Given a compact four dimensional manifold, we prove existence of conformal metrics with constant Q-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure. Since the corresponding Euler functional is in general unbounded from above and from below, we employ topological methods and min-max schemes, jointly with the...

The aim of this study is the investigation of the large amplitude deflection of an Euler-Bernoulli beam subjected to an axial load on a viscoelastic foundation with the strong damping. In order to achieve this purpose, the beam nonlinear frequency has been calculated by homotopy perturbation method (HPM) and Hamilton Approach (HA) and it was compared by the exact solutions for the different bou...

We study the compression of viscous filaments at constant velocity. If slender enough, the filament bends, a viscous analogue of Euler elastic buckling. We measure the characteristic time of this viscous buckling and discuss the link with the elastic critical compression. We show that the analogy only holds in the limit of large capillary numbers. Otherwise capillarity has a stabilizing effect,...

Given a compact four dimensional manifold, we prove existence of conformal metrics with constant Q-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure. Since the corresponding Euler functional is in general unbounded from above and from below, we employ topological methods and minimax schemes, jointly with the...

Prescribing, by conformal transformation, the k-elementary symmetric polynomial of the Schouten tensor σk(P) to be constant is a generalisation of the Yamabe problem. On compact Riemannian n-manifolds we show that, for 3 ≤ k ≤ n, this prescription equation is an Euler-Lagrange equation of some action if and only if the structure is locally conformally flat.

Given a compact four dimensional manifold, we prove existence of conformal metrics with constant Q-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure. Since the corresponding Euler functional is in general unbounded from above and from below, we employ topological methods and min-max schemes, jointly with the...

Abstract: A mathematical model of architecture and learning processes of multilayer artificial neural netwoks is discussed in the paper. Dynamical systems theory is used to describe the learning precess of networks consisting of linear, weakly nonlinear and nonlinear neurons. Conjugacy between a gradient dynamical system with a constant time step and a cascade generated by its Euler method theo...

We present a √ e/( √ e−1)-approximation algorithm for the nonpreemptive scheduling problem to minimize the total weighted completion time of jobs on a single machine subject to release dates and precedence constraints. The previously best known approximation algorithm dates back to 1997; its performance guarantee can be made arbitrarily close to the Euler constant e [18].

We prove the existence of time-quasi-periodic solutions incompressible Euler equation on three-dimensional torus T3, with a small external force. The are perturbations constant (Diophantine) vector fields, and they constructed by means normal forms KAM techniques for reversible quasilinear PDEs.

One of the major industry problems is the flow boiling, where reaching to the critical heat flux (CHF) condition can lead to a temperature jump and damage of the systems. In the present study, the effects of a uniform change in tube diameter on subcooled flow boiling and CHF was numerically investigated. The Euler-Euler model was used to investigate the relationship between the two liquid and v...