Verification of the optimal probabilistic basis of aural processing in pitch of complex tones

Periodicity pitch for complex tones has been quantitatively accounted for by a two-stage process of Fourier-frequency analysis subject to random errors and significant nonlinearities, followed by an harmonic pattern recognizer that makes an optimum probabilistic estimate of the fundamental period of musical and speech sounds. The theory predicts that periodicity pitch is a multimodal probabilistic function of a given stimulus. A clear and empirically supported distinction is made between limitations on the pitch mechanism caused by the stochastic nature of aural frequency representation and by the deterministic resolution bandwidths of aural frequency analysis. This model was developed earlier [J. L. Goldstein, J. Acoust. Soc. Am 54, 1496-1516 (1973)] to account for probabilistic data on pitch errors [A. J. M. Houtsma and J. L. Goldstein, J. Acoust. Soc. Am. 51, 520 (1972)] measured with periodic stimuli comprising two successive harmonics. This paper presents new predictions by the theory that were calculated, with computer simulation where needed, for known probabilistic pitch data from stimuli comprising three to six successive harmonics. Predicted pitch errors increase with increasing errors in estimating the frequencies of stimulus harmonics and decrease as more harmonics are added to the stimulus. Optimum processor theory fully accounts for the multicomponent pitch data on the basis of similar errors in estimating component stimulus frequencies as reported earlier, thus providing further evidence for the optimum probabilistic basis of aural signal processing in pitch of complex tones.     

Synthesis, spectroscopic, and structural properties of spirocyclopropanated bicyclobutylidenes and their radical cations

The spirocyclopropanated bicyclobutylidenes 3-7 have been prepared by McMurry coupling of the corresponding spirocyclopropanated cyclobutanone (3 and 5), Staudinger-Pfenniger reaction (4), oxidative coupling of a Wittig ylide (4) or Wittig olefination of perspirocyclopropanated cyclobutanone (6 and 7). The structure of the parent 2a and the perspirocyclopropanated bicyclobutylidene 5 was determined by X-ray crystallography which disclosed considerable steric congestion around the double bond. As a result 5 did undergo addition of dichlorocarbene, epoxidation with meta-chloroperbenzoic acid, and cyclopropanation with CH2I2/ZnEt2, but did not add the more bulky dibromocarbene. The reaction of 5 with tetracyanoethene proceeded smoothly, but led to a formal [3+2] cycloadduct across the proximal single bond of one of the inner cyclopropane rings. The consecutive spirocyclopropanation of bicyclobutylidene led to a bathochromic shift in the UV spectra of 12 and 17nm, respectively, for each pair of beta- and alpha-spirocyclopropane groups. In the He(I)-photoelectron spectra of these bicyclobutylidenes, the effect of spirocyclopropanation upon their pi-ionization energies (pi-IE,) was found to be almost additive, leading to a lowering of 0.05 eV per any additional beta-spirocyclopropane, and 0.28-0.22 eV per additional alpha-spirocyclopropane group; this indicates an increasing nucleophilicity of the double bonds in the order 1 < 4 < 3 < 5. Following the radical cations of the three symmetrical bicyclobutylidenes without (2a, b) and with six (5) spiroannelated cyclopropane rings, the radical cations of two symmetrical bicyclobutylidenes with two (4) and four (3) such rings were studied by ESR spectroscopy. Whereas 2b.+, 3.+, and 5.+ could be generated by electrolytic oxidation of the corresponding hydrocarbons in solution, the spectra of 2a.+ and 4.+, with unsubstituted 2,2',4,4'-positions, were observed upon radiolysis of their neutral precursors in a Freon matrix. On going from 2a.+ to 4.+, the coupling constant [aH] of the eight beta protons in the 2,2',4,4'-positions of bicyclobutylidene increases from 2.62 to 3.08 mT, and that of the four gamma protons in the 3,3'-positions changes from 0.27 to 0.049 to 0.401 mT on passing from 2a.+ via 2b.+ to 3.+. Computations by means of the density functional theory (DFT) at the B3LYP/6-311+G*//B3LYP/6-31G* level reproduce well the experimental hyperfine data.     

