we describe a variational problem on a surface under a constraintof geometrical character. necessary and sufficient conditions for the existence ofbifurcation points are provided. in local coordinates the problem corresponds toa quasilinear elliptic boundary value problem. the problem can be consideredas a physical model for several applications referring to continuum medium andmembranes.

A modified model has been analytically developed to describe the induction time of an elliptic air bubble in contact with an elliptic hydrophobic oil droplet. The role of hydrophobicity was revealed in the slippage of liquid over the surfaces of bubble and droplet. In this condition, the analytical relationships for pressure distribution and consequently hydrodynamic resistance force through th...

Certain elliptic divisibility sequences are shown to contain only finitely many prime power terms. In some cases the methods prove that only finitely many terms are divisible by a bounded number of distinct primes.

We describe in terms of the j-invariant all elliptic surfaces π : X → C with a section, such that h(X) = rankNS(X) and the Mordell-Weil group of π is finite. We use this to give a complete solution to infinitesimal Torelli for elliptic surfaces over P with a section.

We present an algorithm for the constrained saddle point problem with a convexconcave function L and convex sets with nonempty interior. The method consists of moving away from the current iterate by choosing certain perturbed vectors. The values of gradients of L at these vectors provide an appropriate direction. Bregman functions allow us to define a curve which starts at the current iterate ...

We consider FPU-type atomic chains with general convex potentials. The naive continuum limit in the hyperbolic space-time scaling is the p-system of mass and momentum conservation. We systematically compare Riemann solutions to the p-system with numerical solutions to discrete Riemann problems in FPU chains, and argue that the latter can be described by modified p-system Riemann solvers. We all...

Elliptic curve cryptosystems([19, 25]) are based on the elliptic curve discrete logarithm problem(ECDLP). If elliptic curve cryptosystems avoid FR-reduction([11, 17]) and anomalous elliptic curve over Fq ([34, 3, 36]), then with current knowledge we can construct elliptic curve cryptosystems over a smaller de nition eld. ECDLP has an interesting property that the security deeply depends on elli...

Elliptic curve cryptosystems([19],[25]) are based on the elliptic curve discrete logarithm problem(ECDLP). If elliptic curve cryptosystems avoid FRreduction([11],[17]) and anomalous elliptic curve over Fq ([3], [33], [35]), then with current knowledge we can construct elliptic curve cryptosystems over a smaller definition field. ECDLP has an interesting property that the security deeply depends...

we prove the existence of steady 2-dimensional flows, containing a bounded vortex, and approaching a uniform flow at infinity. the data prescribed is the rearrangement class of the vorticity field. the corresponding stream function satisfies a semilinear elliptic partial differential equation. the result is proved by maximizing the kinetic energy over all flows whose vorticity fields are rearra...

in this paper‎, ‎we prove a multiplicity result for some biharmonic elliptic equation of kirchhoff type and involving nonlinearities with critical exponential growth at infinity‎. ‎using some variational arguments and exploiting the symmetries of the problem‎, ‎we establish a multiplicity result giving two nontrivial solutions‎.