Wyniki wyszukiwania - Biblioteka Nauki

1

Distribution of lattice points on hyperbolic surfaces

100%

Lev V.

Acta Arithmetica

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1996

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tom 75

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nr 1

85-95

EN

Let two lattices $Λ', Λ'' ⊂ ℝ^s$ have the same number of points on each hyperbolic surface $|x₁...x_s| = C$. We investigate the case when Λ', Λ'' are sublattices of $ℤ^s$ of the same prime index and show that then Λ' and Λ'' must coincide up to renumbering the coordinate axes and changing their directions.

2

Two types of ontological structure. Concepts Structures and lattices of elementary situations

80%

Kaczmarek J.

Logic and Logical Philosophy

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2012

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tom 21

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nr 2

165-174

EN

In 1982, Wolniewicz proposed a formal ontology of situations based on the lattice of elementary situations (cf. [7, 8]). In [3], I constructed some types of formal structure - Porphyrian Tree Structures (PTS), Con- cepts Structures (CS) and the Structures of Individuals (U) - that formally represent ontologically fundamental categories: species and genera (PTS), concepts (CS) and individual beings (U) (cf. [3, 4]). From an ontological perspective, situations and concepts belong to different categories. But, unexpectedly, as I shall show, some variants of CS and Wolniewicz’s lattice are similar. The main theorem states that a subset of a modified concepts structure (called CS+) based on CS fulfils the axioms of Wolniewicz’ lattice. Finally, I shall draw some philosophical conclusions and state some formal facts.

3

Identity-based Signatures from Lattices : Simpler, Faster, Shorter

80%

Tian M. , Huang L.

Fundamenta Informaticae

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2016

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tom Vol. 145, nr 2

171--187

EN

Identity-based signature is an important technique for light-weight authentication. Recently, many efforts have been made to construct identity-based signatures over lattice assumptions since they would remain secure in future quantum age. In this paper we present a new identitybased signature scheme from lattice problems. This scheme is more efficient than other lattice-based identity-based signature schemes in terms of both computation and communication complexities. We prove its security in the random oracle model under short integer solution assumption that is as hard as approximating several worst-case lattice problems. We also extend the scheme to an identity-based message recovery signature scheme that has better performance.

4

Point process of clusters for a stationary Gaussian random field on a lattice

80%

Lu Y. , Guo J.

Probability and Mathematical Statistics

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2023

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tom Vol. 43, Fasc. 2

247--262

EN

It is well established that the normalized exceedances resulting from a standard stationary Gaussian triangular array at high levels follow a Poisson process under the Berman condition. To model frequent cluster phenomena, we consider the asymptotic distribution of the point process of clusters for a Gaussian random field on a lattice. Our analysis demonstrates that the point process of clusters also converges to a Poisson process in distribution, provided that the correlations of the Gaussian random field meet certain conditions. Additionally, we provide a numerical example to illustrate our theoretical results.

5

Fuzzification of Rational and Recognizable Sets

80%

Konstantinidis S. , Nicolae S. , Yu S.

Fundamenta Informaticae

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2007

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tom Vol. 76, nr 4

413-447

EN

In this paper we present a different framework for the study of fuzzy finite machines and their fuzzy languages. Unlike the previous work on fuzzy languages, characterized by fuzzification at the level of their acceptors/generators, here we follow a top-down approach by starting our fuzzification with more abstract entities: monoids and particular families in monoids. Moreover, we replace the unit interval (in fact, a finite subset of the unit interval) as support for fuzzy values with the more general structure of a lattice. We have found that completely distributive complete lattices allow the fuzzification at the highest level, that of recognizable and rational sets. Quite surprisingly, the fuzzification process has not followed thoroughly the classical (crisp) theory. Unlike the case of rational sets, the fuzzification of recognizable sets has revealed a few remarkable exceptions from the crisp theory: for example the difficulty of proving closure properties with respect to complement, meet and inverse morphisms. Nevertheless, we succeeded to prove the McKnight and Kleene theorems for fuzzy sets by making the link between fuzzy rational/recognizable sets on the one hand and fuzzy regular languages and FT-NFA languages (languages defined by NFA with fuzzy transitions) on the other. Finally, we have drawn the attention to fuzzy rational transductions, which have not been studied extensively and which bring in a strong note of applicability.

