In this paper, we introduce a determinant-like map $$\mathrm{det}^{S^3}$$ and study some of its properties. For this, define graded vector space $$\Lambda ^{S^3}_V$$ that has similar properties with the exterior algebra _V$$ GSC-operad ^{S^2}_V$$ from Staic. When $$\mathrm{dim}(V_2)=2$$ , show $$\mathrm{dim}_k(\Lambda ^{S^3}_{V_2}[6])=1$$ which gives existence uniqueness . We also give an expli...

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...

While the Euler characteristic χ(G) = ω1(G) = ∑ x ω(x) super counts simplices, the Wu characteristics ωk(G) = ∑ x1∼x2···∼xk ω(x1) · · ·ω(xk) super counts simultaneously pairwise interacting k-tuples of simplices in a finite abstract simplicial complex G. More generally, one can define the k-intersection number ωk(G1, . . . Gk), which is the same sum but where xi ∈ Gi. For every k ≥ 1 we define ...

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 ...

Columns are the key load-bearing elements in frame structures and exterior columns are probably the most vulnerable structural components to terrorist attacks. Column failure is normally the primary cause of progressive failure in frame structures. A high-fidelity physicsbased computer program, LS-DYNA was utilized in this study to provide numerical simulations of the dynamic responses and resi...