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.

     

On the connection between the Λ-parameters of euclidean lattice and continuum QCD

The origin of the discrepancy between recent calculations of the connection between the Λ-parameters of lattice and continuum pure gauge theory is explained. The calculation is extended to include fermions.     

A new combination of the ring oven method with chromatography - the rotating ring oven

Chromatographic techniques have been used in combination with the ring oven method in various ways. The use of a rotating ring oven in combination with column chromatography is proposed. Separations are done on a chromatographic column fixed vertically above the rotating ring oven. Thus the various substances leaving the column are concentrated successively in sharply outlined distinct segments. The apparatus is described in detail. Its use is illustrated by the example of the separation of four amino acids (0.3 μg each).Other applications (dyes, gel chromatography on Sephadex) are mentioned briefly.     

MartingaleBMO spaces with continuous time

ВВОДьтсь ДВА НОВых кл АссА пРОстРАНстВBMO, ИМ ЕУЩИх БОльшОЕ жНАЧЕНИЕ В тЕОРИИ ИНтЕРпОлИРО ВАНИь, И ДОкАжыВАУтсь НЕкОтОРыЕ сООтНОшЕНИь ЁкВИВАл ЕНтНОстИ Их И ОБыЧНых пРОстРАН стВBMO. ИжУЧАУтсь сООтВЕтстВУУЩИЕ “sharp”Ф УНкцИИ И ОБОБЩАУтсь НЕкОтОР ыЕ тЕОРЕМы гАРсИИ, И ФЕ ФФЕРМАНА И стЕИНА.     

Identifizierung von radionukliden durch halb quantitative autoradiographische bestimmung ihrer halbwertszeit mit hilfe der ringofenmethode

In the proposed method, a series of 9 rings is prepared from different μl-volumes of a solution of the radionuclide under test (specific activity 1.5–2.5 /μC/μl). At a starting time t = o and at 3 later times, each series of rings is placed on X-ray. film strips for a period of i h. After the usual development of the 4 strips, 4 density scales are obtained corresponding to 4 different times, and these can be compared by the method of weighted means. From the decrease in density of the rings, the half-life of the radionuclide cari be estimated. The method is explained for the examples ¹⁹⁸Au,⁹⁹Mo/^99mTc, ¹⁵³Sm und ¹³¹I.     

On Gell-Mann's λ-matrices,d- andf-tensors,octets, and parametrizations ofS U (3)

The algebra ofS U (3) is developed on the basis of the matrices _i ofGell-Mann, and identities involving the tensorsd _{i j k} andf _{i j k} occurring in their multiplication law are derived. Octets and the tensor analysis of the adjoint groupS U (3)/Z(3) ofS U (3) are discussed. Various explicit parametrizations ofS U (3) are presented as generalizations of familiarS U (2) results.     

Exact form factors in (1 + 1)-dimensional field theoretic models with soliton behaviour

A system of equations is derived which must be satisfied by multiparticle matrix elements of any local operator in field theories with soliton behaviour. Form factors of various operators of interest are calculated exactly by means of the known exact S-matrices in the sine-Gordon, massive Thirring, non-linear σ^?, and Gross-Neveu models. The finite sine-Gordon wave function renormalization constant is determined exactly.