In this paper, differential invariants of null Cartan curves are studied in (n+2) dimensional Lorentzian similarity geometry. The fundamental theorem for a curve geometry is investigated and the characterization all self-similar parameterized by de Sitter parameter Minkowski space-time given.

We study the classical analog of quantum metric tensor and its scalar curvature for two well-known physics models. First, we analyze geometry parameter space Dicke model with aid metrics find that, in thermodynamic limit, they have same divergent behavior near phase transition, as opposed to their corresponding curvatures which are not there. On contrary, under resonance conditions, both exhibi...

In [Ch1], Chern gives a generalization of projective geometry by considering foliations on the Grassman bundle of p-planes Gr(p, R) → R by p-dimensional submanifolds that are integrals of the canonical contact differential system. The equivalence method yields an sl(n + 1, R)valued Cartan connection whose curvature captures the geometry of such foliation. In the flat case, the space of leaves o...

Background: As the field of transcranial magnetic stimulation (TMS) evolves, there is still debate over optimal therapeutic target for effective treatment depression. Over time, it has become elucidated that left dorsolateral prefrontal cortex (DLPFC) highly heterogenous, and response rates may depend on precise location where in DLPFC rTMS administered. targeting approaches have ranged from a ...

The type II1 unprojection is, by definition, the generic complete intersection type II unprojection, in the sense of [P] Section 3.1, for the parameter value k = 1, and depends on a parameter n ≥ 2. Our main results are the explicit calculation of the linear relations of the type II1 unprojection for any value n ≥ 2 (Theorem 3.16) and the explicit calculation of the quadratic equation for the c...

We examine the derivation of consistent concurrency relations in uncertain geometry. This work extends previous work on parallelism and collinearity. We introduce the concept of a metadomain, which is defined as the set of parameter vectors of lines passing through two domains, where a domain is defined as the uncertainty region of the parameter vector of a line segment. The intersection graph ...

A method of higher-order Laue zone line position measurement in convergent-beam electron diffraction (CBED) is proposed based on Hough transformation. A thorough analysis of the errors introduced by this measurement procedure is performed and their influence on the accuracy of lattice parameter determination is estimated. A criterion is derived which enables the accuracy to be predicted before ...