Extension of a theorem of P. Wolfe on singular integral equations

The integral operator which sends f (ζ) into $$\int_{|\xi |< 1} {\tfrac{{f(\xi )}}{{|x - \xi |^{p - 1} }}} d\xi = g(x)(|x|< 1)$$ x and ζ ∈ R^P, is shown to map the space of functions f (ζ) on |ζ|<1, square integrable with respect to the weight (1-|ξ|²)^1/2 one to one onto the space of functions g (x) on |x|<1 which possess gradients δg(x) in the sense of distribution theory, with both g(x) and δg(x) being square integrable with respect to the weight (1-|x|²)^1/2. This extends to p≥3 a result of P. Wolfe's in the case p=2.     

Further study of theE/f 1 (1420) meson in central production

We have studied the reactions \(({{\pi ^ + } \mathord{\left/ {\vphantom {{\pi ^ + } p}} \right. \kern-0em} p})p \to ({{\pi ^ + } \mathord{\left/ {\vphantom {{\pi ^ + } p}} \right. \kern-0em} p})(K\bar K\pi )p\) where the \(K\bar K\pi \) system is centrally produced, at 85 GeV/c and 300 GeV/c using the CERN Omega spectrometer. A spin-parity analysis of theK _S ⁰ K ^± π ^? system shows the presence of a strongJ ^PC=1⁺⁺ signal which we identify as theE/f ₁ (1420) meson. We also find evidence for the decayE/f ₁(1420)→K _S ⁰ K _S ⁰ π ⁰ which determines theC-parity of this state to be positive. Alternative explanations of the data have been tested and ruled out. Hence we obtain the quantum numbers of theE/f ₁ (1420) to beI ^G(J^PC)=0⁺(1⁺).     

Sur les séries de Taylor et les transformations de Möbius

Given a non-empty closed subsetF of the unit circle |z|=1, and a Möbius transformationM(z) of the unit disc |z|1, such thatM(0)0, there exists a functionf(z) holomorphic in the unit disc,F being the singular set at the boundary, whose Taylor coefficients tend to zero while the Taylor coefficients off(M(z)), do not tend to zero.     

On the asymptotic behavior of solutions of a mildly nonlinear parabolic system

In this paper we study the asymptotic behavior of solutions to the mixed initial boundary value problem for the system of nonlinear parabolic equations

$\text{?u}{}_{\mathrm{t}}\text{+Lu=f(x.t.u.v)}\text{?v}{}_{\mathrm{t}}\text{+Mv=g(x,t,u,v)}$

We show, under suitable technical assumptions, that these solutions converge to solutions of the Dirichlet problem for the corresponding limiting elliptic system, provided that the solution of the Dirichlet problem is unique.     

The refocused INADEQUATE MAS NMR experiment in multiple spin-systems: interpreting observed correlation peaks and optimising lineshapes

The robustness of the refocused INADEQUATE MAS NMR pulse sequence for probing through-bond connectivities has been demonstrated in a large range of solid-state applications. This pulse sequence nevertheless suffers from artifacts when applied to multispin systems, e.g. uniformly labeled (13)C solids, which distort the lineshapes and can potentially result in misleading correlation peaks. In this paper, we present a detailed account that combines product-operator analysis, numerical simulations and experiments of the behavior of a three-spin system during the refocused INADEQUATE pulse sequence. The origin of undesired anti-phase contributions to the spectral lineshapes are described, and we show that they do not interfere with the observation of long-range correlations (e.g. two-bond (13)C-(13)C correlations). The suppression of undesired contributions to the refocused INADEQUATE spectra is shown to require the removal of zero-quantum coherences within a z-filter. A method is proposed to eliminate zero-quantum coherences through dephasing by heteronuclear dipolar couplings, which leads to pure in-phase spectra.     

Limits of chromatic zeros of some families of maps

Two families of maps are considered, one consisting of maps with two pentagons separated by n 5-rings, the other of maps with two n-gons separated by two n-rings. For each family, a homogeneous linear recursion is derived for the corresponding family of chromatic polynomials. It is shown that B₅, B₇, and B₁₀ are limits of sequences of zeros from one or another of the families, where $\text{B}{}_{\mathrm{n}}\text{= 2(1+}\text{cos}\text{2π}\text{n}\text{)}$.     

Allgemeine Methoden

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