Consider a set of continuous maps from the interval [0, 1] to a domain in R. Although the topological boundary of this set in the path space is not smooth in general, by using the theory of functions of bounded variation (BV functions) on the Wiener space and the theory of Dirichlet forms, we can discuss the existence of the surface measure and the Skorokhod representation of the reflecting Orn...

A simple consequence of a theorem of Franks says that whenever a continuous map, g, is homotopic to angle doubling on the circle it is semiconjugate to it. We show that when this semiconjugacy has one disconnected point inverse, then the typical point in the circle has a point inverse with uncountably many connected components. Further, in this case the topological entropy of g is strictly larg...

We derive a new pointwise characterization of the subdifferential of the total variation (TV) functional. It involves a full trace operator which maps certain L vectorfields to integrable functions with respect to the total variation measure of the derivative of a bounded variation function. This full trace operator extents a notion of normal trace, frequently used, for example, to characterize...

Digital signatures provide authenticity and nonrepudiation. They are a standard cryptographic primitive with many applications in higher-level protocols. Groups featuring a computable bilinear map are particularly well suited for signature-related primitives. For some signature variants the only construction known uses bilinear maps. Where constructions based on, e.g., RSA are known, bilinear-m...

Digital signatures provide authenticity and nonrepudiation. They are a standard cryptographic primitive with many applications in higher-level protocols. Groups featuring a computable bilinear map are particularly well suited for signature-related primitives. For some signature variants the only construction known uses bilinear maps. Where constructions based on, e.g., RSA are known, bilinear-m...

let $a$ be an abelian topological group and $b$ a trivial topological $a$-module. in this paper we define the second bilinear cohomology with a trivial coefficient. we show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...

The first dynamic threshold decryption scheme from pairing is presented. It is secure in groups equipped with a bilinear map, and caters to some important requirements in real application; including the needs to renew the master key, or to add/remove or update a decryption sever, without leaking any information on the master key and changing other decryption servers’ secret keys.

1σ(T ) is defined to be the set of λ ∈ C such that v 7→ Tv − λv is not a bijection. It is a fact that if T ∈ B(H) and v 7→ Tv − λv is a bijection then it is an element of B(H). That it is linear can be proved quickly. The fact that it is bounded is proved using the open-mapping theorem, which states that a surjective bounded linear map from one Banach space to another is an open map, from which...

This paper presents a novel diversity-controlled (DC) genetic algorithm (GA) for the optimization of digital Intermediate Frequency (IF) filters over the (finiteprecision) canonical signed-digit (CSD) multiplier coefficient space. This optimization exploits the bilinear-losslessdiscrete-integrator (bilinear-LDI) lattice digital filter design approach for the realization of the required infinite...