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1
Content available Predicate Data Model in the Form of a Linear Space
Shliakhov V., Chetverykov G., Bozhko I., Shliakhova N.
ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes
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2019
|
Vol. 8, No 2
51--54
EN
The restriction of the input set in the form of a positive cone of the space is not always correct. For instance, while studying the organ of vision, people are limited not only to positive, but also to radiation with not very high energies, because excessively intense can disturb the visual organ. In this particular case, a convex body of a linear space is a fairly acceptable model of the set of input signals. Therefore, we consider linear predicates with this domain of definition.
2
Content available remote Elementy teorii Galois w zastosowaniach kryptograficznych w systemie bezpieczeństwa narodowego
Wereński S., Siemieńska B.
Studia Bezpieczeństwa Narodowego
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2016
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R. 6, Nr 9
359--387
PL
Praca dotyczy praktycznego wykorzystania elementów teorii Galois w zastosowaniach kryptograficznych w aspekcie bezpieczeństwa narodowego. W związku z powyższym zaprezentowano historię narodzin matematyki, w tym genezę powstania algebry oraz znaczenie tego terminu. Następnie przedstawiono krótką charakterystykę rozwoju algebry w kierunku abstrakcyjnym oraz omówiono niektóre elementy klasycznej teorii Galois, które mogą być wykorzystywane w implementacjach kryptograficznych na potrzeby bezpieczeństwa i obronności kraju. Szczególną uwagę zwrócono na ciała skończone oraz ich rozszerzenia, wykorzystywane do budowy algorytmów szyfrujących, a także omówiono kilka WAT-owskich wynalazków bazujących na rozwiązaniach tego typu.
EN
The following paper focuses on the practical use of some elements of the Galois’ Theory in the field of cryptography. Therefore, the paper briefly presents the origin of the algebra and the meaning of this term, as well as short characteristic of its development in the abstract aspects and its applicability to security protection. Subsequently, crucial points of the classic Galois’ Theory which can be used in cryptographic implementation for the national defence needs, are discussed here. Special attention is paid to the finite fields and their developments which can constitute the basis of the construction of the cryptographic algorithms. Additionally, some WAT inventions based on the solution of this type are introduced.
3
Content available remote Orthopairs: A Simple and Widely UsedWay to Model Uncertainty
Ciucci D.
Fundamenta Informaticae
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2011
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Vol. 108, nr 3/4
287-304
EN
The term orthopair is introduced to group under a unique definition different ways used to denote the same concept. Some orthopairmodels dealing with uncertainty are analyzed both from a mathematical and semantical point of view, outlining similarities and differences among them. Finally, lattice operations on orthopairs are studied and a survey on algebraic structures is provided.
4
Content available remote Algebraic Structures Related to Many Valued Logical Systems. Part 2, Equivalence Among some Widespread Structures
Cattaneo G., Ciucci D., Giuntini R., Konig M.
Fundamenta Informaticae
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2004
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Vol. 63, nr 4
357--373
EN
Several algebraic structures (namely HW, BZMVdM, Stonean MV and MVΔ algebras) related to many valued logical systems are considered and their equivalence is proved. Four propositional calculi whose Lindenbaum-Tarski algebra corresponds to the four equivalent algebraic structures are axiomatized and their semantical completeness is given.
5
Content available remote Algebraic Structures Related to Many Valued Logical Systems. Part 1, Heyting Wajsberg Algebras
Cattaneo G., Ciucci D., Giuntini R., Konig M.
Fundamenta Informaticae
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2004
|
Vol. 63, nr 4
331--355
EN
A bottom-up investigation of algebraic structures corresponding to many valued logical systems is made. Particular attention is given to the unit interval as a prototypical model of these kind of structures. At the top level of our construction, Heyting Wajsberg algebras are defined and studied. The peculiarity of this algebra is the presence of two implications as primitive operators. This characteristic is helpful in the study of abstract rough approximations.
6
Content available remote Σ-genomorphism of algebraic structures
Emanovský P.
Demonstratio Mathematica
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2003
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Vol. 36, nr 4
785--792
EN
For an algebraic structure A = (A, F, R) of type τ and a set Σ of open formulas of the first order language L(τ), the concept of Σ-closed subset of A was introduced in [3]. The set C Σ(A) of all Σ-closed subsets of A forms a complete lattice whose properties were studied in [3], [4] and [5]. Algebraic structures A, B of type τ are called CΣ-isomorphic (or Σ-isomorphic in [3]) if the lattices CΣ(A) and CΣ(B) are isomorphic. The CΣ-isomorphisms are investigated for so-called Σ-separable algebraic structures in [3]. The study of the Σ-isomorphisms of algebraic structures is continued in this paper. We introduce the concepts of Σ-genomorphism and Σ-isogenomorphism of algebraic structures and we formulate a sufficient condition under which two structures are isomorphic. We show that for Σ-separable structures the condition is also necessary. Further, we introduce the concepts of Σ-morphism, congruential E -morphism and congruence induced by a congruential Σ-morphism. We also prove Theorem on Σ-genomorphism and Theorem on Σ-morphism.
7
Content available remote Varieties of Ordered Semigroups
Kuřil M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2000/2001
|
Vol. 8
45--49
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