In this paper the family of elliptic curves over Q given by the equation Ep :Y2 = (X - p)3 + X3 + (X + p)3 where p is a prime number, is studied. Itis shown that the maximal rank of the elliptic curves is at most 3 and someconditions under which we have rank(Ep(Q)) = 0 or rank(Ep(Q)) = 1 orrank(Ep(Q))≥2 are given.

In this paper we introduce the cone bounded linear mapping and demonstrate a proof to show that the cone norm is continuous. Among other things, we prove the open mapping theorem and the closed graph theorem in TVS-cone normed spaces. We also show that under some restrictions on the cone, two cone norms are equivalent if and only if the topologies induced by them are the same. In the sequel, we...

The operator e−tA and the heat trace Tr e−tA, for t > 0, are investigated in the case when A is an elliptic differential operator on a manifold with conical singularities. Under a certain spectral condition (parameter–ellipticity) we obtain a full asymptotic expansion in t of the heat trace as t → 0+. As in the smooth compact case, the problem is reduced to the investigation of the resolvent (A...

The operator e−tA and the heat trace Tr e−tA, for t > 0, are investigated in the case when A is an elliptic differential operator on a manifold with conical singularities. Under a certain spectral condition (parameter–ellipticity) we obtain a full asymptotic expansion in t of the heat trace as t → 0+. As in the smooth compact case, the problem is reduced to the investigation of the resolvent (A...

in this paper, a method based on binary-coded genetic algorithm is proposed to explore an optimization method, for obtaining an optimal elliptical tank. this optimization method enhances the rollover threshold of a tank vehicle, especially under partial filling conditions. minimizing the overturning moment imposed on the vehicle due to c.g. height of the liquid load, lateral acceleration and ca...

By the Mordell-Weil theorem‎, ‎the group of rational points on an elliptic curve over a number field is a finitely generated abelian group‎. ‎There is no known algorithm for finding the rank of this group‎. ‎This paper computes the rank of the family $ E_p:y^2=x^3-3px $ of elliptic curves‎, ‎where p is a prime‎.

In this paper, Gaussian and elliptic high pass filters are analyzed for image sharpening qualitatively and quantatively . The filters are implemented in frequency domain using matlab software. Experiments are performed to compare the performance of both the filters ,processed images are presented. The results demonstrate that elliptic yields better results.

The propagation time of a signal, emitted by moving along an elliptical orbit satellite from the GPS (or GLONASS) confi gurations is very important ingredient theory, based on formalism null cone and accounting for effects General Relativity Theory. For case satellites, orbiting plane elliptic orbit, it has been proved that signal between satellites given combination integrals first, second thi...

the flow characteristics around an elliptic cylinder with an axis ratio of ar=2 located near a flat plate were investigated experimentally. the elliptic cylinder was located on the inside and outside a turbulent boundary layer region whose thickness (δ) is 0.38b. the reynolds numbers based on the height of the cylinder cross-section were 15000 and 30000. measurements of mean velocity and turbul...