ExplicitN-polynomials of 2-power degree over finite fields,I

For an odd prime powerq the infinite field GF(q ² )= _n0 GF (q ²ⁿ ) is explicitly presented by a sequence (f _n)₁ ofN-polynomials. This means that, for a suitably chosen initial polynomialf ₁, the defining polynomialsf _nGF(q)[x] of degrees2 ⁿ are constructed by iteration of the transformation of variablexx+1/x and have linearly independent roots over GF(q). In addition, the sequences are trace-compatible in the sense that the relative traces map the corresponding roots onto each other. In this first paper the caseq1 (mod 4) is considered and the caseq3 (mod 4) will be dealt with in a second paper. This specific construction solves a problem raised by A. Scheerhorn in [11].     

Proton-neutron interaction at N≅Z — First observation of the Tz=1 nucleus 46 94 Pd48 in-beam

The neutron deficient nucleus⁹⁴Pd was identified and studied for the first time by in-beam spectroscopy. An I=(14⁺) isomer with t_1/2=0.8 (2) s was observed in a recoil catcher setup inside the multi-detector -array OSIRIS. Filter detectors for neutrons and charged particles were used to identify the (2p2n) exit channel of the reaction⁵⁸Ni+⁴⁰Ca, populated with only 0.06% of the total evaporation residue cross section. The structure of the isomer is discussed within the frame work of shell model calculations in the (p_1/2,g_9/2) model space with emphasis on the g ₉ ^2/2 T=0, I=1,9 pairing two-body matrix elements.Communicated by: D. Schwalm     

Effect of a magnetic flux line on the quantum beats in the Henon-Heiles level density

The quantum density of states of the Henon-Heiles potential displays a pronounced beating pattern. This has been explained by the interference of three isolated classical periodic orbits with nearby actions and periods. A singular magnetic flux line, passing through the origin, drastically alters the beats even though the classical Lagrangian equations of motion remain unchanged. Some of the changes can be easily understood in terms of the Aharonov-Bohm effect. However, we find that the standard periodic orbit theory does not reproduce the diffraction-like quantum effects on those classical orbits which intersect the singular flux line, and argue that corrections of relative order variant Planck's over 2pi are necessary to describe these effects. We also discuss the changes in the distribution of nearest-neighbor spacings in the eigenvalue spectrum, brought about by the flux line. (c) 1995 American Institute of Physics.     

Bell-type inequalities in horizontal sums of Boolean algebras

We give a necessary and sufficient condition for a Bell-type inequality to hold in a horizontal sum of finitely many finite Boolean algebras.     

The nature of the C-defects in nickel and their rôle in the interpretation of radiation damage in metals

In previous Perturbed-Angular-Correlation (PAC) studies of the - emission of ¹¹¹In probe nuclei in cold-worked or particle-irradiated nickel, it has been found that thermal annealing in the temperature regime of recovery stage III leads to the formation of so-called C-defects (Cubic defects). This is indicated by the occurrence of a new frequency of about 80 Mrad/s, in addition to the frequency (200 Mrad/s) that is due to ¹¹¹In on substitutional sites. Obviously, the C-defects are complexes consisting of ¹¹¹In and the intrinsic point-defect species that migrates freely in recovery stage III. Therefore, they have played an important rôle in the long-standing controversy on whether the recovery-stage-III defects are vacancies (one-interstitial model) or self-interstitials (two-interstitial model). The present paper reports on a novel experimental effort to reveal the nature of the C-defects by combining PAC studies on nickel samples differently pretreated in a systematic way, investigations of the Extended X-ray Absorption Fine Structure (EXAFS) on In-doped nickel, and measurements of the decay rate of ¹¹¹In nuclei in the Electron-Capture-Induced Decay (ECID). On the basis of the results of these experiments it is concluded that the defects trapped by substitutional ¹¹¹In atoms (In_s) in recovery stage III are self-interstitials (I), as expected according to the two-interstitial model. Moreover, there is evidence that the C-defects are In interstitials on tetrahedral sites (In_i) that form exclusively in the vicinity of the specimen surface from In_s – I pairs via the reaction In_s+I In_i.     

Arsenic speciation in marine organisms: from the analytical methodology to the constitution of reference materials

An analytical procedure for total arsenic and arsenic species quantification in marine organisms has been developed. Fresh materials are freeze-dried and reduced to powders before analysis. Arsenic is determined either by energy dispersive X-ray fluorescence (EDXRF) directly or by inductively coupled plasma optical emission spectrometry (ICP/OES) after microwave digestion. Arsenic speciation is performed on the extracted sample using liquid chromatography coupled to ICP/OES for arsenobetaine and arsenocholine determination and to the hydride generation-quartz furnace atomic absorption spectrometric technique for arsenite, arsenate, monomethylarsonic and dimethylarsinic acids quantification. Special precautions are taken to avoid losses or contaminations as well as to prevent analytical errors during the quantification stage. Other methods are applied and the corresponding results compared for each step of the procedure. The method is finally validated by means of intercomparison studies within the Measurements and Testing Programme of the European Community (formely BCR).     

Convexity theories III. Classification of certain real convexity theories

In this paper we classify all real convexity theories that contain the standard convexity theory _c. For this purpose we consider three subcases: finitary; infinitary and (_sc\_c)Ø; infinitary and _sc=_c. In each of these subcases one encounters a phenomenon resembling bifurcation.This research was supported by the Deutsche Forschungsgemeinschaft.     

Relative entropy maximization and directed diffusion equations

Motivated by the concept of maximum entropy methods in signal and image processing, we introduce and discuss a class of ‘directed diffusion equations’ with suitable boundary conditions. The paradigmatic ‘directed diffusion equation’ is The relative entropy $ Sb[f](t): = - \int_\Omega {f(t,x)} \;\ln \;(f(t,x)/b(x))dx $ is rapidly increasing along solution trajectories of (i). This suggests that solving (i) will yield efficient procedures for entropy maximization. We also discuss the asymptotic behavior of solutions of (i)—this is readily done because (i) has a large family of Ljapunov functionals.