We investigate a particular realization of generalized q-differential calculus of exterior forms on a smooth manifold based on the assumption that d N = 0 while d k = 0 for k < N. It implies the existence of cyclic commutation relations for the differentials of first order and their generalization for the differentials of higher order. Special attention is paid to the cases N = 3 and N = 4. A c...

A 100 km deep liquid water ocean probably underlies the icy exterior of Jupiter’s satellite Europa. The long-term persistence of a liquid ocean beneath an ice shell presents a thermal conundrum: Is the temperature of the ocean equal to the freezing point of water at the bottom of the ice shell, or is it equal to the somewhat warmer temperature at which water attains its maximum density? We argu...

abstract soil pollution with heavy metals like zinc causes increasing concerns about environment. according to distribution in soil, this study was conducted to compare zinc concentration between aggregate exteriors and interiors of some contaminated soils. aggregates were collected from 5 depths of 4 soil profiles with different textures and were separated mechanically into exterior and interi...

Accurate simulation of atmospheric flow in weather and climate prediction models requires the discretization of the governing equations to have a number of desirable properties. Although these properties can be achieved relatively straightforwardly on a latitude-longitude grid, they are much more challenging on the various quasi-uniform spherical grids that are now under consideration. A recent...

After a quick introduction to L cohomology, we discuss recent joint work with Jeff Cheeger where we study, from a mostly topological standpoint, the L-signature of certain spaces with nonisolated conical singularities. The contribution from the singularities is identified with a topological invariant of the link fibration of the singularities, involving the spectral sequence of the link fibrati...

Evolutionary forms, as well as exterior forms, are skew-symmetric differential forms. But in contrast to the exterior forms, the basis of evolutionary forms is deforming manifolds (manifolds with unclosed metric forms). Such forms possess a peculiarity, namely, the closed inexact exterior forms are obtained from that. The closure conditions of inexact exterior form (vanishing the differentials ...

We introduce the wedge product of two polytopes. The wedge product is described in terms of inequality systems, in terms of vertex coordinates as well as purely combinatorially, from the corresponding data of its constituents. The wedge product construction can be described as an iterated “subdirect product” as introduced by McMullen (1976); it is dual to the “wreath product” construction of Jo...

We consider three problems for the Helmholtz equation in interior and exterior domains in R, (d = 2, 3): the exterior Dirichlet-to-Neumann and Neumann-to-Dirichlet problems for outgoing solutions, and the interior impedance problem. We derive sharp estimates for solutions to these problems that, in combination, give bounds on the inverses of the combined-field boundary integral operators for ex...

Abstract-Continuing a recent investigation of interface cracks, attention is paid to the exterior crack. Two elastic solids bonded over a finite segment of their boundary and capable of transmitting shear and tensile tractions are considered. It is found that one of the edge cracks remains completely closed under shear alone, and opens gradually as the level of tension is increased. Both crack ...

The language of modern mechanics is calculus on manifolds, and exterior calculus is an important part of that. It consists of objects like differential forms, general tensors and vector fields on manifolds, and operators that act on these. While the smooth exterior calculus has a long history going back to Cartan, Lie, Grassmann, Hodge, de Rham and many others, the need for a discrete calculus ...