Temat: spectral problem - Prolib Integro

Skocz do pozycji: 1.

Tytuł:: Direct and inverse spectral problems for Dirac systems with nonlocal potentials
Autorzy:: Dębowska, Kamila
Nizhnik, Leonid P.
Tematy:: inverse spectral problem
nonlocal potential
nonlocal boundary conditions
Dirac system; Pokaż więcej
Data publikacji:: 2019
Powiązania:: https://bibliotekanauki.pl/articles/255043.pdf Link otwiera się w nowym oknie
Źródło:: Opuscula Mathematica; 2019, 39, 5; 645-673
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Opis:: The main purposes of this paper are to study the direct and inverse spectral problems of the one-dimensional Dirac operators with nonlocal potentials. Based on information about the spectrum of the operator, we find the potential and recover the form of the Dirac system. The methods used allow us to reduce the situation to the one-dimensional case. In accordance with the given assumptions and conditions we consider problems in a specific way. We describe the spectrum, the resolvent, the characteristic function etc. Illustrative examples are also given.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Shape sensitivity analysis of eigenvalues revisited
Autorzy:: Nazarov, S. A.
Sokolowski, J.
Tematy:: spectral problem
singular perturbation
eigenvalues of Laplacian
shape sensitivity analysis
topology optimization; Pokaż więcej
Data publikacji:: 2008
Powiązania:: https://bibliotekanauki.pl/articles/970311.pdf Link otwiera się w nowym oknie
Źródło:: Control and Cybernetics; 2008, 37, 4; 999-1012
0324-8569
Pojawia się w:: Control and Cybernetics
Opis:: The paper can be considered as a complement to previous papers of the authors. An insight into applied asymptotic analysis of boundary value problems in singularly perturbed domains is presented. As a result, the asymptotic expansions of eigenvalues are obtained and discussed in terms of integral attributes of the geometrical perturbations including the virtual mass tensor, polarization tensor etc. The results are presented in such a way that can be easily employed in numerical methods for shape optimization and inverse problems.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: The Delsarte-Darboux type binary transformations, their differential-geometric and operator structure with applications. Part. 1
Autorzy:: Prykarpatsky, Y.A.
Samoilenko, A.M.
Tematy:: Delsarte transmutation operators
parametric functional spaces
Darboux transformations
inverse spectral transform problem
soliton equations
Zakharov-Shabat equations; Pokaż więcej
Data publikacji:: 2006
Powiązania:: https://bibliotekanauki.pl/articles/254961.pdf Link otwiera się w nowym oknie
Źródło:: Opuscula Mathematica; 2006, 26, 1; 137-150
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Opis:: The structure properties of multidimensional Delsarte-Darboux transmutation operators in parametric functional spaces are studied by means of differential-geometric and topological tools. It is shown that kernels of the corresponding integral operator expressions depend on the topological structure of related homological cycles in the coordinate space. As a natural realization of the construction presented we build pairs of Lax type commutative differential operator expressions related via a Delsarte-Darboux transformation and having a lot of applications in soliton theory.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: The general differential-geometric structure of multidimensional Delsarte transmutation operators in parametric functional spaces and their applications in soliton theory. Pt. 2
Autorzy:: Golenia, J.
Prykarpatsky, Y.A.
Samoilenko, A.M.
Prykarpatsky, A.K.
Tematy:: Delsarte transmutation operators
parametric functional spaces
Darboux transformations
inverse spectral transform problem
soliton equations
Zakharov-Shabat equations
polynomial operator pencils; Pokaż więcej
Data publikacji:: 2004
Powiązania:: https://bibliotekanauki.pl/articles/2050173.pdf Link otwiera się w nowym oknie
Źródło:: Opuscula Mathematica; 2004, 24, 1; 71-83
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Opis:: The structure properties of multidimensional Delsarte transmutation operators in parametric functional spaces are studied by means of differential-geometric tools. It is shown that kernels of the corresponding integral operator expressions depend on the topological structure of related homological cycles in the coordinate space. As a natural realization of the construction presented we build pairs of Lax type commutive differential operator expressions related via a Darboux-Backlund transformation having a lot of applications in soliton theory. Some results are also sketched concerning theory of Delsarte transmutation operators for affine polynomial pencils of multidimensional differential operators.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 5.

