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Tytuł:
Oscillation criteria for second order self-adjoint matrix differential equations
Autorzy:
Parhi, N.
Praharaj, P.
Powiązania:
https://bibliotekanauki.pl/articles/1293939.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
matrix differential equations
self-adjoint
oscillation
Opis:
Some results concerning oscillation of second order self-adjoint matrix differential equations are obtained. These may be regarded as a generalization of results for the corresponding scalar equations.
Źródło:
Annales Polonici Mathematici; 1999, 72, 1; 1-14
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Shape derivatives for general objective functions and the incompressible Navier-Stokes equations
Autorzy:
Schmidt, S.
Schulz, V.
Powiązania:
https://bibliotekanauki.pl/articles/969869.pdf
Data publikacji:
2010
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
shape optimization
shape derivative
Navier-Stokes
adjoint calculus
Opis:
The aim of this paper is to present the shape derivative for a wide array of objective functions using the incompressible Navier-Stokes equations as a state constraint. Most real world applications of computational fluid dynamics are shape optimization problems in nature, yet special shape optimization techniques are seldom used outside the field of elliptic partial differential equations and linear elasticity. This article tries to be self contained, also presenting many useful results from the literature. We conclude with a comparison of different objective functions for the shape optimization of an obstacle in a channel, which can be done quite conveniently when one knows the general form of the shape gradient.
Źródło:
Control and Cybernetics; 2010, 39, 3; 677-713
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Necessary optimality conditions for predator-prey system with a hunter population
Autorzy:
Apreutesei, N. C.
Powiązania:
https://bibliotekanauki.pl/articles/952826.pdf
Data publikacji:
2010
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
predator-prey system
optimal control
adjoint system
Opis:
An optimal control problem is studied for a predator-prey reaction-diffusion system. A hunter population is introduced in the ecosystem and it is interpreted as a control variable. One finds necessary optimality conditions in order that, in the end of a given time interval, the total density of the two populations is maximal.
Źródło:
Opuscula Mathematica; 2010, 30, 4; 389-397
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Adjointness between theories and strict theories
Autorzy:
Vogel, Hans-Jürgen
Powiązania:
https://bibliotekanauki.pl/articles/728926.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
symmetric monoidal category
dhts-category
partial theory
adjoint functor
Opis:
The categorical concept of a theory for algebras of a given type was foundet by Lawvere in 1963 (see [8]). Hoehnke extended this concept to partial heterogenous algebras in 1976 (see [5]). A partial theory is a dhts-category such that the object class forms a free algebra of type (2,0,0) freely generated by a nonempty set J in the variety determined by the identities ox ≈ o and xo ≈ o, where o and i are the elements selected by the 0-ary operation symbols.
If the object class of a dhts-category forms even a monoid with unit element I and zero element O, then one has a strict partial theory.
In this paper is shown that every J-sorted partial theory corresponds in a natural manner to a J-sorted strict partial theory via a strongly d-monoidal functor. Moreover, there is a pair of adjoint functors between the category of all J-sorted theories and the category of all corresponding J-sorted strict theories.
This investigation needs an axiomatic characterization of the fundamental properties of the category Par of all partial function between arbitrary sets and this characterization leads to the concept of dhts- and dhth∇s-categories, respectively (see [5], [11], [13]).
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2003, 23, 2; 163-212
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analysis of wing-engine nacelle aerodynamic interference
Autorzy:
Zalewski, W.
Stalewski, W.
