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Tytuł:
A New Approach to Measurement of Frequency Shifts Using the Principle of Rational Approximations
Autorzy:
Murrieta-Rico, F. N.
Petranovskii, V.
Sergiyenko, O. Y.
Hernandez-Balbuena, D.
Lindner, L.
Powiązania:
https://bibliotekanauki.pl/articles/220851.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
frequency measurement
rational approximations
sensors
Opis:
When a frequency domain sensor is under the effect of an input stimulus, there is a frequency shift at its output. One of the most important advantages of such sensors is their converting a physical input parameter into time variations. In consequence, changes of an input stimulus can be quantified very precisely, provided that a proper frequency counter/meter is used. Unfortunately, it is well known in the time-frequency metrology that if a higher accuracy in measurements is needed, a longer time for measuring is required. The principle of rational approximations is a method to measure a signal frequency. One of its main properties is that the time required for measuring decreases when the order of an unknown frequency increases. In particular, this work shows a new measurement technique, which is devoted to measuring the frequency shifts that occur in frequency domain sensors. The presented research result is a modification of the principle of rational approximations. In this work a mathematical analysis is presented, and the theory of this new measurement method is analysed in detail. As a result, a new formalism for frequency measurement is proposed, which improves resolution and reduces the measurement time.
Źródło:
Metrology and Measurement Systems; 2017, 24, 1; 45-56
0860-8229
Pojawia się w:
Metrology and Measurement Systems
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Global convergence of successive approximations of the Darboux problem for partial functional differential equations with infinite delay
Autorzy:
Człapiński, T.
Powiązania:
https://bibliotekanauki.pl/articles/255121.pdf
Data publikacji:
2014
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
successive approximations
Darboux problem
infinite delay
Opis:
We consider the Darboux problem for the hyperbolic partial functional differential equation with infinite delay. We deal with generalized (in the "almost everywhere" sense) solutions of this problem. We prove a theorem on the global convergence of successive approximations to a unique solution of the Darboux problem.
Źródło:
Opuscula Mathematica; 2014, 34, 2; 327-338
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the Chaplygin method for the Darboux problem
Autorzy:
Jaruszewska-Walczak, Danuta
Powiązania:
https://bibliotekanauki.pl/articles/745871.pdf
Data publikacji:
2007
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
functional differential equation
Newton method
analytical approximations
Opis:
In the paper we deal with the Darboux problem for hyperbolic functional differential equations. We give the sufficient conditions for the existence of the sequence \(\{z^{(m)}\}\) such that if \(\tilde{z}\) is a classical solution of the original problem then \(\{z^{(m)}\}\) is uniformly convergent to z\(\tilde{z}\). The convergence that we get is of the Newton type.
Źródło:
Commentationes Mathematicae; 2007, 47, 1
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Approximation of the probability of insolvability of a portfolio
Autorzy:
Pusz, Robert
Rolski, Tomasz
Powiązania:
https://bibliotekanauki.pl/articles/747757.pdf
Data publikacji:
2005
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Finance, portfolios, investment
Approximations to distributions (nonasymptotic)
Opis:
The authors review and criticize different approaches for calculations of ruin probabilities in one or multiperiod life insurance portfolios. They claim that precise calculations are time-consuming and in some cases (especially in the multiperiod ones) are practically inaccessible even if theoretical formulae are available. The reviewer considers that, because parameters of any such model must be estimated somehow, then precision in calculations cannot be achieved. For example, the authors assume a constant interest rate, which is not precisely the best way of doing things for the multiperiod model, and the precision must be lost anyway. Particularly, the authors show that the use of the central limit theorem is not appropriate; errors are large. The precise recursive method is difficult to perform for a large portfolio. The authors propose the importance of the Monte Carlo sampling method instead of the crude one. Their estimations are based on some probabilistic inequalities such as a version of Chernoff's (saddle point), also analyzed by S. Asmussen [Stochastic simulation with a view toward stochastic processes, Univ. Aarhus, Aarhus, 1999; Zbl 0981.65013], and are related to the approximation from D. Blackwell and J. L. Hodges, Jr. [Ann. Math. Statist. 30 (1959), 1113–1120; MR0112197].
