Thermal Behaviour Studies on Some Heterotrinuclearpolyacids

An improved method for the synthesis of four heterotrinuclearpolyacids of the type: H_x[EM′_yM″_zO₄₀⋅nH₂O (E=P, Si; M′=Mo, W; M″=V, W) was elaborated. The studied compounds were characterized by elemental analysis, IR spectra and thermal behaviour over 20–800°C temperature range. This revised version was published online in August 2006 with corrections to the Cover Date.     

Second quantization of classical nonlinear relativistic field theory

The construction of a relativistic interacting local quantum field is given in two steps: first the classical nonlinear relativistic field theory is written down in terms of Poisson brackets, with initial conditions as canonical variables: next a representation of Poisson bracket Lie algebra by means of linear operators in the topological vector space is given and an explicit form of a local interacting relativistic quantum field \(\hat \Phi \) is obtained. The construction of asymptotic local relativistic fields \(\hat \Phi _{in} \) and \(\hat \Phi _{out} \) associated with \(\hat \Phi \) is also given.     

An Infrared Spectroscopic Study on the Hofmann-diam-type 1,9-Diaminononanemetal(II) Tetracyanonickelate(II)-Aromatic Guest Clathrates: M(H2N(CH2)9NH2)Ni(CN)4 ċG(M = Cd or Ni; G = Benzene, Naphthalene, Anthracene or Phenanthrene

IR spectra of M(1,9-Diaminononane)Ni(CN)₄G (M = Cd or Ni; G = benzene, naphthalene, anthracene or phenanthrene) are reported. The spectral data suggest that the host structures in these clathrates are similar to those of Hofmann-, -diaminoalkane type clathrates.     

Synthesis and electrochemical characterization of biphenyl-malonic ester substituted cobalt,copper, and palladium phthalocyanines

Phthalocyanines with four biphenyl-malonic ester groups on the periphery were synthesized by cyclotetramerization of 4-(1,1-dicarbethoxy-2-(4-biphenyl)-ethyl)-phthalonitrile. The new compounds were characterized by elemental analyses, FT-IR, ¹H NMR, ¹³C NMR, UV–Vis, and MASS spectral data. Electrochemical behaviors of novel Co(II), Cu(II), and Pd(II) phthalocyanines were investigated by cyclic voltammetry, potential differential pulse voltammetry, and applied potential chronocoulometry techniques. While Cu(II) and Pd(II) phthalocyanines give up to four common phthalocyanine ring reductions, Co(II) phthalocyanine gave two ligand-centered and two metal-centered redox processes. HOMO–LUMO gap of the complexes are comparable with the reported MPc papers.     

Predictability and stopping on lattices of sets

Summary As a first step in the development of a general theory of set-indexed martingales, we define predictability on a general space with respect to a filtration indexed by a lattice of sets. We prove a characterization of the predictable -algebra in terms of adapted and left-continuous processes without any form of topology for the index set. We then define a stopping set and show that it is a natural generalization of the stopping time; in particular, the predictable -algebra can be characterized by various stochastic intervals generated by stopping sets.Research supported by a grant from the Natural Sciences and Engineering Research Council of CanadaResearch partially done while the second author was visiting the University of Ottawa. He wishes to thank the Department of Mathematics for its hospitality     

Studies on the Non-Isothermal Decomposition of H3PMo12O40·xH2O and H4PVMo11O40·yH2O

This paper reports a comparative study of the non-isothermal decompositions of the heteropolyacids HPM and HPVM, with structures consisting of Keggin units (KUs). Non-isothermal analysis at low heating rates demonstrated the existence of 4 crystal hydrate species, depending on the temperature. The stability domains of the anhydrous forms of HPM and HPVM were found to be 150–380°C, respectively. Processing of the TG curves obtained at different heating rates by the Ozawa method revealed that the decomposition of anhydrous HPM takes place according to a unitary mechanism, whilst for anhydrous HPVM two mechanisms are observed. Thus, the first part of the constitution water is lost simultaneously with the departure of vanadium from the KU as VO²⁺, while the second part is lost at higher temperatures as in the case HPM. This revised version was published online in August 2006 with corrections to the Cover Date.     

Synthesis of novel rhodium‐xylyl linked N‐heterocyclic carbene complexes as hydrosilylation catalysts

Reaction of ortho‐xylylbis(N‐2,4,6‐trimethylbenzylimidazolinium); xylylbis(N‐butylimidazolinium) and para‐xylylbis(N‐2,4,6‐trimethylbenzylimidazolinium); xylylbis(N‐butylimidazolinium) salts with KOBu^t and [RhCl(COD)]₂ yields ortho‐ and para‐xylylbis{(N‐alkylimidazolidin‐2‐ylidene)chloro(η⁴‐1,5‐cyclooctadiene) rho dium(I)} complexes (2a–d). All compounds synthesized were characterized by elemental analysis and NMR spectroscopy, and the molecular structures of the 2a and 2d were determined by X‐ray crystallography. Triethylsilane reacts with acetophenone derivatives in the presence of catalytic amount of the new rhodium(I)–carbene complexes (2a–d), to give the corresponding silylethers in good yields (83–99%). Copyright © 2008 John Wiley & Sons, Ltd.     

Manufacturer’s mixed pallet design problem

We study a problem faced by a major beverage producer. The company produces and distributes several brands to various customers from its regional distributors. For some of these brands, most customers do not have enough demand to justify full pallet shipments. Therefore, the company decided to design a number of mixed or “rainbow” pallets so that its customers can order these unpopular brands without deviating too much from what they initially need. We formally state the company’s problem as determining the contents of a pre-determined number of mixed pallets so as to minimize the total inventory holding and backlogging costs of its customers over a finite horizon. We first show that the problem is NP-hard. We then formulate the problem as a mixed integer linear program, and incorporate valid inequalities to strengthen the formulation. Finally, we use company data to conduct a computational study to investigate the efficiency of the formulation and the impact of mixed pallets on customers’ total costs.