Angular distributions in the dimuon hadronic production at 150 GeV/c

From π^- interactions at 150 GeV/c on a heavy target, we present the final analysis of the dimuon decay angular distribution in the mass interval 4.5–8.5 GeV/c². Results are presented and discussed in various reference frames and are also given in terms of the density matrix elements. Finally the possible contribution of higher-twist effects at largex ₁ is discussed; we find that our data are not compatible with higher twist contributions as proposed by the Berger and Brodsky Model.     

Uranylacetat als Sprühreagens in der Dünnschichtchromatographie

Zusammenfassung Sprüht man eine l%ige wäßrige Lösung von Uranylacetat auf eine mit Kieselgel G beschichtete Platte, so erhält man nach dem Trocknen eine gelbgrüne Fluoreszenz im UV (254 nm), die durch zahlreiche Stoffe gelöscht wird. Dies kann zum Nachweis der verschiedensten Substanzen nach ihrer dünnschichtchromatographischen Trennung verwendet werden. Beispiele für die Erfassungsgrenzen werden angegeben.

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Summary If a 1% aqueous solution of uranyl acetate is sprayed on a plate carrying a layer of silica gel G and then dried, there results a yellow-green fluorescence in UV (254 nm) that is quenched by numerous materials. This finding can be employed for the detection of the most varied substances after they have been separated by thin layer Chromatographic procedures. Examples of the sensitivity limits are given.

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Résumé Si l'on vaporise une solution aqueuse à 1% d'acétate d'uranyle sur une plaque recouverte de gel de silice G, on obtient après séchage une fluorescence vert-jaune dans l'UV (254 nm), éteinte par de nombreuses substances. On peut utiliser ce phénomène pour la recherche de substances très variées après leur séparation par Chromatographie en couche mince. On donne des exemples pour les limites de dilution.

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Wir danken der Alexander-von-Humboldt-Stiftung, die diese Arbeit durch ein Stipendium (H. S.) ermöglieht hat.     

Duality results and inequalities with respect to Hardy spaces containing function sequences

With the help of two-parameter martingales and strong martingales Hardy spaces consisting of adapted function sequences are considered. The Hardy spaces generated by the square and by the conditional square functions and their dual spaces are investigated. An inequality due to Stein and Lepingle is extended to two parameters.This research was supported by the Hungarian Scientific Research Funds No. 2085 and No. 74189 as well as by DAAD, the lattest with a stay at the Ludwig-Maximilians-Universität in München.     

Inversion of the Short-Time Fourier Transform Using Riemannian Sums

The inversion formula for the short-time Fourier transform is usually considered in the weak sense, or only for specific combinations of window functions and function spaces such as L₂ and modulation spaces. In the present note the Riemannian sums of the inverse short-time Fourier transform are investigated. Under some conditions on the window functions we prove that the Riemannian sums converge to f in the modulation spaces and inWiener amalgam norms, hence also in the L_p sense.     

Triangular Ces??ro summability of two dimensional Fourier series

It is proved that the maximal operator of the triangular Ces??ro means of a two-dimensional Fourier series is bounded from the periodic Hardy space $H_{p}(\mathbb{T}^{2})$ to $L_{p}(\mathbb{T}^{2})$ for all 2/(2+??)<p?Q?? and, consequently, is of weak type (1,1). As a consequence we obtain that the triangular Ces??ro means of a function $f \in L_{1}(\mathbb{T}^{2})$ converge a.e. to?f.     

On a-Posteriori Error Estimate of Approximate Solutions to a Mildly Nonlinear Nonpotential Elliptic Boundary Value Problem

The paper deals with the construction of a computable a-posteriori error estimate of the approximate solution to some nonpotential nonlinear elliptic boundary value problems. The convergence of the presented error estimate to the true error is proved. The method is illustrated on some numerical examples.     

Herz spaces and summability of Fourier transforms

A general summability method is considered for functions from Herz spaces K^α_p,r (?^d ). The boundedness of the Hardy–Littlewood maximal operator on Herz spaces is proved in some critical cases. This implies that the maximal operator of the θ ‐means σ^θ _T f is also bounded on the corresponding Herz spaces and σ^θ _T f → f a.e. for all f ∈ K^{–d /p} _p,∞ (?^d ). Moreover, σ^θ _T f (x) converges to f (x) at each p ‐Lebesgue point of f ∈ K^{–d /p} _p,∞ (?^d ) if and only if the Fourier transform of θ is in the Herz space K^{d /p} _{p ′,1} (?^d ). Norm convergence of the θ ‐means is also investigated in Herz spaces. As special cases some results are obtained for weighted L_p spaces. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Anwendung des Ringofens in der Tüpfelkolorimetrie

Zusammenfassung Die bereits früher beschriebene Ringofenmethode wurde zu tüpfelkolorimetrischen Analysen verwendet. Mehrere Ringe mit verschiedener Zahl von Probetropfen wurden hergestellt und mit Standardringen verglichen. Es ist nicht nötig, genau zu schätzen. Eine annähernde Zuordnung der Proberinge zu den Standardringen reicht aus, um brauchbare Resultate zu erhalten. Als Beispiele wurden beschrieben: Die Bestimmung des Eisens mit Kaliumferrocyanid, des Nickels mit Dimethylglyoxim, des Kobalts mit-Nitroso--Naphthol, des Kupfers mit Schwefelwasserstoffwasser und Umwandlung des Kupfersulfids in eine äquivalente Menge Silbersulfid. — Die Abtrennnng störender Ionen kann in den meisten Fällen auf dem Papier selbst erfolgen.

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Summary The ring furnace method already described was employed for spot colorimetric analyses. Several rings with different numbers of sample drops were prepared and compared with standard rings. An exact estimate is not necessary. An approximate coordination of the test rings to the standard rings is adequate for obtaining usable results. Examples described include determination of: iron with potassium ferrocyanide, nickel with dimethylglyoxime, cobalt with-nitroso-naphtol, copper with hydrogen sulfide water and conversion of the copper sulfide into its equivalent of silver sulfide. In most cases, the removal of interfering ions can be accomplished on the paper itself.

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Résumé On utilise pour des analyses colorimétriques à la goutte, la méthode du four annulaire déjà décrit. On a obtenu plusieurs anneaux avec des gouttes d'essai différentes et on les compare à des anneaux étalons. Il n'est pas nécessaire d'opérer d'une façon précise. Une comparaison approchée des anneaux de la substance et de l'étalon suffit pour obtenir des résultats utilisables. Comme exemples, on décrit: le dosage du fer avec le ferrocyanure de potassium, du nickel avec la diméthylglyoxime, du cobalt avec l'-nitroso-naphtol, du cuivre avec la solution d'hydrogène sulfuré et la transformation du sulfure de cuivre en la quantité équivalente de sulfure d'argent. La séparation des ions gênants peut, dans la plupart des cas, s'effectuer sur le papier lui-même.