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...

We show that the closed-form monotone solution linking two different vacuum states, for exterior Yang–Mills wave equation over extremal Reissner–Nordström spacetime found in recent work of Bizoń and Kahl [Classical Quantum Gravity 33, 175013 (2016)], is unique to an associated domain-wall type energy minimization problem. also derive accompanying interior within same formalism. obtain a few mor...

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...

Abstract The analysis is based on the results of computer simulation by using DesignBUILDER software. In multi dwelling house assessed. There are standard building constructions used like as brick wall with polystyrene thermal insulation, Windows plastic frame and double glazing flat roof insulation from without gravel layer. this considered so called green walls, that localized at eastern, sou...