Relativistic gravastar configurations in which the interior matter distribution is modeled through a Chaplygin fluid

In this paper, we investigate gravastar configurations in which the interior of the compact object is modeled through a Chaplygin fluid. This is motivated by the fact that Chaplygin fluid and the associated exotic equation of state, have often been used as models for the dark energy sector. We derive the relativistic equations of the stellar structure for non-rotating configurations. A special focus is denoted in particular to the mass-radius function and the equation of state for the shell of the gravastars, for which we derive the analytical expressions.

A pair of kinematically related space curves

We investigate the relation between two types of space curves, the Mannheim curves and constant-pitch curves and primarily explicate a method of deriving Mannheim curves and constant-pitch curves from each other by means of a suitable deformation of a space curve. We define a “radius” function and a “pitch” function for any arbitrary regular space curve and use these to characterize the two classes of curves. A few non-trivial examples of both Mannheim and constant pitch curves are discussed. The geometric nature of Mannheim curves is established by using the notion of osculating helices. The Frenet–Serret motion of a rigid body in theoretical kinematics is studied for the special case of a Mannheim curve and the axodes in this case are deduced. In particular, we show that the fixed axode is developable if and only if the motion trajectory is a Mannheim curve.

Natural Produce Classification Using Computer Vision Based on Statistical Color Features and Derivative of Radius Function

In agriculture industry, natural produce classification is used in sorting, grading, measuring, and pricing. Currently, a lot of methods have been developed using computer vision to replace human expert in natural produce classification. However, some of the method used long features descriptor and complex classifier to obtain high classification rate. This paper proposes natural produce classification method using computer vision based on simple statistical color features and derivative of radius function. The k-nearest neighbors (k-NN) and artificial neural network (ANN) were used to classify the produce based on the extracted features. Preliminary experiment results show that the proposed method achieved best result with average classification accuracy of 99.875% using ANN classifier with nine nodes in hidden layer.

Weighted Weak Local Hardy Spaces Associated with Schrödinger Operators

We characterize the weighted weak local Hardy spacesWhρp(ω)related to the critical radius functionρand weightsω∈A∞ρ,∞(Rn)which locally behave as Muckenhoupt’s weights and actually include them, by the atomic decomposition. As an application, we show that localized Riesz transforms are bounded on the weighted weak local Hardy spaces.