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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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On duality of submodule lattices

100%
Czédli G., Takách G.
Discussiones Mathematicae - General Algebra and Applications
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2000
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tom 20
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nr 1
43-49
EN
An elementary proof is given for Hutchinson's duality theorem, which states that if a lattice identity λ holds in all submodule lattices of modules over a ring R with unit element then so does the dual of λ.
2
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Analysis of an isopetype dual algorithm for optimizing control and nonlinear optimization

100%
Tadej W., Tatjewski P.
International Journal of Applied Mathematics and Computer Science
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2001
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tom 11
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nr 2
429-457
EN
First results concerning important theoretical properties of the dual ISOPE (Integrated System Optimization and Parameter Estimation) algorithm are presented. The algorithm applies to on-line set-point optimization in control structures with uncertainty in process models and disturbance estimates, as well as to difficult nonlinear constrained optimization problems. Properties of the conditioned (dualized) set of problem constraints are investigated, showing its structure and feasibility properties important for applications. Convergence conditions for a simplified version of the algorithm are derived, indicating a practically important threshold value of the right-hand side of the conditioning constraint. Results of simulations are given confirming the theoretical results and illustrating properties of the algorithms.
3
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Operator-splitting and Lagrange multiplier domain decomposition methods for numerical simulation of two coupled Navier-Stokes fluids

100%
Bresch D., Koko J.
International Journal of Applied Mathematics and Computer Science
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2006
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tom 16
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nr 4
419-429
EN
We present a numerical simulation of two coupled Navier-Stokes flows, using ope-rator-split-ting and optimization-based non-overlapping domain decomposition methods. The model problem consists of two Navier-Stokes fluids coupled, through a common interface, by a nonlinear transmission condition. Numerical experiments are carried out with two coupled fluids; one with an initial linear profile and the other in rest. As expected, the transmission condition generates a recirculation within the fluid in rest.
4
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Analysis of some dual properties in discrete dynamic systems

88%
Zhirabok A.
International Journal of Applied Mathematics and Computer Science
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2006
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tom 16
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nr 3
297-308
EN
The problem of duality in nonlinear and linear systems is considered. In addition to the known duality between controllability and observability, new dual notions and their properties are investigated. A way to refine these properties through an isomorphic transformation of the original systems is suggested.
5
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The Orthogonal Projection and the Riesz Representation Theorem

88%
Narita K., Endou N., Shidama Y.
Formalized Mathematics
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2015
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tom 23
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nr 3
243-252
EN
In this article, the orthogonal projection and the Riesz representation theorem are mainly formalized. In the first section, we defined the norm of elements on real Hilbert spaces, and defined Mizar functor RUSp2RNSp, real normed spaces as real Hilbert spaces. By this definition, we regarded sequences of real Hilbert spaces as sequences of real normed spaces, and proved some properties of real Hilbert spaces. Furthermore, we defined the continuity and the Lipschitz the continuity of functionals on real Hilbert spaces. Referring to the article [15], we also defined some definitions on real Hilbert spaces and proved some theorems for defining dual spaces of real Hilbert spaces. As to the properties of all definitions, we proved that they are equivalent properties of functionals on real normed spaces. In Sec. 2, by the definitions [11], we showed properties of the orthogonal complement. Then we proved theorems on the orthogonal decomposition of elements of real Hilbert spaces. They are the last two theorems of existence and uniqueness. In the third and final section, we defined the kernel of linear functionals on real Hilbert spaces. By the last three theorems, we showed the Riesz representation theorem, existence, uniqueness, and the property of the norm of bounded linear functionals on real Hilbert spaces. We referred to [36], [9], [24] and [3] in the formalization.
6
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(k,l)-kernels, (k,l)-semikernels, k-Grundy functions and duality for state splittings

88%
Galeana-Sánchez H., Gómez R.
Discussiones Mathematicae Graph Theory
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2007
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tom 27
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nr 2
359-371
EN
Line digraphs can be obtained by sequences of state splittings, a particular kind of operation widely used in symbolic dynamics [12]. Properties of line digraphs inherited from the source have been studied, for instance in [7] Harminc showed that the cardinalities of the sets of kernels and solutions (kernel's dual definition) of a digraph and its line digraph coincide. We extend this for (k,l)-kernels in the context of state splittings and also look at (k,l)-semikernels, k-Grundy functions and their duals.
7
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Useful Four-Valued Extension of the Temporal Logic KtT4

75%
Degauquier V.
Bulletin of the Section of Logic
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2018
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tom 47
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nr 1
EN
The temporal logic KtT4 is the modal logic obtained from the minimal temporal logic Kt by requiring the accessibility relation to be reflexive (which corresponds to the axiom T) and transitive (which corresponds to the axiom 4). This article aims, firstly, at providing both a model-theoretic and a proof-theoretic characterisation of a four-valued extension of the temporal logic KtT4 and, secondly, at identifying some of the most useful properties of this extension in the context of partial and paraconsistent logics.
8
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Duality for some free modes

75%
Pszczoła K., Romanowska A., Smith J.
Discussiones Mathematicae - General Algebra and Applications
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2003
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tom 23
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nr 1
45-61
EN
The paper establishes a duality between a category of free subreducts of affine spaces and a corresponding category of generalized hypercubes with constants. This duality yields many others, in particular a duality between the category of (finitely generated) free barycentric algebras (simplices of real affine spaces) and a corresponding category of hypercubes with constants.
9
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On Compact Sets of Compact Operators on Banach Spaces not Containing a Copy of l^1

75%
Akkouchi M., Université Cadi Ayyad F. d. S.-S., akkouchimo@yahoo.fr
Acta Universitatis Lodziensis. Folia Mathematica
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2010
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tom vol. 17
EN
F. Galaz-Fontes (Proc. AMS., 1998) has established a criterion for a subset of the space of compact linear operators from a reflexive and separable space X into a Banach space Y to be compact. F. Mayoral (Proc. AMS., 2000) has extended this criterion to the case of Banach spaces not containing a copy of l^1 . The purpose of this note is to give a new proof of the result of F. Mayoral. In our proof, we use l^∞ -spaces, a well known result of H. P. Rosenthal and L.E. Dor which characterizes the spaces without a copy of l^1 and a recent result obtained by G. Nagy in 2007 concerining compact sets in normed spaces. We point out that another proof of Mayoral’s result was given by E. Serrano, C. Pineiro and J.M. Delgado (Proc. AMS., 2006) by using a different method.
10

Numerical methods for linear minimax estimation

63%
Gaffke N., Heiligers B.
Discussiones Mathematicae Probability and Statistics
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2000
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tom 20
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nr 1
51-62
EN
We discuss two numerical approaches to linear minimax estimation in linear models under ellipsoidal parameter restrictions. The first attacks the problem directly, by minimizing the maximum risk among the estimators. The second method is based on the duality between minimax and Bayes estimation, and aims at finding a least favorable prior distribution.
11
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Representation of Hilbert algebras and implicative semilattices

63%
Celani S.
Open Mathematics
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2003
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tom 1
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nr 4
561-572
EN
In this paper we shall give a topological representation for Hilbert algebras that extend the topological representation given by A. Diego in [4]. For implicative semilattices this representation gives a full duality. We shall also consider the representation for Boolean ring.
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