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Tytuł:
Pseudo-phase mapping of speckle fields using 2D Hilbert transformation
Autorzy:
Zenkova, C. Y.
Gorsky, M. P.
Ryabiy, P. A.
Powiązania:
https://bibliotekanauki.pl/articles/174971.pdf
Data publikacji:
2016
Wydawca:
Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Tematy:
speckle field
singular points
saddle points
phase problem
Opis:
The use of a "window" 2D Hilbert transform for the reconstruction of the phase distribution of the intensity of a speckle field is proposed. It is shown that the advantage of this approach consists in the invariance of a phase map to a change of the position of the kernel of transformation and in the possibility to reconstruct the structure-forming elements of the skeleton of an optical field, including singular points and saddle points. We demonstrate the possibility to reconstruct the equi-phase lines within a narrow confidence interval, and introduce an additional algorithm for solving the phase problem for random 2D intensity distributions.
Źródło:
Optica Applicata; 2016, 46, 1; 153-162
0078-5466
1899-7015
Pojawia się w:
Optica Applicata
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A note on minimax rates of convergence in the Spektor-Lord-Willis problem
Autorzy:
Szkutnik, Z.
Powiązania:
https://bibliotekanauki.pl/articles/254773.pdf
Data publikacji:
2010
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
poisson inverse problem
rate minimaxity
singular value decomposition
stereology
Opis:
In this note, attainable lower bounds are constructed for the convergence rates in a stereological problem of unfolding spheres size distribution from linear sections, which shows that a spectral type estimator is strictly rate minimax over some Sobolev-type classes of functions.
Źródło:
Opuscula Mathematica; 2010, 30, 2; 203-207
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Unfolding spheres size distribution from linear sections with B-splines and EMDS algorithm
Autorzy:
Szkutnik, Z.
Powiązania:
https://bibliotekanauki.pl/articles/255515.pdf
Data publikacji:
2007
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
inverse problem
singular value expansion
stereology
discretization
quasi-maximum likelihood estimator
Opis:
The stereological problem of unfolding spheres size distribution from linear sections is formulated as a problem of inverse estimation of a Poisson process intensity function. A singular value expansion of the corresponding integral operator is given. The theory of recently proposed B-spline sieved quasi-maximum likelihood estimators is modified to make it applicable to the current problem. Strong L2-consistency is proved and convergence rates are given. The estimators are implemented with the recently proposed EMDS algorithm. Promising performance of this new methodology in finite samples is illustrated with a numerical example. Data grouping effects are also discussed.
Źródło:
Opuscula Mathematica; 2007, 27, 1; 151-165
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Third order singularly perturbed delay differential equation of reaction diffusion type with integral boundary condition
Autorzy:
Sekar, Elango
Tamilselvan, Ayyadurai
Powiązania:
https://bibliotekanauki.pl/articles/122568.pdf
Data publikacji:
2019
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
singular perturbation problem
finite difference scheme
delay
integral boundary condition
error estimate
schemat różnic skończonych
opóźnienie
oszacowanie błędu
metoda numeryczna
metoda równań skończonych
Opis:
A class of third order singularly perturbed delay differential equations of reaction diffusion type with an integral boundary condition is considered. A numerical method based on a finite difference scheme on a Shishkin mesh is presented. The method suggested is of almost first order convergent. An error estimate is derived in the discrete norm. Numerical examples are presented, which validate the theoretical estimates.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 2; 99-110
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solution of the boundary value problem of heat conduction in a cone
Autorzy:
Ramazanov, Murat
Jenaliyev, Muvasharkhan
Gulmanov, Nurtay
Powiązania:
https://bibliotekanauki.pl/articles/2048719.pdf
Data publikacji:
2022
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
non-cylindrical domain
cone
boundary value problem of heat conduction
singular Volterra integral equation
Carleman–Vekua regularization method
Opis:
In the paper we consider the boundary value problem of heat conduction in a non-cylindrical domain, which is an inverted cone, i.e. in the domain degenerating into a point at the initial moment of time. In this case, the boundary conditions contain a derivative with respect to the time variable; in practice, problems of this kind arise in the presence of the condition of the concentrated heat capacity. We prove a theorem on the solvability of a boundary value problem in weighted spaces of essentially bounded functions. The issues of solvability of the singular Volterra integral equation of the second kind, to which the original problem is reduced, are studied. We use the Carleman–Vekua method of equivalent regularization to solve the obtained singular Volterra integral equation.
Źródło:
Opuscula Mathematica; 2022, 42, 1; 75-91
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
P-order necessary and sufficient conditions for optimality in singular calculus of variations
Autorzy:
Prusińska, Agnieszka
Tret'yakov, Alexey
Powiązania:
https://bibliotekanauki.pl/articles/729251.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
singular variational problem
necessary condition of optimality
p-regularity
p-factor operator
Opis:
This paper is devoted to singular calculus of variations problems with constraint functional not regular at the solution point in the sense that the first derivative is not surjective. In the first part of the paper we pursue an approach based on the constructions of the p-regularity theory. For p-regular calculus of variations problem we formulate and prove necessary and sufficient conditions for optimality in singular case and illustrate our results by classical example of calculus of variations problem.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2010, 30, 2; 269-279
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An intial-value technique for self-adjoint singularly perturbed two-point boundary value problems
Autorzy:
Padmaja, P.
