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Wyświetlanie 1-15 z 62
Tytuł:
Positive solutions for nonparametric anisotropic singular solutions
Autorzy:
Papageorgiou, Nikolaos S.
Rădulescu, Vicenţiu D.
Sun, Xueying
Powiązania:
https://bibliotekanauki.pl/articles/29519752.pdf
Data publikacji:
2024
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
anisotropic regularity
variable Lebesgue
Sobolev spaces
anisotropic maximum principle
truncations and comparisons
Hardy inequality
Opis:
We consider an elliptic equation driven by a nonlinear, nonhomogeneous differential operator with nonstandard growth. The reaction has the combined effects of a singular term and of a “superlinear” perturbation. There is no parameter in the problem. Using variational tools and truncation and comparison techniques, we show the existence of at least two positive smooth solutions.
Źródło:
Opuscula Mathematica; 2024, 44, 3; 409-423
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Bayesian estimation of fertility rates under imperfect age reporting
Autorzy:
Verma, Vivek
Nath, Dilip C.
Dwivedi, S. N.
Powiązania:
https://bibliotekanauki.pl/articles/14761323.pdf
Data publikacji:
2023-03-15
Wydawca:
Główny Urząd Statystyczny
Tematy:
Fisher information
square error loss function
age-specific marital fertility rate
Bayes estimator
maximum likelihood principle
Opis:
This article outlines the application of the Bayesian method of parameter estimation to situations where the probability of age misreporting is high, leading to transfers of an individual from one age group to another. An essential requirement for Bayesian estimation is prior distribution, derived for both perfect and imperfect age reporting. As an alternative to the Bayesian methodology, a classical estimator based on the maximum likelihood principle has also been discussed. Here, the age misreporting probability matrix has been constructed using a performance indicator, which incorporates the relative performance of estimators based on age when reported correctly instead of misreporting. The initial guess of performance indicators can either be empirically or theoretically derived. The method has been illustrated by using data on Empowered Action Group (EAG) states of India from National Family Health Survey-3 (2005-2006) to estimate the total marital fertility rates. The present study reveals through both a simulation and real-life set-up that the Bayesian estimation method has been more promising and reliable in estimating fertility rates, even in situations where age misreporting is higher than in case of classical maximum likelihood estimates.
Źródło:
Statistics in Transition new series; 2023, 24, 2; 39-57
1234-7655
Pojawia się w:
Statistics in Transition new series
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Internet digital content pricing and subscribers control
Autorzy:
Mejjouali, Sobhi
Tadj, Lotfi
Powiązania:
https://bibliotekanauki.pl/articles/27315325.pdf
Data publikacji:
2023
Wydawca:
Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Tematy:
maximum principle
model predictive control
optimal control
web content pricing
Opis:
We use optimal control theory to determine the optimal rate of change in the subscription fee and the optimal ratio of ad space to the total web page space for a web content provider. An optimal solution is obtained using the maximum principle approach and the model predictive control approach. Numerical experiments show that it is preferable to use the first approach when the planning horizon is short and the second approach when the planning horizon is long.
Źródło:
Operations Research and Decisions; 2023, 33, 3; 59--73
2081-8858
2391-6060
Pojawia się w:
Operations Research and Decisions
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Network optimality conditions
Autorzy:
Osmolovskii, Nikolai P.
Qian, Meizhi
Sokołowski, Jan
Powiązania:
https://bibliotekanauki.pl/articles/31343935.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
network
optimal control problem
weak local minimum
Pontryagin’s maximum principle
critical cone
quadratic form
second order optimality conditions
Riccati equation
Opis:
Optimality conditions for optimal control problems arising in network modeling are discussed. We confine ourselves to the steady state network models. Therefore, we consider only control systems described by ordinary differential equations. First, we derive optimality conditions for the nonlinear problem for a single beam. These conditions are formulated in terms of the local Pontryagin maximum principle and the matrix Riccati equation. Then, the optimality conditions for the control problem for networks posed on an arbitrary planar graph are discussed. This problem has a set of independent variables xi varying within their intervals [0, li], associated with the corresponding beams at network edges. The lengths li of intervals are not specified and must be determined. So, the optimization problem is non-standard, it is a combination of control and design of networks. However, using a linear change of the independent variables, it can be reduced to a standard one, and we show this. Two simple numerical examples for the single-beam problem are considered.
