Wyniki wyszukiwania - Biblioteka Nauki

Nowa wersja platformy, zawierająca wyłącznie zasoby pełnotekstowe, jest już dostępna.
Przejdź na https://bibliotekanauki.pl

Ograniczanie wyników

Znaleziono wyników: 4

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: linearly independent

Sortuj według:

Ogranicz wyniki do:

Torsion Z-module and Torsion-free Z-module

100%

Futa Y. , Okazaki H. , Nakasho K. , Shidama Y.

nr 4

277-289

In this article, we formalize a torsion Z-module and a torsionfree Z-module. Especially, we prove formally that finitely generated torsion-free Z-modules are finite rank free. We also formalize properties related to rank of finite rank free Z-modules. The notion of Z-module is necessary for solving lattice problems, LLL (Lenstra, Lenstra, and Lov´asz) base reduction algorithm [20], cryptographic systems with lattice [21], and coding theory [11].

Rank of Submodule, Linear Transformations and Linearly Independent Subsets of Z-module

100%

Nakasho K. , Futa Y. , Okazaki H. , Shidama Y.

nr 3

189-198

In this article, we formalize some basic facts of Z-module. In the first section, we discuss the rank of submodule of Z-module and its properties. Especially, we formally prove that the rank of any Z-module is equal to or more than that of its submodules, and vice versa, and that there exists a submodule with any given rank that satisfies the above condition. In the next section, we mention basic facts of linear transformations between two Z-modules. In this section, we define homomorphism between two Z-modules and deal with kernel and image of homomorphism. In the last section, we formally prove some basic facts about linearly independent subsets and linear combinations. These formalizations are based on [9](p.191-242), [23](p.117-172) and [2](p.17-35).

Vector-based Attribute Reduction Method for Formal Contexts

100%

Shao M. , Liu M. , Guo L.

tom Vol. 126, nr 4

397--414

Attribute reduction is one basic issue in knowledge discovery of information systems. In this paper, based on the object oriented concept lattice and classical concept lattice, the approach of attribute reduction for formal contexts is investigated. We consider attribute reduction and attribute characteristics from the perspective of linear dependence of vectors. We first introduce the notion of context matrix and the operations of corresponding column vectors, then present some judgment theorems of attribute reduction for formal contexts. Furthermore, we propose a new method to reducing formal context and show corresponding reduction algorithms. Compared with previous reduction approaches which employ discernibility matrix and discernibility function to determine all reducts, the proposed approach is more simpler and easier to implement.

Eigenvalue problem for multi-degree-of-freedom systems with repeated frequencies

86%

Palej R.

tom Vol. 24

307--312

The paper deals with the eigenvalue problem related with discrete systems, consisting of n identical masses connected with springs in such a way that the stiffness matrix has the form of a multiband symmetric matrix. The eigenvalue problem formulated for such systems is characterized by repeated eigenvalues to which linearly independent eigenvectors correspond. The solution of the eigenvalue problem has been found for an arbitrary, finite number of degrees of freedom for the fully coupled systems and the systems in which masses are connected exclusively with the nearest neighbours.

Praca dotyczy zagadnienia własnego macierzy związanych z układami dyskretnymi, zbudowanymi z n identycznych mas połączonych sprężynami w taki sposób, by macierz sztywności miała budowę wielopasmowej macierzy symetrycznej. Zagadnienie własne tego typu macierzy charakteryzuje się wielokrotnymi wartościami własnymi, którym odpowiadają układy liniowo niezależnych wektorów własnych. W pracy podano analityczne rozwiązanie zagadnienia własnego macierzy dla układu w pełni sprzężonego i układu, w którym każda masa połączona jest wyłącznie z dwiema sąsiednimi.