is called the modulus of (uniform) continuity of f . The mapping f is said to be uniformly continuous if Ω f (d) → 0 as d ↓ 0. In this case the modulus of continuity is a subadditive monotone continuous function. The definition of Ω f implies that f (Br(x)) ⊂ BΩ f (r)( f (x)). (By Bρ(y) and Bρ(y) we denote, respectively, the open and the closed ball of radius ρ, centered at y.) One important cl...

LetX be a Banach space with dualX∗, and letK be a nonempty subset ofX. A gauge function is a continuous strictly increasing function φ : R → R such that φ 0 0 and limt→∞φ t ∞. The duality mapping Jφ : X → X∗ associated with a gauge function φ is defined by Jφ x : {f ∈ X∗ : 〈x, f〉 ‖x‖‖f‖, ‖f‖ φ ‖x‖ }, x ∈ X, where 〈·, ·〉 denotes the generalized duality pairing. In the particular case φ t t, the ...

Suppose that A is a C∗-algebra acting on a Hilbert space H, and φ, ψ are mappings from A into B(H) which are not assumed to be necessarily linear or continuous. By a (φ, ψ)derivation we mean a linear mapping d : A → B(H) such that d(ab) = φ(a)d(b) + d(a)ψ(b) (a, b ∈ A). In this paper, we prove that if φ is a multiplicative(not necessary linear) ∗-mapping, then every ∗-(φ,φ)-derivation is automa...

Two methods for transmission of a continuous amplitude source signal over a continuous amplitude channel with a power constraint are proposed. For both methods, bandwidth reduction is achieved by mapping from a higher dimensional source space to a lower dimensional channel space. In the rst system, a source vector is quantized and mapped to a discrete set of points in a multidimensional PAM sig...

this paper deals with continuous frames and continuous riesz bases. we introduce continuous riesz bases and give some equivalent conditions for a continuous frame to be a continuous riesz basis. it is certainly possible for a continuous frame to have only one dual. such a continuous frame is called a riesz-type frame [13]. we show that a continuous frame is riesz-type if and only if it is a con...

This paper is about the interface between continuous and discrete robot control. We advocate encapsulating continuous actions and their related sensing strategies into structures called situation speciic activities, which can be manipulated by a symbolic reactive planner. The approach addresses the problem of turning symbolic actions into continuous activities, and the problem of mapping contin...

It is a difficult issue to support interactive image processing software in grid environment, which requires special mapping methods over grid architecture. Interactive service packaging, mapping of interactive interface mechanism are reviewed in heterogeneous grid architecture. Grid Service Automated Packaging and Generating System (GS-APGS) for image processing software is designed to provide...

Such a mapping defines by passing to quotients a continuous one-to-one mapping f of the circle-identified with the real numbers modulo the integersto itself. We can define an orientation-preserving homeomorphism of the circle to be a mapping obtained in this way. The mapping f is not quite uniquely determined by the induced mapping f ; two f ' s induce the same f if and only if they differ by a...

In this paper, the generalized variational inequality with multi-valued mapping (GVI) is considered. To solve the problem, we first establish a global error bound estimation for GVI with the underlying multi-valued mapping being   strict monotone and Holder continuous. Based on this, we propose a new type of method to solve the GVI, and its global convergence is also established. Keywords-GVI...