The trace anomaly and low energy phenomenological implications of wormholes

In Coleman's wormhole scenario it is the trace anomaly on S₄ that controls the behavior of fundamental coupling constants, particle masses, mixing angles, etc. We indicate how low energy phenomenology may be derivable from very general properties of wormhole physics and calculable β-functions, etc.     

A general method for the synthesis of 1-substituted (or unsubstituted)-4-carbomethoxy-2-imidazolin-5-ones

A general method for the synthesis of the title compounds by employing the reagent methyl $\text{N}$-(dicarbomethoxymethyl)methanimidate is described. The preparation, properties and reactions of the reagent are also reported.     

Synthesis of dihydroxylated polyamines from an erythronolactone

The opening of protected erythronolactone by an amine or a diamine furnished hydroxy-amides. Their multistep functional conversion led to either selectively protected or free dihydroxy-polyamines.     

Communication-Computation Trade-off in Executing ECDSA in a Contactless Smartcard

Emerging standards specify a communication rate between a contactless smartcard and a terminal that is of the same order of magnitude as the internal clock rate in the card. This gives a natural ground for the known card-terminal communication-computation trade-off, where non-secure operations should rather be performed by the terminal and not in the card. In this paper we treat an implementation of Elliptic Curve Digital Signature Algorithm (ECDSA), the most cost effective digital signature algorithm, which has a potential of being executed under the heavy constraints imposed by a contactless smartcard environment. This algorithm heavily relies on numerous calculations of modular multiplicative inverses. It is shown in this paper that, based on communicating with the terminal, each modular inverse operation needed to be executed in the card during ECDSA signature generation requires only two modular multiplications in the card. Each modular inverse operation performed during signature verification requires only one modular multiplication in the card. A complete ECDSA implementation over integers or over GF(2ⁿ) is then treated in detail AMS Classification: 94A62     

Precoloring Extension of Co-Meyniel Graphs

The pre-coloring extension problem consists, given a graph G and a set of nodes to which some colors are already assigned, in finding a coloring of G with the minimum number of colors which respects the pre-coloring assignment. This can be reduced to the usual coloring problem on a certain contracted graph. We prove that pre-coloring extension is polynomial for complements of Meyniel graphs. We answer a question of Hujter and Tuza by showing that “PrExt perfect” graphs are exactly the co-Meyniel graphs, which also generalizes results of Hujter and Tuza and of Hertz. Moreover we show that, given a co-Meyniel graph, the corresponding contracted graph belongs to a restricted class of perfect graphs (“co-Artemis” graphs, which are “co-perfectly contractile” graphs), whose perfectness is easier to establish than the strong perfect graph theorem. However, the polynomiality of our algorithm still depends on the ellipsoid method for coloring perfect graphs. C.N.R.S. Final version received: January, 2007     

Cavity identification in linear elasticity and thermoelasticity

The aim of this paper is an analysis of geometric inverse problems in linear elasticity and thermoelasticity related to the identification of cavities in two and three spatial dimensions. The overdetermined boundary data used for the reconstruction are the displacement and temperature on a part of the boundary. We derive identifiability results and directional stability estimates, the latter using the concept of shape derivatives, whose form is known in elasticity and newly derived for thermoelasticity. For numerical reconstructions we use a least‐squares formulation and a geometric gradient descent based on the associated shape derivatives. The directional stability estimates guarantee the stability of the gradient descent approach, so that an iterative regularization is obtained. This iterative scheme is then regularized by a level set approach allowing the reconstruction of multiply connected shapes. Copyright © 2007 John Wiley & Sons, Ltd.