Seeing small

This paper reviews a number of used and/or proposed ideas for optical detection of small particles including single-molecules. Different techniques (direct absorption and scattering, interferometry, use of sub Poissonian statistics, cavity enhancement, and thermal lens detection) are compared in terms of signal-to-noise (SNR) ratio. It is shown that scattering (resonance and non-resonance) remains the method of choice for most practical applications. Thermal lens detection can do potentially better, but its performance critically depends on the thermal properties of the particle surroundings.     

The Direct Limits Of The Banach-mazur Compacta

Let 1 p . For each n-dimensional Banach space E = (E, || ·||), we define a norm || · ||_p on E x R as follows: [formula] It is shown that the correspondence (E, || · ||) (Ex R, || · ||_p) defines a topological embedding of oneBanach–Mazur compactum, BM(n), into another, BM(n 1),and hence we obtain a tower of Banach–Mazur compacta:BM(1) BM(2) BM(3) ···. Let BM_p be thedirect limit of this tower. We prove that BM_p is homeomorphicto Q = dir lim Qⁿ, where Q = [0, 1] is the Hilbert cube. 1991Mathematics Subject Classification 46B04, 46B20, 52A21, 57N20,54H15.     

High-spin yrast states in Ce

Yrast states up to spin 18 have been identified in ¹³²Ce. The energies and spins of the levels suggest the existence of two fairly well-behaved collective bands. The results are compared with those obtained in the rare-earth deformed region.     

Functionalized carbo- and heterocycles via Pt-catalyzed asymmetric alkoxycyclization of 1,6-enynes

This paper describes the asymmetric version of highly atom-economical alkoxycyclization of 1,6-enynes, using a combination of silver salts with the Pt(II)/(R)-Ph-BINEPINE system.     

Determination and estimation of risk aversion coefficients

Computational Management Science - In the paper we consider two types of utility functions often used in portfolio allocation problems, i.e. the exponential utility and the quadratic utility. We...     

Moment-angle complexes from simplicial posets

We extend the construction of moment-angle complexes to simplicial posets by associating a certain T ^m -space Z _S to an arbitrary simplicial poset S on m vertices. Face rings ℤ[S] of simplicial posets generalise those of simplicial complexes, and give rise to new classes of Gorenstein and Cohen-Macaulay rings. Our primary motivation is to study the face rings ℤ[S] by topological methods. The space Z _S has many important topological properties of the original moment-angle complex Z _K associated to a simplicial complex K. In particular, we prove that the integral cohomology algebra of Z _S is isomorphic to the Tor-algebra of the face ring ℤ[S]. This leads directly to a generalisation of Hochster’s theorem, expressing the algebraic Betti numbers of the ring ℤ[S] in terms of the homology of full subposets in S. Finally, we estimate the total amount of homology of Z _S from below by proving the toral rank conjecture for the moment-angle complexes Z _S .     

Palladium‐Catalyzed Chain‐Growth Polycondensation of AB‐type Monomers: High Catalyst Turnover and Polymerization Rates

Chain‐growth catalyst‐transfer polycondensations of AB‐type monomers is a new and rapidly developing tool for the preparation of well‐defined π‐conjugated (semiconducting) polymers for various optoelectronic applications. Herein, we report the Pd/PtBu₃‐catalyzed Negishi chain‐growth polycondensation of AB‐type monomers, which proceeds with unprecedented TONs of above 100 000 and TOFs of up to 280 s^?1. In contrast, related AA/BB‐type step‐growth polycondensation proceeds with two orders of magnitude lower TONs and TOFs. A similar trend was observed in Suzuki‐type polycondensation. The key impact of the intramolecular (vs. intermolecular) catalyst‐transfer process on both polymerization kinetics and catalyst lifetime has been revealed.     

A square‐planar NiII complex with an asymmetric coordination of a novel polynucleative 2,6‐diacetylpyridine bis{[2‐(hydroxyimino)propanoyl]hydrazone} ligand

The title compound, (2,6‐diacetylpyridine bis{[2‐(hydroxyimino)propanoyl]hydrazone}(2−))nickel(II) dimethyl sulfoxide solvate monohydrate, [Ni(C₁₅H₁₇N₇O₄)]·C₂H₆OS·H₂O, represents the first example of square‐planar N₄ coordination via N atoms with four different functions, namely amide, azomethine, hydroxyimino and pyridine. The coordination polyhedron of the central Ni atom has a slightly distorted square‐planar geometry. The 2,6‐diacetylpyridine bis{[2‐(hydroxyimino)propanoyl]hydrazone} ligand forms one six‐ and two five‐membered chelate rings, and a pseudo‐chelate ring through an intramolecular hydrogen bond with an amide group as donor and a deprotonated hydroxyimino group as acceptor, resulting in a pseudomacrocyclic arrangement.     

Topological groups and convex sets homeomorphic to non-separable Hilbert spaces

Let X be a topological group or a convex set in a linear metric space. We prove that X is homeomorphic to (a manifold modeled on) an infinite-dimensional Hilbert space if and only if X is a completely metrizable absolute (neighborhood) retract with ω-LFAP, the countable locally finite approximation property. The latter means that for any open cover of X there is a sequence of maps (f _n : X → X) _nεgw such that each f _n is -near to the identity map of X and the family {f _n (X)} _n∈ω is locally finite in X. Also we show that a metrizable space X of density dens(X) < is a Hilbert manifold if X has gw-LFAP and each closed subset A ⊂ X of density dens(A) < dens(X) is a Z _∞-set in X.