Algebraic Interpolation in Uniform Norm

2008 ◽  
pp. 235-318
Keyword(s):  
Uniform Norm

scholarly journals MONOTONE ECONOMICAL SCHEMES FOR QUASILINEAR PARABOLIC EQUATIONS

2002 ◽  
Vol 7 (2) ◽  
pp. 207-216
Author(s):  
N. V. Dzenisenko ◽  
A. P. Matus ◽  
P. P. Matus
Keyword(s):  
A Priori Estimates ◽  
A Priori ◽  
Quasilinear Parabolic Equation ◽  
Uniform Norm ◽  
Additive Scheme ◽  
Quasilinear Parabolic Equations ◽  
The Maximum Principle ◽  
Priori Estimates ◽  
The Difference ◽  
Quasilinear Parabolic

In order to approximate a multidimensional quasilinear parabolic equation with unlimited nonlinearity the economical vector‐additive scheme is constructed. It is shown that its solution satisfies the maximum principle and, hence, the scheme is monotone. The proof is based on the equivalence of the vector‐additive scheme and the scheme of summarized approximation (locally one‐dimensional scheme). The a priori estimates of the difference solution in the uniform norm are obtained.

scholarly journals POSTRZEGANIE ZWYCZAJÓW ODNOSZĄCYCH SIĘ DO OBOWIĄZKU ZACHOWANIA POUFNOŚCI W ARBITRAŻU. ANALIZA WYNIKÓW ANKIETY PRZEPROWADZONEJ PRZEZ SĄD ARBITRAŻOWY LEWIATAN WŚRÓD POLSKICH PRAKTYKÓW ARBITRAŻOWYCH

2016 ◽  
Vol 13 (3) ◽  
pp. 89
Author(s):  
Beata Gessel-Kalinowska vel Kalisz
Keyword(s):  
Public Opinion ◽  
Legal System ◽  
Uniform Norm ◽  
Professional Group ◽  
Controversial Issues ◽  
The Social ◽  
The Subject ◽  
The Right ◽  
Confidentiality And Privacy

THE PERCEPTION OF THE PRACTICE OF CONFIDENTIALITY IN ARBITRATION. AN ANALYSIS OF THE RESULTS OF A SURVEY CARRIED OUT BY THE LEWIATAN COURT OF ARBITRATION AMONG POLISH ARBITRATION PRACTITIONERS Summary As with numerous other systems of law, such as Norwegian, Swedish or Australian law, the Polish legal system does not have a clear and uniform norm of law governing confidentiality and privacy in arbitration. Public opinion frequently refers to the role of custom as the source of the obligation to preserve confidentiality, although usually it does so without a detailed analysis of the subject and object of this obligation. This fact provided the inspiration for a survey carried out among Polish arbitration practitioners. The results of the survey present an interesting picture of what is subjectively perceived by arbitration practitioners as forming part of the confidentiality canons in arbitration proceedings. In principle, they reflect the worldwide trends, i.e. as far as the object of the confidentiality obligation is concerned – in camera sessions and the confidentiality of awards, and as regards its subject – the confidentiality obligation imposed on arbitrators and arbitration institutions. In addition, the customary practice of keeping confidential any information obtained in the course of proceedings is perceived as the right conduct as far as the object of the obligation is concerned. One of the very controversial issues is the matter of parties’ responsibilities, which leads to further questions as to individual arbitrators’ membership of the social (professional) group known as “arbitration practitioners”.

Simultaneous Approximations of Polynomials and Derivatives and Their Applications to Neural Networks

2008 ◽  
Vol 20 (11) ◽  
pp. 2757-2791 ◽  
Author(s):  
Yoshifusa Ito
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Uniform Norm ◽  
Degree Of Approximation ◽  
Probability Measures ◽  
Compact Sets ◽  
Network Parameters ◽  
Whole Space ◽  
Hidden Layer ◽  
Approximating Polynomials

We have constructed one-hidden-layer neural networks capable of approximating polynomials and their derivatives simultaneously. Generally, optimizing neural network parameters to be trained at later steps of the BP training is more difficult than optimizing those to be trained at the first step. Taking into account this fact, we suppressed the number of parameters of the former type. We measure degree of approximation in both the uniform norm on compact sets and the Lp-norm on the whole space with respect to probability measures.

Talagrand’s quadratic transportation cost inequalities for SPDEs driven by fractional noises with two reflection walls

2021 ◽  
pp. 2250004
Author(s):  
Yumeng Li
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Transportation Cost ◽  
Uniform Norm ◽  
Continuous Functions ◽  
Partial Differential ◽  
Girsanov’S Transformation ◽  
Fractional Noises

Using the method of Girsanov’s transformation, we investigate Talagrand’s quadratic transportation cost inequalities for the laws of the solutions of stochastic partial differential equations (SPDEs) with two reflection walls under the uniform norm on the continuous functions space. These equations are driven by fractional noises.

The Best Interpolating Approximation is a Limit of Best Weighted Approximations

1982 ◽  
Vol 25 (4) ◽  
pp. 502-503 ◽  
Author(s):  
Lee L. Keener
Keyword(s):  
Uniform Norm ◽  
Weight Functions

AbstractUnder appropriate conditions it is shown that the best interpolating approximation to a given function in the uniform norm is a limit of best unconstrained approximations with respect to a certain sequence of discontinuous weight functions.

Weak Solutions for Semi-Martingales

1981 ◽  
Vol 33 (5) ◽  
pp. 1165-1181 ◽  
Author(s):  
J. Pellaumail
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Weak Solution ◽  
Stochastic Differential Equation ◽  
Marginal Distribution ◽  
Uniform Norm ◽  
Section 8 ◽  
Initial Space ◽  
Sample Paths ◽  
The Given

The fundamental theorem of this paper is stated in Section 8. In this theorem, the stochastic differential equation dX = a(X)dZ is studied when Z is a *-dominated (cf. [15]) Banach space valued process and a is a predictable functional which is continuous for the uniform norm.For such an equation, the existence of a “weak solution” is stated; actually, the notion of weak solution here considered is more precise than this one introduced by Strook and Varadhan (cf. [30], [31], [23]).Namely, this weak solution is a probability, so-called “rule,” defined on (DH × Ω), DH being the classical Skorohod space of all the cadlag sample paths and Ω is the initial space which Z is defined on: the marginal distribution of R on Ω is the given probability P on Ω. This concept of rule is defined in Section 3.

scholarly journals The Role of Nonpolynomiality in Uniform Approximation by RBF Networks of Hankel Translates

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Isabel Marrero
Keyword(s):  
Uniform Approximation ◽  
Linear Span ◽  
Uniform Norm ◽  
Continuous Functions ◽  
Rbf Networks

Givenμ>-1/2andc∈I=]0,∞[, let the spaceCμ,c(respectively,Cμ) consist of all those continuous functionsuon]0,c](respectively,I) such that the limitlimz→0+⁡z-μ-1/2u(z)exists and is finite;Cμ,cis endowed with the uniform normuμ,∞,c=supz∈[0,c]⁡z-μ-1/2u(z)  (u∈Cμ,c).Assumeϕ∈Cμdefines an absolutely regular Hankel-transformable distribution. Then, the linear span of dilates and Hankel translates ofϕis dense inCμ,cfor allc∈Iif, and only if,ϕ∉πμ, whereπμ=span{t2n+μ+1/2:n∈Z+}.

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