6

An Energy Efficient QAM Modulation with Multidimensional Signal Constellation

80%

Markiewicz T. G.

International Journal of Electronics and Telecommunications

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2016

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tom Vol. 62, No. 2

159--165

EN

Packing constellations points in higher dimensions, the concept of multidimensional modulation exploits the idea drawn from geometry for searching dense sphere packings in a given dimension, utilising it to minimise the average energy of the underlying constellations. The following work analyses the impact of spherical shaping of the constellations bound instead of the traditional, hyper-cubical bound. Balanced constellation schemes are obtained with the N-dimensional simplex merging algorithm. The performance of constellations of dimensions 2, 4 and 6 is compared to the performance of QAM modulations of equivalent throughputs in the sense of bits transmitted per complex (twodimensional) symbols. The considered constellations give an approximately 0.7 dB to 1 dB gain in terms of BER over a standard QAM modulation.

7

W-irreducible Lattices

80%

Grygiel J.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2005

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tom Vol. 10

77--81

EN

A finite lattice is W-irreducible if it cannot be split into two overlapping lattices, one of them being an ideal and the other a filter of the lattice. We give some characterization of finite W-irreducible lattices.

8

Geometric properties of the lattice of polynomials with integer coefficients

80%

Lipnicki A. , Śmietański M. J.

Opuscula Mathematica

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2024

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tom Vol. 44, no. 4

565--585

EN

This paper is related to the classic but still being examined issue of approximation of functions by polynomials with integer coefficients. Let r, n be positive integers with n ≥ 6r. Let Pn ∩Mr be the space of polynomials of degree at most n on [0, 1] with integer coefficients such that P(k)(0)/k! and P(k)(1)/k! are integers for k = 0, . . . , r − 1 and let PZn ∩Mr be the additive group of polynomials with integer coefficients. We explore the problem of estimating the minimal distance of elements of PZn ∩Mr from Pn ∩Mr in L2(0, 1). We give rather precise quantitative estimations for successive minima of PZn in certain specific cases. At the end, we study properties of the shortest polynomials in some hyperplane in Pn ∩Mr.

9

Quantifiers on lattices with an antitone involution

80%

Chajda I. , Langer H.

Demonstratio Mathematica

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2009

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tom Vol. 42, nr 2

241-246

EN

Quantifiers on lattices with an antitone involution are considered and it is proved that the poset of existential quantifiers is antiisomorphic to the poset of relatively complete sublattices.

10

Two Infinite Sequences of Pre-Maximal Extensions of the Relevant Logic E

80%

Typańska-Czajka L.

Bulletin of the Section of Logic

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2019

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tom 48

|

nr 1

EN

The only maximal extension of the logic of relevant entailment E is the classical logic CL. A logic L ⊆ [E,CL] called pre-maximal if and only if L is a coatom in the interval [E,CL]. We present two denumerable infinite sequences of premaximal extensions of the logic E. Note that for the relevant logic R there exist exactly three pre-maximal logics, i.e. coatoms in the interval [R,CL].

11

Some characterizations of pseudo-BL-chains

80%

Walendziak A. , Wojciechowska-Rysiawa M.

Commentationes Mathematicae

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2011

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tom Vol. 51, [Z] 2

121-124

EN

Pseudo-BL-chains are linearly ordered pseudo-BL-algebras. Characterizations of them in terms of concepts of lattice theory are given.

12

Uniform approximation by polynomials with integer coefficients

80%

Lipnicki A.

