A）, are obtained. For a topologically simple A, in the infinite-dimensional case we have Ltaut（A）0 = Aut（A） implying Ltder（A） = Der（A）. In the finite-dimensional case Ltaut（A）0 is a direct product of Aut（A） and a certain subgroup of Lie derivations δ from A to its center, annihilating commutators.

Orders of Automorphism Groups of the p^6 Groups of Family Φ_(24)

Using the metabelian property, regularity, p-commutativity and some properties of congruence, this paper gave the orders of automorphism groups of family Ф24, which are the groups of order p^6 determined by Rodney James, where p denotes an odd prime.

Two Important Classes of p-groups and the Orders of Their Automorphism Groups

In the paper we obtain two infinite classes of p-groups, calculate the orders of their automorphism groups and correct a mistake（perhaps misprinted） of Rodney James＇ paper in 1980.

The Automorphism Group of the Lie Group T（D（V_N,F））

In this paper,the authors determine maximal connected automorphism group of the Lie transformation group T（D（VN,F））,which acting on the normal Siegel domain D（VN,F）is simple and transitive,and prove that the maximal connected automorphism group of T（D（VN,F））is its maximal connected inner automorphism group.

ON COLEMAN OUTER AUTOMORPHISM GROUPS OF FINITE GROUPS

Let G be a finite group and Outcoz（G） the Coleman outer automorphism group of G（for the definition, see below）. The question whether Outcol（G） is a p′-group naturally arises from the study of the normalizer problem for integral group rings, where p is a prime. In this article, some sufficient conditions for OutCol（G） to be a p＇-group are obtained. Our results generalize some well-known theorems.

THE HOLOMORPHIC AUTOMORPHISM GROUP OF HIGHER DIMENSION THULLEN DOMAIN

In this paper, we give the holomorphic automorphism group of the higher-dimensional generalization of Thullen domain.

Invariants for Automorphisms of the Underlying Algebras Relative to Lie Algebras of Cartan Type

Let X denote a finite or infinite dimensional Lie algebra of Cartan type W, S, H or K over a field of characteristic p 〉 3. In this paper it is proved that certain filtrations of the underlying algebras are invariant under the admissible groups relative to Lie algebras of Cartan type X.

LOCAL AUTOMORPHISMS OF SEMISIMPLE ALGEBRAS AND GROUP ALGEBRAS

Let F be a field of characteristic not 2, and let A be a finite-dimensional semisimple F -algebra. All local automorphisms of A are characterized when all the degrees of A are larger than 1. If F is further assumed to be an algebraically closed field of characteristic zero, K a finite group, F K the group algebra of K over F , then all local automorphisms of F K are also characterized.

Notes on Automorphisms of Prime Rings

Let R be a prime ring, L a noncentral Lie ideal and a nontrivialautomorphism of R such that us（u）ut = 0 for all u 2 L, where s; t are fixednon-negative integers. If either charR 〉 s ＋ t or charR = 0, then R satisfies s4, thestandard identity in four variables. We also examine the identity （σ（[x; y]）-[x; y]）n =0 for all x; y ∈ I, where I is a nonzero ideal of R and n is a fixed positive integer. Ifeither charR 〉 n or charR = 0, then R is commutative.

Boolean Automorphisms of a Hypercube Coincide with the Linear Isometries

Boolean homomorphisms of a hypercube, which correspond to the morphisms in the category of finite Boolean algebras, coincide with the linear isometries of the category of finite binary metric vector spaces.

The Automorphism Group of U（4,Z）

In this paper,the automorphism group of G is determined,where G is a 4 × 4 upper unitriangular matrix group over Z.Let K be the subgroup of AutG consisting of all elements of AutG which act trivially on G/G,G /ζG and ζG,then (i) InnG ■ K ■ AutG;(ii) AutG/K≌=G_1×D_8×Z_2,where G_1=(a,b,c|a^4=b^2=c^2=1,a^b=a^(-1),[a,c]= [b,c]=1 ;(iii) K/Inn G≌=Z×Z×Z.

Orders of Automorphism Groups of Some p-Groups

The orders of automorphism groups of the groups of order p^6 in the twelve family Ф12 axe produced, where p is an odd prime. Every group is analysed by utilizing the properties of metabelian, regularity and p-commutativity of finite p-groups, and the structure of the generators of its automorphism groups is obtained. Then the orders of automorphism groups are determined through some properties of equivalence in number theory.