A note on Pall partitions over finite fields

A Pall partition for a quadratic space V is a collection of disjoint (except for {0}) maximal totally isotropic subspaces whose union contains all of the isotropic vectors in V. In this paper it is shown that no non-degenerate quadratic space of dimension 4k+1, k?1, over a finite field of odd characteristic can have a Pall partition. The method of proof consists of assuming such a partition exists and showing by various counting arguments that this leads to the existence of an impossible array of ordered pairs.     

The Split of the Dirac Hamiltonian into Precisely Predictable Energy Components

We are dealing with the Dirac Hamiltonian H = H₀ + V with no magnetic field and radially symmetric electrostatic potential V = V(r), preferably the Coulomb potential. While the observable H is precisely predictable, its components H₀ (relativistic mass) and V (potential energy) are not. However they both possess precisely predictable approximations H₀ and V which approximate accurately if the particle is not near its nucleus. On the other hand, near 0, H₀ and V are practically unpredictable, perhaps in agreement with the fact, that a neutrino also should be in the game. [We have not yet studied the corresponding observables for the ( 12-dimensional) problem of electro-weak interaction.] Mathematically we are focusing on the spectral theory of the unbounded self-adjoint operators H₀ and V . We can prove that V is unitarily equivalent to V(r) again, by a unitary map given as Wiener-Hopf-type singular integral operator in the standard separation of variables for radially symmetric Dirac Hamiltonians. [This is, as far as the continuous spectrum is concerned.] Very similar unitary equivalence holds for H ₀ and H ₀. We are tempted to regard this as a form of renormalization.     

Structure of chlorohydroxonitrosyl(terpyridine)ruthenium(II) hexafluorophosphate

The title complex has the NO grouptrans to the hydroxyl ligand and the chloride ion in the plane of the tripyridyl ligand. The Ru?O and Ru?N(O) distances are 1.939(5) Å and 1.764(6) Å, respectively; the Ru?N?O bond angle is 171.7(6)⁰. These values are consistent with previously reported shortening of Ru?O distances whentrans to a linear NO ligand. The space group of the structure isP2₁/c, witha=9.7213(9) Å,b=13.9318(11) Å,c=14.523(4) Å, and β=105.820(13)⁰.     

Pancyclic orderings of in-tournaments

An in-tournament is an oriented graph such that the negative neighborhood of every vertex induces a tournament. In this paper, pancyclic orderings of a strong in-tournament D are investigated. This is a labeling, say x₁,x₂,…,x_n, of the vertex set of D such that D[{x₁,x₂,…,x_t}] is Hamiltonian for t=3,4,…,n. Moreover, we consider the related problem on weak pancyclic orderings, where the same holds for t4 and x₁ belongs to an arbitrary oriented 3-cycle. We present sharp lower bounds for the minimum indegree ensuring the existence of a pancyclic or a weak pancyclic ordering in strong in-tournaments.     

Psychometric Evaluation of Disease Specific Quality of Life Instruments in Voice Disorders

The objective of this study was to compare the psychometric properties of voice disordered quality of life (VQOL) instruments. Nine VQOL instruments were identified through a comprehensive literature search. Based on specific criteria, four were selected for comprehensive review: Voice Handicap Index (VHI), Voice Activity and Participation Profile (VAPP), Voice-Related Quality of Life (V-RQOL) and Voice Outcome Survey (VOS). Selected instruments were evaluated based on 11 measurement standards related to item information, versatility, practicality, breadth and depth of health measure, reliability, validity, and responsiveness. VHI and V-RQOL each met 7 of 11 criteria, with VHI showing additional preferable item information, practicality, and reliability over V-RQOL and V-RQOL showing preferable responsiveness properties over VHI. These study results do not support the Social Security Administration's recent conclusion that the VHI meets reliability and validity standards for individual decision making. Nevertheless, the present results do support the use of VHI total scores for clinical use with individual patients, and the use of V-RQOL total scores or individual dimension scores for use with groups of patients.     

Manganese(IV) Corroles with σ‐Aryl Ligands

Different pathways for the preparation of organometallic manganese(IV) corroles with σ‐aryl ligands have been evaluated. The treatment of a manganese(III) corrole with Grignard reagents PhMgX (X = Cl, Br), followed by aerial oxidation yields oxidized halogenido complexes [(cor)Mn^IVX] instead of the anticipated organometallic compounds. Reaction of these halogenido species, especially the bromido compound, with excess Grignard reagents or with lithium aryls results in the formation of the desired σ‐aryl compounds via salt metatheses. Three examples of this class of rare complexes have been characterized by means of optical and ¹H NMR spectroscopy, and in two cases single crystal X‐ray diffraction studies have been carried out. In the crystal, the molecular structures of the σ‐phenyl‐ and the σ‐(p‐bromophenyl) derivatives were observed to be very similar, albeit both species pack in different pattern.     

A nickel hydride complex in the active site of methyl-coenzyme m reductase: implications for the catalytic cycle

Methanogenic archaea utilize a specific pathway in their metabolism, converting C1 substrates (i.e., CO2) or acetate to methane and thereby providing energy for the cell. Methyl-coenzyme M reductase (MCR) catalyzes the key step in the process, namely methyl-coenzyme M (CH3-S-CoM) plus coenzyme B (HS-CoB) to methane and CoM-S-S-CoB. The active site of MCR contains the nickel porphinoid F430. We report here on the coordinated ligands of the two paramagnetic MCR red2 states, induced when HS-CoM (a reversible competitive inhibitor) and the second substrate HS-CoB or its analogue CH3-S-CoB are added to the enzyme in the active MCR red1 state (Ni(I)F430). Continuous wave and pulse EPR spectroscopy are used to show that the MCR red2a state exhibits a very large proton hyperfine interaction with principal values A((1)H) = [-43,-42,-5] MHz and thus represents formally a Ni(III)F430 hydride complex formed by oxidative addition to Ni(I). In view of the known ability of nickel hydrides to activate methane, and the growing body of evidence for the involvement of MCR in "reverse" methanogenesis (anaerobic oxidation of methane), we believe that the nickel hydride complex reported here could play a key role in helping to understand both the mechanism of "reverse" and "forward" methanogenesis.