Źródło:
Control and Cybernetics; 2023, 52, 2; 129-180
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Preliminary optimization technique in the design of steel girders according to Eurocode 3
Metoda wstępnej optymalizacji w projektowaniu dźwigarów stalowych zgodnie z Eurokodem 3
Autorzy:
Szeptyński, Paweł
Mikulski, Leszek
Powiązania:
https://bibliotekanauki.pl/articles/2203444.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
efekt drugiego rzędu
Eurokod
imperfekcja
konstrukcja stalowa
optymalizacja
zasada maksimum Pontriagina
dźwigar stalowy
Eurocode
imperfection
Pontryagin’s maximum principle
second order effect
steel structure
structural optimization
steel girder
Opis:
The problem of optimal design of a steel plated girder according to the Eurocode 3 is considered. Code regulations admit the Finite Element Analysis (FEA) in designing plated structures with variable cross-sections. A technique of determining an approximate solution to the optimization problem is presented. It is determined a solution of a control theory optimization task, in which Eurocode requirements regarding the Ultimate Limit State (bearing capacity, local and global stability) as well as Serviceability Limit State (flexural rigidity) are used as appropriate inequality constraints. Static analysis is performed within the framework of linear elasticity and Bernoulli-Euler beam theory making an account for second-order effects due to prescribed imperfections. Obtained solutions, after regularization, may be used for direct verification with the use of FEA or as the first guess for iterative topology optimization algorithms. Code requirements governing the determination of optimal shape are visualized in the constraint activity diagram, which is a proposed tool for analysis of optimization process.
Rozważany jest problem optymalnego projektowania blachownicy stalowej zgodnie z Eurokodem 3. Zapisy normowe dopuszczają stosowanie Metody Elementów Skończonych (MES) w projektowaniu blachownic o zmiennym przekroju poprzecznym. Przedstawiono metodę wyznaczania przybliżonego rozwiązania zagadnienia optymalizacji. Jest ono wyznaczane jako rozwiązanie problemu optymalizacyjnego teorii sterowania, w którym wymagania Eurokodu dotyczące Stanu Granicznego Nośności (nośność, lokalna i globalna stateczność) i Stanu Granicznego Użytkowalności (sztywność giętna) wykorzystane są jako ograniczenia nierównościowe. Analiza statyczna przeprowadzona jest w ramach liniowej teorii sprężystości dla modelu belki Bernoulliego - Eulera z uwzględnieniem efektów drugiego rzędu z uwagi na zadane imperfekcje. Uzyskane rozwiązania, po stosownych modyfikacjach, mogą podlegać weryfikacji z wykorzystaniem MES lub mogą zostać wykorzystane jako pierwsze przybliżenie w iteracyjnych algorytmach optymalizacji topologicznej. Wymagania normowe rządzące wyznaczaniem optymalnego kształtu zostały zwizualizowane na schemacie aktywności ograniczeń, który proponowany jest jako narzędzie analizy procesu optymalizacji.
Źródło:
Archives of Civil Engineering; 2023, 69, 1; 71--89
1230-2945
Pojawia się w:
Archives of Civil Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Simplest Models of the Macroeconomics Dynamics in a Composition with the Principle of the Subjective Entropy Maximum
Autorzy:
Kasianov, Vladimir Aleksandrovich
Goncharenko, Andriy Viktorovich
Powiązania:
https://bibliotekanauki.pl/articles/36811490.pdf
Data publikacji:
2023
Wydawca:
Sieć Badawcza Łukasiewicz - Instytut Lotnictwa
Tematy:
aviation transportation
operational effectiveness
objective functional optimisation
simplest macroeconomic problem
entropy
Opis:
This paper proposes a solution to a certain macroeconomic model. A multi-alternative problem of aviation transportation optimal organisation in conditions of uncertainty of the subjective preference functions is considered. Conditional optimisation of the objective functional containing the entropy of the individuals’ operational effectiveness functions preferences is carried out in the framework of the simplest macroeconomic problem. The principle of the Solow and Cobb-Douglas models, similar to the approach adopted for the estimation of economic growth, is modified with the subjective entropy maximum principle. The advantages of the described optimisation approach are demonstrated in the generalised terms of the operational effectiveness functions for aviation transportation organisation.
Źródło:
Transactions on Aerospace Research; 2023, 1 (270); 10-21
0509-6669
2545-2835
Pojawia się w:
Transactions on Aerospace Research
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A second-order sufficient condition for a weak local minimum in an optimal control problem with an inequality control constraint
Autorzy:
Osmolovskii, Nikolai P.
