Let K be a finite, connected, abstract simplicial complex. The Morse complex of K, first introduced by Chari and Joswig, is the constructed from all gradient vector fields on K. We show that if neither boundary n-simplex nor cycle, then Aut(M(K))≅Aut(K). In case where K=Cn, cycle length n, we Aut(M(Cn))≅Aut(C2n). When K=∂Δn, prove Aut(M(∂Δn))≅Aut(∂Δn)×Z2. These results are based recent work Cap...

We report on the first far–IR detection of H 2 D + , using the Infrared Space Observatory, in the line of sight toward Sgr B2 in the galactic center. The transition at λ=126.853 µm connecting the ground level of o-H 2 D + , 1 1,1 , with the the 2 1,2 level at 113 K, is observed in absorption against the continuum emission of the cold dust of the source. The line is broad, with a total absorptio...

Let U be a set of elements and d a distance function defined among them. Let NNk(u) be the k elements in U−{u} having the smallest distance to u. The k-nearest neighbor graph (knng) is a weighted directed graph G(U, E) such that E = {(u, v), v ∈ NNk(u)}. Several knng construction algorithms are known, but they are not suitable to general metric spaces. We present a general methodology to constr...

It was proved earlier that there are constants M, c > 0 such that for every n M (resp., every n M , n / ≡ 0, 3mod 12) there are at least c2n/6 nonisomorphic nonorientable (resp., orientable) genus embeddings ofKn. In the present paper we show that for s 6 there are at least 2s−6 nonisomorphic OT-embeddings of K12s . As a byproduct, we give a relatively simple method of constructing index four c...

Gravity in d dimensions is formulated as the gauge theory of local SO(2,d-1) gauge group. The Chern-Pontryagin index P2n plays a crucial role in both gravity and gauge theories. P2n(gravity) gives the gravitational Lagrangian in 2n dimensions, having the vacuum solution AdS2n. The same but global symmetry is shared with the gauge theories and 0,1-cochains of the Chern-Simon index C2n(gauge) tak...