Powiązania:
https://bibliotekanauki.pl/articles/243801.pdf
Data publikacji:
2017
Wydawca:
Instytut Techniczny Wojsk Lotniczych
Tematy:
air transport
nacelle-wing integration
flow separation
adjoint solver
parametric design
Opis:
The article presents an analysis of the wing-engine nacelle flow interference phenomenon on the example of a light twin-engine commuter aircraft. The problems of propulsion system integration with the wing in airplanes are now frequently the subject of advanced optimization research performed by aircraft manufacturers. The shape of the engine nacelle and its connection with the wing determines the quality of the flow around the wing in that area. This is important for high-lift devices placed at the wing trailing edge behind engine nacelle used during the take-off and landing process. Additionally the flow is effected by the disturbances generated by working propellers, the presence of air inlets and an exhaust system of the engine. The article presents a process of numerical optimization of an engine nacelle rear part shape. The main goal of the process was to eliminate the flow disturbances caused by the engine nacelle-wing interference phenomenon. During analysis, the Adjoint Solver method was used to designate nacelle body areas where modification should have the most important impact on the flow quality. The results obtained from adjoint solver were used in the process of finding the optimum shape of the rear part of the nacelle using a parametric geometry generator powered by Ansys Design Modeler and PARADES software. Comparative computational analysis for selected geometries of the engine nacelle was performed using commercial Ansys Fluent solver. Ansys Fluent is an advanced computational solver based on the finite volume method for solving the Navier-Stokes flow equations. Several dozen of geometric shapes were analysed in the optimization process of the nacelle rear part. The final result was the shape of the engine nacelle with correct flow without separation and vortex structures. The article presents results of calculations and visualization of the flow pattern for analysed cases.
Źródło:
Journal of KONES; 2017, 24, 3; 339-344
1231-4005
2354-0133
Pojawia się w:
Journal of KONES
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Approximation of eigenvalues of some unbounded self-adjoint discrete Jacobi matrices by eigenvaules of finite submatrices
Autorzy:
Malejki, M.
Powiązania:
https://bibliotekanauki.pl/articles/255561.pdf
Data publikacji:
2007
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
self-adjoint unbounded Jacobi matrix
asymptotics
point spectrum
tridiagonal matrix
eigenvalue
Opis:
We investigate the problem of approximation of eigenvalues of some self-adjoint operator in the Hilbert space l2(N) by eigenvalues of suitably chosen principal finite submatrices of an infinite Jacobi matrix that defines the operator considered. We assume the Jacobi operator is bounded from below with compact resolvent. In our research we estimate the asymptotics (with n → ∞) of the joint error of approximation for the first n eigenvalues and eigenvectors of the operator by the eigenvalues and eigenvectors of the finite submatrix of order n x n. The method applied in our research is based on the Rayleigh-Ritz method and Volkmer's results included in [7]. We extend the method to cover a class of infinite symmetric Jacobi matrices with three diagonals satisfying some polynomial growth estimates.
Źródło:
Opuscula Mathematica; 2007, 27, 1; 37-49
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Il ne faut pas se laisser tromper par la langue : entre syntaxe et sémantique
Don’t Be Fooled by the Language: Between Syntax and Semantics
Autorzy:
Śmigielska, Beata
Powiązania:
https://bibliotekanauki.pl/articles/31341237.pdf
Data publikacji:
2022
Wydawca:
Wydawnictwo Uniwersytetu Śląskiego
Tematy:
Semantic grammar
predicate
argument
adjoint
modifier
valence
semantic implication
paraphrase
contradiction
Opis:
In this article, Beata Śmigielska describes the questions used to determine the number and nature of arguments of predicates within the framework of Stanisław Karolak’s semantics-based grammar. Since syntactic structures do not directly reflect the semantic structures of predicates, the distinction between arguments and adjunct elements (modifiers) often becomes problematic. This fact is related to the lack of a single methodology by which this can be done in a simple and unambiguous way, resulting in different results of analyses of the same predicates. To solve this problem, it is necessary clearly to define the theory within which we work, because it is the adopted perspective and its well-defined principles that will decide both the path of thought during the research and its results. In her analyses of the selected predicates, Śmigielska defines the tools that can be used in predicate description such as the semantic decomposition of predicates into simpler elements, supplemented, where necessary, by contradiction tests and paraphrasing.