Quantum superchemistry: dynamical quantum effects in coupled atomic and molecular Bose-Einstein condensates

We show that in certain parameter regimes there is a macroscopic dynamical breakdown of the Gross-Pitaevskii equation. Stochastic field equations for coupled atomic and molecular condensates are derived using the functional positive- P representation. These equations describe the full quantum state of the coupled condensates and include the commonly used Gross-Pitaevskii equation as the noiseless limit. The full quantum theory includes the spontaneous processes which will become significant when the atomic population is low. The experimental signature of the quantum effects will be the time scale of the revival of the atomic population after a near total conversion to the molecular condensate.     

Synthesis of functionalized 2-alkoxybenzoates, 2-aryloxybenzoates and xanthones based on formal [3+3] cyclocondensations of 3-alkoxy- and 3-aryloxy-1-silyloxy-1,3-butadienes with 3-silyloxy-2-en-1-ones

Functionalized 2-alkoxy- and 2-aryloxybenzoates were prepared by formal [3+3] cyclocondensations of 3-alkoxy- and 3-aryloxy-1-silyloxy-1,3-butadienes with 3-silyloxy-2-en-1-ones. The reaction of 2-aryloxybenzoates with concentrated sulfuric acid resulted in the formation of xanthones.     

X‐ray photoelectron spectroscopic chemical state quantification of mixed nickel metal,oxide and hydroxide systems

Quantitative chemical state X‐ray photoelectron spectroscopic analysis of mixed nickel metal, oxide, hydroxide and oxyhydroxide systems is challenging due to the complexity of the Ni 2p peak shapes resulting from multiplet splitting, shake‐up and plasmon loss structures. Quantification of mixed nickel chemical states and the qualitative determination of low concentrations of Ni(III) species are demonstrated via an approach based on standard spectra from quality reference samples (Ni, NiO, Ni(OH)₂, NiOOH), subtraction of these spectra, and data analysis that integrates information from the Ni 2p spectrum and the O 1s spectra. Quantification of a commercial nickel powder and a thin nickel oxide film grown at 1‐Torr O₂ and 300 °C for 20 min is demonstrated. The effect of uncertain relative sensitivity factors (e.g. Ni 2.67 ± 0.54) is discussed, as is the depth of measurement for thin film analysis based on calculated inelastic mean free paths. Copyright © 2009 John Wiley & Sons, Ltd.     

Production of entanglement in Raman three-level systems using feedback

We examine the theoretical limits of the generation of entanglement in a damped coupled ion-cavity system using jump-based feedback. Using Raman transitions to produce entanglement between ground states reduces the necessary feedback bandwidth, but does not improve the overall effect of the spontaneous emission on the final entanglement. We find that the fidelity of the resulting entanglement will be limited by the asymmetries produced by vibrations in the trap, but that the concurrence remains above 0.88 for realistic ion trap sizes.     

INTERFACIAL FREE ENERGIES,ZETA POTENTIALS AND THROMBORESI STANCE IN BOVINE AND OVINE CAROTID ARTERIES

The physical properties of the intimal surfaces of both natural and artificial arteries are important In the prevention of thrombosis and clotting. It Is expected thati a) the interface between the blood plasma and the intima should be highly negatively charged, to repel negatively charged platelets and other blood constituents, and b) the interfacial free energy at the plasma-intima interface should be as low as possible, to prevent adhesion If the charge barrier is breached. Few measurements of either the zeta potential or the interfacial free energy at the intimal surface can be found in the literature. Zeta potentials of natural and cross-linked bovine carotid intima, and of an expanded Teflon prosthesis were determined by a streaming potential method in 0.9% (w/v) NaC1. Interfacial free energies of both bovine and ovine carotid intima, and of an expanded Teflon prosthesis were also determined by a contact-angle method using water immiscible liquid drops on the intimal surface Immersed in 0.9% (w/v) NaC1.     

Global solvability on the torus for certain classes of formally self-adjoint operators

In this paper we prove a necessary and sufficient condition for global solvability on the torus for two classes of formally self-adjoint operators. For the first class of operators we prove that global solvability is equivalent to an algebraic condition involving Liouville vectors and simultaneous approximability. For the second class of operators, when the coefficients are not identically zero, an independence condition on the coefficients is shown to be necessary and sufficient for global solvability. Received: 21 June 1999 / Revised version: 8 May 2000     

Global Solvability and Simultaneously Approximable Vectors

We consider a class of sum of squares operators on a torus and we prove that global solvability is equivalent to an algebraic condition involving simultaneously approximable vectors.