Freeze-out conditions in ultrarelativistic heavy-ion collisions

We present recent results on single particle transverse momentum distributions of pions, kaons and protons, measured in CERN Experiment NA44, of 200 AGeV/c S+S and 158 AGeV/c Pb+Pb central collisions. By comparing these data with thermal and transport models, freeze-out parameters like the temperatureT _fo and the chemical potentials (μ _q ,μ _s ) are extracted and discussed.     

On a problem of H. N. Gupta

It is shown that the axiom For any points x, y, z such that y is between x and z, there is a right triangle having x and z as endpoints of the hypotenuse and y as foot of the altitude to the hypotenuse, when added to three-dimensional Euclidean geometry over arbitrary ordered fields, is weaker than the axiom Every line which passes through the interior of a sphere intersects that sphere.     

Constructing nonresidues in finite fields and the extended Riemann hypothesis

We present a new deterministic algorithm for the problem of constructing th power nonresidues in finite fields , where is prime and is a prime divisor of . We prove under the assumption of the Extended Riemann Hypothesis (ERH), that for fixed and , our algorithm runs in polynomial time. Unlike other deterministic algorithms for this problem, this polynomial-time bound holds even if is exponentially large. More generally, assuming the ERH, in time we can construct a set of elements that generates the multiplicative group . An extended abstract of this paper appeared in Proc. 23rd Ann. ACM Symp. on Theory of Computing, 1991.

     

Splitting the Pasch axiom

On the basis of the theory ^– of Pasch-free 2-dimensional geometry, Pasch's axiom is shown to be equivalent to the conjunction of the following two axioms: In any right triangle the hypotenuse is greater than the leg and If AOB is right, B lies between O and C, and D is the footpoint of the perpendicular from B to AC, then the segment OA is greater than the segment BD. This represents an attempt to split the Pasch axiom with respect to ^–. Only the question whether the second of the above two axioms is really weaker than Pasch's axiom, remains open.     

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.     

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.