A note on smooth toral reductions of spheres

In this paper we show that there exist mod 2 obstructions to the smoothness of 3-Sasakian reductions of spheres. Specifically, ifS is a smooth 3-Sasakian manifold obtained by reduction of the 3-Sasakian sphereS ⁴ⁿ⁻¹ by a torus, and if the second Betti numberb ₂(S)≥2 then dimS=7, 11, 15, whereas, ifb ₂ (S)≥5 then dimS=7. We also show that the above bounds are sharp, in that we construct explicit examples of 3-Sasakian manifolds in the cases not excluded by these bounds. During the preparation of this work the authors were partially supported by an NSF grant. This article was processed by the author using the L^AT_EX style file from Springer-Verlag.     

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.     

Equipartite Gregarious 5-Cycle Systems and Other Results

A k-cycle decomposition of a complete multipartite graph is said to be gregarious if each k-cycle in the decomposition has its vertices in k different partite sets. Equipartite 3-cycle systems are 3-GDDs (and so are automatically gregarious), and necessary and sufficient conditions for their existence are known. The cases of equipartite gregarious 4-, 6- and 8-cycle systems have also been dealt with (using techniques that could be applied in the case of any even length cycle). Here we give necessary and sufficient conditions for the existence of a gregarious 5-cycle decomposition of the complete equipartite graph K_m(n) (in effect the first odd length cycle case for which the gregarious constraint has real meaning). In doing so, we also define some general cyclic constructions for the decomposition of certain complete equipartite graphs into gregarious p-cycles (where p is an odd prime).     

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