Representations of Positive Projections II

In this paper we obtain a number of Maharam-type slice integral representations, with respect to scalar measures, for positive projections in Dedekind complete vector lattices and f-algebras. AMS Classification: 47B65, 46A40, 06F25     

Leptonic constant of the pseudoscalar <Emphasis Type="Italic">B</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript> meson

We calculate the leptonic constant for the pseudoscalar ground state of the B _c meson in the framework of a QCD-motivated potential model taking into account the two-loop anomalous dimension for the heavy quark current in nonrelativistic QCD as matched with full QCD.     

Fonctions analytiques Cliffordiennes

We define analytic functions within Clifford Algebras CL, and study their trigonometric properties. We write the addition formulas when their arguments, A and B in CL, commute, this generalizes ordinary trigonometry. We examine in particular the case A² = 1.      

Isometric Isomorphisms Between Banach Algebras Related to a Certain Class of Clifford Topological Semigroups

In the present paper it is shown that if S₁ and S₂ are two Clifford topological semigroups satisfying certain conditions and T is an isometric isomorphism of LUC(S₁*) onto LUC(S₂*), then T maps S₁ topologically isomorphically onto S₂. Furthermore, T maps M ^l _n(S₁) (M(S₁), respectively) isometrically isomorphically onto M ^l _n(S₂) (M(S₂), respectively). Indeed, we have obtained a generalization of a well-known result of Ghahramani, Lau and Losert for locally compact groups to a more general setting of Clifford topological semigroups.     

Experiences in Expert Systems

This paper describes some work carried out in the Scientific Research and Development Branch (SRDB) of the Home Office, intended to contribute to an overall aim of building up internal expertise in the field of expert systems. This was done by carrying out a number of pilot and demonstrator projects, two of which are described in some detail. The plan, which proved successful, was to build as far as possible on the relevant skills already possessed by an OR group in the branch. The lessons learned from these are summarized in the hope that they will be of use to other groups who wish to become involved in this important area.     

Program explanations and causal relevance

Frank Jackson and Philip Pettit have defended a non-reductive account of causal relevance known as the ‘program explanation account’. Allegedly, irreducible mental properties can be causally relevant in virtue of figuring in non-redundant program explanations which convey information not conveyed by explanations in terms of the physical properties that actually do the ‘causal work’. I argue that none of the possible ways to spell out the intuitively plausible idea of a program explanation serves its purpose, viz., defends non-reductive physicalism against Jaegwon Kim’s Causal Exclusion Argument according to which non-reductive physicalism is committed to epiphenomenalism because irreducible mental properties are ‘screened off’ from causal relevance by their physical realizers. Jackson and Pettit’s most promising explication of a program explanation appeals to the idea of invariance of effect under variation of realization, but I show that invariance of effect under variation of realization is neither necessary nor sufficient for causal relevance.     

Certificateless signature and proxy signature schemes from bilinear pairings

Due to avoiding the inherent escrow of identity-based cryptography and yet not requiring certificates to guarantee the authenticity of public keys, certificateless public key cryptography has received a significant attention. Due to various applications of bilinear pairings in cryptography, numerous pairing-based encryption schemes, signature schemes, and other cryptographic primitives have been proposed. In this paper, a new certificateless signature scheme based on bilinear pairings is presented. The signing algorithm of the proposed scheme is very simple and does not require any pairing computation. Combining our signature scheme with certificateless public key cryptography yields a complete solution of certificateless public key system. As an application of the proposed signature scheme, a certificateless proxy signature scheme is also presented. We analyze both schemes from security point of view.__________Published in Lietuvos Matematikos Rinkinys, Vol. 45, No. 1, pp. 95–103, January–March, 2005.