Chiral Charged Fermions,One-Dimensional Quantum Field Theory and Vertex Algebras

We give an explicit L ²-representation of chiral charged fermions using the Hardy–Lebesgue octant decomposition. In the pure case such a representation has already been used by M. Sato in holonomic field theory. We study both pure and mixed cases. In the compact case, we rigorously define unsmeared chiral charged fermion operators inside the unit circle. Using chiral fermions, we orient our findings towards a functional analytic study of vertex algebras as one-dimensional quantum field theory.     

Finite generation properties for fuchsian group von Neumann algebras tensor

We prove that the algebra , a free group with finitely many generators, contains a subnormal operator such that the linear span of the set is weakly dense in . This is the analogue for the factor , finite, of a well known fact about the unilateral shift on a Hilbert space : the linear span of all the monomials is weakly dense in .

We also show that for a suitable space of square summable analytic functions, if is the projection from the Hilbert space of all square summable functions onto and is the unbounded operator of multiplication by on , then the (unbounded) operator is nonzero (with nonzero domain).

     

Exponential decay of derivatives of covariance operators on the lattice

We prove exponential decay for derivatives of covariance operators on the lattice. This result is obtained by using random walk methods on the v-dimensional lattice and a certain estimate on the generating function of the one-dimensional random walk. The result is useful in the frame of the cluster and mean field expansion of continuous spin models on the lattice.     

Ethylene-hexene-1 copolymers through modified phillips catalysis

Copolymerization of ethylene and hexene has been carried out using Phillips' catalysts (chromium oxide deposited on silica) modified with small amounts of triethylaluminium [Al(C₂H₅)₃], without solvent other than hexene itself and under constant ethylene pressure. The copolymers are highly disperse, not only in molecular weight but also in composition; the amount of hexene incorporated in the solid fraction is always less than 4%. Most of the hexene units are in a waxy fraction, which may account for a very high proportion of the copolymer produced. The behaviour of the catalyst is strongly dependent upon the amount of Al(C₂H₅)₃ used.     

Pyrolysis gas chromatography of some fluorine-containing polymers

Pyrolysis gas chromatography of the polymers of 1,3,3,3-tetrafluoropropene, 3,3,4,4,5,5,5-heptafluoropentene-1 and of the copolymers of tetrafluoroethylene with the above and with 3,3,3-trifluoropropene and with isobutene in all instances gave only 3 to 19% of volatiles below C₁₆, distributed among many peaks. This and the absence of significant char indicate predominantly a random scission mechanism of decomposition.     

Nontriviality of the scattering matrix for weakly coupled Φ34 models

It is shown that the weakly coupled, three space-time dimensions, boson quantumfield-theory model with Φ⁴ self-interaction has a scattering matrix which is different from $\text{1}$.     

Scanning electrochemical microscopy (SECM) of nanolitre droplets using an integrated working/reference electrode assembly

Scanning electrochemical microscopy (SECM) has been performed in the restricted space of nanolitre droplets with a robust and easy-to-handle coaxial electrode assembly centring a Pt microdisk in a circular Ag electrode. Straightforward and reproducible fabrication of the specially designed probe tips was achieved by using Tollens reaction to chemically deposit a uniform and well-adhering layer of silver on the body of a glass-insulated Pt microdisk electrode. The suitability of the novel dual-electrode SECM tip for measurement in small volumes was evaluated by imaging an array of four Pt band microelectrodes in 500 nL electrolyte.     

On the Weyl tensor of a self-dual complex 4-manifold

We study complex 4-manifolds with holomorphic self-dual conformal structures, and we obtain an interpretation of the Weyl tensor of such a manifold as the projective curvature of a field of cones on the ambitwistor space. In particular, its vanishing is implied by the existence of some compact, simply-connected, null-geodesics. We also show that the projective structure of the -surfaces of a self-dual manifold is flat. All these results are illustrated in detail in the case of the complexification of .