Third‐order WENO scheme with a new smoothness indicator

In this article, we have devised a new reference smoothness indicator for third‐order weighted essentially non‐oscillatory (WENO) scheme to achieve desired order of convergence at critical points. In the context of the weighted essentially non‐oscillatory scheme, reference smoothness indicator is constructed in such a way that it satisfies the sufficient condition on the weights for the third‐order convergence. The goal is to construct a reference smoothness indicator such that the resulted scheme have to achieve the required order of accuracy even if the first two derivatives vanish but not the third derivative. The construction of such reference smoothness indicator is not possible through a linear combination of local smoothness indicators only. We have proposed a reference smoothness indicator to be of the fourth order of accuracy on three‐point stencil that contains the linear combination of the first derivative information of the local and global stencils. The performance enhancement of the WENO scheme through this reference smoothness indicator is verified through the standard numerical experiments. Numerical results indicate that the new scheme provides better results in comparison with the earlier third‐order WENO schemes like WENO‐JS and WENO‐Z. Copyright © 2017 John Wiley & Sons, Ltd.     

Weighted estimates for strongly singular integral operators with rough kernels

The Fourier transform and the Littlewood-Paley theory are used to give the weighted boundedness of a strongly singular integral operator defined in this paper. The paper shows that the strongly singular integral operator is bounded from the Sobolev space to the Lebesgue space.     

Determination of molecular weights and Mark–Houwink constants for soluble electronically conducting polymers

Intrinsic viscosities and gel permeation chromatography data were used to evaluate the Mark–Houwink constants of the soluble electronically conducting polymer, poly(3-hexylthiophene) (P3HT):K and a are 2.28 × 10^-3 cm³/g and 0.96, respectively, in tetrahydrofuran (THF) at 25°C. Mark–Houwink constants were used to calibrate gel permeation chromatography (GPC) columns for P3HT. Number-average molecular weights of P3HT determined with modified calibration curves agreed well with those determined by an absolute method, embulliometry. Molecular weights estimated using unmodified polystyrene calibration procedures were significantly larger than true values.     

The Mixed Norm Spaces of Polyharmonic Functions

Let be a bounded domain with C ² boundary. And let H _k be the set of all polyharmonic functions f with order k on Ω. For 0<p, q≤∞ and ϕ a normal weight, the mixed-norm space consists of all function f in H _k for which the mixed-norm ||·|| _{p, q, ϕ} <∞. The main result of the paper is the norm equivalence:

Commutators of weighted lipschitz functions and multilinear singular integrals with non-smooth kernels

This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained.     

Some Indeterminate Moment Problems and Freud-Like Weights

We study two indeterminate Hamburger moment problems and the corresponding orthogonal polynomials. The coefficients in their recurrence relations are of exponential growth or are polynomials of degree 2. The entire functions in the Nevanlinna parametrization are found. The orthogonal polynomials with polynomial recurrence coefficients resemble the Freud polynomials with a = 1/2 . Inequalities are given for the largest zero and the asymptotic behavior of the largest zero is established. April 24, 1996. Date revised: March 3, 1997.     

Mikroprozessor-Interface zur on-line Erfassung von Wägedaten

Zusammenfassung Als ergänzender Schritt für die Automatisierung der Flüssigkeitschromatographie wurde in unseren analytischen Laboratorien für Routinemessungen die automatische Erfassung von Wägedaten während der Probenvorbereitung eingeführt. Zu diesem Zweck wurde ein von einem Mikroprozessor gesteuertes Datenerfassungsgerät entwickelt, welches die Gewichtswerte von der Analysenwaage on-line in das Hewlett-Packard Lab-Data-System 3354 übermittelt. Das bedienungsfreundliche Konzept bringt eine wesentliche Arbeitserleichterung und schließt Fehlermöglichkeiten weitgehendst aus. Mit Geräten, welche seit über einem Jahr in Betrieb stehen konnten die Erwartungen voll erfüllt werden.

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Microprocessor-interface for the on-line aquisition of weight data

Summary With the on-line data aquisition of sample weights an additional step to the automation of liquid chromatography was introduced in our analytical laboratories. A new developed microprocessor controlled equipment connects a balance to the Hewlett-Packard Lab-Data-System 3354 and controls the on-line transfer of the weight data. The design is based on an easy application for users and gives essential reductions of workload and of error possibilities. Equipment are now in use with excellent results for over one year.

     

On bornologicalC $$\overline V $$ (X) spaces

Archiv der Mathematik -     

关于加权的帐篷空间

本文建立了加权的帐篷空间，把帐篷空间中的一些主要结果推广到加权的情形，同时刻划了Ap权函数与Carleson测度的一种新的关系。     

Antisymmetry of solutions for some weighted elliptic problems

This article concerns the antisymmetry, uniqueness, and monotonicity properties of solutions to some elliptic functionals involving weights and a double well potential. In the one-dimensional case, we introduce the continuous odd rearrangement of an increasing function and we show that it decreases the energy functional when the weights satisfy a certain convexity-type hypothesis. This leads to the antisymmetry or oddness of increasing solutions (and not only of minimizers). We also prove a uniqueness result (which leads to antisymmetry) where a convexity-type condition by Berestycki and Nirenberg on the weights is improved to a monotonicity condition. In addition, we provide with a large class of problems where antisymmetry does not hold. Finally, some rather partial extensions in higher dimensions are also given.