Diborane (4) derivatives via coupling of amine monobromocyanoboranes: Study of the bromination of amine cyanoborane and molecular structures of the amine dibromocyanoboranes

The first examples of diborane (4) compounds derived from amine cyanoboranes are described. A series of monobromo derivatives of amine cyanoboranes (A:BHBrCN), and dibromo derivatives (A:BBr₂CN), 1-7, were prepared. Lithiation of the monobromo derivative of trimethylamine cyanoborane, using n-BuLi, did not produce the C-lithiated intermediate Li⁺ [CH₂NMe₂BHBrCN]⁻, but instead the B-lithiated intermediate Li⁺ [Me₃NBHCN]⁻, was obtained. This intermediate, when allowed to react for 16 h, coupled with the un-lithiated trimethylamine monobromocyanoborane (Me₃NBHBrCN) and resulted in diborane (4) derivative formation as the 2LiBr complex. The same result was obtained when one equiv of the trimethylamine monobromocyanoborane was added to the reaction mixture 1 h after lithiation. Following the same procedure, novel diborane (4) derivatives of amine cyanoboranes were successfully obtained, 8-11, as their 2LiBr complexes from the monobromo derivatives of the corresponding amine cyanoboranes. Molecular structures of the trimethylamine dibromocyanoborane, 6, and the triethylamine dibromocyanoborane, 7, were determined using X-ray crystallography.     

A new general-purpose isothermal microcalorimeter for use at temperatures up to 200 °C

The design and some properties of a new general-purpose isothermal microcalorimeter are reported. The instrument is a twin thermopile heat conduction calorimeter, which is designed for use up to 200 °C. The calorimetric units and surrounding heat sink are suspended inside a hollow aluminium construction, which is thermostated. Above that unit a second thermostated block is positioned and the whole assembly is suspended inside a Dewar vessel. When the instrument is used at room temperature and below, the thermostated units are cooled by use of an insertion Peltier effect cooler. The instrument can be used with a wide range of different reaction vessels (diameter 14 mm). Baseline experiments have been conducted in the temperature range 15-200 °C. Typical values obtained during 10 h periods at 200 °C are ±3 and ±10 nW for the baseline drift and baseline fluctuations, respectively. The heat detection limit, determined by release of electrical energy, is about 2 μJ. Preliminary stability measurements have been conducted at 100 °C on samples of stabilised and non-stabilised polyamide film.     

Local structure of graphs with λ=μ=2,a 2=4

Several properties of graphs with ==2,a ₂=4 are studied. It is proved that such graphs are locally unions of triangles, hexagons or heptagons. As a consequence, a distance regular graph with intersection array (13,10,7;1,2,7) does not exist.     

Symmetric Skorohod topology onn-variable functions and hierarchical Markov properties ofn-parameter processes

Summary We introduce a new Skorohod topology for functions of several variables. Since ann-variable function may be viewed as a one-variable function with values in the set of (n–1)-variable functions, this topology is defined by induction from the classical Skorohod topology for one-variable functions. This allows us to define the notion of completen-parameter symmetric Markov processes: Such processes are, for any 1pn, rawp-parameter Markov processes (in the sense of our previous paper [17]) with values in the space of (n–p)-variable functions. We prove, for these processes and their Bochner subordinates, a maximal inequality which implies the continuity of additive functionals associated with finite energy measures. We finally present several important examples.     

A Banach space where minimal weak cuscos are generically compact-valued

The space of continuous functions on the double arrow space has long been of interest in differentiability theory since many convex functions on this space are densely but not generically Gâteaux differentiable. We show that this space has the property that minimal weak* cuscos into its dual take compact values at the points of a denseG set.     

Densest packings of eleven congruent circles in a circle

In 1969 Pirl provided the densest packings ofn equal circles in a circle forn 10. We will prove the optimality for the packings that were conjectured forn=11. The proof is based on elementary combinatorial and analytical techniques.     

Shock fluctuations in the asymmetric simple exclusion process

Summary We consider the one dimensional nearest neighbors asymmetric simple exclusion process with ratesq andp for left and right jumps respectively;q<p. Ferrari et al. (1991) have shown that if the initial measure isv _, , a product measure with densities and to the left and right of the origin respectively, <, then there exists a (microscopic) shock for the system. A shock is a random positionX _t such that the system as seen from this position at timet has asymptotic product distributions with densities and to the left and right of the origin respectively, uniformly int. We compute the diffusion coefficient of the shockD=lim _t t ^–1(E(X _t )²–(EX _t )²) and findD=(p–q)(–)^–1((1–)+(1–)) as conjectured by Spohn (1991). We show that in the scale the position ofX _t is determined by the initial distribution of particles in a region of length proportional tot. We prove that the distribution of the process at the average position of the shock converges to a fair mixture of the product measures with densities and . This is the so called dynamical phase transition. Under shock initial conditions we show how the density fluctuation fields depend on the initial configuration.     

Optical spectra of an intracavity two-photon medium with sequeezed inputs

We consider an ensemble of three-level configuration atoms in an optical cavity, interacting through two-photon transitions with a cavity mode, driven by a broad-band squeezed input of finite amplitude. The atom-cavity system is coupled to reservoirs to describe the losses of the atoms and the cavity. Optical spectra in the transmitted and the reflected field are calculated and analysed in the good cavity limit, for the purely absorptive resonant case and the general case, respectively.     

Zero cycles on conic fibrations and a conjecture of Bloch

Let X be a smooth projective surface over a number field k. Let (CH₀(X)) denote the Chow group of zero-cyles modulo rational equivalence on X. Let CH₀(X) be the subgroup of CH ₀(X) consisting of classes which vanish when going over to an arbitrary completion of k. Bloch put forward a conjecture asserting that this group is isomorphic to the Tate-Shafarevich group of a certain Galois module atttached to X. In this paper, we disprove this general conjecture. We produce a conic bundle X over an elliptic curve, for which the group (CH₀(X) is not zero, but the Galois-theoretic Tate-Shafarevich group vanishes.     

Theq-harmonic oscillator and the Al-Salam and Carlitz polynomials

One more model of aq-harmonic oscillator based on theq-orthogonal polynomials of Al-Salam and Carlitz is discussed. The explicit form ofq-creation andq-annihilation operators,q-coherent states and an analog of the Fourier transformation are established. A connection of the kernel of this transform with a family of self-dual biorthogonal rational functions is observed.