Źródło:
Neophilologica; 2022, 34; 1-19
0208-5550
2353-088X
Pojawia się w:
Neophilologica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Spontaneous decay of level from spectral theory point of view
Autorzy:
Ianovich, Eduard
Powiązania:
https://bibliotekanauki.pl/articles/2048989.pdf
Data publikacji:
2021
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
spectral theory
quantum field theory
self-adjoint operators
absolutely continuous spectrum
spontaneous decay
Opis:
In quantum field theory it is believed that the spontaneous decay of excited atomic or molecular level is due to the interaction with continuum of field modes. Besides, the atom makes a transition from upper level to lower one so that the probability to find the atom in the excited state tends to zero. In this paper it will be shown that the mathematical model in single-photon approximation may predict another behavior of this probability generally. Namely, the probability to find the atom in the excited state may tend to a nonzero constant so that the atom is not in the pure state finally. This effect is due to that the spectrum of the complete Hamiltonian is not purely absolutely continuous and has a discrete level outside the continuous part. Namely, we state that in the corresponding invariant subspace, determining the time evolution, the spectrum of the complete Hamiltonian when the field is considered in three dimensions may be not purely absolutely continuous and may have an eigenvalue. The appearance of eigenvalue has a threshold character. If the field is considered in two dimensions the spectrum always has an eigenvalue and the decay is absent.
Źródło:
Opuscula Mathematica; 2021, 41, 6; 849-859
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Asymptotic expansion of large eigenvalues for a class of unbounded Jacobi matrices
Autorzy:
Harrat, Ayoub
Zerouali, El Hassan
Zielinski, Lech
Powiązania:
https://bibliotekanauki.pl/articles/255073.pdf
Data publikacji:
2020
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
tridiagonal matrix
band matrix
unbounded self-adjoint operator discrete spectrum
large eigenvalues
asymptotics
Opis:
We investigate a class of infinite tridiagonal matrices which define unbounded self-adjoint operators with discrete spectrum. Our purpose is to establish the asymptotic expansion of large eigenvalues and to compute two correction terms explicitly.
Źródło:
Opuscula Mathematica; 2020, 40, 2; 241-270
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On roots of the automorphism group of a circular domain in $ℂ^n$
Autorzy:
Myszewski, Jan
Powiązania:
https://bibliotekanauki.pl/articles/1312644.pdf
Data publikacji:
1991
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
circular domain
automorphism group
maximal torus
Lie algebra
adjoint representation
root
root subspace
Opis:
We study the properties of the group Aut(D) of all biholomorphic transformations of a bounded circular domain D in $ℂ^n$ containing the origin. We characterize the set of all possible roots for the Lie algebra of Aut(D). There exists an n-element set P such that any root is of the form α or -α or α-β for suitable α,β ∈ P.
Źródło:
Annales Polonici Mathematici; 1991, 55, 1; 269-276
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An inverse backward problem for degenerate two-dimensional parabolic equation
Autorzy:
Atifi, Khalid
Essoufi, El-Hassan
Khouiti, Bouchra
Powiązania:
https://bibliotekanauki.pl/articles/255085.pdf
Data publikacji:
2020
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
data assimilation
adjoint method
regularization
heat equation
inverse problem
degenerate equations
optimization
Opis:
This paper deals with the determination of an initial condition in the degenerate two-dimensional parabolic equation [formula], where Ω is an open, bounded subset of R2, a [formula] with a ≥0 everywhere, and [formula], with initial and boundary conditions [formula] from final observations. This inverse problem is formulated as a minimization problem using the output least squares approach with the Tikhonov regularization. To show the convergence of the descent method, we prove the Lipschitz continuity of the gradient of the Tikhonov functional. Also we present some numerical experiments to show the performance and stability of the proposed approach.
