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Tytuł:
Greens functions and existence of solutions of nonlinear fractional implicit difference equations with Dirichlet boundary conditions
Autorzy:
Cabada, Alberto
Dimitrov, Nikolay D.
Jonnalagadda, Jagan Mohan
Powiązania:
https://bibliotekanauki.pl/articles/29519501.pdf
Data publikacji:
2024
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
fractional difference
Dirichlet conditions
Green’s function
existence of solutions
Opis:
This article is devoted to deduce the expression of the Green’s function related to a general constant coefficients fractional difference equation coupled to Dirichlet conditions. In this case, due to the points where some of the fractional operators are applied, we are in presence of an implicit fractional difference equation. So, due to such a property, it is more complicated to calculate and manage the expression of the Green’s function than in the explicit case studied in a previous work of the authors. Contrary to the explicit case, where it is shown that the Green’s function is constructed as finite sums, the Green’s function constructed here is an infinite series. This fact makes necessary to impose more restrictive assumptions on the parameters that appear in the equation. The expression of the Green’s function will be deduced from the Laplace transform on the time scales of the integers. We point out that, despite the implicit character of the considered equation, we can have an explicit expression of the solution by means of the expression of the Green’s function. These two facts are not incompatible. Even more, this method allows us to have an explicit expression of the solution of an implicit problem. Finally, we prove two existence results for nonlinear problems, via suitable fixed point theorems.
Źródło:
Opuscula Mathematica; 2024, 44, 2; 167-195
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the blowing up solutions of the 4-d general q-Kuramoto-Sivashinsky equation with exponentially “dominated” nonlinearity and singular weight
Autorzy:
Baraket, Sami
Mahdaoui, Safia
Ouni, Taieb
Powiązania:
https://bibliotekanauki.pl/articles/29519212.pdf
Data publikacji:
2023
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
singular limits
Green’s function
nonlinearity
gradient
nonlinear domain decomposition method
Opis:
Let Ω be a bounded domain in $ \mathbb{R}^4 $ with smooth boundary and let $ x^1, x^2, . . . , x^m $ be m-points in Ω. We are concerned with the problem $ \Delta^2 u - H(x, u, D^k u)=\rho^4 \prod_{i=1}^n | x - p_i |^{4 \alpha_i } f(x)g(u), $ where the principal term is the bi-Laplacian operator, $ H(x, u, D^k u)$ is a functional which grows with respect to $ Du $ at most like $ |Du|^q, 1 ≤ q ≤ 4, f : Ω → [0,+∞[ $ is a smooth function satisfying f(pi) > 0 for any i = 1, . . . , n, $ α_i $ are positives numbers and $ g : \mathbb{R} → [0,+∞[ $ satisfy $ |g(u)| ≤ ce^u $. In this paper, we give sufficient conditions for existence of a family of positive weak solutions $ (u_ρ)_{ρ>0} $ in Ω under Navier boundary conditions u = Δu = 0 on ∂Ω. The solutions we constructed are singular as the parameters ρ tends to 0, when the set of concentration $ S = {x^1, . . . , x^m} ⊂ Ω $ and the set $ Λ := {p_1, . . . , p_n} ⊂ Ω $ are not necessarily disjoint. The proof is mainly based on nonlinear domain decomposition method.
Źródło:
Opuscula Mathematica; 2023, 43, 1; 5-18
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Region of existence of multiple solutions for a class of robin type four-point bvps
Autorzy:
Verma, Amit K.
Urus, Nazia
Agarwal, Ravi P.
