Euclidean ramsey theorems. I

The general Ramsey problem can be described as follows: Let A and B be two sets, and R a subset of A × B. For a?A denote by R(a) the set {b?B | (a, b) ?R}. R is called r-Ramsey if for any r-part partition of B there is some a?A with R(a) in one part. We investigate questions of whether or not certain R are r-Ramsey where B is a Euclidean space and R is defined geometrically.     

Practical scheme for polarization-insensitive and frequency-conversion interval independent four-wave mixing in semiconductor optical amplifiers

A practical scheme for polarization-insensitive and frequency-conversion interval-independent four-wave mixing in an optical loop configuration is proposed that uses one conventional semiconductor optical amplifier device and two perpendicular polarized pump sources. The significant advantages of this technique are simplicity of configuration, efficient conjugate power generation, effective suppression of the signal and one pump wave at the output port, and reduction in noise.     

A [3+2] annulation procedure for methylenecyclopentanes

A two step sequence converts certain cyclic enones to fused methylenecyclopentanes using the annulation reagent 2-chloromethyl-3-trimethylsilylpropene.     

Lattice systems with a continuous symmetry

We consider perturbations of a massless Gaussian lattice field on ? ^d ,d≧3, which preserves the continuous symmetry of the Hamiltonian, e.g., $$ - H = \sum\limits_{< x,y > } {(\phi _x - \phi _y )^2 + T(\phi _x - \phi _y )^4 ,\phi _x \in \mathbb{R}.} $$ It is known that for allT>0 the correlation functions in this model do not decay exponentially. We derive a power law upper bound for all (truncated) correlation functions. Our method is based on a combination of the log concavity inequalities of Brascamp and Lieb, reflection positivity and the Fortuin, Kasteleyn and Ginibre (F.K.G.) inequalities.     

Chemical investigation of three plutonium–beryllium neutron sources

Thorough physical and chemical characterization of plutonium–beryllium (PuBe) neutron sources is an important capability with applications ranging from material accountancy to nuclear forensics. Characterization of PuBe sources is not trivial owing to range of existing source designs and the need for adequate infrastructure to deal with radiation and protect the analyst. This study demonstrates a method for characterization of three PuBe sources that includes physical inspection and imaging followed by controlled disassembly and destructive analysis.     

Impulsive loading of ideal fibre-reinforced rigid-plastic beams—III Cantilever beam

The theory outlined in Part I is applied to the problem of a cantilever beam struck transversely at any point by a mass which subsequently adheres to the beam. In the subsequent motion, slope and velocity discontinuities propagate outwards from the point of impact. Solutions for the velocity and deflection of the various segments of the beam are obtained for the case of linear strain-hardening, and simpler approximate solutions are derived for the case of low impact velocity and/or slight strain-hardening. The discontinuity propagating towards the free end of the beam always comes to rest before it reaches this end, but for sufficiently high values of impact mass and velocity, and a strain-hardening parameter, one or more reflections of the discontinuity may occur at the fixed end of the beam and at the point of impact.     

Copper-free palladium-catalyzed Sonogashira and Hiyama cross-couplings using aryl imidazol-1-ylsulfonates

Aryl imidazylates are effective electrophilic partners in copper-free palladium-catalyzed Hiyama and Sonogashira cross-coupling reactions. The Sonogashira cross-coupling of estron-3-yl imidazylate afforded the corresponding phenylacetylene derivative in excellent yield.     

On Motives Associated to Graph Polynomials

The appearance of multiple zeta values in anomalous dimensions and β-functions of renormalizable quantum field theories has given evidence towards a motivic interpretation of these renormalization group functions. In this paper we start to hunt the motive, restricting our attention to a subclass of graphs in four dimensional scalar field theory which give scheme independent contributions to the above functions.     

Efficiency enhancement of high power vacuum BWO's using nonuniformslow wave structures

The Sinus-6, a high-power relativistic repetitively-pulsed electron beam accelerator, is used to drive various slow wave structures in a BWO configuration in vacuum. Peak output power of about 550 MW at 9.45 GHz was radiated in an 8-ns pulse. We describe experiments which study the relative efficiencies of microwave generation from a two-stage nonuniform amplitude slow wave structure and its variations without an initial stage. Experimental results are compared with 2.5 D particle-in-cell computer simulations. Our results suggest that prebunching the electron beam in the initial section of the nonuniform BWO results in increased microwave generation efficiency, Furthermore, simulations reveal that, in addition to the backward propagating surface harmonic of the TM₀₁ mode, backward and forward propagating volume harmonics with phase velocity twice that of the surface harmonic play an important role in high-power microwave generation and radiation