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Wyświetlanie 1-15 z 53
Tytuł:
A maximal function characterization of weighted Besov-Lipschitz and Triebel-Lizorkin spaces.
Autorzy:
-Q. Bui, H.
Paluszyński, M.
Taibleson, M.
Powiązania:
https://bibliotekanauki.pl/articles/1287511.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Besov-Lipschitz space
Triebel-Lizorkin space
Littlewood-Paley function
Calderón representation theorem
$A_∞$ weight
Opis:
We give characterizations of weighted Besov-Lipschitz and Triebel-Lizorkin spaces with $A_∞$ weights via a smooth kernel which satisfies "minimal" moment and Tauberian conditions. The results are stated in terms of the mixed norm of a certain maximal function of a distribution in these weighted spaces.
Źródło:
Studia Mathematica; 1996, 119, 3; 219-246
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A new Kantorovich-type theorem for Newtons method
Autorzy:
Argyros, Ioannis
Powiązania:
https://bibliotekanauki.pl/articles/1338842.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Newton's method
Lipschitz-Hölder condition
Kantorovich hypothesis
Banach space
Opis:
A new Kantorovich-type convergence theorem for Newton's method is established for approximating a locally unique solution of an equation F(x)=0 defined on a Banach space. It is assumed that the operator F is twice Fréchet differentiable, and that F', F'' satisfy Lipschitz conditions. Our convergence condition differs from earlier ones and therefore it has theoretical and practical value.
Źródło:
Applicationes Mathematicae; 1999, 26, 2; 151-157
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A special case of generalized Hölder functions
Autorzy:
Lupa, M.
Powiązania:
https://bibliotekanauki.pl/articles/122471.pdf
Data publikacji:
2014
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
Lipschitz condition
generalized Hölder condition
equivalency of norms
Opis:
In this paper some properties of a special case of generalized Hölder functions, which belong to the space W γ [a, b], are considered. These functions are r-times differentiable and their r-th derivatives satisfy the generalized Hölder condition. The main result of the paper is a proof of the theorem that product of two functions belonging to the space W γ [a, b] also belongs to this space.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2014, 13, 4; 81-89
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A stable homotopy approach to horizontal linear complementarity problems
Autorzy:
Ralph, D.
Powiązania:
https://bibliotekanauki.pl/articles/206132.pdf
Data publikacji:
2002
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
ciągłość pseudo-Lipschitza
metoda homotopii
rozwiązanie stałe
system kawałkami afiniczny
active set method
global metric regularity
homotopy method
horizontal linear complementarity problem
mathematical program with complementarity constraints
MPCC
MPCC-LICQ
MPEC
path following
piecewise affine system
pseudo-Lipschitz continuity
QPCC
stable solution
Opis:
We are interested in the solution of Horizontal Linear Complementarity Problems, HLCPs, that is complementarity problems with more variables than equations. Globally metrically regular HLCPs have nonempty solution sets that are stable with respect to "right-hand-side perturbations" of the data, hence are numerically attractive. The main purpose of the paper is to show how the stability on conditioning properties of globally metrically regular HLCPs are preserved by a homotopy framework for solving the HLCP that finds a "stable" direcaion at each iteration as a local minimizer of a strongly convex quadratic program with linear complementarity constraints, QPCC. Apart from intrinsic interest in numerical solution of HLCPs, this investigation has application in solving horizontal nonlinear complementarity problems and more broadly in the area of mathematical programs with complementarity constraints, MPCCs.
Źródło:
Control and Cybernetics; 2002, 31, 3; 575-599
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A sufficient condition for optimality in nondifferentiable invex programming
Autorzy:
Antczak, T.
Powiązania:
https://bibliotekanauki.pl/articles/205838.pdf
Data publikacji:
2001
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
funkcja półwypukła
uogólniony gradient Clarka
Clarke's generalized gradient
invex function
locally Lipschitz function
semiconvex function
Opis:
In this paper sufficient optimality condition are established for a nonlinear programming problem without differentiability assumption on the data wherein Clarke's generalized gradient is used to define invexity.
Źródło:
Control and Cybernetics; 2001, 30, 4; 431-437
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A survey on Lipschitz-free Banach Spaces
Autorzy:
Godefroy, Gilles
Powiązania:
https://bibliotekanauki.pl/articles/746348.pdf
Data publikacji:
2015
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Lipschitz maps
geometry of Banach spaces
Opis:
This article is a survey of Lipschitz\dywiz free Banach spaces and recent progress in the understanding of their structure. The results we present have been obtained in the last fifteen years (and quite often in the last five years). We give a self\dywiz contained presentation of the basic properties of Lipschitz\dywiz free Banach spaces and investigate some specific topics: non-linear transfer of asymptotic smoothness, approximation properties, norm\dywiz attainment. Section 5 consists mainly of unpublished results. A list of open problems with comentary is provided.
