Hammett studies of enantiocontrol by PHOX ligands in Pd-catalyzed allylic substitution reactions

Electronically modified PHOX ligands 3a-e were synthesized to probe the mechanism of the enantioselective palladium-catalyzed allylic alkylation and amination reactions. Alkylation with dimethyl sodiomalonate produced only a small variation in the ee (89.3% to 93.4%), but amination with benzylamine gave a much wider variation in the ee (16.4% to 66.6%). Hammett analysis suggests that the substituents interact more significantly with phosphorus and supports a combined electronic and steric basis for enantioselection. [reaction: see text]     

Lateralization produced by envelope-based interaural temporal disparities of high-frequency, raised-sine stimuli: empirical data and modeling

An acoustic pointing task was used to measure extents of laterality produced by ongoing interaural temporal disparities (ITDs) conveyed by the envelopes of 4-kHz-centered raised-sine stimuli while varying, parametrically, their peakedness, depth of modulation, and frequency of modulation. One purpose of the study was to determine whether such manipulations would produce changes in laterality logically consistent with those found for ITD-discrimination thresholds reported by Bernstein and Trahiotis [J. Acoust. Soc. Am. 125, 3234-3242 (2009)]. The data obtained revealed that they did in that (1) increasing depth of modulation, peakedness, or frequency of modulation between 32 and 128 Hz produced smaller threshold ITDs and greater laterality and (2) increasing frequency of modulation to 256 Hz produced modest increases in threshold ITDs and modest decreases in laterality. The extents of laterality measured were successfully accounted for via an augmentation of the cross-correlation-based "position-variable" modeling approach developed by Stern and Shear [J. Acoust. Soc. Am. 100, 2278-2288 (1996)] to account for ITD-based extents of laterality obtained at low spectral frequencies.     

Mechanism of meerwein-pondorf-verley type reductions

The reduction of benzophenone by lithium and chloromagnesium alkoxides has been studied as well as the transformation of certain lithium alkoxides to the corresponding ketones by electron transfer. Fluorenone was reduced by lithium sec-butoxide to the corresponding lithium ketyl to the extent of 65%. Lithium 9-fluoroenolate underwent in tetrahydrofuran a spontaneous transformation to lithium fluorenone ketyl. This process was interpreted as involving 1,2-hydrogen shift in an oxygen-centred radical. A mechanism for the Meerwein-Pondorf-Verley-type reductions is proposed, invoking single electron as well as 1,2-hydrogen shift steps.     

Cooperative and interference effects in the resonance fluorescence of two identical three-level atoms at high photon densities

The excitation spectrum of two identical three-level atoms is considered when a strong electromagnetic field operates resonantly between two levels of the atoms. While undergoing the transition into the excited state, the atoms interact through their dipole-dipole interaction and radiate to each other as well, and subsequently, they decay radiatively into another excited state. For such a system, the spectral functions are calculated describing the cooperative and interference spectra for the symmetric and antisymmetric modes arising from the decay of the atoms from one excited state into another. In the absence of the pump field, the spectral function for the symmetric modes consists of two peaks, which are described by Lorentzian lines peaked at the frequencies ω = ω₂₃ + V_AB and ω = ω₂₃ ? V_AB and having spectral widths of the order of γ⁰₂₁ + γ⁰₂₃ and γ⁰₂₃, respectively, where ω₂₃ is the transition frequency between the two excited states, V_AB is the dipole-dipole interaction and $\text{1}\text{2}\text{γ}{}^0{}_{21}$ is the natural width for a photon spontaneously emitted from the 2 → 1 transition of an isolated atom. The splitting of the central peak for the transition in question and the broadening of the spectral widths are due entirely to the dipole-dipole and radiative interactions between the atoms. The spectral function for the antisymmetric modes describes a stable mode at the frequency ω = ω₂₃ ? V_AB, which has a delta-function distribution, and a Lorentzian line peaked at the frequency ω = ω₂₃ + V_AB and has a spectral width of the order of γ⁰₂₁. In the presence of the pump field, the spectral function for the symmetric modes contains, in addition to the central peaks, two pairs of sidebands, one pair of which is induced by the pump field with an energy shift equal to $\text{Ω}{}_{\mathrm{<mtext>a</mtext>}}\text{/√2}$, while the other pair of sidebands is due to the dipole-dipole interaction between the atoms; the probability of occurrence of the latter pair of sidebands is proportional to $\text{V}{}_{\mathrm{AB}}\text{/Ω}{}_{\mathrm{<mtext>a</mtext>}}$, while the induced energy shift is equal to $\text{3Ω}{}_{\mathrm{<mtext>a</mtext>}}\text{/√2}$, where $\text{√2Ω}{}_{\mathrm{<mtext>a</mtext>}}$ is the induced by the laser field energy shift (Rabi frequency) for a single two-level atom. The spectral widths for both pairs of sidebands are of the order of γ⁰₂₁ + γ⁰₂₃. The excitation spectrum of the antisymmetric modes consists of, in addition to the central peaks, a pair of stable sidebands, which have delta-function distributions, and two pairs of sidebands, which are similar but sharper than those for the symmetric modes. Detail comparisons are given between the one- and two-atom excitation spectra for the systems under investigation.     

An experimental approach to the analysis of electric field gradients in ionic crystals

The spectrum of a partially oriented sample of ethanol has been analysed by making use of the simpler spectra obtained from the species CD₃CH₂OH and CH₃CD₂OH, together with ¹H?{²H} double resonance. With p-ethoxy-benzylidene-p-n-butylaniline (EBBA) as the nematic solvent the dipolar couplings of CH₃ and CH₂ protons with the OH proton can be observed, and their magnitudes are compared with values calculated assuming different models for C-O-H internal rotation. Information on the quadrupole coupling constant tensor elements for CD₃ and CD₂ deuterium nuclei is obtained.     

Perturbation theory for the double sine-Gordon equation

This paper presents a perturbation theory for the double sine-Gordon equation. We obtain a system of differential equations that shows the soliton parameters modification under the influence of the perturbation. For the particular case λ=0 the results transform into the well-known perturbation theory for the sine-Gordon equation.     

Continuous solutions for balance laws

Abstract The paper employs the method of characteristics to show that continuous solutions of scalar conservation laws do not incur entropy production and to recover, in a direct and elementary way the (known) properties of solutions to the Hunter-Saxton equation. Keywords: Balance laws, Characteristics, Hunter-Saxton equation Mathematics Subject Classification (2000): 35L65, 35Q58     

Dancy Cartwright: Particularism in the philosophy of science

This paper aims to explore the space of possible particularistic approaches to Philosophy of Science by examining the differences and similarities between Jonathan Dancy’s moral particularism—as expressed in both his earlier writings (e.g., Moral Reasons, 1993), and, more explicitly defended in his book Ethics without Principles (2004)—and Nancy Cartwright’s particularism in the philosophy of science, as defended in her early collection of essays, How the Laws of Physics Lie (1983), and her later book, The Dappled World: A Study of the Boundaries of Science (1999). I shall argue that Dancy’s particularism is more radical, but also more plausible, than Cartwright’s, concluding that we have good reason to embrace a scientific particularism that is far closer to Dancy’s ethical particularism than any view defended by Nancy Cartwright, or any other philosopher from the ‘Stanford school’ of scientific theory.