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The Background and Significance of 'Crises' in the Foundations of Mathematics

100%

Mrozek J.

nr 3(67)

49-60

The watersheds in the development of mathematics that lay bare the ambiguities and contradictions among its very basic notions and conceptions are commonly described as 'crises' in mathematics. They coincide with periods of intense mathematical research, often inspired by philosophical doctrines which help to clarify the notions and methods with the use of which many fundamental theorems are proved. The paper presents three best known and most widely discussed crises in the foundations of mathematics, reviews the causes of their appearance and discusses the difficulties that they have led to as well as possible ways of their resolution. The three crises arose in connection with the discovery of the incommensurable line segments in the Pythagorean School, in connection with the operations on the infinitesimals by the creators of the differential calculus (17th-18th centuries) and with respect to the foundations of mathematics connected with operations on the actually infinite sets (19th and 20th centuries).

Rola anty-Muller hormonu w roznicowaniu meskiego ukladu rozrodczego

63%

Mrozek J.

tom 97

nr 12

275-277

Exploring bonding patterns of molecular systems using quantum mechanical bond multiplicities

51%

Mrozek J. , Nalewajski R. F. , Michalak A.

tom Vol. 72, nr 7S

1779-1791

One of the fundamental chemical concepts, the structural formula of a chemical species, which visualizes bonding patterns in a given molecular system, can also given a more flexible and quantified form in terms of alternative quantum-mechanical measures of bond-orders. The recently developed difference approach, based upon the one-determinantal wavefunction [Hartree-Fock(HF) and Kohn-Sham (KS) theories], compares the charge-and-bond-order matrix in a molecule (P) and that in the separated atoms limit (P(0), SAL) defined in the orthogonal basis set of atomic functions. In this approach the atomic and diatomic contibutions to the molecularly averaged difference between these matrices, /2 = 1/2tr[P(P(0) - P)], are used to define bond multiplicities. THe main purpose of this work is to examine the overall performance of such KS and HF bonding indices, when applied to the set of chemically well defined reference systems, and to use them to investigate bond-orders in more challenging molecules, which have recently been the subject of independent studies. Manifestations of changing bond ionicity by these effective bond-orders are examined for a series of diatomics. Some methodological aspects associated with alternative SAL choices are discussed and tested.

Kalibrowanie szyn tramwajowych z wykorzystaniem wspólnych wykrojów kształtujących

38%

Nowakowski A. , Turczyn A. , Okoń R. , Kuźmiński Z. , Madej W. , Mrozek J. , Dziwisz A.

tom nr 2

68-74

W artykule przedstawiono przegląd stosowanych metod walcowania szyn tramwajowych. Przegląd ten obejmuje analizę kalibrowań w złożeniach dwuwalcowych oraz kalibrowania walców do walcowania szyn z wykorzystaniem klatek czterowalcowych. Omówiono zagadnienia technologii walcowania szyn tramwajowych 180 S, Ri59 i Ri60. Przedstawiono zunifikowane (z wykorzystaniem wspólnych wykrojów kształtujących) kalibrowanie wymienionych szyn oraz wytyczne prawidłowego ich walcowani w warunkach Walcowni Dużej Huty Katowice S.A.

A review of used methods of tram rails rolling is presented. The review includes sizing analysis in two-roll assemblies and roll pass design for rail rolling in four-high stands. Rolling technology of 180 S, Ri59 and Ri60 tram rails was discussed. Unified sizing of specified rails (by using common shape passes) and instructions for correct rolling in heavy-section mill of Katowice steelworks SA are presented.