Common supports as fixed points

A family S of sets in R ^d is sundered if for each way of choosing a point from rd+1 members of S, the chosen points form the vertex-set of an (r–1)-simplex. Bisztriczky proved that for each sundered family S of d convex bodies in R ^d , and for each partition (S , S ), of S, there are exactly two hyperplanes each of which supports all the members of S and separates the members of S from the members of S . This note provides an alternate proof by obtaining each of the desired supports as (in effect) a fixed point of a continuous self-mapping of the cartesian product of the bodies.     

Gradient- and Sensitivity-Enhanced TOCSY Experiments

A pulsed field gradient version of the sensitivity-enhanced 2D TOCSY experiment is proposed which yields high-quality spectra with improved sensitivity and a minimum of two scans pert₁increment. For rapid acquisition of 1D TOCSY spectra, the 1D DPFGSE–TOCSY experiment was modified to include phase-encoded multiple-selective excitation followed by a simple spectral editing. Combination of these two building blocks is used in a sensitivity-enhanced 2D analog of the 3D TOCSY–TOCSY experiment which provides an efficient tool for resolving severely overlapped signals of oligomers in short experimental time.     

Fermion–Antifermion Condensate Contribution to the Anomalous Magnetic Moment of a Fundamental Dirac Fermion

We consider the contribution offermion–antifermion condensates to the anomalousmagnetic moment of a fermion in a vacuum in which suchcondensates exist. The real part of the condensatecontribution to the anomalous magnetic moment is shown to bezero. A nonzero imaginary part is obtained below thekinematic threshold for intermediatefermion–antifermion pairs. The calculation isshown to be gauge-parameter independent provided a single fermion masscharacterizes both the fermion propagator andcondensate-sensitive contributions, suggestive of adynamically generated fermion mass. The nonzeroimaginary part is then argued to correspond to the kinematicproduction of the intermediatestate Goldstone bosonsanticipated from a chiral-noninvariant vacuum. Finally,speculations are presented concerning the applicability of these results to quark electromagneticproperties.     

Fluorescence Properties of Intercalating Neutral Chromophores in Complexes with Polynucleotides of Various Base Compositions and Secondary Structures

Changes in the relative quantum yield and polarization degree of steady-state fluorescence of daunomycin (DM) on its binding to six synthetic single- and double-stranded polynucleotides of various nucleotide compositions were measured over a wide range of molar polymer-to-dye ratios, in solutions of low ionic strength. Guanine base was found to be an effective quencher of DM fluorescence [in the DM–poly(G) complex the intensity of residual emission was ~0.5% of the free dye intensity]. The quenching of DM fluorescence by another purine base, i.e., adenine, was also revealed. But, unlike guanine, adenine exhibits quenching activity when it is in close contact with the DM chromophore, as realized in the complex with single-stranded poly(A). In intercalative complexes with double-stranded nucleic acids, where such contact is lacking, the quenching ability of adenine does not manifest itself, which has been demonstrated with the DM–poly(A) · poly(U) complex. It was found that the interaction with pyrimidine bases does not substantially change the DM quantum yield. The quenching feature of DM fluorescence is identical to that observed earlier by us for a glycoside phenazine dye containing, like DM, a neutral chromophore.     

High-field DNP and ENDOR with a novel multiple-frequency resonance structure.

We describe a new triply tuned (e(-), (1)H, and (13)C) resonance structure operating at an electron Larmor frequency of 139.5 GHz for dynamic nuclear polarization (DNP) and electron nuclear double-resonance (ENDOR) experiments. In contrast to conventional double-resonance structures, the body of the microwave cavity simultaneously acts as a NMR coil, allowing for increased efficiency of radiofrequency irradiation while maintaining a high quality factor for microwave irradiation. The resonator design is ideal for low-gamma-nuclei ENDOR, where sensitivity is limited by the fact that electron spin relaxation times are on the order of the RF pulse lengths. The performance is demonstrated with (2)H ENDOR on a standard perdeuterated bis-diphenylene-phenyl-allyl stable radical. In DNP experiments, we show that the use of this resonator, combined with a low microwave power setup (17 mW), leads to significantly higher (1)H signal enhancement (epsilon approximately 400 +/- 50) than previously achieved at 5-T fields. The results emphasize the importance of optimizing the microwave B(1) field by improving either the quality factor of the microwave resonator or the microwave power level.     

Non-ergodicity of Two Particles Interacting via a Smooth Potential

We examine two point particles interacting via a smooth Lennard-Jones-type potential of finite range on a two-dimensional torus. We find situations under which this system contains a stable, elliptic periodic orbit and hence is not ergodic. This result is in contrast to the case of hard spheres interacting via inelastic collision, which are always ergodic for two particles, are conjectured to be ergodic for arbitrarily many particles, and can never contain elliptic periodic orbits.     

Features of X-ray fluorescence determination of rock-forming elements in powder samples of peat sediments

The features of rock-forming elements determination in powder samples of peat sediments are considered. Based on theoretical calculations and experimental data, the mineralogical and particle size effects on the X-ray fluorescence intensity have been estimated. For routine analysis, powder rock samples are usually milled to a particle size of 10–60 μm. Theoretically, estimated variations of rock-forming elements analytical lines intensities in different minerals are up to 30%, and the particle size effect cannot be eliminated simultaneously for all rock-forming elements. Experimental estimation shows that the impossibility of the particle size distribution control can lead to significant variations in the intensities of the analytical lines (3%–18%) that is mainly corresponding to theoretical estimation. Fine milling allowed us to achieve an average particle size of fewer than 20 μm and reduce the measurement uncertainty by 1.5–2 times. 12 samples of peat sediments with organic matter content up to 70 wt% were analyzed by X-ray fluorescence analysis using different sample preparation techniques, as well as by certified methods. The accuracy of X-ray fluorescence analysis of peat sediments prepared as pressed pellets varies from 1.5 to 11 rel% depending on compound contents. It is more than for samples prepared as fused beads, however, the proposed method can be used to determine the variations of rock-forming elements contents in peat sediments where the content variations exceed the measurement uncertainty, and accuracy of analysis is sufficient for further paleoecological reconstructions.     

Prescriptions for gravitational initial data as judged by a simple radiating model

Several methods of prescribing initial data for gravitational and matter fields, which are intended to eliminate extraneous radiation that is not produced by the matter source, are analysed in a simple exactly soluble radiating model. The model consists of an harmonic oscillator coupled to a scalar field along future light cones of Minkowski space time. In particular we analyze the asymptotic regime of the oscillator and find it is characterized essentially by two distinct decay modes. They differ in the way they behave both in the limit of small coupling constant and in a certain Newtonian limit. As a criterion to select initial data for the field with no extra radiation, we require that these initial data sets should put the oscillator from the start into the asymptotic regime. The underlying hypothesis here is that initial transients result from excitation of the oscillator by incoming radiation. We then see that the requirement of a uniform Newtonian limit leads to unique data for the scalar field for each arbitrary data set for the oscillator. We further find that this unique data set indeed satisfies our criterion.     

Stable radially symmetric and azimuthally modulated vortex solitons supported by localized gain

We discover that a spatially localized gain supports stable vortex solitons in media with cubic nonlinearity and two-photon absorption. The interplay between nonlinear losses and gain in amplifying rings results in the suppression of otherwise ubiquitous azimuthal modulation instabilities of radially symmetric vortex solitons. We find that the topology of the gain profile imposes restrictions on the maximal possible charge of vortex solitons. Symmetry breaking occurs at high gain levels, resulting in the formation of necklace vortex solitons composed of asymmetric bright spots.