Unions and Intersections of Families of Lp-Spaces

Let L^Ψ and E^Ψ be the ORLICZ space and the space of finite elements respectively, on a measure space (Ω, Σ, μ), and let T ? (0, ∞). It is proved that if inf {p: p ? T} ? T or sup {p: p ? T} ? T and μ is an infinite atomless measure, then there is no ORLICZ function Ψ such that: \documentclass{article}\pagestyle{empty}\begin{document}$ L^\varphi = Lin\mathop { \cup L^p }\limits_{p\varepsilon T} $\end{document} or \documentclass{article}\pagestyle{empty}\begin{document}$ E^\varphi = Lin\mathop { \cup L^p }\limits_{p\varepsilon T} $\end{document} and moreover, there is no ORLICZ function Ψ such that: \documentclass{article}\pagestyle{empty}\begin{document}$ L^\varphi = Lin\mathop { \cap L^p }\limits_{p\varepsilon T} $\end{document} or \documentclass{article}\pagestyle{empty}\begin{document}$ E^\varphi = Lin\mathop { \cap L^p }\limits_{p\varepsilon T} $\end{document}.     

Final results on μe-pair production in neutrino interactions in the SKAT freon bubble chamber experiment

We present the final results from the search for μe pairs produced in neutrino interactions using the freon filled bubble chamber SKAT. The rate of μ^? e ⁺ pairs to charged current events above the charm threshold is \(R_{\mu ^ - e^ + } = (4.8 \pm 1.1)10^{ - 3} \) . Assuming charm particle production to be the origin of the positron we calculate \(R_{\Lambda _c^ + } = (6.2 \pm 3.1)10^{ - 2} \) andR _D =(2.8±0.9)10^?2. We observe no considerable μ^? e ^? pair production above the background. In the regionE _v >3 GeV,p _μ,e >1.0 GeV/c andp _μ>p _e we find with a 90% confidence level the limit \(R_{\mu ^ - e^ - }< 1.7 10^{ - 4} \) .     

On Calderón-Toeplitz operators

We discuss boundedness and Schatten ideal criteria for a class of Toeplitz style operators based on the Calderón reproducing formula. These operators are a variation on Calderón-Zygmund operators but our results also apply to classical Toeplitz operators acting on the weighted Bergman space of the upper half plane.     

An analogue to a conjecture of S. Chowla and H. Walum

It is proved that (for every ε > 0)

$\text{∑}\text{n?T}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{∑n<}\text{T}\text{n}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{n}{}^{\mathrm{a}}\text{m}{}^{\mathrm{b}}\text{B}{}_{\mathrm{k}}\text{({}\text{T}\text{nm}\text{}) = O(T}{}^{\mathrm{<mtext>(a+b+1)</mtext><mtext>3?</mtext>}}\text{)}$

(where {·} denotes the fractional part and B_k the Bernoulli polynomial of order k) under the suppositions that k ≥ 2 and 2a ? 1 ≥ b ≥ 1. If (1) were true for k = 1, a = b = 0, then Piltz' divisor problem (for n = 3) would be readily solved. This is an analog to a conjecture formulated by S. Chowla and H. Walum in 1963 and settled in the affirmative (under suitable suppositions) quite recently by S. Kanemitsu and R. Sita Rama Chandra Rao.     

Properties of multiplicity distributions in νA and\bar v A intersections atE_{\begin{array}{*{20}c} {( - )} \\ v \\ \end{array} }< 30GeV

We present data on the multiplicity structure of inclusive charged hadron production in charged current neutrino and antineutrino freon interactions in the energy range 3–30 GeV resulting from an experiment with the bubble chamber SKAT. Average multiplicities, dispersions and correlation coefficients are investigated. Furthermore, KNO-scaling is studied and average net charges are calculated in different kinematical regions. Our data are compared with results from \(\begin{array}{*{20}c} {( - )} \\ v \\ \end{array} \) -interactions on an isoscalar target of “free” nucleons to study the influence of nuclear effects.     

A biosensor for monitoring formaldehyde using a new lipophilic tetrathiafulvalene-tetracyanoquinodimethane salt and a polyurethane membrane

The fabrication and application of an end-column amperometric detection (AD) system with a carbon electrode for capillary-column liquid chromatography (CLC) were described. This new amperometric detector showed good sensitivity and stability in detecting the thiocompounds and other analytes with CLC. In order to obtain the better separation and detection performance for analytes, several operational parameters had been investigated: the working potentials, pH and flow rate. Under the optimum conditions, the method could effectively separate and determine cysteine (Cys), glutathione (GSH), dopamine (DA) and 6-thiopurine (6-TP). Good repeatability for retention time was obtained with a relative standard deviation (R.S.D.) value of 0.5%. The linear range covered over three orders of magnitude and the limits of detection were 8 fmol for cysteine, 20 fmol for glutathione, 8 fmol for dopamine and 20 fmol for 6-thiopurine. This method was successfully applied in determination of urinary sample with characteristics of simplicity, high sensitivity and good repeatability.     

Lattice points in a circle and divisors in arithmetic progressions

Let A(x) denote the number of lattice points in the circle u²+v²x and define as the infimum of all reals for which . The objective of this paper is to show that 35/108 which improves upon all previously known results. This estimate is an immediate consequence of a surprisingly easy generalization of KOLESNIK's work on Dirichlet's divisor problem to divisor functions with respect to arithmetic progressions.