We consider linear codes associated to Schubert varieties in Grassmannians. A formula for the minimum distance of these codes was conjectured in 2000 and after having been established in various special cases, it was proved in 2008 by Xiang. We give an alternative proof of this formula. Further, we propose a characterization of the minimum weight codewords of Schubert codes by introducing the n...

This paper discusses the so called holographic solution, in short ”holostar”. The holostar is the simplest exact, spherically symmetric solution of the original Einstein field equations with zero cosmological constant, including matter. The interior matter-distribution follows an inverse square law ρ = 1/(8πr). The interior principal pressures are Pr = −ρ and P⊥ = 0, which is the equation of st...

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...

We study the exterior depth of an E-module and its exterior generic annihilator numbers. For the exterior depth of a squarefree E-module we show how it relates to the symmetric depth of the corresponding S-module and classify those simplicial complexes having a particular exterior depth in terms of their exterior shifting. We define exterior annihilator numbers analogously to the annihilator nu...

Skew-symmetric differential forms play an unique role in mathematics and mathematical physics. This relates to the fact that closed exterior skew-symmetric differential forms are invariants. The concept of “Exterior differential forms” was introduced by E.Cartan for a notation of integrand expressions, which can create the integral invariants. (The existence of integral invariants was recognize...

A general method for studying boundary value problems for linear and for integrable nonlinear partial differential equations in two dimensions was introduced in Fokas, 1997. For linear equations in a convex polygon (Fokas and Kapaev (2000) and (2003), and Fokas (2001)), this method: (a) expresses the solution q(x, y) in the form of an integral (generalized inverse Fourier transform) in the comp...

In an evaluation of foetal hearts in II and III pregnancy semester, correlation with exterior foetal dimensions should be taken into consideration. It is interesting also if all exterior heart dimensions are correlated at the same level with overall body dimensions. The subject of examination was 204 foetuses of both sexes, including 106 males and 98 females, in 5th and 6th month of foetal life...

This setting can be generalized by replacing E by a differential 1-form ω, subject to the Maxwell-type equation (δd− k)ω = 0 [7]. Herein, d denotes the exterior derivative, and δ the co-derivative, its formal L adjoint [2,8]. The latter equation seamlessly extends to dimensions n other than 3. Moreover, it can be posed in Riemannian manifolds, while the original double curl equation relies on f...