On direct sum decompositions of hestenes algebras

In a *-linear Hestenes algebra, the elements with *-reciprocals are characterized by means of certain direct sum decompositions of the algebra. Research partly supported by the Office of Naval Research, contract Nonr-1228(10) project NR 047-021, and by the National Science Foundation, project B-14102.     

Entropy and stability in a stochastic laser model

The asymptotic stability of a microscopic stochastic laser model in the Heisenberg picture is discussed using Liapounov's direct method. By reducing the laser Langevin equations to a classical van der Pol equation for the photon number in the rotating wave approximation, it may be shown that the above-threshold steady state characterized by the cubic non-linearity in the van der Pol equation, is stable. This leads to the definition of a monotonic increasing entropy function far from thermal equilibrium.     

Complexes in polymers: FT-IR spectra and photochemistry of some monomeric organometallic carbonyl complexes in polystyrene,poly(methyl methacrylate), polystyrene—poly(methyl methacrylate) and polystyrene—polyacrylonitrile copolymers

A convenient method for embedding organometallic complexes in polymer films has been developed and the FT-IR spectra of these films have been investigated at room temperature. Infrared data in the n?(CO) stretching region are reported for M(CO)₆ (M = Cr, Mo, W), CpMn(CO)₃ (Cp = η⁵-C₅H₅), η-C₆H₆Cr(CO)₂L [L = CO, P(n-Bu)₃], (η₆-C₆H₅NH₂)Cr(CO)₃, [η⁶-o-C₆H₄(NH₂)MeCr(CO)₃], CpFe(CO)LR [L = CO, PPh₃; R = Me, C(O)Me] embedded in poly(methyl methacrylate) (PMMA), polystyrene (PS), polystyrene-poly(methyl methacrylate) (PS-PMMA), and polystyrene–polyacrylonitrile (PS-AN) plastic films. These matrices appear to approximate the common solvents ethyl acetate, toluene, toluene–ethyl acetate, and toluene–acetonitrile, respectively, with respect to n?(CO) vibrational band behavior. Several of the films have been subjected to UV irradiation and the photoproducts formed have been identified by FT-IR spectroscopy. PS-AN effectively traps photogenerated coordinatively unsaturated species via coordination of its pendant nitrile groups.     

Construction of C1-symmetric zirconium complexes by the design of new Salan ligands. Coordination chemistry and preliminary polymerisation catalysis studies

The first synthesis of achiral and chiral [ONNO']-type Salan ligands featuring two different phenol arms, and the diastereoselective formation of the corresponding octahedral C1-symmetric zirconium complexes is described; the activity and isospecificity induction of the [ONNO']Zr(bn)2 complexes in 1-hexene polymerisation reflected those of the parent symmetric compounds.     

Pd catalysis on dendronized solid support: generation effects and the influence of the backbone structure

Recent studies revealed that catalysts, prepared on dendronized support, frequently exhibit enhanced activity and selectivity as compared to their non-dendronized analogues. Regretfully, in early studies of the supported dendritic catalysis, no particular attention was paid to the coordinative nature of the dendritic backbone. In this study, we functionalized Wang polystyrene support with three types of dendritic templates: poly(aril benzyl ether), poly(aryl benzyl thioether), and poly(aryl benzyl amine). These dendronized resins were further decorated with phosphine ligands on the periphery and complexed with a Pd(0) catalytic precursor. The catalysis of the Heck and Suzuki reactions of bromobenzene with the first to third generation supported dendritic catalysts was examined and compared to that of the non-dendritic analogues. All of the examined reactions revealed a positive dendritic effect, reflected in up to 5-fold increase in yield, in the most prominent case. The reasons for the observed effect are the proximity of the ligating sites translated into reduced cross-linking and, probably, the increased distance of the catalyst from the polymer matrix. We proved, however, that the latter could not be achieved with a linear spacer. Although the Suzuki reaction was rather insensitive to the backbone structure, the Heck reaction catalysis at 80 degrees C exhibited substantial sensitivity to the nature of the dendritic backbone, with the polyether structure demonstrating the best outcome. This is the first demonstration of the influence of the coordinative ability of the backbone on the activity of a supported dendritic catalyst.     

Dwell time of a Brownian molecule in a microdomain with traps and a small hole on the boundary

We calculate the mean time a Brownian particle spends in a domain with traps and the number of bonds it makes before escaping through a small hole in the boundary. This mean time, called the Dwell time, depends on the backward binding rate (with the trap, e.g., scaffolding molecules), the mean time to reach the trap (forward binding rate), and the size of the hole. We estimate the mean and variance of the number of bonds made prior to exit. In a biochemical context, a quantitative signal occurs when the mean number of bonds exceeds a certain threshold, which may initiate a cascade of chemical reactions that have physiological consequences. We apply the present results to obtain estimates of the mean time a Brownian receptor spends inside a synaptic domain, when it moves freely by lateral diffusion on the membrane of a neuron and interacts at a synapse with scaffolding molecules.     

Complexity measures of sign matrices

In this paper we consider four previously known parameters of sign matrices from a complexity-theoretic perspective. The main technical contributions are tight (or nearly tight) inequalities that we establish among these parameters. Several new open problems are raised as well. Supported by the ISF. Supported by the ARC.