Źródło:
Mathematica Applicanda; 2005, 33, 47/06
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Continuous selections and approximations in α-convex metric spaces
Autorzy:
Kowalska, A.
Powiązania:
https://bibliotekanauki.pl/articles/729415.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
generalized convexity
selections
relative selections
graph-approximations
Opis:
In the paper, the notion of a generalized convexity was defined and studied from the view-point of the selection and approximation theory of set-valued maps. We study the simultaneous existence of continuous relative selections and graph-approximations of lower semicontinuous and upper semicontinuous set-valued maps with α-convex values having nonempty intersection.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 2; 265-294
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The finite difference approximation for the Dirichlet problem with a non-uniform mesh on a boundary
Autorzy:
Morawiec, Grażyna
Powiązania:
https://bibliotekanauki.pl/articles/747719.pdf
Data publikacji:
1987
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Derivation of finite difference approximations
Error bounds
Opis:
.
The author describes a construction of the positive difference scheme, which is the approximation of the Dirichlet problem for an elliptic second order equation with mixed derivatives in an arbitrary region in R2. The a priori estimation for the approximate solution is proved and the estimation of the rate of convergence in maximum norm is established.
Źródło:
Mathematica Applicanda; 1987, 16, 30
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Teoretyczne podstawy metody Newtona przybliżonego rozwiązywania równań nieliniowych
On theoretical foundations of newton’s method of solving nonlinear equations
Autorzy:
Strasburger, Aleksander
Tempczyk, Wacława
Powiązania:
https://bibliotekanauki.pl/articles/453740.pdf
Data publikacji:
2011
Wydawca:
Szkoła Główna Gospodarstwa Wiejskiego w Warszawie. Katedra Ekonometrii i Statystyki
Tematy:
wielowymiarowa metoda Newtona
metoda kolejnych przybliżeń
aproksymacja numeryczna.
multidimensional Newton’s method
method of successive approximations
numerical approximations
Opis:
Artykuł przedstawia podstawowe pojęcia teoretyczne i sformułowania leżące u podstaw wielowymiarowej metody Newtona konstruowania przybliżonych rozwiązań układu równań nieliniowych, a użytej w pracach [Strasburger i inni (2009), Strasburger i inni (2011)] dla modelowania pewnych aspektów teorii konsumpcji. Metoda ta korzysta ze stosunkowo prostych pojęć matematycznych i stanowi bardzo elastyczne narzędzie zarówno do rozważań teoretycznych jak i obliczeń numerycznych. Metoda ta z pewnością zasługuje na to, by być lepiej znaną w społeczności ekonomistów matematycznych.
The paper surveys basic theoretical concepts and formulations underlying the multidimensional Newton’s method of constructing approximate solutions to systems of nonlinear equations., which was used in the papers [Strasburger et al. (2009), Strasburger et al. (2011)] for modeling certain aspects of consumer’s theory. This method is based on relatively simple mathematical concepts and is a very flexible tool for both theoretical arguments as well as for numerical computations. It certainly deserves to be better known in the community of mathematical economists.
Źródło:
Metody Ilościowe w Badaniach Ekonomicznych; 2011, 12, 2; 357-364
2082-792X
Pojawia się w:
Metody Ilościowe w Badaniach Ekonomicznych
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the approximation theorem of Wong-Zakai type for the Lasota operator
Autorzy:
Dawidowicz, A. L.
Twardowska, K.
Powiązania:
https://bibliotekanauki.pl/articles/255461.pdf
Data publikacji:
2010
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
stochastic evolution equations
Wong-Zakai approximations
Lasota operator
Opis:
We consider in this paper a stochastic evolution equation with Professor A. Lasota's operator as the infinitesimal generator of a strongly continuous semigroup of transformations and with Hammerstein operator connected with a noise being the Wiener process. We show that such evolution equation satisfies the Wong-Zakai type approximation theorem. The idea of the definition of the Lasota operator has the origin in the mathematical model of the creation and differentiation of cells in biology and medicine.
