Magnetic properties of group VIB hexacarbonyls. Suggestion of a new diamagnetic susceptibility standard

Summary Careful measurements of the magnetic susceptibilities of group VI B metal hexacarbonyls show an ideal diamagnetic behaviour. The properties of W(CO)₆, together with the relatively low price, lead to the suggestion of W(CO)₆ as a new calibration standard for the diamagnetic region.

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Magnetische Eigenschaften von Hexacarbonylen der Gruppe VI B. Vorschlag zu einem neuen diamagnetischen Suszeptibilitätsstandard

Zusammenfassung Sorgfältige Messungen der magnetischen Suszeptibilität der Metallhexacarbonyle der Gruppe VI B zeigen deren ideal diamagnetisches Verhalten. Die physikalischen Eigenschaften des W(CO)₆, zusammen mit dem relativ niedrigen Preis, prädestinieren es als diamagnetischen Eichstandard.

     

A reduction theorem for the McKay conjecture

The McKay conjecture asserts that for every finite group G and every prime p, the number of irreducible characters of G having p’-degree is equal to the number of such characters of the normalizer of a Sylow p-subgroup of G. Although this has been confirmed for large numbers of groups, including, for example, all solvable groups and all symmetric groups, no general proof has yet been found. In this paper, we reduce the McKay conjecture to a question about simple groups. We give a list of conditions that we hope all simple groups will satisfy, and we show that the McKay conjecture will hold for a finite group G if every simple group involved in G satisfies these conditions. Also, we establish that our conditions are satisfied for the simple groups PSL₂(q) for all prime powers q≥4, and for the Suzuki groups Sz(q) and Ree groups R(q), where q=2 ^e or q=3 ^e respectively, and e>1 is odd. Since our conditions are also satisfied by the sporadic simple group J ₁, it follows that the McKay conjecture holds (for all primes p) for every finite group having an abelian Sylow 2-subgroup.     

Inequalities for some blocks of finite groups

We analyze some inequalities for numbers of characters in p-blocks of finite groups and prove them in the case of blocks with a normal defect group, as well as in the case of certain blocks in non-abelian simple groups. Received: 27 October 2005     

The spin-1/2XXZ Heisenberg chain,the quantum algebra Uq[sl(2)], and duality transformations for minimal models

The finite-size scaling spectra of the spin-1/2XXZ Heisenberg chain with toroidal boundary conditions and an even number of sites provide a projection mechanism yielding the spectra of models with a central chargec < 1, including the unitary and nonunitary minimal series. Taking into account the half-integer angular momentum sectors—which correspond to chains with an odd number of sites—in many cases leads to new spinor operators appearing in the projected systems. These new sectors in theXXZ chain correspond to new types of frustration lines in the projected minimal models. The corresponding new boundary conditions in the Hamiltonian limit are investigated for the Ising model and the 3-state Potts model and are shown to be related to duality transformations which are an additional symmetry at their self-dual critical point. By different ways of projecting systems we find models with the same central charge sharing the same operator content and modular invariant partition function which, however, differ in the distribution of operators into sectors and hence in the physical meaning of the operators involved. Related to the projection mechanism in the continuum there are remarkable symmetry properties of the finiteXXZ chain. The observed degeneracies in the energy and momentum spectra are shown to be the consequence of intertwining relations involvingU _q [sl(2)] quantum algebra transformations.     

Topological Fixed Point Theorems Do Not Hold for Random Dynamical Systems

The aim of this paper is to demonstrate that topological fixed point theorems have no canonical generalization to the case of random dynamical systems. This is done by using tools from algebraic ergodic theory. We give a criterion for the existence of invariant probability measures for group valued cocycles. With that, examples of continuous random dynamical systems on a compact interval without random invariant points, which are an appropriate generalization of fixed points, are constructed.     

A rapid and sensitive assay for determining human brain levels of farnesyl-(FPP) and geranylgeranylpyrophosphate (GGPP) and transferase activities using UHPLC–MS/MS

The isoprenoids farnesyl-(FPP) and geranylgeranylpyrophosphate (FPP and GGPP) are two major lipid intermediates in the mevalonate pathway. They participate in post-translational modification of members of the superfamily of small guanosine triphosphatases (GTPases; Ras, Rab, Rac, etc.) via prenylation reactions. Due to the important role of these proteins in a number of cell processes, in particular cell growth, division, and differentiation, investigation of the involvement of isoprenoids in these processes is of great interest. In a previously published report, we described a fully validated assay for the quantitation of the two isoprenoids using a high-performance liquid chromatography (HPLC)–fluorescence detection (FLD) method. The current work expands on the previous method and enhances it greatly by using a much faster state-of-the-art ultrahigh-performance liquid chromatography (UHPLC) technique coupled to tandem mass spectrometry (MS/MS). The method exhibited a linear concentration range of 5–250 ng/mL for FPP and GGPP in human brain tissue; it was shown to be unaffected by ion suppression and provided results almost six times faster than the HPLC–FLD assay. Comparison of UHPLC–MS/MS and HPLC–FLD yielded excellent comparability of the two assays for both isoprenoids. Based on the UHPLC–MS/MS assay, a novel in vitro test system was implemented to study enzyme specificity for distinct amino acid CAAX motifs, which is potentially useful for investigating target interactions of new therapeutics for diseases involving pathological regulation of isoprenoids and/or small GTPases.