Powiązania:
https://bibliotekanauki.pl/articles/2052065.pdf
Data publikacji:
2021
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Green’s function
monotone iterative technique
maximum principle
multi-point problem
Opis:
This article aims to prove the existence of a solution and compute the region of existence for a class of four-point nonlinear boundary value problems (NLBVPs) defined as \[ \begin{array}{lr} -u^{\prime\prime}(x) = \psi(x,u,u^{\prime}), & x \in (0,1) \\ u^{\prime}(0) = \lambda_{1}u(\xi), & u^{\prime}(1) = \lambda_{2}u(\eta) \end{array} \] where $I = [0, 1], 0 < \xi \leq \eta < 1 \text{ and } \lambda_{1} ,\lambda_{2} > 0$. The nonlinear source term $\psi \in C(I \times \mathbb{R}^{2}, \mathbb{R})$ is one sided Lipschitz in $u$ with Lipschitz constant $L_{1}$ and Lipschitz in $u^{\prime}$, such that $\vert \psi(x, u, u^{\prime}) - \psi(x, u, v^{\prime})\vert$. We develop monotone iterative technique (MI-technique) in both well ordered and reverse ordered cases. We prove maximum, anti-maximum principle under certain assumptions and use it to show the monotonic behaviour of the sequences of upper-lower solutions. The sufficient conditions are derived for the existence of solution and verified for two examples. The above NLBVPs is linearised using Newton’s quasilinearization method which involves a parameter k equivalent to $\text{max}_{u} \frac{\delta\psi}{\delta_{u}}$. We compute the range of $k$ for which iterative sequences are convergent.
Źródło:
Opuscula Mathematica; 2021, 41, 4; 571-600
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Exact and approximate controllability conditions for the micro-swimmers deflection governed by electric field on a plane: The Green’s function approach
Autorzy:
Khurshudyan, A. Zh.
Powiązania:
https://bibliotekanauki.pl/articles/229564.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
run
tumble
micro-swimmers
Green’s function of nonlinear equation
discontinuous
Opis:
We study the exact and approximate controllabilities of the Langevin equation describing the Brownian motion of particles with a white noise. The Langevin equation is shown to describe also the bacterial run-and-tumble motion. Applying the Green’s function approach to the Green’s function representation of the Langevin equation, we obtain necessary and sufficient conditions for exact controllability in the form of a finite-dimensional problem of moments. For the approximate controllability, we obtain only sufficient conditions. The sets of resolving controls are characterized in both cases. The theoretical derivations are supported by a numerical analysis.
Źródło:
Archives of Control Sciences; 2018, 28, 3; 335-347
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Surface Green’s function of a soft elastomer with the gravity effect
Autorzy:
Liang, Xiaodong
Liu, Junxiu
Xu, Peibao
Li, Kai
Powiązania:
https://bibliotekanauki.pl/articles/280502.pdf
Data publikacji:
2020
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
surface Green’s function
gravity
distributed pressure
soft materials
neo-Hookean model
Opis:
Gravity can play a tremendous effect on deformation of rubberlike materials and biological soft tissues. In this paper, considering the gravity effect, we proposed a surface Green’s function of a soft elastomer based on the neo-Hookean model. The proposed surface Green’s function is applied to analyze the elastic deformation of a soft elastomer subjected to uniform pressure. The surface normal displacement of the soft elastomer is calculated and the results show that gravity has a large impact on the surface deformation of the elastomer. Generally, the surface normal displacement decreases with the increasing gravitational force.
Źródło:
Journal of Theoretical and Applied Mechanics; 2020, 58, 1; 35-44
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Resonant Greens function for Euler-Bernoulli beams by means of the Fredholm Alternative Theorem
Autorzy:
Hozhabrossadati, S. M.
Sani, A. A.
Mofid, M.
Powiązania:
https://bibliotekanauki.pl/articles/973616.pdf
Data publikacji:
2013
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
Fredholm Alternative Theorem
modified Green’s function
resonance
Euler-Bernoulli beam
rezonans
Opis:
This paper presents the Green's function for a uniform thin beam which is assumed to obey the Euler-Bernoulli theory at resonant condition. The beam under study has a simple support at one end and a sliding support at the other. First, the differential equation governing the free vibration of the beam is obtained in the frequency domain using the Fourier transform. Then, we try to find the corresponding Green's function of the problem. But a contradiction occurs due to the special properties of resonance. In order to overcome this hurdle, the Fredholm Alternative Theorem is utilized. Remarkably, it is shown that this theorem, by adding a particular term to the Green's function, can remedy this problem and the modified Green's function is consequently established. Moreover, the deformation function of the beam is found in an integral equation form. Some diagrams and tables conclude this study.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2013, 12, 3; 55-67
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Approximate controllability of second order infinite dimensional systems
Autorzy:
Klamka, Jerzy
Khurshudyan, Asatur Zh.