Źródło:
Opuscula Mathematica; 2010, 30, 3; 255-270
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the local Cauchy problem for nonlinear hyperbolic functional differential equations
Autorzy:
Człapiński, Tomasz
Powiązania:
https://bibliotekanauki.pl/articles/1294574.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
functional differential equations
weak solutions
bicharacteristics
successive approximations
Opis:
We consider the local initial value problem for the hyperbolic partial functional differential equation of the first order (1) $Dₓz(x,y) = f(x,y,z(x,y),(Wz)(x,y),D_y z(x,y))$ on E, (2) z(x,y) = ϕ(x,y) on [-τ₀,0]×[-b,b], where E is the Haar pyramid and τ₀ ∈ ℝ₊, b = (b₁,...,bₙ) ∈ ℝⁿ₊. Using the method of bicharacteristics and the method of successive approximations for a certain functional integral system we prove, under suitable assumptions, a theorem on the local existence of weak solutions of the problem (1),(2).
Źródło:
Annales Polonici Mathematici; 1997, 67, 3; 215-232
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Difference melt model
Autorzy:
Kazhikenova, Saule Sh.
Shaltakov, Sagyndyk N.
Nussupbekov, Bekbolat R.
Powiązania:
https://bibliotekanauki.pl/articles/1845514.pdf
Data publikacji:
2021
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
Navier-Stokes equations
hydrodynamic
approximations
mathematical models
melt
Opis:
The basic objective of the research is to construct a difference model of the melt motion. The existence of a solution to the problem is proven in the paper. It is also proven the convergence of the difference problem solution to the original problem solution of the melt motion. The Rothe method is implemented to study the Navier-Stokes equations, which provides the study of the boundary value problems correctness for a viscous incompressible flow both numerically and analytically.
Źródło:
Archives of Control Sciences; 2021, 31, 3; 607-627
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Difference melt model
Autorzy:
Kazhikenova, Saule Sh.
Shaltakov, Sagyndyk N.
Nussupbekov, Bekbolat R.
Powiązania:
https://bibliotekanauki.pl/articles/1845525.pdf
Data publikacji:
2021
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
Navier-Stokes equations
hydrodynamic
approximations
mathematical models
melt
Opis:
The basic objective of the research is to construct a difference model of the melt motion. The existence of a solution to the problem is proven in the paper. It is also proven the convergence of the difference problem solution to the original problem solution of the melt motion. The Rothe method is implemented to study the Navier-Stokes equations, which provides the study of the boundary value problems correctness for a viscous incompressible flow both numerically and analytically.
Źródło:
Archives of Control Sciences; 2021, 31, 3; 607-627
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A computationally inexpensive algorithm for determining outer and inner enclosures of nonlinear mappings of ellipsoidal domains
Autorzy:
Rauh, Andreas
Jaulin, Luc
Powiązania:
https://bibliotekanauki.pl/articles/2055165.pdf
Data publikacji:
2021
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
bounded uncertainty
guaranteed enclosures
ellipsoidal enclosures
inner approximations
outer approximations
nonlinear system
confidence interval
niepewność ograniczona
układ nieliniowy
przedział ufności
Opis:
A wide variety of approaches for set-valued simulation, parameter identification, state estimation as well as reachability, observability and stability analysis for nonlinear discrete-time systems involve the propagation of ellipsoids via nonlinear functions. It is well known that the corresponding image sets usually possess a complex shape and may even be nonconvex despite the convexity of the input data. For that reason, domain splitting procedures are often employed which help to reduce the phenomenon of overestimation that can be traced back to the well-known dependency and wrapping effects of interval analysis. In this paper, we propose a simple, yet efficient scheme for simultaneously determining outer and inner ellipsoidal range enclosures of the solution for the evaluation of multi-dimensional functions if the input domains are themselves described by ellipsoids. The Hausdorff distance between the computed enclosure and the exact solution set reduces at least linearly when decreasing the size of the input domains. In addition to algebraic function evaluations, the proposed technique is-for the first time, to our knowledge-employed for quantifying worst-case errors when extended Kalman filter-like, linearization-based techniques are used for forecasting confidence ellipsoids in a stochastic setting.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2021, 31, 3; 399--415
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The unique solvability of stationary and non-stationary incompressible melt models in the case of their linearization
Autorzy:
Kazhikenova, Saule Sh.
