The basic objective of this work is to construct an efficient and secure mechanism for mobile commerce applying the concept of financial cryptography and secure multi-party computation. The mechanism (MCM) is defined by various types of elements: a group of agents or players, actions, a finite set of inputs of each agent, a finite set of outcomes as defined by output function, a set of objectiv...

A multi-secret sharing scheme (MSS) allows a dealer to share multiple secrets among a set of participants. in such a way a multi-secret sharing scheme (MSS) allows a dealer to share multiple secrets among a set of participants, such that any authorized subset of participants can reconstruct the secrets. Up to now, existing MSSs either require too long shares for participants to be perfect secur...

We show that the Wyman’s solution may be obtained from the fourdimensional Einstein’s equations for a spherically symmetric, minimally coupled, massless scalar field by using the continuous self-similarity of those equations. The Wyman’s solution depends on two parameters, the mass M and the scalar charge Σ. If one fixes M to a positive value, say M0, and let Σ 2 take values along the real line...

Mobile guards on the vertices of a graph are used to defend the graph against an infinite sequence of attacks on vertices. A guard must move from a neighboring vertex to an attacked vertex (we assume attacks happen only at vertices containing no guard and that each vertex contains at most one guard). More than one guard is allowed to move in response to an attack. The m-eternal domination numbe...

We show that the Willmore ow for smoothly immersed initial surfaces has eternal solutions in a weak sense, which are smooth except at nitely many times. Furthermore we study the set of singularities of such a weak solution.

Abstract. Eternal solutions of parabolic equations (those which are defined for all time) are typically rather rare. For example, the heat equation has exactly one eternal solution – the trivial solution. While solutions to the heat equation exist for all forward time, they cannot be extended backwards in time. Nonlinearities exasperate the situation somewhat, in that solutions may form singula...

AbSTRACT With the rapid growth in mobile commerce (m-commerce) applications, the need for providing suitable infrastructure to support these applications has become critical. Secure multicast is a key element of this infrastructure, in particular, to support group m-commerce applications such as mobile auctions, product recommendation systems , and financial services. Despite considerable atten...