Weak distributive laws and their role in lattices of congruences and equational theories

By a result of Pigozzi and Kogalovskii, every algebraic latticeL having a completely join —irreducible top element can be represented as the lattice L() of equational theories extending some fixed theory . Conversely, strengthening a recent result due to Lampe, we show that such a representationL=L() forcesL to satisfy the following condition: if the top element ofL is the join of a nonempty subsetB ofL then there are elementsb..., B such thata=(... (((b₁ a) b₂) a) ... b_n) a for alla L. In presence of modularity, this equation reduces to the identitya=(a b₁) ... (a b_n). Motivated by these facts, we study several weak forms of distributive laws in arbitrary lattices and related types of prime elements. The main tool for applications to universal algebra is a generalized version of Lampe's Zipper Lemma.Presented by Ralph Freese.     

Gorenstein curves and symmetry of the semigroup of values

LetO be the local ring of a irreducible algebroid curve and S its semigroup of values, Kunz in [7] proves thatO is a Gorenstein ring if and only if S is symmetrical. In this paper we give a generalization of this fact for the case of reduced curves with an arbitrary number of branches, d. For it we introduce a concept of symmetry for the semigroup of values S₊ ^d which generalizes the well known symmetry for d=1 (i.e. the irreducible case). This concept of symmetry is also closely related to the symmetry introduced by García in [4] (for the d=2 case) and the author in [3] (for arbitrary d) with the main goal of the explicit determination of S (in the case of plane curves).     

Laser properties of coactivated YAP: Nd free of colour centres

YAP:Nd, Cr grown under Ar-H₂ or Ar-He-H₂ atmosphere possesses good energy transfer from Cr³⁺ to Nd³⁺ but suffers from the colour centre formation. The centre formation was completely prevented using further admixture of Ce³⁺ and 10^–4–10^–3 wt. % Fe. Small luminescence quenching of Cr³⁺ or Nd³⁺ due to iron ions is negligible in the presence of Ce³⁺. The crystals may be also heavily doped with Nd³⁺ because the increased pumping efficiency compensates the shortening of the luminescence lifetime. YAP: Nd, Ce, Cr, Fe is advisible active laser material particularly for all the types of pulsed lasers.     

A variational expression for the relative entropy

We prove that for the relative entropy of faithful normal states ? and ω on the von Neumann algebraM the formula $$S(\varphi ,\omega ) = \sup \{ \omega (h) - \log \varphi ^h (I):h = h^* \in M\}$$ holds.     

The magnetic moment of the 10+ isomer in140Ce andE1 transitions inN=82 isotones caused by outer subshell configurations

Using the reaction¹³⁸Ba(α,2n)¹⁴⁰Ce the magnetic moment of the 10 ₁ ⁺ isomer atE _x =3714.7 keV in theN=82 nucleus¹⁴⁰Ce has been determined by means of the TDPAD method toμ=+10.3(4)μ _N . Measuredg-factors in¹⁴⁰Ce are compared to calculations within the shell model with configuration mixing. For the 10 ₁ ⁺ isomer in¹⁴⁰Ce the four proton configuration π(1g ₇ ^2/2 ,2d ₅ ^2/2 ) has been found to be dominant. From theg-factor measurement strong contributions of multiparticle excitations to thegp2d _3/2,π3s ₁ ² or π1h ₁₁ ² shells and admixtures of neutron excitations to the wave function of the 10 ₁ ⁺ state could be excluded. The strongE1γ-branch of the deexcitation of the 10 ₁ ⁺ isomer in¹⁴⁰Ce can be explained by means of small admixtures of configurations which contain the outer subshell excitationsπ2f _7/2 andπ1h _9/2. On this basisE1 transitions experimentally observed in theN=82 nuclei¹⁴⁰Ce,¹⁴¹Pr and¹⁴⁵Eu may be understood.     

Characterization of reaction products formed during thin-layer chromatographic detection of thiocarbamate herbicides

The reaction between thiocarbamate herbicides and 2,6-dichlorobenzoquinone-N-chloroimine or 2,6-dibromobenzoquinone-N-chloroimine is suitable for the detection of these herbicides on thin-layer plates with high sensitivity. The reactions were followed by infrared, nuclear magnetic resonance and mass spectrometry. We have established the formation of 2,6-dichlorobenzoquinone-S-alkyl sulphenylimines. In the case of the bromo-derivative, halogen exchange and substitution on the quinone ring took place simultaneously leading to the formation of mixed halogenated 2,6-dihalo- and, in addition, 2,3,6-trihalobenzoquinone-S-alkyl sulphenylimines. The final product of the detection reaction, i.e. 2,6-dichlorobenzoquinone-S-alkyl sulphenylimine was reacted with 2,6-dibromobenzoquinone-N-chloroimine where 2,6-dichloro-3-bromobenzoquinone-S-alkyl sulphenylimine formed as a consequence of the looser bromine-carbon linkage on the 2 and 6 positions of the quinone ring.