Powiązania:
https://bibliotekanauki.pl/articles/1409079.pdf
Data publikacji:
2021
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
infinite dimensional systems
approximate controllability
Green’s function approach
flexible Kirchhoff–Love plate
Opis:
In the paper approximate controllability of second order infinite dimensional system with damping is considered. Applying linear operators in Hilbert spaces general mathematical model of second order dynamical systems with damping is presented. Next, using functional analysis methods and concepts, specially spectral methods and theory of unbounded linear operators, necessary and sufficient conditions for approximate controllability are formulated and proved. General result may be used in approximate controllability verification of second order dynamical system using known conditions for approximate controllability of first order system. As illustrative example using Green function approach approximate controllability of distributed dynamical system is also discussed.
Źródło:
Archives of Control Sciences; 2021, 31, 1; 165-184
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Matrix Greens function of double-diffusivity problem and its applications to problems with inner point source
Autorzy:
Chaplya, Yevhen
Chernukha, Olha
Bilushchak, Yurii
Powiązania:
https://bibliotekanauki.pl/articles/1954454.pdf
Data publikacji:
2014
Wydawca:
Politechnika Gdańska
Tematy:
Green’s function
double-diffusivity
initial-boundary value problem
point mass source
random coordinate
Opis:
The matrix Green’s function of the initial-boundary value problem of admixture double-diffusivity is defined. The initial-boundary value problem with a point source is formulated for the matrix elements for determination of the matrix Green’s function. Formulae for matrix elements are obtained and the behavior of Green’s functions is investigated. It is shown that the surface generated by the Green’s function has a typical sharp peak in the vicinity of the point of action of the point mass source, and in the vicinity of the top boundary of the layer ,the values of the second element of the Green’s function are times higher than the values of the first one the state of which is corresponding to the quick migration way. On this basis the solutions of the initial-boundary value problems under the action of the internal point source of mass are found. The cases of the deterministic source as well as stochastic ones under uniformand triangular distributions of the coordinate of the mass source location are considered.
Źródło:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2019, 23, 1; 75-99
1428-6394
Pojawia się w:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fizyczne podstawy metody interferometrii sejsmicznej
Physical derivation of the seismic interferometry method
Autorzy:
Czarny, R.
Powiązania:
https://bibliotekanauki.pl/articles/394167.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Instytut Gospodarki Surowcami Mineralnymi i Energią PAN
Tematy:
interferometria sejsmiczna
funkcja Greena
korelacja wzajemna
akustyka odwróconego czasu
seismic interferometry
Green’s function
cross-correlation
time-reversed acoustics
Opis:
Interferometria sejsmiczna jest dynamicznie rozwijającą się metodą, której pierwsze zastosowania sięgają początków obecnego stulecia. Aktualnie znajduje coraz szersze zastosowanie w zagadnieniach m.in. obrazowania głębokich struktur ziemi oraz utworów przypowierzchniowych, monitorowania procesów wulkanicznych oraz analizowania wpływu silnych trzęsień ziemi na obiekty budowlane. Metoda ta pozwala na odtworzenie odpowiedzi impulsowej tzw. funkcji Greena ośrodka pomiędzy parą odbiorników na podstawie zarejestrowanych w tym samym czasie sejsmicznych pól falowych na tych odbiornikach. W wyniku odpowiednich operacji matematycznych metoda ta zamienia zarejestrowane na odbiornikach koherentne fale sejsmiczne o nieznanym czasie oraz miejscu ich wzbudzenia na układ tzw. wirtualnych źródeł emitujących sejsmiczne pole falowe z dowolnego odbiornika. W artykule przedstawiono fizyczne uzasadnienie wyników eksperymentu akustyki odwróconego czasu (ang. time-reversed acoustics) według Derode i in. (2003), które jest zarazem wytłumaczeniem metody interferometrii sejsmicznej. Eksperyment laboratoryjny w pierwszym etapie polegał na rejestracji akustycznego pola falowego wyemitowanego na brzegu naczynia wypełnionego cieczą i stalowymi prętami. Następnie rejestracje zostały odwrócone w czasie i wysłane powtórnie do wewnątrz naczynia i odebrany po przeciwnej stronie. Zarejestrowany na końcu sygnał okazał się zbliżony do sygnału wyemitowanego, pomimo przejścia przez ośrodek wielokrotnie rozpraszający. Doświadczenie to uzasadniono wykorzystując technikę korelacji wzajemnej (ang. cross-correlation), zasadę superpozycji pola falowego oraz zasadę wzajemności Rayleigha.