Powiązania:
https://bibliotekanauki.pl/articles/2183496.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
critical cone
quadratic form
first order tangent
second order tangent
second order optimality conditions
weak local minimum
inequality control constraint
Pontryagin’s maximum principle
Opis:
This paper is devoted to a sufficient second-order condition for a weak local minimum in a simple optimal control problem with one control constraint G(u) ≤ 0, given by a C2-function. A similar second-order condition was obtained earlier by the author for a strong minimum in a much more general problem. In the present paper, we would like to take a narrower perspective than before and thus provide shorter and simpler proofs. In addition, the paper uses the first and second order tangents to the set U, defined by the inequality G(u) ≤ 0. The main difficulty of the proof, clearly shown in the paper, refers to the set, where the gradient Hu of the Hamiltonian is small, but the condition of quadratic growth of the Hamiltonian is satisfied. The paper can be valuable for self-explanation and provides a basis for extensions.
Źródło:
Control and Cybernetics; 2022, 51, 2; 151--169
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Double phase problems: a survey of some recent results
Autorzy:
Papageorgiou, Nikolaos S.
Powiązania:
https://bibliotekanauki.pl/articles/2048893.pdf
Data publikacji:
2022
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
double phase integrand
generalized Orlicz spaces
regularity theory
maximum principle
Nehari manifold
Opis:
We review some recent results on double phase problems. We focus on the relevant function space framework, which is provided by the generalized Orlicz spaces. We also describe the basic tools and methods used to deal with double phase problems, given that there is no global regularity theory for these problems.
Źródło:
Opuscula Mathematica; 2022, 42, 2; 257-278
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence of positive continuous weak solutions for some semilinear elliptic eigenvalue problems
Autorzy:
Zeddini, Noureddine
Sari, Rehab Saeed
Powiązania:
https://bibliotekanauki.pl/articles/2216186.pdf
Data publikacji:
2022
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Green function
Kato class
nonlinear elliptic systems
positive solution
maximum principle
Schauder fixed point theorem
Opis:
Let D be a bounded $C^(1,1)$ -domain in $R^d$, d ≥ 2. The aim of this article is twofold. The first goal is to give a new characterization of the Kato class of functions $K(D)$ that was defined by $N$. Zeddini for $d = 2$ and by $H$. Mâagli and M. Zribi for $d ≥ 3$ and adapted to study some nonlinear elliptic problems in $D$. The second goal is to prove the existence of positive continuous weak solutions, having the global behavior of the associated homogeneous problem, for sufficiently small values of the nonnegative constants $λ$ and $μ$ to the following system $Δu = λf(x, u, v)$, $Δv = μg(x, u, v)$ in D, $u = ϕ_1$ and $v = ϕ_2$ on $∂D$, where $ϕ_1$ and $ϕ_2$ are nontrivial nonnegative continuous functions on $∂D$. The functions $f$ and g are nonnegative and belong to a class of functions containing in particular all functions of the type $f(x, u, v) = p(x)u^(α) h_1 (v)$ and $g(x, u, v) = q(x)h_2 (u)v^β$ with $α ≥ 1$, $β ≥ 1$, $h_1$, $h_2$ are continuous on $[0,∞)$ and $p$, $q$ are nonnegative functions in $K(D)$.
Źródło:
Opuscula Mathematica; 2022, 42, 3; 489-519
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Application of maximum principle to optimization of production and storage costs
Autorzy:
Popescu, Liviu
Dimitrov, Ramona
Powiązania:
https://bibliotekanauki.pl/articles/2083467.pdf
Data publikacji:
2021
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
optimal control
Pontryagin Maximum Principle
controllability
production
storage
Opis:
A problem of optimization for production and storge costs is studied. The problem consists in manufacture of n types of products, with some given restrictions, so that the total production and storage costs are minimal. The mathematical model is built using the framework of driftless control affine systems. Controllability is studied using Lie geometric methods and the optimal solution is obtained with Pontryagin Maximum Principle. It is proved that the economical system is not controllable, in the sense that we can only produce a certain quantity of products. Finally, some numerical examples are given with graphical representation.
Źródło:
Archives of Control Sciences; 2021, 31, 4; 865-881
1230-2384
Pojawia się w:
Archives of Control Sciences
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:
A multiplicity theorem for parametric superlinear (p, q)-equations
Autorzy:
Onete, Florin-Iulian
Papageorgiou, Nikolaos S.
