Wyniki wyszukiwania - BazTech

1

On linear chaos in function spaces

Jimenez John M., Markin Marat V.

Demonstratio Mathematica

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2022

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Vol. 55, nr 1

119--135

EN

We show that, in Lp(0,∞) ( 1≤p<∞ ), bounded weighted translations as well as their unbounded counterparts are chaotic linear operators. We also extend the unbounded case to C0[0,∞) and describe the spectra of the weighted translations provided the underlying spaces are complex.

2

On the Representation of Human Motions and Distance-based Retargeting

Hengeveld Simon, Mucherino Antonio

Annals of Computer Science and Information Systems

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2021

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Vol. 25

181--189

EN

Distance-based motion adaptation leads to the formulation of a dynamical Distance Geometry Problem (dynDGP) where the involved distances simultaneously represent the morphology of the animated character, as well as a possible motion. The explicit use of inter-joint distances allows us to easily verify the presence of joint contacts, which one generally wishes to preserve when adapting a given motion to characters having a different morphology. In this work, we focus our attention on suitable representations of human-like animated characters, and study the advantages (and disadvantages) in using some of them. In the initial works on distance-based motion adaptation, a 3ndimensional vector was employed for representing the positions of the n joints of the character at a given frame. Here, we investigate the use of another, very popular in computer graphics, representation that basically replaces every joint position in the three-dimensional space with a set of three sorted Euler angles. We show that the latter can in fact be useful for avoiding some of the artifacts that were observed in previous computational experiments, but we argue that this Euler-angle representation, from a motion adaptation point of view, does not seem to be the optimal one. By paying particular attention to the degrees of freedom of the studied representations, it turns out that a novel character representation, inspired by representations used in structural biology for molecules, may allow us to reduce the character degrees of freedom to their minimal value. As a result, statistical analysis on human motion databases, where the motions are given with this new representation, can potentially provide important insights on human motions. This study is an initial step towards the identification of a full set of constraints capable of ensuring that unnatural postures for humans cannot be created while tackling motion adaptation problems.

3

Daleko i dokładnie

Królikowski Jerzy

Geodeta : magazyn geoinformacyjny

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2020

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nr 1

17--20

4

A New Optimized Stochastic Approach for Multidimensional Integrals in Machine Learning

Todorov Venelin, Apostolov Stoyan, Dimov Ivan, Fidanova Stefka

Annals of Computer Science and Information Systems

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2020

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Vol. 21

337--340

EN

Stochastic techniques have been developed over many years in a range of different fields, but have only recently been applied to the problems in machine learning. A fundamental problem in this area is the accurate evaluation of multidimensional integrals. An introduction to the theory of the stochastic optimal generating vectors has been given. A new optimized lattice sequence with a special choice of the optimal generating vector have been applied to compute multidimensional integrals up to 30-dimensions. Clearly, the progress in the area of machine learning is closely related to the progress in reliable algorithms for multidimensional integration.

5

Vectors in school mathematics

Jędrzejewski J., Kostrzewski T.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2015

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Vol. 20

9--13

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.

6

On the almost sure central limit theorems in the joint version for the maxima and minima of some random variables

Dudziński M., Furmańczyk K.

Demonstratio Mathematica

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2008

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Vol. 41, nr 3

705-722

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.

7

On the Dual Darboux rotation axis of the spacelike Dual space curve

Ayyildiz N., Çöken A. C., Yücesan A.

Demonstratio Mathematica

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2004

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Vol. 37, nr 1

197--202

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].

8

O analizie tensorowej czyli o pochodnej kowariantnej

Kordecki Z.

Czasopismo Techniczne. Środowisko

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2003

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R. 100, z. 1-Ś

103--120

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 R3 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.

9

Podstawy mnogościowe przestrzeni wektorowej wielomianów symetrycznych wielu zmiennych w notacji spektralnej : zarys teorii

Piwowarczyk T.

Czasopismo Techniczne. Elektrotechnika

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2000

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R. 97, z. 4-E

61--79

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.

10

Interval eigenvalue problems - new concepts

Skrzypczyk J., Witek H.

Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska

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1998

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z. 7

329-324

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.