Opuscula Mathematica

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2016

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tom Vol. 36, no. 4

489--498

EN

Let r, n be positive integers with n ≥ 6r. Let P be a polynomial of degree at most n on [0,1] with real coefficients, such that [formula] are integers for k = 0,…, r — 1. It is proved that there is a polynomial Q of degree at most n with integer coefficients such that [formula] for x ∈ [0,1], where C1, C2 are some numerical constants. The result is the best possible up to the constants.

13

The uncountable cofinality of the automorphism group of the countable universal distributive lattice

80%

Droste M. , Truss J. K.

Demonstratio Mathematica

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2011

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tom Vol. 44, nr 3

473-479

EN

We show that the automorphism group of the countable universal distributive lattice has strong uncountable cofinality, and we adapt the method to deduce the strong uncountable cofinality of the automorphism group of the countable universal generalized boolean algebra.

14

On varieties of orgraphs

80%

Haviar A. , Monoszová G.

Discussiones Mathematicae Graph Theory

|

2001

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tom 21

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nr 2

207-221

EN

In this paper we investigate varieties of orgraphs (that is, oriented graphs) as classes of orgraphs closed under isomorphic images, suborgraph identifications and induced suborgraphs, and we study the lattice of varieties of tournament-free orgraphs.

15

On a complete lattice of retracts of a free monoid generated by three elements

80%

Foryś W.

Opuscula Mathematica

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2008

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tom Vol. 28, no. 2

123-127

EN

We prove that the family of retracts of a free monoid generated by three elements, partially ordered with respect to the inclusion, is a complete lattice.

16

Many Faces of Lattice Tolerances

70%

Grygiel J.

Bulletin of the Section of Logic

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2019

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tom 48

|

nr 4

EN

Our aim is to overview and discuss some of the most popular approaches to the notion of a tolerance relation in algebraic structures with the special emphasis on lattices.

17

Badania nad zastosowaniem systemu klasyfikatorów do optymalizacji kratownicy

70%

Rabijasz M.

Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska

|

2004

|

tom z. 23

357-362

PL

Zaprezentowano badania nad zastosowaniem systemu klasyfikatorów do optymalizacji kratownicy. Określono zasady działania algorytmu iteracyjnego i zobrazowano jego działanie na przykładach. Wskazano na praktyczne zastosowanie oraz potencjał obranej metody.

EN

This paper presents research on classifier system (CS) application possibilities in truss structural optimization. Algorithm has been explained and results have been shown in examples. Practical application possibilities and potential for improvement have been pointed out.

18

Externalization of lattices

70%

Chajda I. , Wismath S.

Demonstratio Mathematica

|

2006

|

tom Vol. 39, nr 4

731-736

EN

Let r be a type of algebras. An identity s = t of type r is said to be externally compatible, or simply external, if the terms s and t are either the same variable or both start with the same operation symbol fj of the type. A variety is called external if all of its identities are external. For any variety V , there is a least external variety E(V ) containing V , the variety determined by the set of all external identities of V . External identities and varieties have been studied by [4], [5] and [2], and a general characterization of the algebras in E(V ) has been given in [3]. In this paper we study the algebras of the variety E(V ) where V is the type (2, 2) variety L of lattices. Algebras in L may also be described as ordered sets, and we give an ordered set description of the algebras in E(L). We show that on any algebra in E(L) there is a natural quasiorder having an additional property called externality, and that any set with such a quasiorder can be given the structure of an algebra in E(L). We also characterize algebras in E(L) by an inflation construction.

19

Flat semilattices

70%

Grätzer G. , Wehrung F.

Colloquium Mathematicum

|

1999

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tom 79

|

nr 2

185-191

20

Linear model genealogical tree application to an odontology experiment

70%

Covas R.

Discussiones Mathematicae Probability and Statistics

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2007

|

tom 27

|

nr 1-2

47-77

EN

Commutative Jordan algebras play a central part in orthogonal models. We apply the concepts of genealogical tree of an Jordan algebra associated to a linear mixed model in an experiment conducted to study optimal choosing of dentist materials. Apart from the conclusions of the experiment itself, we show how to proceed in order to take advantage of the great possibilities that Jordan algebras and mixed linear models give to practitioners.