Seismic interferometry is a geophysical method which has been developing very rapidly over the last decade. It has been applied to image deep structures of the Earth as well as near-surface, monitor volcanic processes, geothermal reservoirs within exploitation, rock mass deformation induced by mining, landslides, ground water storage, ice sheet or the impact of strong earthquakes to buildings. The vast majority of these applications use ambient seismic noise as a seismic source. This method involves reconstructing thte impulse response, the socalled Green’s function, between pair of receivers based on the wave field registered by them. Using seismic interferometry with various data processing flows the registered coherent seismic waves by the receivers can be changed to virtual sources which are placed in the receiver locations. In the article, the physical derivation of the time-reversed acoustics experiment which was introduced by Derode et. al. (2003) is presented. This derivation also explains the seismic interferometry method. The laboratory experiment contained two phases. First, an acoustics signal was emitted into the medium with hundreds of scatterers (cube with liquid and rods) and registered on the opposite side of the medium. Then, registrations were reversed and emitted back. Finally, the wave field refocused exactly in the point of initial excitation. Derode et. al. explain these results using the cross-correlation technique, superposition and Rayleigh’s reciprocity principles.
Źródło:
Zeszyty Naukowe Instytutu Gospodarki Surowcami Mineralnymi i Energią PAN; 2017, 101; 195-202
2080-0819
Pojawia się w:
Zeszyty Naukowe Instytutu Gospodarki Surowcami Mineralnymi i Energią PAN
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Quantum simulations of band-to-band tunnelling in a type-II broken-gap superlattice diode
Autorzy:
Makowiec, Marcin
Kolek, Andrzej
Powiązania:
https://bibliotekanauki.pl/articles/2204215.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Stowarzyszenie Elektryków Polskich
Tematy:
type-II superlattice
broken-gap superlattice diode
band-to-band tunnelling
quantum transport
nonequilibrium Green’s function
twoband Hamiltonian
Opis:
In recent years, type-II superlattice-based devices have completed the offer of the electronic industry in many areas of applications. Photodetection is one of them, especially in the midinfrared wavelength range. It is due to the unique feature of a superlattice material, which is a tuneable bandgap. It is also believed that the dark current of superlattice-based photodetectors is strongly suppressed due to the suppression of the band-to-band tunnelling current in a superlattice material. This argument relies, however, on a semi-classical approach that treats superlattice as a bulk material with effective parameters extracted from the k·p analysis. In the paper, a superlattice device is analysed on a quantum level: the nonequilibrium Green’s function method is applied to the two-band Hamiltonian of the InAs/GaSb superlattice p-i-n diode. The analysis concentrates on the band-to-band tunnelling with the aim to validate the correctness of a semi-classical description of the phenomenon. The results of calculations reveal that in a superlattice diode, the inter-band tunnelling occurs only for certain values of energy and in-plane momentum, for which electronic and hole sub-bands cross. The transitions occurring for vanishing in-plane momentum produce resonances in the current-voltage characteristics - the feature which was reported in a few experimental observations. This scenario is quite different from that occurring in bulk materials, where there is a range of energy-momentum pairs for which the band-to-band tunnelling takes place, and so current-voltage characteristics are free from any resonances. However, simulations show that, while not justified for a detailed analysis, the semi-classical description can be applied to superlattice-based devices for an ‘order of magnitude’ estimation of the band-to-band tunnelling current.
Źródło:
Opto-Electronics Review; 2023, 31, Special Issue; art. no. e144558
1230-3402
Pojawia się w:
Opto-Electronics Review
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Heating control of a finite rod with a mobile source
Autorzy:
Jilavyan, Samvel H.
