Spectroscopic detection and theoretical confirmation of the role of Cr2(CO)5(C5R5)2 and .Cr(CO)2(ketene)(C5R5) as intermediates in carbonylation of N=N=CHSiMe3 to O=C=CHSiMe3 by .Cr(CO)3(C5R5) (R = H, CH3)

Conversion of N=N=CHSiMe3 to O=C=CHSiMe3 by the radical complexes .Cr(CO)3C5R5 (R = H, CH3) derived from dissociation of [Cr(CO)3(C5R5)]2 have been investigated under CO, Ar, and N2 atmospheres. Under an Ar or N2 atmosphere the reaction is stoichiometric and produces the Cr[triple bond]Cr triply bonded complex [Cr(CO)2(C5R5)]2. Under a CO atmosphere regeneration of [Cr(CO)3(C5R5)]2 (R = H, CH3) occurs competitively and conversion of diazo to ketene occurs catalytically as well as stoichiometrically. Two key intermediates in the reaction, .Cr(CO)2(ketene)(C5R5) and Cr2(CO)5(C5R5)2 have been detected spectroscopically. The complex .Cr(13CO)2(O=13C=CHSiMe3)(C5Me5) has been studied by electron spin resonance spectroscopy in toluene solution: g(iso) = 2.007; A(53Cr) = 125 MHz; A(13CO) = 22.5 MHz; A(O=13C=CHSiMe3) = 12.0 MHz. The complex Cr2(CO)5(C5H5)2, generated in situ, does not show a signal in its 1H NMR and reacts relatively slowly with CO. It is proposed to be a ground-state triplet in keeping with predictions based on high level density functional theory (DFT) studies. Computed vibrational frequencies are also in good agreement with experimental data. The rates of CO loss from 3Cr2(CO)5(C5H5)2 producing 1[Cr(CO)2(C5H5)]2 and CO addition to 3Cr2(CO)5(C5H5)2 producing 1[Cr(CO)3(C5H5)]2 have been measured by kinetics and show DeltaH approximately equal 23 kcal mol(-1) for both processes. Enthalpies of reduction by Na/Hg under CO atmosphere of [Cr(CO)n(C5H5)]2 (n = 2,3) have been measured by solution calorimetry and provide data for estimation of the Cr[triple bond]Cr bond strength in [Cr(CO)2(C5H5)]2 as 72 kcal mol(-1). The complex [Cr(CO)2(C5H5)]2 does not readily undergo 13CO exchange at room temperature or 50 degrees C implying that 3Cr2(CO)5(C5H5)2 is not readily accessed from the thermodynamically stable complex [Cr(CO)2(C5H5)]2. A detailed mechanism for metalloradical based conversion of diazo and CO to ketene and N2 is proposed on the basis of a combination of experimental and theoretical data.     

Kinetics of the thermal unimolecular decomposition of hex-1-ene-3-yne. Heat of formation and resonance stabilization energy of the 3-ethenylpropargyl radical

The thermal unimolecular decomposition of hex-1-ene-3-yne (HEY) has been investigated over the temperature range 949–1230 K using the technique of very low-pressure pyrolysis (VLPP). One reaction pathway is the expected C₅? C₆ bond fission to form the resonance-stabilized 3-ethenylpropargyl radical. There is a concurrent process producing molecular hydrogen which probably occurs via the intermediate formation of hexatrienes and cyclohexa-1,3-diene. RRKM calculations yield the extrapolated high-pressure rate parameters at 1100 K given by the expressions 10^16.0±0.3 exp(?300.4 ± 12.6 kJ mol^?1/RT) s^?1 for bond fission and 10^13.2+0.4 exp(?247.7 ± 8.4 kJ mol^?1/RT) for the overall formation of hydrogen. The A factors were assigned from the results of previous studies of related alkynes, alkenes, and alkadienes. The activation energy for the bond fission reaction leads to ΔH [H₂CCHCC?H₂] = 391.9, DH [H₂CCHCCCH₂? H] = 363.3, and a resonance stabilization energy of 56.9 ± 14.0 kJ mol^?1 for the 3-ethenylpropargyl radical, based on a value of 420.2 kJ mol^?1 for the primary C? H bond dissociation energy in alkanes. Comparison with the revised value of 46.6 kJ mol^?1 for the resonance energy of the unsubstituted propargyl radical indicates that the ethenyl substituent (CH₂?CH) on the terminal carbon atom has only a small effect on the propargyl resonance energy. © John Wiley & Sons, Inc.     

