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...

Building 3D models using terrestrial laser scanner (TLS) data is currently an active area of research, especially in the fields of heritage recording and site documentation. Multiple TLS scans are often required to generate an occlusion-free 3D model in situations where the object to be recorded has a complex geometry. The first task associated with building 3D models from laser scanner data in...

In this work we study the asymptotic behavior of viscous incompressible 2D flow in the exterior of a small material obstacle. We fix the initial vorticity ω0 and the circulation γ of the initial flow around the obstacle. We prove that, if γ is sufficiently small, the limit flow satisfies the full-plane Navier-Stokes system, with initial vorticity ω0 + γδ, where δ is the standard Dirac measure. ...

One crucial point during the application of direct georeferencing is the accuracy and reliability of directly measured orientation parameters using integrated GPS/inertial systems in an operational photogrammetric airborne environment. In order to investigate the potential of direct georeferencing for standard photogrammetric applications the accuracy of a commercially available GPS/inertial sy...

An n-Venn diagram is a Venn diagram on n sets, which is defined to be a collection of n simple closed curves (Jordan curves) C1, C2, ..., Cn in the plane such that any two intersect in finitely many points and each of the 2n sets of the form Ë Cie is nonempty and connected, where ei is one of "interior" or "exterior". Thus the Venn regions are all bounded except for the region exterior to all c...

Abstract. The purpose of this paper is to study the shapes and stabilities of biomembranes within the framework of exterior differential forms. After a brief review of the current status in theoretical and experimental studies on the shapes of biomembranes, a geometric scheme is proposed to discuss the shape equation of closed lipid bilayers, the shape equation and boundary conditions of open l...

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...

The simplex method is perhaps the most widely used method for solving linear programming (LP) problems. The computation time of simplex type algorithms depends on the basis inverse that occurs in each iteration. Parallelizing simplex type algorithms is one of the most challenging problems. The aim of this paper is to present a parallel implementation of the primal exterior point simplex algorit...

Probabilistic latent-variable models are a fundamental tool in statistics and machine learning. Despite their widespread use, identifying the parameters of basic latent variable models continues to be an extremely challenging problem. Traditional maximum likelihood-based learning algorithms find valid parameters, but suffer from high computational cost, slow convergence, and local optima. In co...

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...