Перестановки систем ы Хаара в пространств ахℒ p

Linear operators of the form are studied, where { _n ^k } denotes the Haar system and _n a permutation of the integers 1, 2, ..., 2 ⁿ . Conditions ensuring boundedness of these operators in the Lorentz spacesL _p,q , and in particular inL _p , are found.     

Arithmetic properties of the Markov function for the Jacobi weight

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Hydroxy- and alkoxymethylation of polyfluoroalkyl pyrazoles

A synthetic route to 1-hydroxy- and 1-alkoxymethyl-3-polyfluoroalkylpyrazoles via regioselective N-hydroxy- and alkoxymethylation of N-unsubstituted pyrazoles with paraformaldehyde has been proposed. The alkoxyalkylation of polyfluoroalkylpyrazoles proceeds in aqueous-alcohol medium, whereas hydroxymethylation requires anhydrous conditions.     

О ДИФФЕРЕНцИРОВАНИИ ИНтЕгРАлОВ От ФУНкцИ И Иж сИММЕтРИЧНых пРОс тРАНстВ ДИФФЕРЕНцИАльНыМИ Б АжИсАМИ

We consider new methods of constructing differential bases. Symmetric spaces with essentially different fundamental functions at zero can be defined by means of differential bases. Even the Lorentz and Marcinkiewicz or the Lebesgue and Marcinkiewicz spaces can be defined by means of differential bases.     

Многомерные вариаци и множеств и их контин генции

LetE be a compact set inR ⁿ (n≧2), and denote byV ₀(E) the number of the components ofE. Letp=1,2, ...,n?1;k=0,1, ...,p, and $$V_k (E;n,p) = \int\limits_{\Omega _k^n } {V_0 (E \cap \tau )^{{{(n - p)} \mathord{\left/ {\vphantom {{(n - p)} {(n - k)}}} \right. \kern-\nulldelimiterspace} {(n - k)}}} d\mu _\tau ,}$$ whereΩ _k ⁿ is the set of all (n-k)-dimensional hyperplanesτ?R ⁿ anddμ _τ is the Haar measure on the spaceΩ _k ⁿ ; furthermore, let $$V_n (E;n,n - 1) = mes_n E.$$ . Theorem. Let E?Rⁿ, p=1, 2 ..., n?1, V_p+1(E;n,p)=0, and V_k(E; n, p)<∞ for k= =0,1, ..., p. Then the contingency of the set E at a point x∈E coincides with a certain p-dimensional hyperplane for almost all points x∈E in the sense of Hausdorff p-measure.     

Получение изотопа С13 методом ректиФикации окиси углерода

A prompt activation technique – detection of the α-particles with surface barrier silicon and solid state track detectors, detection of the γ rays with (GeLi) detector – based on the ¹⁰B(n, α)⁷Li nuclear reaction was applied for boron determination using a time-of-flight technique on the IBR-30 pulsing reactor. The method was used for measurement of the boron concentration and distribution in bean and maize leaves.     

Functionalized polynorbornenes with organosilicon groups in the side chains. Synthesis and photophysical properties

Using the method of metathesis polymerization carbon-chain homopolymers containing triрhenylsilyl, tritolylsilyl and trithienylsilyl groups in the side chains, as well as their copolymers with additional carbazole-containing units have been synthesized. Photophysical properties of the obtained compounds were investigated. All polymer products show an intense photoluminescence in the blue region of the spectrum. The largest quantum yield (61.4%) was shown by the copolymer with triphenylsilyl and carbazole side groups.