Given a path geometry on surface $\mathcal{U}$, we construct causal structure four-manifold which is the configuration space of non-incident pairs (point, path) $\mathcal{U}$. This corresponds to conformal if and only $\mathcal{U}$ real projective plane, paths are lines. We give example given by symmetric sextic, an ${\rm SL}(2,{\mathbb R})$-invariant where ellipses area $\pi$ centred at origin...

Let $\pi$ be a group equipped with an action of second $G$ by automorphisms. We define the equivariant cohomological dimension $\mathsf{cd}\_G(\pi)$, geometric $\mathsf{cat}\_G(\pi)$, and Lusternik–Schnirelmann category $\mathsf{gd}\_G(\pi)$ in terms Bredon dimensions classifying space family subgroups semi-direct product $\pi\rtimes G$ consisting sub-conjugates $G$. When is finite, we extend t...

We consider a finite set of alternatives A = {a1, a2, . . . , am} evaluated on a family of n criteria F = {g1, g2, . . . , gn}. Let N = {1, 2, . . . , n}. To each criterion gi ∈ F is assigned a positive weight wi. It is supposed wlog that the weights are normalized so that ∑n i=1wi = 1. Let Xi = {gi(a) : a ∈ A} be the set of evaluations of the alternatives on the ith criterion. It is supposed t...

The Minimum Linear Arrangement problem (MLA) consists of finding a mapping $\pi$ from vertices graph to distinct integers that minimizes $\sum_{\{u,v\}\in E}|\pi(u) - \pi(v)|$. In setting, are often assumed lie on horizontal line and edges drawn as semicircles above said line. For trees, various algorithms available solve the in polynomial time $n=|V|$. There exist variants MLA which arrangemen...

in this paper, we present some inequalities for the co-pi index involving the some topological indices, the number of vertices and edges, and the maximum degree. after that, we give a result for trees. in addition, we give some inequalities for the largest eigenvalue of the co-pi matrix of g.

The connection between semi-classical orthogonal polynomials and discrete integrable systems is well established. The earliest example of a discrete integrable system in semi-classical orthogonal polynomials can be attributed first to Shohat in 1939 [16], then second by Freud [10] in 1976. However it wasn’t until the 1990’s, when the focus within integrable systems shifted from continuous to di...

In this study we introduce a new tensor in semi-Riemannian manifold, named the M*-projective curvature which generalizes m-projective tensor. We start by deducing some fundamental geometric properties of After that, pseudo symmetric manifolds (PM?S)n. A non-trivial example has been used to show existence such manifold. series interesting conclusions. establish, among other things, that if scala...

We apply a quantum version of dimensional reduction to Gaussian coherent states in Bargmann space obtain squeezed on complex projective spaces. This leads definition family spin with excellent semi-classical properties, governed by symbol calculus. prove semiclassical norm estimates and propagation result.

Projective techniques are unusual and often intriguing for respondents to complete, permitting them to express thoughts and feelings which can be difŽ cult to access by direct and structured questioning. This is achieved by presenting respondents with ambiguous verbal or visual stimulus materials, such as bubble cartoons, which they need to make sense of by drawing from their own experiences, t...