We continue Mizar formalization of general topology according to the book [16] by Engelking. In the article, we present the final theorem of Section 4.1. Namely, the paper includes the formalization of theorems on the correspondence between the cardinalities of the basis and of some open subcover, and a discreet (closed) subspaces, and the weight of that metrizable topological space. We also de...

Základné vlastnosti sadrovca pre odsírenie spalín Several hundred thousand of FGD gypsum is produced annually at the Matra Power Plant (Hungary) as a byproduct of generating electricity and protecting the environment. Chemical and mechanical characteristics of this material were studied of the Department of Mining and Geotechnical Engineering, University of Miskolc (Hungary). The material in qu...

This paper provides a an introduction to some basic properties of Brownian motion. In particular, it shows that Brownian motion exists, that Brownian motion is nowhere differentiability, and that Brownian motion has finite quadratic variation.

High-resolution spectrographs for very large telescopes lead to new challenges in grating technology to achieve optimum matching of the slit width to the seeing disc. This has led elsewhere to the development of long echelles of high blaze angle produced by mosaicking technology. An alternative approach, pursued in this paper and adopted for the Gemini HighResolution Optical Spectrograph, is to...

Mathematical population models are constructed based on plausible explicit and implicit biological assumptions. While it is easy to incorporate explicit assumptions correctly in the models, those implicit ones are often ill treated or forgotten. Indeed, this happens to some well known models in the literature and examples of such will be mentioned and discussed. For a model to be logically cred...

Lyapunov functions for basic virus dynamics models are introduced, and global stability of the models are thereby established.

In this paper S, X denote non empty sets and R denotes a binary relation on X. We consider orthorelational structures, extensions of relational structure and ComplStr, as systems 〈 a carrier, an internal relation, a complement operation 〉, where the carrier is a set, the internal relation is a binary relation on the carrier, and the complement operation is a unary operation on the carrier. Let ...

A Introduction This paper outlines some of the basic mechanical and thermal properties of silicon. B Crystalline Structure and Elastic Properties Three values for the lattice parameter of pure Silicon at 22.500 °C are given below. The values were determined in independent studies through X-ray and optical interferometry (XROI). a= 543102.032 +/0.033 fm [2] a= 543102.044 +/0.017 fm [3] a= 543101...

This technical report summarized facts from the basic theory of filter convergence spaces and gives detailed proofs for them. Many of the results collected here are well known for various types of spaces. We have made no attempt to find the original proofs.