Powiązania:
https://bibliotekanauki.pl/articles/1409389.pdf
Data publikacji:
2021
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
Navier-Stockes equations
hydrodynamic
approximations
mathematical models
incompressible melt
Opis:
The article presents ε-approximation of hydrodynamics equations’ stationary model along with the proof of a theorem about existence of a hydrodynamics equations’ strongly generalized solution. It was proved by a theorem on the existence of uniqueness of the hydrodynamics equations’ temperature model’s solution, taking into account energy dissipation. There was implemented the Galerkin method to study the Navier-Stokes equations, which provides the study of the boundary value problems correctness for an incompressible viscous flow both numerically and analytically. Approximations of stationary and non-stationary models of the hydrodynamics equations were constructed by a system of Cauchy-Kovalevsky equations with a small parameter ε. There was developed an algorithm for numerical modelling of the Navier-Stokes equations by the finite difference method.
Źródło:
Archives of Control Sciences; 2021, 31, 2; 307-332
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
PRECISE ESTIMATES OF RUIN PROBABILITIES
Autorzy:
Rudź, Marcin
Powiązania:
https://bibliotekanauki.pl/articles/453317.pdf
Data publikacji:
2015
Wydawca:
Szkoła Główna Gospodarstwa Wiejskiego w Warszawie. Katedra Ekonometrii i Statystyki
Tematy:
discrete time risk models
ruin probabilities
approximations
Solvency II
Opis:
In this paper we investigate a sequence of accurate approximations of ruin probabilities in discrete time models. We prove its convergence to the exact ruin probability without any restrictive assumptions on the claim distribution. Numerical studies show that the sequence, from the first term on, accurately approximates ruin probabilities. A formula for ruin probabilities in the finite horizon is also proposed.
Źródło:
Metody Ilościowe w Badaniach Ekonomicznych; 2015, 16, 2; 80-88
2082-792X
Pojawia się w:
Metody Ilościowe w Badaniach Ekonomicznych
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Computational Methods for Stochastic Differential Equations and Stochastic Partial Differential Equations Involving Standard Brownian and Fractional Brownian Motion
Autorzy:
Shea, J.
Zachariou, I.
Pasik-Duncan, B.
Powiązania:
https://bibliotekanauki.pl/articles/115867.pdf
Data publikacji:
2011
Wydawca:
Fundacja na Rzecz Młodych Naukowców
Tematy:
Brownian Motion (BM)
fractional Brownian Motion (fBM)
SDEs
SPDEs
Numerical Approximations
Opis:
As more applied science researchers are attempting to use Stochastic Differential Equations (SDEs) as well as Stochastic Partial Differential Equations (SPDEs) in their modeling, especially when involving Fractional Brownian Motion (fBM), one common issue appears: an exact solution cannot always be found. For cases involving SPDEs, exact solutions commonly do not exist and approximation schemes for their solution are typically still in development. Therefore, in this paper, we test various Numerical methods in solving SDEs and SPDEs with standard BM that have non-linear coeffi cients. In addition we extend our results to problems with fBM.
Źródło:
Challenges of Modern Technology; 2011, 2, 2; 3-12
2082-2863
2353-4419
Pojawia się w:
Challenges of Modern Technology
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fuzzy relation-based approximation techniques in supporting medical diagnosis
Autorzy:
Radzikowska, A. M.
Powiązania:
https://bibliotekanauki.pl/articles/385167.pdf
Data publikacji:
2017
Wydawca:
Sieć Badawcza Łukasiewicz - Przemysłowy Instytut Automatyki i Pomiarów
Tematy:
fuzzy modal operators
fuzzy set approximations
Intuitionistic fuzzy sets
medical diagnosis
Opis:
In this paper we present an application of fuzzy approximation operators in supporting medical diagnosis. These operators are compositions of fuzzy modal operators. The underlying idea is based on the observation that approximations of fuzzy sets may be viewed as intuitionistic fuzzy sets. Reasoning scheme is determined by distances between intuitionistic fuzzy sets proposed by Szmidt and Kacprzyk.