Aparna, P.
Gorla, R. S. R.
Powiązania:
https://bibliotekanauki.pl/articles/264933.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
wartość początkowa
wartość brzegowa
perturbacja procesu
initial value technique
boundary value problem
singular perturbation problem
Opis:
In this paper, we present an initial value technique for solving self-adjoint singularly perturbed linearvboundary value problems. The original problem is reduced to its normal form and the reduced problem is converted to first order initial value problems. This replacement is significant from the computational point of view. The classical fourth order Runge-Kutta method is used to solve these initial value problems. This approach to solve singularly perturbed boundary-value problems is numerically very appealing. To demonstrate the applicability of this method, we have applied it on several linear examples with left-end boundary layer and rightend layer. From the numerical results, the method seems accurate and solutions to problems with extremely thin boundary layers are obtained.
Źródło:
International Journal of Applied Mechanics and Engineering; 2020, 25, 1; 106-126
1734-4492
2353-9003
Pojawia się w:
International Journal of Applied Mechanics and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On singular arcs in nonsmooth optimal control
Autorzy:
Oberle, H. J.
Rosendahl, R.
Powiązania:
https://bibliotekanauki.pl/articles/969559.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
nonsmooth optimal control problems
necessary conditions
singular state subarcs
Zermelo's problem
Opis:
In this paper we consider general optimal control problems (OCP) which are characterized by a nonsmooth ordinary state differential equation. However, we allow only mild types of nonsmoothness. More precisely, we assume that the right-hand side of the state equation is piecewise smooth and that the switching points, which separate these pieces, are determined as points, where a state-and possibly control-dependent (smooth) switching function changes sign. For this kind of optimal control problems necessary optimality conditions are developed. Attention is paid to the situation when the switching function vanishes identically along a nontrivial subarc. Such subarcs, which we call singular state subarcs, are investigated with respect to necessary conditions and to junction conditions. In extension to earlier results of the authors, Oberle and Rosendhal (2006), in this paper nonsmooth OCPs are considered with respect to the order of the switching function. Especially, the case of a zero-order switching function is included and examples of order zero, one and two are treated.
Źródło:
Control and Cybernetics; 2008, 37, 2; 429-450
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Shape sensitivity analysis of eigenvalues revisited
Autorzy:
Nazarov, S. A.
Sokolowski, J.
Powiązania:
https://bibliotekanauki.pl/articles/970311.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
spectral problem
singular perturbation
eigenvalues of Laplacian
shape sensitivity analysis
topology optimization
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.
Źródło:
Control and Cybernetics; 2008, 37, 4; 999-1012
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Interaction between a stratified elastic half-space and an irregular base allowing for the intercontact gas
Oddziaływanie sprężystej półprzestrzeni warstwowej na sztywną przeszkodę oddzielona szczeliną wypełnioną gazem
Autorzy:
Machyshyn, I.
Nagórko, W.
Powiązania:
https://bibliotekanauki.pl/articles/280251.pdf
Data publikacji:
2003
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
contact problem
laminated half-space
gas
complex potentials
singular integral equations
Opis:
The paper is devoted to the investigation of contact interaction of a laminated half-space and a rigid body with a smooth cylindrical depression under conditions of plane deformation allowing for an intercontact ideal gas. To describe the homogenized model of the laminated body with microlocal parameters and to describe the behavior of the gas - equations of ideal gas state are used. Applying the method of comlex potentials the problem is reduced to the singular integral equation for the height of intercontact gap and its solution is obtained in a closed form. To find the lenght of the gap, its volume and the gas pressure a system of three equations is derived. With the aid of this system the dependence of the external loading and amount of the gas in the gap on the contact pressure and geometrical parameters of the gap is analyzed.
W pracy analizuje się oddziaływanie sprężystej półprzestrzeni warstwowo-niejednorodnej na ciało sztywne z walcową szczeliną wypełnioną gazem. Półprzestrzeń sprężystą poddaje się homogenizacji mikrolokalnej, a do rozwiązania otrzymanych równań modelowych stosuje się metodę potencjałów zespolonych. Analizowany problem sprowadza się do poszukiwania rozwiązania równania całkowego. W pracy uzyskuje się rozwiązania w postaci zamkniętej oraz przeprowadza analizę numeryczną zależności rozwartości szczeliny oraz jej objętości od obciążenia zewnętrznego.
Źródło:
Journal of Theoretical and Applied Mechanics; 2003, 41, 2; 271-288
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Positive solutions of a singular fractional boundary value problem with a fractional boundary condition
Autorzy:
Lyons, J. W.
