Immanant positivity for Catalan-Stieltjes matrices

We give some sufficient conditions for the nonnegativity of immanants of square submatrices of Catalan-Stieltjes matrices and their corresponding Hankel matrices. To obtain these sufficient conditions, we construct new planar networks with a recursive nature for Catalan-Stieltjes matrices. As applications, we provide a unified way to produce inequalities for many combinatorial polynomials, such as the Eulerian polynomials, Schröder polynomials, and Narayana polynomials.     

Existence theorems for π/n vortex scattering

The analysis of 90° vortex-vortex scattering is extended to /n scattering in all head-on collisions ofn vortices in the Abelian Higgs model. A Cauchy problem with initial data that describe the scattering ofn vortices is formulated. It is shown that this Cauchy problem has a unique global finite-energy solution. The symmetry of the solution and the form of the local analytic solution then show that /n scattering is realized.     

A floating spherical Gaussian orbital model of molecular structure

The FSGO model has been used to make ab initio calculations of the geometrical structures of borazane and diborane. Where experimental data are available there is good agreement between calculated and observed values.

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Zusammenfassung Für ab initio-Rechnungen zur geometrischen Struktur des Borazans und Diborans wurde das FSGO-Modell benutzt. Soweit experimentelle Werte vorhanden sind, stimmen die berechneten und beobachteten Werte gut überein.

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Résumé La méthode FSGO a été utilisée pour effectuer des calculs ab-initio sur les structures géométriques du borazane et du diborane. Un bon accord est obtenu entre les valeurs calculées et les valeurs expérimentales existantes.

     

Reactivity patterns of thermally stable, terminal, electrophilic phosphinidene complexes towards diazoalkanes: oxidation at the phosphorus centre and formation of P-bound eta1-phosphaazine, eta1-phosphaalkene and eta3-diazaphosphaallene complexes

The thermally stable, terminal phosphinidene complexes [CpM(CO)2(eta1-PNiPr2)]AlCl4(Cp= Cp, Cp*; M = Fe) and [Cp*M(CO)3(eta1-PNiPr2)]AlCl4 (M = Cr, Mo, W) react with Ph2C=N=N to form terminal P-coordinated eta1-phosphaazine and eta3-diazaphosphaallene ligands, respectively, whereas [CpFe(CO)2(eta1-PNiPr2)]AlCl4 reacts with Me3SiCHN2 affording a terminal phosphorus bound eta1-phosphaalkene complex.     

Direct observation of eta 2-imine formation through beta-H abstraction between amide ligands. Neutron and X-ray diffraction structure of a dihydride imine ditantalum complex

Reactions of Ta(NMe2)5 with D2SiR'Ph (R' = Me, Ph) were found to give a dideuteride eta 2-imine complex (Me2N)3Ta(mu-D)2(mu-N-eta 2-N,C-CH2NMe)Ta(NMe2)3(1-d2) through C-H activation of an amide ligand via beta-H abstraction, and the structure of 1 was confirmed by single crystal neutron and X-ray diffraction.     

A Markov model for relaxation and exchange in NMR spectroscopy

A two-state Markov noise process for lattice fluctuations and chemical exchange dynamics is used to derive a stochastic Liouville equation describing the evolution of the spin-density operator in nuclear magnetic resonance spectroscopy. Relaxation through lattice fluctuations and chemical exchange processes is incorporated into the theory at the same fundamental level, and the results are valid for all time scales provided that lattice fluctuations are much faster than chemical exchange kinetics. Time-scale separation emerges as an essential feature from the lowest-order perturbation expansion of the average resolvent in the Laplace domain.     

MECHANISMS OF 1,2-DIOXETANE DECOMPOSITION: THE ROLE OF ELECTRON TRANSFER

Abstract— The chemiluminescence from the cleavage of a number of 1,6-diaryl-2,5,7,8-tetraoxabicyclo[4.2.0]octanes 1 has been examined. The ease of oxidation of (object) the aryl moiety strongly influences both the stability and chemiluminescence efficiency of these 1,2-dioxetanes. When Ar is difficult to oxidize, 1 is comparable in stability to simple. alkyl-substituted 1,2-dioxe-tanes and affords triplet excited states in moderate yield. Both biradical and concerted cleavage mechanisms have been suggested to explain this behavior. However, when Ar is a readily oxidized group, 1 is substantially destahilized and gives excited singlet states in high yield. In this instance 1 is analogous to a number of bioluminescent systems. Cleavage mechanisms involving intramolecular electron transfer are proposed to account for this observation. In certain cases thermolysis of 1 occurs by both types of mechanism in competition, and the electron transfer mechanism may be selectively catalyzed by polar, protic media.     

Counterexamples in optimal quadrature

It is widely believed that order of exactness is a good measure of the quality of an algorithm for numerical quadrature. We show that this is not the case, by exhibiting a situation in which the optimal algorithm does not even integrate constants exactly. We also show that there are situations in which the penalty for using equidistant nodes is unbounded. Finally, we show that the complexity of obtaining an -approximation can be an arbitrary function of , i.e., there is no hardest quadrature problem.