Grigoryan, Edmon R.
Khurshudyan, Asatur Zh.
Powiązania:
https://bibliotekanauki.pl/articles/1409386.pdf
Data publikacji:
2021
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
null-controllability
mobile control
nonlinear constraints
triangular wave
rectangular wave
Green’s function approach
heuristic control
lack of exact controllability
Opis:
The Green’s function approach is applied for studying the exact and approximate null-controllability of a finite rod in finite time by means of a source moving along the rod with controllable trajectory. The intensity of the source remains constant. Applying the recently developed Green’s function approach, the analysis of the exact null-controllability is reduced to an infinite system of nonlinear constraints with respect to the control function. A sufficient condition for the approximate null-controllability of the rod is obtained. Since the exact solution of the system of constraints is a long-standing open problem, some heuristic solutions are used instead. The efficiency of these solutions is shown on particular cases of approximate controllability.
Źródło:
Archives of Control Sciences; 2021, 31, 2; 417-430
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Distributed controllability of one-dimensional heat equation in unbounded domains: The Greens function approach
Autorzy:
Khurshudyan, Asatur Zh.
Powiązania:
https://bibliotekanauki.pl/articles/229527.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
lack of controllability
exact controllability
approximate controllability
nullcontrollability
Green’s function
heuristic method
infinite system of algebraic equations
regularity
fully regularity
Opis:
We derive exact and approximate controllability conditions for the linear one-dimensional heat equation in an infinite and a semi-infinite domains. The control is carried out by means of the time-dependent intensity of a point heat source localized at an internal (finite) point of the domain. By the Green’s function approach and the method of heuristic determination of resolving controls, exact controllability analysis is reduced to an infinite system of linear algebraic equations, the regularity of which is sufficient for the existence of exactly resolvable controls. In the case of a semi-infinite domain, as the source approaches the boundary, a lack of L2-null-controllability occurs, which is observed earlier by Micu and Zuazua. On the other hand, in the case of infinite domain, sufficient conditions for the regularity of the reduced infinite system of equations are derived in terms of control time, initial and terminal temperatures. A sufficient condition on the control time, heat source concentration point and initial and terminal temperatures is derived for the existence of approximately resolving controls. In the particular case of a semi-infinite domain when the heat source approaches the boundary, a sufficient condition on the control time and initial temperature providing approximate controllability with required precision is derived.
Źródło:
Archives of Control Sciences; 2019, 29, 1; 57-71
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Comparison of heating curves of a rectangular busbar in different conditions of heat abstraction during the short-circuit heating
Autorzy:
Zaręba, M.
Powiązania:
https://bibliotekanauki.pl/articles/201224.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
analytical methods
field theory
transient heat flow
short-circuit in leads
Green’s function
metody analityczne
teoria pola
nieustalony przepływ ciepła
funkcja Greena
Opis:
The paper compares heating curves for a rectangular busbar in the conditions of convective and adiabatic heat transfer during short-circuit heating. Different coefficients of heat transfer from the external surface of the busbar and different busbar cross-sections have been assumed. This has allowed determining the error value occurring when the adiabatic rather than convective boundary condition is presumed at short circuit. The analysis takes into account a change of resistivity in the temperature function. The respective boundary-initial problems have been solved with analytical methods using Green’s function. The calculated results show that no considerable errors occur for long-lasting short circuits with an adiabatic rather than convective boundary condition.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 1; 79-85
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Problem on extremal decomposition of the complex plane
O problemie ekstremalnej dekompozycji płaszczyzny zespolonej
Autorzy:
Denega, Iryna
Powiązania:
https://bibliotekanauki.pl/articles/699882.pdf
Data publikacji:
2018
Wydawca:
Łódzkie Towarzystwo Naukowe
Tematy:
inner radius of domain, non-overlapping domains, radial system of points, separating transformation, quadratic differential, Green’s function
promień wewnętrzny obszaru, ekstremalna dekompozycja płaszczyzny zespolonej
Opis:
https://doi.org/10.26485/0459-6854/2018/68.3/6 Rozpatrujemy funkcjonał określony na układzie niezachodzących na siebie obszarów. Wynik dotyczy problemu Dubinina-poszukiwania maksimum iloczynu promieni wpisanych kół w niezachodzące na siebie obszary zawierające punkty okręgu jednostkowego i potęgę promienia wpisanego kola w obszar zawierający początek układu współrzędnych. Problem został sformułowany w 1994r. w pracy Dubinina, a następnie powtórzony w monografii tegoż autora z roku 2014. Problem nie jest rozwiązany w ogólnym przypadku. W obecnej pracy problem w postaci dotyczącej bardziej ogólnego układu punktów jest uzyskany dla pewnych konkretnych wartości n oraz y.