Vetro, Calogero
Powiązania:
https://bibliotekanauki.pl/articles/254965.pdf
Data publikacji:
2020
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
superlinear reaction
constant sign and nodal solutions extremal solutions
nonlinear regularity
nonlinear maximum principle
critical groups
Opis:
We consider a parametric nonlinear Robin problem driven by the sum of a p-Laplacian and of a q-Laplacian ((p, q)-equation). The reaction term is (p — 1)-superlinear but need not satisfy the Ambrosetti-Rabinowitz condition. Using variational tools, together with truncation and comparison techniques and critical groups, we show that for all small values of the parameter, the problem has at least five nontrivial smooth solutions, all with sign information.
Źródło:
Opuscula Mathematica; 2020, 40, 1; 131-149
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Growth of a polynomial not vanishing in a disk
Autorzy:
Mir, Abdullah
Powiązania:
https://bibliotekanauki.pl/articles/2078964.pdf
Data publikacji:
2019
Wydawca:
Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
Tematy:
Polynomial
maximum modulus principle
zeros
Opis:
This paper deals with the problem of finding some upper bound estimates for the maximum modulus of the derivative and higher order derivatives of a complex polynomial on a disk under the assumption that the polynomial has no zeros in another disk. The estimates obtained strengthen the well-known inequality of Ankeny and Rivlin about polynomials.
Źródło:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2019, 73, 1; 41-48
0365-1029
2083-7402
Pojawia się w:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Hybrid-optional effectiveness functions entropy conditional extremization doctrine contributions into engineering systems reliability assessments
Autorzy:
Goncharenko, Andriy Viktorovich
Powiązania:
https://bibliotekanauki.pl/articles/36404766.pdf
Data publikacji:
2019
Wydawca:
Sieć Badawcza Łukasiewicz - Instytut Lotnictwa
Tematy:
effectiveness functions entropy
hybrid-optional effectiveness
multi-optionality
optimal distribution
variational principle
probability
reliability
entropy maximum principle
optimal periodicity
Opis:
In this publication a Doctrine for the Conditional Extremization of the Hybrid-Optional Effectiveness Functions Entropy is discussed as a tool for the Reliability Assessments of Engineering Systems. Traditionally, most of the problems having been dealt with in this area relate with the probabilistic problem settings. Regularly, the optimal solutions are obtained through the probability extremizations. It is shown a possibility of the optimal solutions “derivation”, with the help of a model implementing a variational principle which takes into account objectively existing parameters and components of the Markovian process. The presence of an extremum of the objective state probability is observed and determined on the basis of the proposed Doctrine with taking into account the measure of uncertainty of the hybrid-optional effectiveness functions in the view of their entropy. Such approach resembles the well known Jaynes’ Entropy Maximum Principle from theoretical statistical physics adopted in subjective analysis of active systems as the subjective entropy maximum principle postulating the subjective entropy conditional optimization. The developed here with Doctrine implies objective characteristics of the process rather than subjective individual’s preferences or choices, as well as the states probabilities maximums are being found without solving a system of ordinary linear differential equations of the first order by Erlang corresponding to the graph of the process. Conducted numerical simulation for the proposed mathematical models is illustrated with the plotted diagrams.
Źródło:
Transactions on Aerospace Research; 2019, 2 (255); 96-106
0509-6669
2545-2835
Pojawia się w:
Transactions on Aerospace Research
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On a Robin (p, q)-equation with a logistic reaction
Autorzy:
Papageorgiou, Nikolaos S.
Vetro, Calogero
Vetro, Francesca
Powiązania:
https://bibliotekanauki.pl/articles/254839.pdf
Data publikacji:
2019
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
positive solutions
superdiffusive reaction
local minimizers
maximum principle
minimal positive solutions
Robin boundary condition
indefinite potential
Opis:
We consider a nonlinear nonhomogeneous Robin equation driven by the sum of a p-Laplacian and of a q-Laplacian ((p,q)-equation) plus an indefinite potential term and a parametric reaction ol logistic type (superdiffusive case). We prove a bilurcation-type result describing the changes in the set ol positive solutions as the parameter λ > 0 varies. Also, we show that lor every admissible parameter λ > 0, the problem admits a smallest positive solution. Keywords: positive solutions, superdiffusive reaction, local minimizers, maximum principle, min
Źródło:
Opuscula Mathematica; 2019, 39, 2; 227-245
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 62

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