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Vectors in school mathematics
EN
Vectors have several meanings in the science. Mathematicians, physicists and other scientists make use of the notion of a vector. The notions they make use of are different in different subjects. Here we present different meanings of vectors and give some hints how to understand them in different subjects of science.
EN
Let: {Xi} be a sequence of r.v.'s, and: Mn := max (X1,..., Xn), mn := min (X1,..., Xn). Our goal is to prove the almost sure central limit theorem for the properly normalized vector {Mn,mn}, provided: 1) {Xi} is an i.i.d. sequence, 2) {Xi} is a certain standardized stationary Gaussian sequence.
4
On the Dual Darboux rotation axis of the spacelike Dual space curve
EN
In this paper, the Dual Darboux rotation axis for spacelike dual space curve in the semi-dual space D3 is decomposed in two simultaneous rotations. The axis of these simultaneous rotations are joined by a simple mechanism. This study is original corresponding in the semi-dual space D3 of the article entitled On the Dual Darboux Rotation Axis of the Dual Space Curve [6].
5
O analizie tensorowej czyli o pochodnej kowariantnej
EN
This paper outlines the origin of the notion of the covariant derivative of the tensor field. What has been particularly emphasised are the conditions and causes of the fact that the notion "the ordinary R^3 derivative" has become inadequate, since it does not produce a tensor nor its field. The work has been based on original sources, as well as on references which give a currrent view on the question. What has been taken into consideration is the lack of equivalence between covariant and contravariant representations of a vector, with reference to the problem of the derivative of the vector field.
EN
All symmetric polynomials of multiple variables, with the variables belonging to the fixed, final set, are the elements of the vector space of infinite dimension. The vector space contains numerous finite subspaces. These subspaces are subjected to a standard analysis. Set theory classifications and ordering relations indicate how to choose the basis. The investigation of transient matrices reveals sets of algebra identities. The unlimited set of these identities is particularly useful when it comes to engineering applications.
PL
W pracy przedstawiono nowe pojęcia i wyniki dotyczące metodologii analizy zagadnień związanych z wartościami własnymi i wektorami i własnymi macierzy rzeczywistych o współczynnikach interwałowych postaci A = { A ; AC - A < A < A C + A } , gdzie A jest miarą niepewności . Przedstawione ujęcie jest prawdopodobnie najprostszym sposobem aproksymacji w modelowaniu drgań i ich własności w systemach o parametrach niepewnych.
EN
In the paper, we are concerned with interval - oriented methodology to mode l uncertaintie s o f eigenvalues , and eigenvectors of an nx n interva l rea l matrix A = { A ;AC - A< A< AC + A }, where A i s a measure of uncertainty. Presented methodology is probably the simples t way to model an d to approximate vibration properties of systems with uncertain parameters.
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