Tandem silylformylation-allyl(crotyl)silylation: a new approach to polyketide synthesis

Tandem intramolecular silylformylation-allyl(crotyl)silylation reactions have been developed that allow the highly efficient synthesis of polyketide fragments. The substrates are subjected to Rh(I)-catalyzed silylformylation to afford β-(diallyl)silyl aldehydes which undergo spontaneous uncatalyzed allylsilylation. This unusual spontaneous allylsilylation reaction is driven by strain release Lewis acidity, which arises from the ∼95° O-Si-C bond angle in the oxasilacyclopentane product of the silylformylation reaction. The methodology has been developed both for alkene and alkyne substrates, may be used to establish as many as three stereocenters, and has been shown to be amenable to use in an iterative fashion.     

Dispersion relations and Omnès representations for $K\to \pi \pi$ decay amplitudes

We derive dispersion relations for decay, using the Lehmann-Symanzik-Zimmermann formalism, which allows the analytic continuation of the amplitudes with respect to the momenta of the external particles. No off-shell extrapolation of the field operators is assumed. We obtain generalized Omnès representations, which incorporate the and S-wave phase shifts in the elastic region of the direct and crossed channels, according to the Watson theorem. The contribution of the inelastic final-state and initial-state interactions is parameterized by the technique of conformal mappings. We compare our results with previous dispersive treatments and indicate how the formalism can be combined with lattice calculations to yield physical predictions. Received: 14 October 2002 / Published online: 14 February 2003     

Substantiation of the two-temperature kinetic model by comparing calculations within the kinetic and fluid models of the positive column plasma of a dc oxygen discharge

Results from kinetic and fluid simulations of the positive column plasma of a dc oxygen discharge are compared using commercial CFDRC software (), which enables one to perform numerical simulations in an arbitrary 3D geometry with the use of both the fluid equations for all the components (fluid model) and the kinetic equation for the electron energy distribution function (kinetic model). It is shown that, for both the local and nonlocal regimes of the formation of the electron energy distribution function (EEDF), the non-Maxwellian EEDF can satisfactorily be approximated by two groups of electrons. This allows one to take into account kinetic effects within the conventional fluid model in the simplest way by using the proposed two-temperature approximation of the nonequilibrium and nonlocal EEDF (2T fluid model).     

Probability Space of Stochastic Fractals

We develop a general method for the construction of a probability structure on the space F of random sets in ℝ. For this purpose, by using the introduced notion of c-system, we prove a theorem on the unique extension of a finite measure from a c-system to the minimal c-algebra. The obtained structure of measurability enables one to determine probability distributions of the c-algebra of random events sufficient, e.g., for the so-called fractal dimensionality of random realizations to be considered as a measurable functional on F.__________Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 11, pp. 1467–1483, November, 2004.     

Two-color resonance photoionization spectrum of nickelocene in a supersonic jet

Two-color photoionization of nickelocene molecules cooled in a supersonic jet is performed using a tunable nanosecond pulsed laser. The first stage of the multiphoton excitation is the transition from the highest occupied molecular orbital of nickelocene to the lowest Rydberg level. Conditions are found under which molecular ions (η ⁵-C₅H₅)₂Ni⁺ are the only product of the multiphoton ionization in the one-color experiment. Irradiation of an excited molecule by an intense pulse of another laser increases significantly the yield of molecular ions. The dependence of the yield of (η⁵-C₅H₅)₂Ni⁺ ions on the frequency of the second laser makes it possible to determine the adiabatic ionization potential of nickelocene as 6.138±0.012eV.     

Stress Tensor Fluctuations and Passive Quantum Gravity

The quantum fluctuations of the stress tensor of a quantum field are discussed, as are the resulting space-time metric fluctuations. Passive quantum gravity is an approximation in which gravity is not directly quantized, but fluctuations of the space-time geometry are driven by stress tensor fluctuations. We discuss a decomposition of the stress tensor correlation function into three parts, and consider the physical implications of each part. The operational significance of metric fluctuations and the possible limits of validity of semiclassical gravity are discussed.     

On similarity and scaling of the radiative transfer equation

The present paper shows how the well-known similarity and scaling concepts are properties of the radiative transfer equation and not specifically of the degree of anisotropy of the phase function. It is shown that the key assumption regarding the angular dependence of the radiative field is essential in determining both the value for the parameter used to scale the radiative transfer, as well as the number of streams used in calculating the radiances for various atmospheric problems. Simulations performed on realistic type of cirrus clouds, characterized by strongly anisotropic functions, demonstrates the superior computational advantage for accurately simulating radiances. A new approach for determining the scaling parameter is introduced.     

Microtraps and Atom Chips: Toolboxes for Cold Atom Physics

Magnetic microtraps and Atom Chips are safe, small-scale, reliable and flexible tools to prepare ultra-cold and degenerate atom clouds as sources for various atom-optical experiments. We present an overview of the possibilities of the devices and indicate how a microtrap can be used to prepare and launch a Bose-Einstein condensate for use in an atom clock or an interferometer.