‎In the present study‎, ‎we consider a regular curve in Galilean‎ ‎$4$-space $mathbb{G}_{4}$ whose position vector is written as a‎ ‎linear combination of its Frenet vectors‎. ‎We characterize such‎ ‎curves in terms of their curvature functions‎. ‎Further‎, ‎we obtain‎ ‎some results of rectifying‎, ‎constant ratio‎, ‎$T$-constant and‎ ‎$N$-constant curves in $mathbb{G}_{4}$‎.

Global convergence results are derived for well-known conjugate gradient methods in which the line search step is replaced by a step whose length is determined by a formula. The results include the following cases: 1. The Fletcher-Reeves method, the Hestenes-Stiefel method, and the Dai-Yuan method applied to a strongly convex LC objective function; 2. The Polak-Ribière method and the Conjugate ...

perfused organs to examine sugar catabolism and metabolism, Holmes underscores the relationship between the laboratory elucidation of a significant intermediate compound like acetone and the clinical knowledge of ketone body production in diabetes. But, he concludes, the early-twentieth-century integrative optimism evaporated, to be re-formulated in the 1930s with the announcement of the "Embde...

The object of this paper is the theta divisor of the compactified Jacobian of a nodal curve of genus g. We determine its irreducible components and give it a geometric interpretation. A characterization of hyperelliptic irreducible curves in M g is appended as an application.

In this paper (part three of the trilogy) we use low degree G 1 and G 2 continuous regular algebraic spline curves deened within parallelograms, to interpolate an ordered set of data points in the plane. We explicitly characterize curve families whose members have the required interpolating properties and possess a minimal number of innection points. The regular algebraic spline curves consider...

The creep anisotropy of nickel-base superalloys with a cubic y' morphology is studied with a composite model. Creep curves and the internal stress distribution in the microstructure under [Oll] load are calculated with a Finite Element Procedure. Analytical considerations are made for arbitrary loading directions. y' cubes (with their interfaces aligned parallel to (001) planes) under [OOl] loa...

In this paper we model shape objects variability and spatial relationships between characteristics of this object. What is an object? We consider that an object is a set of shapes and points. We establish here a formalism unifying shapes and points by approximating shape contours by composite Bézier curves. These are equivalent to their control points. We then propose a non linear invariant sta...

A clothoid has the property that its curvature varies linearly with arclength. This is a useful feature for the path of a vehicle whose turning radius is controlled as a linear function of the distance travelled. Highways, railways and the paths of car-like robots may be composed of straight line segments, clothoid segments and circular arcs. Control polylines are used in computer aided design ...

Starting from scanning electron microscope images of some food products, we generate binary images of composite materials. After measuring the covariance and the probability for segments and for squares to be included in the dominant component, we develop a modelling of the microstructure from random sets obtained by thresholding Gaussian random functions. The covariance function of the underly...