Minimum order of loop networks of given degree and girth

Behzad, Chartrand and Wall proposed the conjecture that any regular digraph of degreer and girthg has ordern r(g – 1) + 1. The conjecture was proved in [3] for vertex transitive graphs. For Loop Networks the conjecture is equivalent to a theorem of Shepherdson in additive number theory. We show that, except for graphs of a particular structure, Loop Networks, and in general Abelian Cayley graphs, verify the stronger inequalityn (r + 1)(g – 1) – 1. This bound is best possible.Supported by the Spanish Research Council (CICYT) under project TIC 90-0712 and Acción Integrada Hispanofrancesa, TIC 79B.     

Transport of charged particle pulses in interplanetary magnetic fields

The charged particle scattering in the presence of a regular magnetic field is considered starting from the Boltzmann kinetic equation in the case of an arbitrary relation between the mean free path and the distance from a particle source. It is shown that the Green function for the kinetic equation can be represented as the sum of the distribution functions of non-scattered particles which propagate with the injection pitch angle and of the scattered ones. The obtained Green function of the Boltzmann equation and also the particle density describe the space-time-pitch angle cosmic ray distribution that corresponds to an instantaneous particle injection at a particular pitch angle.This work was supported by International Science Foundation (grant N UC 8000) and by Slovak Grant Agency for Science (grant No. 1353/95).     

The anomalous Mössbauer fraction of ferritin and polysaccharide iron complex (PIC)

Mössbauer studies of the ubiquitous protein molecule ferritin and its synthetic biomimic polysaccharide iron complex (PIC) exhibit an anomaly in the Mössbauer spectrum wherein the recoil free fraction orf-factor has a sharp drop with respect to temperature as the temperature rises above 30 K for mammalian ferritin and 60 K for PIC. The anomaly coincides with the disappearance of hyperfine splitting, which is due to superparamagnetic relaxation above the blocking temperature. Different absorbers were used to experimentally investigate the effect of absorber thickness on the Mössbauer spectrum. The anomaly persists for thin absorbers. Also, spectra treated with FFT procedures to eliminate the thickness effect still exhibit this anomaly. Motion of the core with respect to the protein shell was also eliminated as a possible source for this phenomenon, by comparing the Debye temperature obtained from the temperature dependence of thef-factor and the isomer shift. A comparison of the magnetic anisotropy constants from magnetization studies with those obtained by relating the hyperfine fieldH of the Mössbauer spectra to the fluctuations of the magnetization imply that the ferritin and PIC molecules possess magnetic anisotropy energy which may not be strictly uniaxial. This, we believe, may be intimately connected with the mechanism causing thef-factor anomaly.This work was carried out in partial fulfilment of the requirements of the PhD degree at Tufts University.     

Determination of the atmospheric neutrino spectra with the Fréjus detector

The combined analysis of the final event set of data on neutrino interactions inside the detector, upward going stopping muons and horizontal muons recorded in the Fréjus experiment is presented. The absolute atmospheric neutrino spectra in the energy range for electron neutrinos and for muon neutrinos are determined. Based on the parameterization of Volkova for thev ^µ a spectral index of =2.66±0.05 is obtained from the ratio of horizontal muons over upward going stopping muons and from the measurement of the energy loss of horizontal muons inside the detector. The neutrino spectra are compared with various flux calculations. They do not show any evidence for neutrino oscillations in agreement with earlier analyses of the Fréjus data.Now atUniversity of Michigan, Ann Arbor, USA     

Study of short-lived silver isotopes with a laser ion source

The continuum part of the⁶Li (a,a)⁶Li (1.47–2.47 MeV) scattering data at E_a=50 MeV are extracted in two discretized bins. Coupled-channel calculations are carried out coupling the 1⁺ ground state of⁶Li with both the resonant, 3⁺ ₁ state, and two non-resonant continuum states. The discretized continuum of the⁶Li (p,p)⁶Li (1.75–3.25 MeV) scattering data at E_p=65 MeV are also analysed on the same footing. In both the cases the effect of coupling is found to be minimal.     

Non-isovalent alkali metal “substitution” in YBa2Cu3O7−y granular ceramics

The aim of this paper is to study the influence of non-isovalent doping in YBa₂Cu₃O_7–y in particular on its synthesis conditions and on the resistive properties both with and without a magnetic field. We concentrate on the study of possible alkali ions (Na, K, Cs) substitution at the barium sites. A low temperature sintering process is used in order to induce a reactive liquid phase. The final chemical composition is discussed as a function of the amount of the liquid phase. No alkali ion is substituted. Carbonate layers are present. However, this (lack of) substitution leads to induced vacancies and improved electrical transport properties which are as good as in highly pure materials. For conciseness the case of Na substitution only is illustrated. The use of such data in order to probe the microstructure is emphasized.     

Snowballs of radioactive ions — nuclear spin polarization of core ions

Short-lived ions¹²B (beta-radioactive, T_1/2=20.3 ms) sustaining nuclear spin polarization were introduced into superfluid helium at 1.7 K. It was found that the¹²B ions were transported as charged entities under a static electric field and that the nuclear polarization was maintained throughout the lifetime of¹²B nuclei. Polarization of¹²B was determined through beta-NMR method. Snowball, a singly charged microcluster of helium atoms formed around an impurity ion, is responsible for the behaviour and thus constitutes a suitable environment for preserving nuclear polarization of the core ions¹²B. In a separate experiment snowballs were produced by implanting⁸Li (T_1/2=830 ms) into liquid helium and detected by means of alpha particles from the core ions to guarantee that the snowballs survive longer than the lifetime of¹²B.