In the context of effective Friedmann equation we classify the cosmologies in multiscalar models with an arbitrary scalar potential V according to their geometric properties. It is shown that all flat cosmologies are geodesics with respect to a conformally rescaled metric on the ‘augmented’ target space. Non-flat cosmologies with V = 0 are also investigated. It is shown that geodesics in a ‘dou...

Nonlinear stability for a class of doubly warped spacetimes is proved. The background spacetimes have negative Einstein factors. It shown that for dimension D ≥ 11 there is a full parameter family of solutions to the vacuum Einstein equations which has Kasner-like singularity and Friedmann like asympotics in the future. In particular, these spacetimes have crushing singularity and are globally ...

In this paper, we derived recurrence relations for joint moment generating functions of nonadjacent generalized order statistics (GOS) of random samples drawn from doubly truncated class of continuous distributions. Recurrence relations for joint moments of nonadjacent GOS (ordinary order statistics (OOS) and k-upper records (k-RVs) as special cases) are obtained. Single and product moment gene...

There has been a considerable amount of work carried out on two-dimensional laser forming. In order to advance the process further for industrial applications, however, it is necessary to consider more general cases and especially their process planning aspect. This paper presents an optimal approach to laser scanning paths and heating condition determination for laser forming of doubly curved ...

Structural parameters of doubly clamped microfabricated beams such as initial curvature, boundary compliance, thickness and mean residual stress are often critical to the performance of microelectromechanical systems (MEMS) and need to be estimated as a part of quality control of the microfabrication process. However, these parameters couple and influence many metrics of device response and thu...

A non-linear theory is presented for stretching and inplane-bending of isotropic beams which have constant initial curvature and lie in their plane of symmetry. For the kinematics, the geometrically exact one-dimensional (1-D) measures of deformation are specialized for small strain. The 1-D constitutive law is developed in terms of these measures via an asymptotically correct dimensional reduc...

We prove an existence result for the prescribed Ricci curvature equation certain doubly warped product metrics on $$\mathbb {S}^{d_1+1}\times \mathbb {S}^{d_2}$$ , where $$d_i \ge 2$$ . If T is a metric satisfying assumptions, we show that can be scaled independently two factors so as to itself tensor of some metric. This first global problem closed cohomogeneity one manifolds since work Hami...

We prove existence and uniqueness for a two-parameter family of translators mean curvature flow. get additional examples by taking limits at the boundary parameter space. Some resemble well-known minimal surfaces (Scherk’s doubly periodic surfaces, helicoids), but others have no surface analogs. A one-parameter subfamily (the pitchforks) finite topology quadratic area growth, thus might arise a...