Źródło:
Commentationes Mathematicae; 2015, 55, 2
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Tikhonov-type theorem for abstract parabolic differential inclusions in Banach spaces
Autorzy:
Gudovich, Anastasie
Kamenski, Mikhail
Nistri, Paolo
Powiązania:
https://bibliotekanauki.pl/articles/729318.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
singular perturbations
differential inclusions
analytic semigroups
multivalued compact operators
Lipschitz selections
Opis:
We consider a class of singularly perturbed systems of semilinear parabolic differential inclusions in infinite dimensional spaces. For such a class we prove a Tikhonov-type theorem for a suitably defined subset of the set of all solutions for ε ≥ 0, where ε is the perturbation parameter. Specifically, assuming the existence of a Lipschitz selector of the involved multivalued maps we can define a nonempty subset $Z_L(ε)$ of the solution set of the singularly perturbed system. This subset is the set of the Hölder continuous solutions defined in [0,d], d > 0 with prescribed exponent and constant L. We show that $Z_L(ε)$ is uppersemicontinuous at ε = 0 in the C[0,d]×C[δ,d] topology for any δ ∈ (0,d].
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2001, 21, 2; 207-234
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Adaptive observer-based fault estimation for a class of Lipschitz nonlinear systems
Autorzy:
Oucief, N.
Tadjine, M.
Labiod, S.
Powiązania:
https://bibliotekanauki.pl/articles/229517.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
nonlinear adaptive observer
fault estimation
strictly positive real
Lipschitz systems
observer matching condition
LMI
Opis:
Fault input channels represent a major challenge for observer design for fault estimation. Most works in this field assume that faults enter in such a way that the transfer functions between these faults and a number of measured outputs are strictly positive real (SPR), that is, the observer matching condition is satisfied. This paper presents a systematic approach to adaptive observer design for joint estimation of the state and faults when the SPR requirement is not verified. The proposed method deals with a class of Lipschitz nonlinear systems subjected to piecewise constant multiplicative faults. The novelty of the proposed approach is that it uses a rank condition similar to the observer matching condition to construct the adaptation law used to obtain fault estimates. The problem of finding the adaptive observer matrices is formulated as a Linear Matrix Inequality (LMI) optimization problem. The proposed scheme is tested on the nonlinear model of a single link flexible joint robot system.
Źródło:
Archives of Control Sciences; 2016, 26, 2; 245-259
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
All solenoids of piecewise smooth maps are period doubling
Autorzy:
Alsedà, Lluís
Jiménez López, Víctor
Snoha, L’ubomír
Powiązania:
https://bibliotekanauki.pl/articles/1205307.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Markov graph
periodic point
piecewise smooth map with nowhere vanishing Lipschitz continuous derivative
piecewise linear map
solenoid
Opis:
We show that piecewise smooth maps with a finite number of pieces of monotonicity and nowhere vanishing Lipschitz continuous derivative can have only period doubling solenoids. The proof is based on the fact that if $p_1 < ... < p_n$ is a periodic orbit of a continuous map f then there is a union set ${q_1,..., q_{n-1}}$ of some periodic orbits of f such that $p_i < q_i < p_{i+1}$ for any i.
Źródło:
Fundamenta Mathematicae; 1998, 157, 2-3; 121-138
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Approximation by nonlinear integral operators in some modular function spaces
Autorzy:
Bardaro, Carlo
Musielak, Julian
Vinti, Gianluca
Powiązania:
https://bibliotekanauki.pl/articles/1311190.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
modular space
nonlinear integral operator
generalized Lipschitz condition
approximation by singular integrals
Opis:
Let G be a locally compact Hausdorff group with Haar measure, and let L⁰(G) be the space of extended real-valued measurable functions on G, finite a.e. Let ϱ and η be modulars on L⁰(G). The error of approximation ϱ(a(Tf - f)) of a function $f ∈ (L⁰(G))_{ϱ+η} ∩ Dom T$ is estimated, where $(Tf)(s) = ∫_G K(t-s,f(t))dt$ and K satisfies a generalized Lipschitz condition with respect to the second variable.
Źródło:
Annales Polonici Mathematici; 1996, 63, 2; 173-182
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Approximation of functions from \(L^p(\omega)_\beta\) by linear operators of their Fourier series
Autorzy:
Łenski, Włodzimierz
Szal, Bogdan
Powiązania:
https://bibliotekanauki.pl/articles/744850.pdf
Data publikacji:
2011
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Rate of approximation
Summability of Fourier series
Lipschitz classes
Opis:
We show the results corresponding to theorems of S. Lal [Appl. Math. Comput., 209 (2009) 346-350] on the rate of approximation of functions from the generalized integral Lipschitz classes by matrix summability means of their Fourier series as well as to the authors theorems [Acta Comment. Univ. Tartu. Math., 13 (2009), 11-24] also on such approximations.
