The rational Bézier form has become a standard in CAD-CAM packages and data exchange formats, because it encompasses both conic segments (in the quadratic case) and general free-form geometry. We present several results on the relationship between the quadratic rational Bézier form and the classical definition of conics in terms of their characteristics, such as foci, centre, axis and eccentric...

Scalar-tensor theories of gravity are known to allow significant deviations from general relativity through various astrophysical phenomena. In this paper, we formulate a scalar-connection by setting up scalars and connection configurations instead metric. Since the matter sector is not straightforward conceive without metric, invoke cosmological fluids in terms their one-form velocity volume e...

Abstract We propose a new formulation of f ( R ) gravity, dubbed scalarized in which the Legendre transform is included as dynamical term. This leads to theory with second-order field equations that describes general relativity self-interacting scalar field, without requiring introduction conformal frames. demonstrate quadratic version gravity reduces massive and we explore its implications for...

In this paper, proper optimality concepts in vector optimization with variable ordering structures are introduced for the first time and characterization results via scalarizations are given. New type of scalarizing functionals are presented and their properties are discussed. The scalarization approach suggested in the paper does not require convexity and boundedness conditions.

In the presence of certain non-minimal couplings between a scalar field and Gauss-Bonnet curvature invariant, Kerr black holes can scalarize, as long they are spinning fast enough. This provides distinctive violation hypothesis, occurring only for some high spin range. this paper we assess if strong magnetic fields, that may exist in vicinity astrophysical holes, could facilitate effect, by bri...

Hough Transform (HT) is a method for shape extraction from images based on accumulator array of the most voted form. This paper introduces a unique methodology to detect any conic equation parameters using HT idea. Based on the analysis of generic conic equation it is observed that is possible to unify its identification on images if some aspects are considered. The bases of the formulation her...

Infinite-dimensional linear conic formulations are described for nonlinear optimal control problems. The primal linear problem consists of finding occupation measures supported on optimal relaxed controlled trajectories, whereas the dual linear problem consists of finding the largest lower bound on the value function of the optimal control problem. Various approximation results relating the ori...

The problem of the generation of homogeneous grids for spherical domains is considered in the class of conformal conic mappings. The equivalence between secant and tangent projections is shown and splitting the set of conformal conic mappings into equivalence classes is presented. The problem of minimization of the mapping factor variation is solved in the class of conformal conic mappings. Obt...