Full-text resources of CEJSH and other databases are now available in the new Library of Science.
Visit https://bibliotekanauki.pl

Results found: 5

first rewind previous Page / 1 next fast forward last

Search results

help Sort By:

help Limit search:
first rewind previous Page / 1 next fast forward last
1
Publication available in full text mode
Content available

Multidimensional Data Classification - Comparison of Isodata and Approximation by Points Methods

100%
Maciuk A., Department of Mathematics and Cybernetics U. o. E.
Acta Universitatis Lodziensis. Folia Oeconomica
|
2009
|
vol. 228
PL
Efekt podziału zależy nie tylko od ustalenia kryteriów podziału, ale także od wyboru metody dzielenia. Standardowy algorytm klasyfikacji wielowymiarowych danych ISODATA dzieli wyjściowy zbiór na ustaloną liczbę rozłącznych podzbiorów tak, aby podział ten jak najkorzystniej spełniał przyjęte kryteria. Alternatywą wobec niego jest algorytm oparty na metodzie aproksymacji ustaloną liczbą punktów, którego efektem jest wskazanie obszarów zbioru o dużym stopniu zagęszczenia elementów. Artykuł zawiera porównanie efektów użycia tych metod ze wskazaniem zalet i wad. Omawia też pewne własności klasyfikacji wynikające z konsekwencji wyboru jednej z dwóch omawianych metod.
EN
The effect of division is dependent not only on the criteria of division but also on the chosen method. The standard algorithm of multidimensional data classification ISODATA divides the given set into an assumed number of separable subsets in such a way that the division fulfills best the accepted criteria. An alternative method is approximation by the chosen number of points which in result indicates the areas of a set with large congestion o f the elements. The paper compares effects of using both methods listing their advantages and drawbacks. Apart from presenting the results of division of various sets some characteristics of classification are discussed which are an effect of the choice of one of the above mentioned methods.
2

Wpływ standardów kształcenia na poziom nauczania matematyki w wyższych szkołach ekonomicznych

100%
Maciuk A.
Didactics of Mathematics
|
2011
|
issue 8 (12)
81-90
EN
The education standards introduced in Poland in 2005 by the new higher education law significantly changed rules of teaching of majority of subject taught at universities. From the perspective of teaching mathematics at universities of economics those standards have several serious drawbacks such as reduction of the number at maths teaching hours without significant modifications of curriculum or bad correlation with what is being taught in high schools. The law of 2005 was supposed to improve the effectiveness of teaching and make students better prepared for challenges of the work market. Teaching of mathematics at the universities of economics should, apart from providing necessary tools for further study, help students become independent and develop abilities of analytical thinking. Unfortunately, practice is different and to a very large extent this is due to the present standards. Few years after they were introduced we are trying to indicate what actions should be taken to improve the quality of mathematics teaching and in consequence facilitate students’ independent conclusions and enhance their analytical thinking skills.
3
Publication available in full text mode
Content available

Vortices and complex numbers

63%
Maciuk A., Smoluk A.
Mathematical Economics
|
2015
|
issue 11(18)
77-88
EN
The paper emphasizes that complex numbers are objects with their equivalents commonly occurring in nature. Just like real numbers measure lengths in a physical world, complex numbers measure vortices observed in nature. The spiral orbits in this paper are exponential spirals (also called logarithmic spirals). A vortex is identified by determining a complex number that generates it. To determine this number, we need two snap-reading observations that provide the argument of a complex number, while the ratio of radiuses – the modulus of a complex number. Therefore, we also deal with the area of a complex number. Complex numbers involve a meaningful description of the laws of nature, i.e. of vortices and of equilibrium.
4
Publication available in full text mode
Content available

Two proofs of Stokes’ theorem in new clothes

63%
Maciuk A., Smoluk A.
Didactics of Mathematics
|
2015
|
issue 12(16)
85-92
EN
The paper presents two proofs of Stokes’ theorem that are intuitively simple and clear. A manifold, on which a differential form is defined, is reduced to a three-dimensional cube, as extending to other dimensions is straightforward. The first proof reduces the integral over a manifold to the integral over a boundary, while the second proof extends the integral over a boundary to the integral over a manifold. A new idea consists in the definition of Sacała’s line that inspired the authors to taking a different look at the proof of Stokes’ theorem.
5
Publication available in full text mode
Content available

Partitions and branching processes

63%
Maciuk A., Smoluk A.
Mathematical Economics
|
2015
|
issue 11(18)
69-76
EN
A partition, i.e. a division of a finite set into nonempty subsets, is a simple and essential concept of quantitatively understanding the reality. A partition of a number n is a decreasing sequence of natural numbers whose sum equals n. Greater numbers are seen only in terms of the union of partitions. The most important processes such as stochastic processes of branching processes can be expressed most simply using the language of partitions. By means of partitions any Sacała’s line defines a wide class of related quasibranching processes which are more general than Markov processes. Didactically such an approach is extremely useful.
first rewind previous Page / 1 next fast forward last
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.