Źródło:
Journal of Automation Mobile Robotics and Intelligent Systems; 2017, 11, 1; 21-29
1897-8649
2080-2145
Pojawia się w:
Journal of Automation Mobile Robotics and Intelligent Systems
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Maximal Inequalities for a Best Approximation Operator in Orlicz Spaces
Autorzy:
Favier, Sergio
Zó, Felipe
Powiązania:
https://bibliotekanauki.pl/articles/745344.pdf
Data publikacji:
2011
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Best \(\varphi\)-approximations by constants
extended best approximation operator
maximal inequalities
Opis:
In this paper we study a maximal operator \(\mathcal{M}f\) related with the best \(\varphi\) approximation by constants for a function \(f\in L^{\varphi'}_{\text{loc}}(\mathbb{R}^n)\), where we denote by \(\varphi'\) derivative function of the \(C^1\) convex function \(\varphi\). We get a necessary and sufficient condition which assure strong inequalities of the type \(\int_{\mathbb{R}^n} \theta(\mathcal{M}|f|)dx\leq K \int_{\mathbb{R}^n} \theta(|f|) dx\), where \(K\) is a constant independent of \(f\). Some pointwise and mean convergence results are obtained. In the particular case \(\varphi (t) = t^{p+1}\) we obtain several equivalent conditions on the functions \(\theta\) that assures strong inequalities of this type.
Źródło:
Commentationes Mathematicae; 2011, 51, 1
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimality conditions in set-valued optimization using approximations as generalized derivatives
Autorzy:
Gadhi, Nazih Abderrazzak
Ichatouhane, Aissam
Powiązania:
https://bibliotekanauki.pl/articles/31342744.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
approximations
set-valued optimization
local weak l-minimal solutions
optimality conditions
Opis:
The set criterion is an appropriate defining approach regarding the solutions for the set-valued optimization problems. By using approximations as generalized derivatives of set-valued mappings, we establish necessary optimality conditions for a constrained set-valued optimization problem in the sense of set optimization in terms of asymptotical pointwise compact approximations. Sufficient optimality conditions are then obtained through first-order strong approximations of data set-valued mappings.
Źródło:
Control and Cybernetics; 2022, 51, 4; 425-444
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Error estimates for finite element approximations of elliptic control problems
Autorzy:
Alt, Walter
Bräutigam, Nils
Rösch, Arnd
Powiązania:
https://bibliotekanauki.pl/articles/729441.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Linear quadratic optimal control problems
elliptic equations
finite element approximations
error estimates
Opis:
We investigate finite element approximations of one-dimensional elliptic control problems. For semidiscretizations and full discretizations with piecewise constant controls we derive error estimates in the maximum norm.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 1; 7-22
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Generalized method of Lie-algebraic discrete approximations for solving Cauchy problems with evolution equation
Autorzy:
Kindybaliuk, A.
Powiązania:
https://bibliotekanauki.pl/articles/122439.pdf
Data publikacji:
2014
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
generalized method of Lie-algebraic discrete approximations
dynamical systems
evolution equation
finite dimensional quasi representation
approximations
Lagrange’s polynomial
factorial convergence
układy dynamiczne
aproksymacje
wielomian Lagrange'a
Opis:
We consider solving the Cauchy problem with an abstract linear evolution equation by means of the Generalized Method of Lie-algebraic discrete approximations. Discretization of the equation is performed by all variables in equation and leads to a factorial rate of convergence if Lagrange interpolation is used for building quasi representation of differential operator. The rank of a finite dimensional operator and approximation properties have been determined. Error estimations and the factorial rate of convergence have been proved.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2014, 13, 2; 51-62
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On application of Newton’s Method to solve optimization problems in the consumer theory. Expansion’s Paths and Engel Curves
Autorzy:
Strasburger, Aleksander
Zembrzuski, Andrzej
Powiązania:
https://bibliotekanauki.pl/articles/453630.pdf
Data publikacji:
2011
Wydawca:
Szkoła Główna Gospodarstwa Wiejskiego w Warszawie. Katedra Ekonometrii i Statystyki
Tematy:
neoclassical theory of consumption
numerical approximations
multidimensional Newton method
expansion path
Engel curve
Opis:
The paper continues investigations concerned with numerical modeling of the neoclassical theory of consumption begun in our previous paper [Strasburger et al. (2009)] This time we are interested in expansion’s paths and Engel curves for separable utility functions.. The used numerical procedure is based on Newton’s approximation method, implemented in the MATLAB environment. Based on the prior determination of the approximate solutions of the optimum problem we determine in this paper the expansion paths and Engel curves and compare them with their standard form studied in econometrics.
