We define the notions of unilateral metric derivatives and “metric derived numbers” in analogy with Dini derivatives (also referred to as “derived numbers”) and establish their basic properties. We also prove that the set of points where a path with values in a metric space with continuous metric derivative is not “metrically differentiable” (in a certain strong sense) is σsymmetrically porous ...

The effectiveness of a commercial absolute air filter for removal of viruses from air was tested with an actinophage, under the usual conditions of a laminar airflow clean room. A new method of dry phage dispersion is described. The filter showed an average reduction of 99.996% of airborne actinophage.

Predictor-corrector (PC) methods for the numerical solution of stiff ODEs can be extended to include the second derivative of the solution. In this paper, we consider second derivative PC methods with the three-step second derivative Adams-Bashforth as predictor and two-step second derivative Adams-Moulton as corrector which both methods have order six. Implementation of the proposed PC method ...

The present study aims at indicating the existence and uniqueness result of system in extended colombeau algebra. The Caputo fractional derivative is used for solving the system of ODEs. In addition, Riesz fractional derivative of  Colombeau generalized algebra is considered. The purpose of introducing Riesz fractional derivative is regularizing it in Colombeau sense. We also give a solution to...

Corner detection is a critical component of many image analysis and understanding tasks, such as object recognition matching. Our research indicates that existing corner algorithms cannot properly depict the difference between edges corners this results in wrong detections. In paper, capability second-order generalized (isotropic anisotropic) Gaussian directional derivative filters to suppress ...

We complete the study of Manin triples of real simple Lie algebras. In the Part 2 of the article we classify the Manin triples (g(R), W, g(R) ⊕ g(R)) (case 2 of the doubles) up to weak and gauge equivalence. First we recall the main definitions of the Part 1. Definition 1. Let g 1 , g 2 , d be Lie algebras over a field K and let Q be a symmetric nondegenerate bilinear form on d. A triple (g 1 ,...

Thyristor rectifiers are widely used in electric railways in order to control the speed. As a consequence of their usage in addition to substantial input lead current, an enormous amount of harmonics is injected into the grid. To avoid such harmonics as well as reactive power compensation, reactive power hybrid filters consisting of active and passive filters are utilized. Regarding different p...