The conformal thin-sandwich (CTS) equations are a set of four of the Einstein equations, which generalize the Laplace-Poisson equation of Newton's theory. We examine numerically solutions of the CTS equations describing perturbed Minkowski space, and find only one solution. However, we find two distinct solutions, one even containing a black hole, when the lapse is determined by a fifth ellipti...

wireless sensors having limited capabilities, because of these factors sensors possess huge attacks like sinkhole, worm hole, Sybil, flooding, etc. a lot of research work already done, but no one implemented secure routing protocol to mitigate all these attacks. Some proposals came on security of wireless sensor network which controlled only one or two attacks. We proposed Secure Routing in Clu...

We consider the following generalization of the decomposition theorem for polycycles. A (R, q)-polycycle is, roughly, a plane graph, whose faces, besides some disjoint holes, are i-gons, i ∈ R, and whose vertices, outside of holes, are q-valent. Such polycycle is called elliptic, parabolic or hyperbolic if 1 q + 1 r − 1 2 (where r = maxi∈Ri) is positive, zero or negative, respectively. An edge ...

Elliptic curve cryptosystems (ECC) are new generations of public key cryptosystems that have a smaller key size for the same level of security. The exponentiation on elliptic curve is the most important operation in ECC, so when the ECC is put into practice, the major problem is how to enhance the speed of the exponentiation. It is thus of great interest to develop algorithms for exponentiation...

The Woods Hole fixed point theorem is a farreaching extension of the classical Lefschetz fixed point theorem to vector bundles. It has as corollaries a holomorphic Lefschetz formula for complex manifolds and the Weyl character formula for the irreducible representations of a compact Lie group. Apart from its importance in its own right, the Woods Hole fixed point theorem is crucial in the histo...

The thermoelectroelastic solution for an elliptic piezoelectric inclusion embedded in an in®nite matrix and its application to crack±inclusion problems are investigated in this paper. By combining the method of Stroh's formalism, the technique of conformal mapping, the concept of perturbation and the method of analytical continuation, a general analytical thermoelectroelastic solution for an el...

‎In this paper‎, ‎we propose some Diffie-Hellman type key exchange protocols using isogenies of elliptic curves‎. ‎The first method which uses the endomorphism ring of an ordinary elliptic curve $ E $‎, ‎is a straightforward generalization of elliptic curve Diffie-Hellman key exchange‎. ‎The method uses commutativity of the endomorphism ring $ End(E) $‎. ‎Then using dual isogenies‎, ‎we propose...

We prove a black hole rigidity result for slowly rotating stationary solutions of the Einstein vacuum equations. More precisely, we prove that the domain of outer communications of a regular stationary vacuum is isometric to the domain of outer communications of a Kerr solution, provided that the stationary Killing vector-field T is small (depending only on suitable regularity properties of the...

Two approaches are proposed for solving inverse problems in shape optimization. We are looking for the unknown position of a small hole in a domain Ω. First, the asymptotic analysis of the underlying p.d.e. defined in a perturbed domain is performed and the so-called topological derivative is defined. Then, in the first approach, the self-adjoint extensions of elliptic operators are used to mod...