Źródło:
Metody Ilościowe w Badaniach Ekonomicznych; 2011, 12, 1; 135-146
2082-792X
Pojawia się w:
Metody Ilościowe w Badaniach Ekonomicznych
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Error analysis of discrete approximations to bang-bang optimal control problems: the linear case
Autorzy:
Veliov, V. M.
Powiązania:
https://bibliotekanauki.pl/articles/970563.pdf
Data publikacji:
2005
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
liniowy system sterowania
aproksymacja dyskretna
szacowanie błędów
linear control systems
discrete approximations
error estimates
Opis:
The paper presents an error estimate for Runge-Kutta direct discretizations of terminal optimal control problems for linear systems. The optimal control for such problems is typically discontinuous, and Lipschitz stability of the solution with respect to perturbations does not necessarily hold. The estimate (in terms of the optimal controls) is of first order if certain recently obtained sufficient conditions for structural stability hold, and of fractional order, otherwise. The main tool in the proof is the established relation between the local convexity index of the reachable set and the multiplicity of zeros of appropriate switching functions associated with the problem.
Źródło:
Control and Cybernetics; 2005, 34, 3; 967-982
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Finite-dimensional approximations of distributed RC networks
Autorzy:
Mitkowski, W.
Powiązania:
https://bibliotekanauki.pl/articles/201214.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
ladder and ring electrical networks
finite-dimensional approximations
eigenvalues of ladder networks
Jacobi matrix
Opis:
Spectral properties of ladder and spatial electrical networks are considered. Dynamic properties of the networks are characterised by eigenvalues of the Jacobi cyclic state matrix. The effective formulas for eigenvalues of appropriate uniform systems are given. Numerical calculations were made using MATLAB.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2014, 62, 2; 263-269
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the construction of two-sided approximations to positive solutions of some elliptic problem
Autorzy:
Kolosova, S.
Lukhanin, V.
Powiązania:
https://bibliotekanauki.pl/articles/411231.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Oddział w Lublinie PAN
Tematy:
two-sided approximations
operator equation
positive solution
concave operator
conical interval
Green's functions
Green's quasifunction
Opis:
In this paper we have investigated the existence, uniqueness and possibility of constructing of two-sided approximations to the positive solution of a heat conduction problem with two sources. The investigation is based on methods in operator equations theory in half-ordered spaces. In this case we have considered a nonlinear operator equation that corresponds to the initial boundary value problem in a cone of non-negative continous functions. The properties of the corresponding operator define conditions which provide the existence and uniqueness of the solution. The conditions link the parameters of the problem implicitly meaning that they don’t provide the range of allowed values but need to be verified for each specific parameters value set separately. During the investigation we have provided the scheme of a two-sided iteration process which must satisfy the conditions in order to converge to the positive solution from both sides. The computational experiment have been conducted in two domains – unit disk and unit half disk. We have applied both two-sided approximations method and Green’s quasifunction method for the problem solving. The obtained results are presented as a surface and level lines plots and also as a table. The results in corresponding domains obtained by different methods have been compared with each other.
Źródło:
ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes; 2016, 5, 4; 11-19
2084-5715
Pojawia się w:
ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Discrete-time feedback stabilization
Autorzy:
Mitkowski, W.
Bauer, W.
Zagórowska, M.
Powiązania:
https://bibliotekanauki.pl/articles/229169.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
stabilization
feedback stabilization
finite dimensional stabilization
infinite dimensional systems
finite dimensional approximations
continuous-discrete system
Opis:
This paper presents an algorithm for designing dynamic compensator for infinitedimensional systems with bounded input and bounded output operators using finite dimensional approximation. The proposed method was then implemented in order to find the control function for thin rod heating process. The optimal sampling time was found depending on discrete output measurements.
Źródło:
Archives of Control Sciences; 2017, 27, 2; 309-322
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
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