We consider the problem of constructing the middle surface of a deformed elastic shell from its first and second fundamental forms, âαβ and b̂αβ . The undeformed shell is a spherical cap of radius R and thickness h with an angular width 2θ0 where 0 < θ0 < π/2. The cap is subjected to a constant uniform load λ and is simply supported at its edge. We seek to compute the one–parameter families of b...

We study synchrony-breaking local steady-state bifurcation in networks of dynamical systems when the critical eigenvalue is real and simple, using singularity theory to transform the bifurcation into normal form. In a general dynamical system, a generic steady-state local bifurcation from a trivial state is transcritical, or, in the presence of symmetry, a pitchfork (if the action on the critic...

We continue the study of a model for heat conduction [6] consisting of a chain of non-linear oscillators coupled to two Hamiltonian heat reservoirs at different temperatures. We establish existence of a Liapunov function for the chain dynamics and use it to show exponentially fast convergence of the dynamics to a unique stationary state. Ingredients of the proof are the reduction of the infinit...

Reduction can be important to aid quickly attaining the integer least squares (ILS) estimate from noisy data. We present an improved Lenstra-Lenstra-Lovasz (LLL) algorithm with fixed complexity by extending a parallel reduction method for positive definite quadratic forms to lattice vectors. We propose the minimum angle of a reduced basis as an alternative quality measure of orthogonality, whic...

This paper is concerned with a cyclic predator-prey system with Sigmoidal type functional response. By using the differential inequality theory, some sufficient conditions are derived for the permanence of the system. By constructing a suitable Liapunov function, we obtain that the system has a unique asymptotically periodic solution which is globally asymptotically stable. Some numerical simul...