Źródło:
Opuscula Mathematica; 2020, 40, 4; 427-449
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the numerical discretization of optimal control problems for conservation laws
Autorzy:
Schäfer Aguilar, Paloma
Schmitt, Johann Michael
Ulbrich, Stefan
Moos, Michael
Powiązania:
https://bibliotekanauki.pl/articles/1839148.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
conservation laws
adjoint state
linear transport equation
discontinuous coefficients
finite difference schemes
Opis:
We analyze the convergence of discretization schemes for the adjoint equation arising in the adjoint-based derivative computation for optimal control problems governed by entropy solutions of conservation laws. The difficulties arise from the fact that the correct adjoint state is the reversible solution of a transport equation with discontinuous coefficient and discontinuous end data. We derive the discrete adjoint scheme for monotone difference schemes in conservation form. It is known that convergence of the discrete adjoint can only be expected if the numerical scheme has viscosity of order O(h) with appropriate 0 < α < 1, which leads to quite viscous shock profiles. We show that by a slight modification of the end data of the discrete adjoint scheme, convergence to the correct reversible solution can be obtained also for numerical schemes with viscosity of order O(h) and with sharp shock resolution. The theoretical findings are confirmed by numerical results.
Źródło:
Control and Cybernetics; 2019, 48, 2; 345-376
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Gauss sum for the adjoint representation of $GL_{n}(q)$ and $SL_{n}(q)$
Autorzy:
Jeong, Yeon-Kwan
Lee, In-Sok
Oh, Hyekyoung
Park, Kyung-Hwan
Powiązania:
https://bibliotekanauki.pl/articles/1206803.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
adjoint representation
$GL_{n}(q)$
$SL_{n}(q)$
Gauss sum
$PGL_{n}(q)$
Źródło:
Acta Arithmetica; 2000, 95, 1; 1-16
0065-1036
Pojawia się w:
Acta Arithmetica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On one condition of absolutely continuous spectrum for self-adjoint operators and its applications
Autorzy:
Ianovich, E.
Powiązania:
https://bibliotekanauki.pl/articles/254841.pdf
Data publikacji:
2018
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
self-adjoint operators absolutely continuous spectrum
equi-absolute continuity
spectral density
Jacobi matrices
Opis:
In this work the method of analyzing of the absolutely continuous spectrum for self-adjoint operators is considered. For the analysis it is used an approximation of a self-adjoint operator A by a sequence of operators An with absolutely continuous spectrum on a given interval [a, b] which converges to A in a strong sense on a dense set. The notion of equi-absolute continuity is also used. It was found a sufficient condition of absolute continuity of the operator A spectrum on the finite interval [a, b] and the condition for that the corresponding spectral density belongs to the class Lp[a,b] (p ≥ 1). The application of this method to Jacobi matrices is considered. As one of the results we obtain the following assertion: Under some mild assumptions, suppose that there exist a constant C > 0 and a positive function g(x) ∈ Lp[a, b] (p ≥ 1).such that for all n sufficiently large and almost all [formula] the estimate [formula] holds, where Pn(x) are 1st type polynomials associated with Jacobi matrix (in the sense of Akhiezer) and bn is a second diagonal sequence of Jacobi matrix. Then the spectrum of Jacobi matrix operator is purely absolutely continuous on [a, b] and for the corresponding spectral density ƒ (x) we have ƒ (x) ∈ Lp[a,b].
Źródło:
Opuscula Mathematica; 2018, 38, 5; 699-718
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Towards theory of C-symmetries
Autorzy:
Kuzhel, S.
Sudilovskaya, V.
Powiązania:
https://bibliotekanauki.pl/articles/255003.pdf
Data publikacji:
2017
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Krein space
J-self-adjoint operator
J-symmetric operator
Friedrichs extension
C-symmetry
Opis:
The concept of C-symmetry originally appeared in PT-symmetric quantum mechanics is studied within the Krein spaces framework.
Źródło:
Opuscula Mathematica; 2017, 37, 1; 65-80
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 29

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