The existence of an embedding in R satisfying a set of exact distances can be verified by the Cayley-Menger conditions [2]. In the MDGP, a set of distances is embeddable if and only if all Cayley-Menger determinants of 3 and 4 points have the correct sign(corresponding to the triangular and tetrangular inequalities) and the ones of 5 and 6 points vanish. Another way to verify the embeddability ...

In this review we examine the dynamics and gravitational wave detectability of rotating strained neutron stars. The discussion is divided into two halves: triaxial stars, and precessing stars. We summarise recent work on how crustal strains and magnetic fields can sustain triaxiality, and suggest that Magnus forces connected with pinned superfluid vortices might contribute to deformation also. ...

Studying spatial patterns and habitat association of plant communities may provide understanding the ecological mechanisms processes that maintain species coexistence. To conduct assessments correlation between community compositions association, we used data from two topographically different plots with 2 ha area in tropical evergreen forests variables recorded via grid systems 10 × m subplots...

The objective of this article is to highlight certain features of a number of coefficients that appear in models of phenomena of transport in anisotropic porous media, especially the coefficient of dispersion, the 2nd rank tensor Dij , and the dispersivity coefficient, the 4th rank tensor aijkl , that appear in models of solute transport. Although we shall focus on the transport of mass of a di...

This paper discwwes th,e dynamics computation, oj strw tu,re ml-yang kin, em,dic chains which, amply m,ech,an,icd link systems wh,ose strudwe may ch,ange from open kinematic chain, to C1O,IA one o,n.d vice I) e rs 0,. The proposed dgorith,rn, can, h,an,dle strwiure chtanges in, o, seo,m,kss manm,er u)ith,out MA ch,an,g among rdgorathm,s for dij%ren.t kinematic ch,ain.s. The ,$tr?!,ct?~.re-?)fl....

A signed k-partite graph (signed multipartite graph) is a k-partite graph in which each edge is assigned a positive or a negative sign. If G(V1, V2, · · · , Vk) is a signed k-partite graph with Vi = {vi1, vi2, · · · , vini}, 1 ≤ i ≤ k, the signed degree of vij is sdeg(vij) = dij = d + ij − d − ij , where 1 ≤ i ≤ k, 1 ≤ j ≤ ni and d + ij(d − ij) is the number of positive (negative) edges inciden...

An alternative perspective on dimensionality reduction is offered by Multidimensional scaling (MDS). MDS is another classical approach that maps the original high dimensional space to a lower dimensional space, but does so in an attempt to preserve pairwise distances. That is MDS addresses the problem of constructing a configuration of t points in Euclidean space by using information about the ...

We present a spatial and temporal logic based on Duration Calculus for the specification and verification of mobile real-time systems. We demonstrate the use of the formalism and apply it to a case study. We extend a pure Duration Calculus specification for the controller by spatial assumptions to reason about spatial system properties. We prove that the formalism is undecidable in general for ...

In this paper we present the main achievements of UNU/IIST during the project “Design Techniques for Real-time Systems” carried out since 1993 by its staff and fellows. Duration Calculus was originally introduced in 1991 as a powerful logic for specifying the safety of realtime systems. During the project, it has evolved to a set of calculi that can capture many important aspects in real-time s...

We have developed a microscopic theory on phonon energy dispersion in chiral crystals within harmonic approximation. One of the main issues is about splitting sound velocity acoustic phonons with opposite “crystal” angular momenta. shown that must be zero even and difference starts from order at least k2 or higher their dispersion. Splitting evident for optical phonons, we derived formula k-lin...