Adjoint classes of functions in the H<Subscript>1</Subscript> sense

Using the concept of the H₁-integral, we consider a similarly defined Stieltjes integral. We prove a Riemann-Lebesgue type theorem for this integral and give examples of adjoint classes of functions.     

Kunststoffe

Ohne Zusammenfassung     

Zur Harnstoffbestimmung nach Liebig

Ohne Zusammenfassung     

Über Paraldol und zähflüssiges Acetaldol

Ohne ZusammenfassungZum Schlüsse obliegt mir noch die angenehme Pflicht, Herrn Hofrath Lieben für die Unterstützung und Antheilnahme an meiner Arbeit, wie dem Herrn Dr. Leopold Kohn meinen tiefgefühlten Dank auszusprechen.     

Approximation algorithms for MAX–MIN tiling

The MAX–MIN tiling problem is as follows. We are given A[1,…,n][1,…,n], a two-dimensional array where each entry A[i][j] stores a non-negative number. Define a tile of A to be a subarray A[ℓ,…,r][t,…,b] of A, the weight of a tile to be the sum of all array entries in it, and a tiling of A to be a collection of tiles of A such that each entry A[i][j] is contained in exactly one tile. Given a weight bound W the goal of our MAX–MIN tiling problem is to find a tiling of A such that: (1) each tile is of weight at least W (the MIN condition), and (2) the number of tiles is maximized (the MAX condition). The MAX–MIN tiling problem is known to be NP-hard; here, we present first non-trivial approximations algorithms for solving it.     

Multinuclear magnetic resonance studies of fluoronitroanilines

Ten fluoronitroanilines have been synthesized and the ¹H, ¹³C, ¹⁵N and, ¹⁹F NMR spectra of these compounds have been recorded and fully assigned. Density functional theory(DFT) calculations have been performed for all compounds studied. Experimental and theoretical results are compared and the structure and atom character influence on the accuracy of the calculation discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Relating transplantation and multipliers for Dunkl and Hankel transforms

By expressing the Dunkl transform of order α of a function f in terms of the Hankel transforms of orders α and α + 1 of even and odd parts of f, respectively, we show that a considerable part of harmonic analysis of the Dunkl transform on the real line may be reduced to known results for the Hankel transform. In particular, defining the modified Dunkl transform and then considering the Dunkl transplantation operator we transfer known multiplier results for the Hankel transform to the Dunkl transform setting. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

TG study on real role of active carbon support in propane dehydrogenation with CO2

Active carbon was used as a support for chromium(III) oxide phase. The synthesized materials appeared to be very active catalysts of the propane dehydrogenation in the presence of CO₂. An influence of the Cr content on the catalytic activity and selectivity was observed. The best results were achieved over the sample containing about 5 wt.% of Cr. A negative effect of activity decay with time-on-stream was found. The reasons of the observed deactivation were explained using the thermal analysis method. A behavior of the fresh and used samples was tested in a temperature range of 25–1000 °C in different atmospheres (inert gas, air or CO₂). It was found that the catalytic runs resulted in a partial decomposition of surface O-containing groups, which together with CrO_x species play a role of active centers. Moreover, a formation of inactive carbonaceous deposit on the catalyst surface was observed.