https://doi.org/10.26485/0459-6854/2018/68.3/6  The paper is devoted to one extremal problem in geometric function theory of complex variables associated with estimates of functionals defined on the systems of non-overlapping domains. We consider Dubinin’s problem of the maximum of product of inner radii of n non-overlapping domains containing points of the unit circle and the power of the inner radius of a domain containing the origin. The problem was formulated in 1994 in the work of Dubinin and then repeated in his monograph in 2014. Currently it is not solved in general. In this paper we generalized it to the case of the more general system of points and obtained a solution of this problem for some concrete values of n and y.
Źródło:
Bulletin de la Société des Sciences et des Lettres de Łódź, Série: Recherches sur les déformations; 2018, 68, 3
1895-7838
2450-9329
Pojawia się w:
Bulletin de la Société des Sciences et des Lettres de Łódź, Série: Recherches sur les déformations
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The problem of external decomposition of a complex plane with three poles
Problem ekstremalnego rozkładu płaszczyzny zespolonej z dowolnymi biegunami
Autorzy:
Bakhtin, Aleksandr
Vyhivska, Liudmyla
Powiązania:
https://bibliotekanauki.pl/articles/1837649.pdf
Data publikacji:
2021-08-12
Wydawca:
Łódzkie Towarzystwo Naukowe
Tematy:
inner radius of domain
non-overlapping domains
radial system of points
separating transformation
quadratic differential
Green’s function
wewnętrzny promień obszaru
rozłączne obszary
promieniowy system punktów
transformacja rozdzielająca
różniczka kwadratowa
funkcja Greena
Opis:
Although much research (f. e. [1], [3], [5], [7–15]) has been devoted to the extremal problems of a geometric function theory associated with estimates of functionals defined on systems of non-overlapping domains, however, in the general case the problems remain unsolved. The paper describes the problem of finding the maximum of a functional. This problem is to find a maximum of the product of inner radii of mutually non-overlapping symmetric domains with respect to a unit circle and the inner radius in some positive certain degree of the domain with respect to zero and description of extreme configurations. The topic of the paper is devoted to the study of the problem of the classical direction of the geometric theory of complex variable functions, namely, the extremal problems for non-overlapping domains
Chociaż wiele badań (zob. [1], [3], [5], [7–15]) zostało poświęconych problemom ekstremalnym geometrycznej teorii funkcji, związanych z oszacowaniem funkcjonałów zdefiniowanych na układach rozłącznych obszarów, to jednak w ogólnym przypadku problemy te pozostają nadal otwarte. Praca opisuje problem znalezienia maksimum pewnego funkcjonału. Ten problem, to znalezienie maksimum iloczynu wewnętrznych promieni wzajemnie rozłącznych symetrycznych obszarów (względem okręgu jednostkowego) i wewnętrznego promienia w pewnej dodatniej potędze w obszarze względem zera oraz opis tych ekstremalnych konfiguracji. Tematem pracy jest badanie problemu z klasycznych zagadnień geometrycznej teorii funkcji, a mianowicie problemów ekstremalnych w wzajemnie rozłącznych obszarach
Źródło:
Bulletin de la Société des Sciences et des Lettres de Łódź, Série: Recherches sur les déformations; 2020, 70, 1; 145-152
1895-7838
2450-9329
Pojawia się w:
Bulletin de la Société des Sciences et des Lettres de Łódź, Série: Recherches sur les déformations
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 16

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