Neugebauer, J. T.
Powiązania:
https://bibliotekanauki.pl/articles/255965.pdf
Data publikacji:
2017
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
fractional differential equation
singular problem
fixed point
Opis:
For α ∈ (1,2] the singular fractional boundary value problem [formula] satisfying the boundary conditions [formula] where β ∈ (0,α - 1], μ ∈ (0,α - 1], and [formula] are Riemann-Liouville derivatives of order α, β, and μ respectively, is considered. Here ƒ satisfies a local Carathéodory condition, and ƒ (t, x, y) may be singular at the value 0 in its space variable x. Using regularization and sequential techniques and Krasnosel’skii’s fixed point theorem, it is shown this boundary value problem has a positive solution. An example is given.
Źródło:
Opuscula Mathematica; 2017, 37, 3; 421-434
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Bolza optimal synthesis problem for singular estimate control systems
Autorzy:
Lasiecka, I.
Tuffaha, A.
Powiązania:
https://bibliotekanauki.pl/articles/970760.pdf
Data publikacji:
2009
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
Bolza problem
Riccati equation
singular estimate control systems
fluid-structure interaction
Opis:
Bolza problem governed by PDE control systems with unbounded controls is considered. The motivating example is fluid structure interaction model with boundary-interface controls. The aim of the work is to provide optimal feedback synthesis associated with well denned gain operator constructed from the Riccati equation. The dynamics considered is of mixed parabolic-hyperbolic type which prevents applicability of tools developed earlier for analytic semigroups. It is shown, however, that the control operator along with the generator of the semigroup under consideration satisfy singular estimate referred to as Revisited Singular Estimate (RSE). This estimate, which measures "unboundedness" of control actions, is a generalization and a weaker form of Singular Estimate (SE) treated in the past literature. The main result of the paper provides Riccati theory developed for this new class of control systems labeled as RSECS (Revisited Singular Estimate Control Systems). The important feature is that the gain operator, constructed via Riccati operator, is consistent with the optimal feedback synthesis. The gain operator, though unbounded, has a controlled algebraically singularity at the terminal point. This enables one to establish well-posedness of the Riccati solutions and of the optimal feedback representation. An application of the theoretical framework to boundary control of a fluid-structure interaction model is given.
Źródło:
Control and Cybernetics; 2009, 38, 4B; 1429-1460
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Multiple positive solutions to singular boundary value problems for superlinear second order FDEs
Autorzy:
Jiang, Daqing
Powiązania:
https://bibliotekanauki.pl/articles/1207893.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
superlinear
fixed point theorem
singular boundary value problem
existence
Opis:
We study the existence of positive solutions to the singular boundary value problem for a second-order FDE

⎧ u'' + q(t) f(t,u(w(t))) = 0, for almost all 0 < t < 1,
⎨ u(t) = ξ(t), a ≤ t ≤ 0,
⎩ u(t) = η(t), 1 ≤ t ≤ b,

where q(t) may be singular at t = 0 and t = 1, f(t,u) may be superlinear at u = ∞ and singular at u = 0.
Źródło:
Annales Polonici Mathematici; 2000, 75, 3; 257-270
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A singular nonlinear boundary value problem with Neumann conditions
Autorzy:
Janus, J.
Powiązania:
https://bibliotekanauki.pl/articles/255233.pdf
Data publikacji:
2005
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
singular nonlinear boundary value problem
Neumann boundary conditions
second order equations
maximal and minimal solutions
Opis:
We study the existence of solutions for the equations x" plmin g(t, x) = h(t), t mem (0, 1) with Neumann boundary conditions, where g: [0, 1] x (0, +infin) arr [0, +infin] and h: [0, 1] arr R are continuous and g(t, ·) is singular at 0 for each t mem [0, 1].
Źródło:
Opuscula Mathematica; 2005, 25, 2; 227-241
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Correctness of a constrained control Mayers problem for a class of singularly perturbed functional-differential systems
Autorzy:
Glizer, V. Y.
Powiązania:
https://bibliotekanauki.pl/articles/969600.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
functional differential system
time delay
Mayer's problem
bounded control
singular perturbation
correctness
suboptimal control
Opis:
A Mayer's problem for a singularly perturbed controlled system with the general type of a small state delay is considered. The control is subject to geometrical constraints. The cost functional is a function of the terminal value of the slow state variable. A simpler parameter-free optimal control problem (the reduced problem) is associated with the original problem. A convergence of the optimal value of the cost functional in the original problem to the optimal value of the cost functional in the reduced problem, as a parameter of singular perturbation tends to zero, is established. An asymptotic suboptimality of the optimal control of the reduced problem in the original problem is shown. These results are extended to some more general optimal control problems. An illustrative example is presented.
Źródło:
Control and Cybernetics; 2008, 37, 2; 329-351
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 22

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