Źródło:
Commentationes Mathematicae; 2011, 51, 2
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Automatic simplification of the geometry of a cartographic line using contractive self-mapping – illustrated with an example of a polyline band
Autorzy:
Bac-Bronowicz, Joanna
Banasik, Piotr
Chrobak, Tadeusz
Powiązania:
https://bibliotekanauki.pl/articles/29433667.pdf
Data publikacji:
2023-12-07
Wydawca:
Oddział Kartograficzny Polskiego Towarzystwa Geograficznego
Tematy:
digital generalization
contractive self-mapping
Salichtchev’s minimum measures
geometry of a polyline in the binary tree structure
Lipschitz’s contraction triangle
Banach theorem
Opis:
The present article is another attempt to adapt map geometry to automatic digital cartography. The paper presents a method of digital polyline generalisation that uses contractive self-mapping. It is a method of simplification, not just an algorithm for simplification. This method in its 1996 version obtained a patent entitled “Method of Eliminating Points in the Process of Numerical Cartographic Generalisation” – Patent Office of the Republic of Poland, No. 181014, 1996. The first results of research conducted using the presented method, with clearly defined data (without singular points of their geometry), were published in the works of the authors in 2021 and 2022. This article presents a transition from the DLM (Digital Landscape Model) to the DCM (Digital Cartographic Model). It demonstrates an algorithm with independent solutions for the band axis and both its edges. The presented example was performed for the so-called polyline band, which can represent real topographic linear objects such as rivers and boundaries of closed areas (buildings, lakes, etc.). An unambiguous representation of both edges of the band is its axis, represented in DLM, which can be simplified to any scale. A direct consequence of this simplification is the shape of the band representing the actual shape of both edges of the object that is classified in the database as a linear object in DCM. The article presents an example performed for the so-called polyline band, which represents real topographic linear objects (roads, rivers) and area boundaries. The proposed method fulfils the following conditions: the Lipschitz condition, the Cauchy condition, the Banach theorem, and the Salichtchev’s standard for object recognition on the map. The presented method is objective in contrast to the previously used approximate methods, such as generalisations that use graph theory and fractal geometry, line smoothing and simplification algorithms, statistical methods with classification of object attributes, artificial intelligence, etc. The presented method for changing the geometry of objects by any scale of the map is 100% automatic, repeatable, and objective; that is, it does not require a cartographer’s intervention.
Źródło:
Polish Cartographical Review; 2023, 55, 1; 73-86
2450-6974
Pojawia się w:
Polish Cartographical Review
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Averages of uniformly continuous retractions
Autorzy:
Jiménez-Vargas, A.
Mena-Jurado, J.
Nahum, R.
Navarro-Pascual, J.
Powiązania:
https://bibliotekanauki.pl/articles/1217171.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
uniformly retraction
Lipschitz retraction
extreme point
Opis:
Let X be an infinite-dimensional complex normed space, and let B and S be its closed unit ball and unit sphere, respectively. We prove that the identity map on B can be expressed as an average of three uniformly retractions of B onto S. Moreover, for every 0≤ r < 1, the three retractions are Lipschitz on rB. We also show that a stronger version where the retractions are required to be Lipschitz does not hold.
Źródło:
Studia Mathematica; 1999, 135, 1; 75-81
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Bernstein and van der Corput-Schaake type inequalities on semialgebraic curves
Autorzy:
Baran, M.
Pleśniak, W.
Powiązania:
https://bibliotekanauki.pl/articles/1219584.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Bernstein and van der Corput-Schaake type inequalities
semialgebraic curves
algebraic manifolds
pluricomplex Green function
Lipschitz functions
Opis:
We show that in the class of compact, piecewise $C^1$ curves K in $ℝ^n$, the semialgebraic curves are exactly those which admit a Bernstein (or a van der Corput-Schaake) type inequality for the derivatives of (the traces of) polynomials on K.
Źródło:
Studia Mathematica; 1997, 125, 1; 83-96
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Characterizations and classification of paraconvex multimaps
Autorzy:
Mokhtar-Kharroubi, Hocine
Powiązania:
https://bibliotekanauki.pl/articles/2183481.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
support function
paraconvex multimap
Lipschitz property
generalized convexities
submonotonicity
Opis:
Paraconvex multimaps are revisited in normed vector space setting. A parallel is provided with the studies conducted for real valued paraconvex functions on generalized convexities and monotonicities. Several characterizations are then obtained. The links with some generalized convexities for multimaps are examined and a first classification is achieved. In addition, two representation results for 2-paraconvex multimaps are given.
Źródło:
Control and Cybernetics; 2022, 51, 3; 303--325
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 53

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