Tytuł:: A numerical approach to predict the rotating stall in the vaneless diffuser of a centrifugal compressor using the eigenvalue method
Autorzy:: Hu, C.
Liu, P.
Zhu, X.
Chen, H.
Du, Z.
Tematy:: instability
vaneless diffuser
eigenvalue problem
spectral method; Pokaż więcej
Data publikacji:: 2017
Powiązania:: https://bibliotekanauki.pl/articles/281006.pdf Link otwiera się w nowym oknie
Źródło:: Journal of Theoretical and Applied Mechanics; 2017, 55, 2; 635-647
1429-2955
Pojawia się w:: Journal of Theoretical and Applied Mechanics
Opis:: A two-dimensional incompressible flow model is presented to study the occurrence of rotating stall in vaneless diffusers of centrifugal compressors. The diffuser considered has two parallel walls, and the undisturbed flow is assumed to be circumferentially uniform, isentropic, and to have no axial velocity. The linearized 2D Euler equations for an incompressible flow in a fixed frame of the coordinate system are considered. After discretization by a spectral collocation method based on Chebyshev-Gauss-Lobatto points, the generalized eigenvalue problem is solved through the QZ algorithm. The compressor stability is judged by the imaginary part of the eigenvalue obtained. Based on the 2D stability analysis, the influence of inflow angle, radius ratio and wave number are studied. The results from the present stability analysis are compared with some experimental measurement and Shen’s model. It is showed that diffuser instability increases rapidly and the stall rotational speed decreases quickly with an increase in the diffuser radius ratio. The largest critical inflow angle can be obtained when the wave number is around 3 ∼ 5 for the radius ratio between 1.5 to 2.2. It is also verified that the stability model proposed in this paper agrees well with experimental data and has the capability to predict the onset of rotating stall, especially for wide diffusers.
Dostawca treści:: Biblioteka Nauki

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na półce

Skocz do pozycji: 6.

Tytuł:: The motion planning problem and exponential stabilization of a heavy chain. Part II
Autorzy:: Grabowski, P.
Tematy:: infinite-dimensional control systems
semigroups
motion planning problem
exponential stabilization
spectral methods
Riesz bases
exact observability; Pokaż więcej
Data publikacji:: 2008
Powiązania:: https://bibliotekanauki.pl/articles/255394.pdf Link otwiera się w nowym oknie
Źródło:: Opuscula Mathematica; 2008, 28, 4; 481-505
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Opis:: This is the second part of paper [8], where a model of a heavy chain system with a punctual load (tip mass) in the form of a system of partial differential equations was interpreted as an abstract semigroup system and then analysed on a Hilbert state space. In particular, in [8] we have formulated the problem of exponential stabilizability of a heavy chain in a given position. It was also shown that the exponential stability can be achieved by applying a stabilizer of the colocated-type. The proof used the method of Lyapunov functionals. In the present paper, we give other two proofs of the exponential stability, which provides an additional intrinsic insight into the exponential stabilizability mechanism. The first proof makes use of some spectral properties of the system. In the second proof, we employ some relationships between exponential stability and exact observability.
Dostawca treści:: Biblioteka Nauki

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na półce

Skocz do pozycji: 7.

Tytuł:: On the central limit theorem for some birth and death processes
Autorzy:: Chojecki, Tymoteusz
Tematy:: Central limit theorem
Markov chain
Lamperti’s problem
birth and death processes
Kipnis-Varadhan theory
spectral gap; Pokaż więcej
Data publikacji:: 2011
Powiązania:: https://bibliotekanauki.pl/articles/747125.pdf Link otwiera się w nowym oknie
Źródło:: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2011, 65, 1
0365-1029
2083-7402
Pojawia się w:: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
Opis:: Suppose that \(\{Xn: n \geq 0\}\) is a stationary Markov chain and \(V\) is a certain function on a phase space of the chain, called an observable. We say that the observable satisfies the central limit theorem (CLT) if \(Y_n :=N^{-1/2}\sum_{n=0}^N V (X_n)\) converge in law to a normal random variable, as \(N \to+\infty\). For a stationary Markov chain with the \(L^2\) spectral gap the theorem holds for all \(V\) such that \(V (X_0)\) is centered and square integrable, see Gordin [7]. The purpose of this article is to characterize a family of observables \(V\) for which the CLT holds for a class of birth and death chains whose dynamics has no spectral gap, so that Gordin’s result cannot be used and the result follows from an application of Kipnis-Varadhan theory.
Dostawca treści:: Biblioteka Nauki

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