Let R be a commutative ring. Unless indicated otherwise, all modules are R-modules and all tensor products are taken over R, so we abbreviate ⊗R to ⊗. A bilinear function out of M1 × M2 turns into a linear function out of the tensor product M1 ⊗ M2. In a similar way, a multilinear function out of M1 × · · · ×Mk turns into a linear function out of the k-fold tensor product M1 ⊗ · · · ⊗Mk. We wil...

The minimal projective bimodule resolutions of the exterior algebras are explicitly constructed. They are applied to calculate the Hochschild (co)homology of the exterior algebras. Thus the cyclic homology of the exterior algebras can be calculated in case the underlying field is of characteristic zero. Moreover, the Hochschild cohomology rings of the exterior algebras are determined by generat...

The minimal projective bimodule resolutions of the exterior algebras are explicitly constructed. They are applied to calculate the Hochschild (co)homology of the exterior algebras. Thus the cyclic homology of the exterior algebras can be calculated in case the underlying field is of characteristic zero. Moreover, the Hochschild cohomology rings of the exterior algebras are determined by generat...

The motive of this paper is to present an outline of mathematics for biophysical scientists who care the morphology of bio-membranes. After a brief review of the current status in theoretical and experimental studies of the shapes of bio-membranes, the mathematical schemes to obtain the shape equation of closed lipid bilayers, the shape equation and boundary conditions of open lipid bilayers an...

Some problems concerning the decomposition of certain characters of SL( n, C) are studied from a combinatorial point of view. The specific characters considered include those of the exterior and symmetric algebras of the adjoint representation and the Euler characteristic of Hanlon's so-called "Macdonald complex." A general recursion is given for computing the irreducible decomposition of these...

Survivors trapped in void spaces formed when buildings collapse in an earthquake may be saved if search and rescue (SAR) operations are quick. A novel computational approach aims to provide building information that can guide SAR teams, thus minimizing their risk and accelerating operations. The inputs are an ‘as-built’ BIM model of the building before an earthquake and a partial ‘as-damaged’ B...

We construct spherically symmetric static solutions to the Einstein–Vlasov system with nonvanishing cosmological constant Λ. The results are divided as follows. For small Λ > 0 we show the existence of globally regular solutions which coincide with the Schwarzschild–deSitter solution in the exterior of the matter regions. For Λ < 0 we show via an energy estimate the existence of globally regula...

I Recently a new hybrid EMP simtilator has been developed where the signal is transmitted by a high-quality coaxial cable from a RF source on the ground to a point above the ground where the cable is cut to create a gap source. The cable is made part of the antenna by passing it through chokes which provide a frequency dependent inductively coupled impedance, thus making the cable-shield exteri...