Let W denote a simply-laced Coxeter group with n generators. We construct an n-dimensional representation φ of W over the finite field F2 of two elements. The action of φ(W ) on F n 2 by left multiplication is corresponding to a combinatorial structure extracted and generalized from Vogan diagrams. In each case W of types A, D and E, we determine the orbits of F 2 under the action of φ(W ), and...

In this paper a new class of mappings, known as locally λ-strongly φ-accretive mappings, where λ and φ have special meanings, is introduced. This class of mappings constitutes a generalization of the well-known monotone mappings, accretive mappings and strongly φ-accretive mappings. Subsequently, the above notion is used to extend the results of Park and Park, Browder and Ray to locally λ-stron...

Let Φ be an finite root system with corresponding reflection group W and let m be a nonnegative integer. We consider the generalized cluster complex ∆(Φ) defined by S. Fomin and N. Reading and the poset NC(m)(W ) of m-divisible noncrossing partitions defined by D. Armstrong. We give a characterization of the faces of ∆(Φ) in terms of NC(m)(W ), generalizing that of T. Brady and C. Watt given in...

In 2006, I. Beg and M. Abbas have studied the existence of coincidence and common fixed points for two mappings satisfying a weak contractive condition. Their results were extended in 2008 by A. Azam and M. Shakeel to the case of three mappings. Recently M. Abbas and D. Dorić employed the contractive conditions introduced in [Q. Zhang and Y. Song, Fixed point theory for generalized φ-weak contr...

Let (X,⟨⋅,⋅⟩) be a Hilbert C∗-module over C∗-algebra A and let S(A) the set of states on A. In this paper, we first compute norm derivative for nonzero elements x y X as follows: limt→0+‖x+ty‖−‖x‖t=1‖x‖max{Reφ(⟨x,y⟩):φ∈S(A),φ(⟨x,x⟩)=‖x‖2}.We then apply it to characterize different concepts orthogonality in X. particular, present simpler proof classical characterization Birkhoff–James C∗-modules...

In the paper we discuss a stability in the sense of the generalized Hyers-Ulam-Rassias for functional equations ∆n(p, c)φ(x) = h(x), which is called generalized Newton difference equations, and give a sufficient condition of the generalized Hyers-Ulam-Rassias stability. As corollaries, we obtain the generalized Hyers-Ulam-Rassias stability for generalized forms of square root spirals functional...

let φ be a w  -continuous homomorphism from a dual banach algebra to c. the notion of φ-connes amenability is studied and some characterizations is given. a type of diagonal for dual banach algebras is de ned. it is proved that the existence of such a diagonal is equivalent to φ-connes amenability. it is also shown that φ-connes amenability is equivalent to so-called φ-splitting of a certain s...

The φ 4 field model is generalized to the case when the field φ(x) is defined on a Lie group: S[φ] = x∈G L[φ(x)]dµ(x), dµ(x) is the left-invariant measure on a locally compact group G. For the particular case of the affine group G : x ′ = ax +b, a ∈ R+, x, b ∈ R n the Feynman perturbation expansion for the Green functions is shown to have no ultraviolet divergences for certain choice of λ(a) ∼ ...

In this paper, we will obtain the strong type and weak type estimates for vector-valued analogs of intrinsic square functions in the generalized weighted Morrey spacesM w (l2). We study the boundedness of intrinsic square functions including the Lusin area integral, the Littlewood-Paley g-function and gλ -function, and their multilinear commutators on vector-valued generalized weighted Morrey s...

The generalized Schoenflies theorem asserts that if φ ∶ Sn−1 → S is a topological embedding and A is the closure of a component of Sn∖φ(Sn−1), then A ≅ D as long as A is a manifold. This was originally proved by Barry Mazur and Morton Brown using rather different techniques. We give both of these proofs.