Complement of forms

The notions of the parallel sum, the parallel difference, and the complement of two nonnegative sesquilinear forms were introduced and studied by Hassi, Sebestyé and de Snoo in Hassi et al. (Oper Theory Adv Appl 198:211–227, 2010) and Hassi et al. (J Funct Anal 257(12):3858–3894, 2009). In this paper we continue these investigations. The Galois correspondence induced by the map ${\mathfrak{m} \mapsto \mathfrak{m}_\mathfrak{t}}$ (where ${\mathfrak{m}_\mathfrak{t}}$ denotes the ${\mathfrak{t}}$ -complement of ${\mathfrak{m}}$ ) is also studied. Inspired by the work of Eriksson and Leutwiler Eriksson and Leutwiler (Math Ann 274:301–317, 1986), we introduce the notion of quasi-unit for nonnegative sesquilinear forms. The quasi-units are characterized by means of the complement and the disjoint part. It is also shown that the ${{\mathfrak{t}}}$ -quasi-units coincide with the extreme points of the convex set ${\mathfrak{z}: 0 \leq \mathfrak{z} \leq \mathfrak{t}\}}$ .     

Polynomiality of primal-dual affine scaling algorithms for nonlinear complementarity problems

This paper provides an analysis of the polynomiality of primal-dual interior point algorithms for nonlinear complementarity problems using a wide neighborhood. A condition for the smoothness of the mapping is used, which is related to Zhu’s scaled Lipschitz condition, but is also applicable to mappings that are not monotone. We show that a family of primal-dual affine scaling algorithms generates an approximate solution (given a precision ε) of the nonlinear complementarity problem in a finite number of iterations whose order is a polynomial ofn, ln(1/ε) and a condition number. If the mapping is linear then the results in this paper coincide with the ones in Jansen et al., SIAM Journal on Optimization 7 (1997) 126–140. Research supported in part by Grant-in-Aids for Encouragement of Young Scientists (06750066) from the Ministry of Education, Science and Culture, Japan. Research supported by Dutch Organization for Scientific Research (NWO), grant 611-304-028     

On the Optimal Value Function of a Linearly Perturbed Quadratic Program

The optimal value function of the quadratic program , where is a given symmetric matrix, a given matrix, and are the linear perturbations, is considered. It is proved that is directionally differentiable at any point in its effective domain . Formulae for computing the directional derivative of at in a direction are obtained. We also present an example showing that, in general, is not piecewise linear-quadratic on W. The preceding (unpublished) example of Klatte is also discussed.     

Quaternionic geometry of matroids

Building on a recent paper [8], here we argue that the combinatorics of matroids are intimately related to the geometry and topology of toric hyperkähler varieties. We show that just like toric varieties occupy a central role in Stanley’s proof for the necessity of McMullen’s conjecture (or g-inequalities) about the classification of face vectors of simplicial polytopes, the topology of toric hyperkähler varieties leads to new restrictions on face vectors of matroid complexes. Namely in this paper we will give two proofs that the injectivity part of the Hard Lefschetz theorem survives for toric hyperkähler varieties. We explain how this implies the g-inequalities for rationally representable matroids. We show how the geometrical intuition in the first proof, coupled with results of Chari [3], leads to a proof of the g-inequalities for general matroid complexes, which is a recent result of Swartz [20]. The geometrical idea in the second proof will show that a pure O-sequence should satisfy the g-inequalities, thus showing that our result is in fact a consequence of a long-standing conjecture of Stanley.     

Strengthened splitting methods for computing resolvents

Computational Optimization and Applications - In this work, we develop a systematic framework for computing the resolvent of the sum of two or more monotone operators which only activates each...