A very special nonexistence theorem for abelian difference sets

It is wellknown that the technique of character sums together with the tools of algebraic number theory is the adequate method for the study of difference sets in abelian groups, compare for instance Ott [5] or Turyn [6]. In this paper we use this method to prove a new non-existence theorem for certain difference sets in abelian groups of order rp^a rp^a , where r 1 2 r \neq 2 and p are distinct primes.     

The mathematics of playing golf, or: a new class of difficult non-linear mixed integer programs

We consider a class of non-linear mixed integer programs with n integer variables and k continuous variables. Solving instances from this class to optimality is an NP-hard problem. We show that for the cases with k=1 and k=2, every optimal solution is integral. In contrast to this, for every k≥3 there exist instances where every optimal solution takes non-integral values. Received: August 2001 / Accepted: January 2002?Published online March 27, 2002     

Existence and Nonlinear Stability of Stationary States of the Schrödinger–Poisson System

We consider the Schrödinger–Poisson system in the repulsive (plasma physics) Coulomb case. Given a stationary state from a certain class we prove its nonlinear stability, using an appropriately defined energy-Casimir functional as Lyapunov function. To obtain such states we start with a given Casimir functional and construct a new functional which is in some sense dual to the corresponding energy-Casimir functional. This dual functional has a unique maximizer which is a stationary state of the Schrödinger–Poisson system and lies in the stability class. The stationary states are parameterized by the equation of state, giving the occupation probabilities of the quantum states as a strictly decreasing function of their energy levels.     

Conformal field algebras with quantum symmetry from the theory of superselection sectors

According to the theory of superselection sectors of Doplicher, Haag, and Roberts, field operators which make transitions between different superselection sectors—i.e. different irreducible representations of the observable algebra—are to be constructed by adjoining localized endomorphisms to the algebra of local observables. We find the relevant endomorphisms of the chiral algebra of observables in the minimal conformal model with central chargec=1/2 (Ising model). We show by explicit and elementary construction how they determine a representation of the braid groupB which is associated with a Temperley-Lieb-Jones algebra. We recover fusion rules, and compute the quantum dimensions of the superselection sectors. We exhibit a field algebra which is quantum group covariant and acts in the Hilbert space of physical states. It obeys local braid relations in an appropriate weak sense.     

Nachweise verwandter Elemente nebeneinander in einem Tropfen. II. Mitteilung: Der mikrochemische Nachweis von Aluminium und Beryllium mittels Ammoniummolybdats

Zusammenfassung Entgegen den Auffassungen von van Zijp über den von ihm veröffentlichten Nachweis des Aluminiums mit Ammoniummolybdat wurde gezeigt, daß ein derartiger Nachweis Empfindlichkeit und Störungsfreiheit in hohem Grade vereint.Der Nachweis durch Ammoniummolybdat konnte auf Beryllium ausgedehnt werden. Eine Reihe von Versuchen zeigte, daß Aluminium- und Berylliummolybdat in zwei verschiedenen Krystallformen ohne gegenseitige Beeinträchtigung selbst nebeneinander auszukrystallisieren vermögen.Es ist mir eine angenehme Pflicht, Herrn Prof. Dr. Wilhelm Böttger für sein stets färderndes Interesse und für die mikrochemische Arbeitsmäglichkeit überhaupt zu danken. Zu Dank verpflichtet bin ich auch der Fa. Otto Perutz, München für die freundliche überlassung von Pervola-Platten zu den Mikrophotographien.     

Untersuchungen an reagenzien zur photometrischen zinnbestimmung

The formation of complexes between tin(IV) and o-diphenols, and o-hydroxyquinones, has been studied spectrophotometrically. Simple o-hydroxyquinones do not react with tin(IV), chloranilic acid gives an SnR₂ complex, and o-diphenols give SnR₃ complexes. The reactions of tin(IV) with hydroxyxanthene dyes to give coloured products were considered for their possible analytical utility: the pH range, absorption spectrum, solubility and composition of the complexes were investigated, and the stability constants determined. Analytical procedures have been developed for tin and checked for precision and sensitivity: gallein and hydroxyhydroquinonephthalein (dihydroxyfluorescein) are to be recommended.     

Connectedness properties of polynomial maps between affine spaces

Let f:A^mAⁿ be a polynomial map between affine spaces. We give some sufficient conditions for the connectedness of the difference kernel of f and relate this to the Jacobian Conjecture.     

High-p T αα andαp interactions

Properties of secondaries associated with a high-p _T charged trigger particle (3<p _T <5 GeV/c) were studied for αp and αα interactions at c.m. energies \(\sqrt s = 88\) GeV and 125 GeV, respectively. Thep _T distributions of secondaries in the away-jet and trigger-jet regions were compared with those for high-p _{T pp} interactions. No statistically significant differences were seen, except at lowp _T . Momentum and angular distributions of spectator and leading protons were studied as a function of charge and rapidity of the trigger hadron. The observed correlations between trigger charge and number of spectator protons provide evidence of valence quark contributions to the trigger jet.