A -normal, not densely normal Tychonoff space

We give an example of a -normal space which is not densely normal.

     

Synthese arylsubstituierter 2-Pyrimidinamine,Dihydro-2-pyrimidinamine und Pyrimido[1,2-a]pyrimidine durch Reaktion von Guanidin mit Chalkonen

4- and 4-methoxy-, 4-hydroxy- and 2-hydroxychalcone4 e,k,f andg, respectively, are transformed by action of guanidine in benzene to yield 4-(4-methoxyphenyl)-6-phenyl-2-pyrimidinamine (6 e=6 k) and hydroxyphenylpyrimidinamines6 f andg, respectively. In contrast, 4- and 4-chlor-, 4-brom- and 4-phenylchalcone4 h,l–n resp. react with guanidine under analogous conditions to give 4,6-diaryl-1,4-dihydro-2-pyrimidinamines5 h,l–n. The bases5 h,l–n also tend to aromatize, but they can be stabilized by transformation into salts5 h,l–n · HCl with hydrochloric acid. Heating of5 n inDMF under atmospheric oxygen yields 4-(4-biphenyl)-6-phenyl-2-pyrimidinamine (6 n). Action of guanidine on 4-nitrochalcone4 o in chloroform affords 2-amino-4-nitrophenyl-6-phenyl-tetrahydro-4-pyrimidinol8 o, which is transformed by hydrochloric acid into 6-nitrophenyl-dihydropyrimidinamine-hydrochloride5 o · HCl. Treating of the latter with sodiummethylat in methanol yields the very stable dihydropyrimidinamine5 o. Action of guanidine on 4-chlor- and 4-bromchalcone4 h andm respectively (in addition to5 h andm) yields 2,4,6,8-tetraaryl-1,4-dihydro-2H-pyrimido[1,2-a]pyrimidines7 h andm, respectively.

Herrn Prof. Dr.Erwin Schauenstein mit den besten Wünschen zum 65. Geburtstag gewidmet.     

Optical metrics and birefringence of anisotropic media

The material tensor of linear response in electrodynamics is constructed out of products of two symmetric second rank tensor fields which in the approximation of geometrical optics and for uniaxial symmetry reduce to “optical” metrics, describing the phenomenon of birefringence. This representation is interpreted in the context of an underlying internal geometrical structure according to which the symmetric tensor fields are vectorial elements of an associated two-dimensional space.     

Total and differential cross-sections for the pp\rightarrow pp\eta^\prime reaction near threshold

The -meson production in the reaction has been studied at excess energies of Q = 26.5, 32.5 and 46.6 MeV using the internal beam facility COSY-11 at the cooler synchrotron COSY. The total cross-sections as well as one angular distribution for the highest Q-value are presented. The excitation function of the near-threshold data can be described by a pure s-wave phase space distribution with the inclusion of the proton-proton final-state interaction and Coulomb effects. The obtained angular distribution of the -mesons is also consistent with pure s-wave production.Received: 11 August 2003, Revised: 14 November 2003, Published online: 6 April 2004PACS: 13.60.Le Meson production - 13.75.-n Hadron-induced low- and intermediate-energy reactions and scattering (energy GeV) - 13.85.Lg Total cross-sections - 25.40.-h Nucleon-induced reactions     

A Short Remark on Weierstrass Points at Infinity on <Emphasis Type="Italic">X</Emphasis><Subscript>0</Subscript>(<Emphasis Type="Italic">N</Emphasis>)

We point out that the formalism of the trace map and reduction modulo p can be used to give a short proof for the fact first proved by Ogg that is not a Weierstrass point on X₀(pM) where p is a prime not dividing M and the genus of X₀(M) is zero.     

Eta physics at threshold

The production of - and -mesons in elementary nucleon-nucleon collisions has been investigated at the synchrotrons CELSIUS, COSY and SATURNE. The high-quality proton beam with low emittance and small momentum spread permits to study the creation of these mesons very close to the kinematical threshold, where --due to the rapid growth of the phase space volume-- the total cross-section increases by orders of magnitude over a few MeV range of the excess energy. The magnitude and energy dependence of the total cross-section as well as the occupation distribution of the phase space serve as observables for investigating the mechanisms underlying the production processes and the interaction of mesons with nucleons. The precise data on the and creation via the reactions allowed to settle the general features of the - and -meson production and revealed the sensitivity of the mentioned observables to the nucleon-nucleon-meson final-state interaction. The particular production properties, like for example, the determination of the dominating exchange processes which lead to the excitation of the S ₁₁ nucleon isobar in the case of creation, must be established by confrontation with other observables. The present status of this investigation with an emphasis on the results of the COSY-11 Collaboration is briefly presented. The available data are interpreted in view of the production mechanism and the meson-nucleon interaction.Received: 30 September 2002, Published online: 22 October 2003PACS: 13.60.Le Meson production - 13.75.-n Hadron-induced low- and intermediate-energy reactions and scattering (energy GeV) - 13.85.Lg Total cross sections - 25.40.-h Nucleon-induced reactions