Gravitational self-force on a particle orbiting a Kerr black hole

We present a practical method for calculating the gravitational self-force, as well as the electromagnetic and scalar self-forces, for a particle in a generic orbit around a Kerr black hole. In particular, we provide the values of all the regularization parameters needed for implementing the (previously introduced) mode-sum regularization method. We also address the gauge-regularization problem, as well as a few other issues involved in the calculation of gravitational radiation reaction in Kerr spacetime.     

(+)-Rimocidin synthetic studies. Construction of an advanced C(1-18) polyol fragment

[structure: see text] The synthesis of an appropriately functionalized advanced C(1-18) polyol fragment of the mycosamine-glycosylated polyene macrolide, (+)-rimocidin (1), has been achieved in a highly efficient manner. Highlights of the strategy include the S(N)2/S(N)2' addition of dithiane anions to vinyl epoxides and the multicomponent linchpin union of 2-TBS-1,3-dithiane with two advanced epoxides.     

Spherical maximal operator on symmetric spaces of constant curvature

We prove an endpoint weak-type maximal inequality for the spherical maximal operator applied to radial funcions on symmetric spaces of constant curvature and dimension . More explicitly, in the Lorentz space associated with the natural isometry-invariant measure, we show that, for every radial function ,

The proof uses only geometric arguments and volume estimates, and applies uniformly in every dimension.

     

Ratio of jet cross sections at square root of s = 630 GeV and 1800 GeV

The D0 Collaboration has measured the inclusive jet cross section in barpp collisions at square root of s = 630 GeV. The results for pseudorapidities (eta)<0.5 are combined with our previous results at square root of s = 1800 GeV to form a ratio of cross sections with smaller uncertainties than either individual measurement. Next-to-leading-order QCD predictions show excellent agreement with the measurement at 630 GeV; agreement is also satisfactory for the ratio. Specifically, despite a 10% to 15% difference in the absolute magnitude, the dependence of the ratio on jet transverse momentum is very similar for data and theory.     

Analyses of electron and proton scattering to low-excitation isoscalar states in 20Ne, 24Mg and 28Si

The excitation of low-lying isoscalar 2⁺ and 4⁺ states in ²⁰Ne, ²⁴Mg and ²⁸Si by electron and proton scattering is studied. Large basis models of nuclear structure are used to determine both the electromagnetic and hadronic transition densities. The analyses of the longitudinal form factors obtained from electron scattering show that little or no effective charges are required with these nuclear structure models. Proton inelastic scattering to these states then is analysed to test effective forces based upon the Paris and Hamada-Johnston interactions. At intermediate energies (155 MeV) density-dependent t-matrices from both potentials were used with fits to data giving a clear preference for that based upon the Paris interaction. For lower energies only the Hamada-Johnston t-matrix is available and comparison of analyses of 24 and 49 MeV data made using this (complex) t-matrix with those in which the (real) Paris G-matrix is used as the effective force show a clear preference for the t-matrix. This is particularly the case with analyses of polarization data and suggests that the use of the G-matrix as an effective force in nuclear reaction calculations is inadequate even at low energies.     

Fourier transform infrared study of two truxene-based discotic liquid crystals

We have used FTIR absorption to study the crystalline and liquid-crystalline phases of 2,3,7,8,12,13-hexa-n-tetradecanoyloxy-truxene (HATX) and 2,3,7,8,12,13-hexa(4-n-undecyloxybenzoyloxy)truxene (HBTX). Both materials show pronounced changes in the CH₂ stretching mode frequencies at their melting points. In addition, HATX shows a transition at about 20°C below the nominal melting point in which the alkyl tails gain significant disorder. Benzene stretching modes and the CH₂ deformation modes show subtle changes at the D_rd → N transition of HBTX and at the D_rd → D_hd transition of HATX.     

The effect of photoperiod and prey density on long-term survival of larvae—a data analytic approach where no parametric model is assumed and individual follow-up is not available

A data analytic approach for analysing differences in long-term survival and identifying treatment combinations which provide high survival in a factorial design set-up is presented. The methods are particularly appropriate when individual follow-up data are not available and no simple model fits the data. Upper quantiles of the survival distributions are used as the response variable and within and between-treatment differences are analysed through both a structured ANOVA model and subset-selection procedure. The methods are used to study the effects of several photoperiods and prey density treatments on the long-term survival of the larvae of gilthead seabream, Sparus aurata. The two approaches used are shown to lead to similar conclusions.     

Factorization theorems for univariate splines on regular grids

For a given univariate compactly supported distributionφ, we investigate here the spaceS(φ) spanned by its integer translates, the subspaceH(φ) of all exponentials inS(φ) and the kernelK _ϕ of the associated semi-discrete convolutionφ*. The paper addresses a variety of results including a complete structure ofH(φ) andK _ϕ and a characterization of splines of minimal support. The main result shows that eachφ can be expressed asφ = p(∇)τ * M, wherep(∇) is a finite difference operator,τ is a distribution of smaller support satisfyingH(τ) =K _τ = {0}, andM is a spline which depends onH(φ) but not onφ itself, and which in the generic case (termed here “regular”) is the exponential B-spline associated withH(φ). The approach chosen is direct and avoids entirely the Fourier analysis arguments. The fact that a distribution is examined, rather than a function, is essential for the methods employed.     

Synthesis of geiparvarin: a novel antitumor agent possessing a 3(2H)-furanone ring

The first synthesis of geiparvarin as well as assignment of configuration of the previously undefined trisubstituted olefinic bond has been achieved.