Convexity preserving interpolation by algebraic curves and surfaces

The problem of interpolation by a convex curve to the vertices of a convex polygon is considered. A natural 1-parameter family ofC algebraic curves solving this problem is presented. This is extended to a solution, of a general Hermite-type problem, in, which the curve also interpolates to one or two prescribedtangents at any desired vertices of the polygon. The construction of these curves is a generalization of well known methods for generatingconic sections. Several properties of this family of algebraic curves are discussed. In addition, the method is generalized to convexC interpolation of strictly convex data sets inR ³ by algebraicsurfaces.     

Wind-generated ambient noise in a topographically isolated basin: a pre-industrial era proxy

During the mid-1980s, calibrated measurements of ambient noise and wind speed were made in the Tongue of the Ocean in the Bahamas to quantify the spectra and statistics of wind-generated noise. This deep basin is topographically isolated from the Atlantic Ocean and, therefore, largely acoustically decoupled from the Atlantic Ocean deep sound channel. The quantitative effects of contaminating (non-surface wind-generated) noise sources within the basin were eliminated by careful measurement and robust statistical analysis methodologies. Above 500 Hz, the spectral slopes are approximately -5 dB per octave and independent of wind speed. Below 500 Hz, the ambient noise is no longer a linear function of wind speed. Below 100 Hz and for wind speeds greater than 18.5 knots (kt), the ambient noise is independent of frequency. The minimum observed ambient noise level falls 13 dB below Urick's "light shipping" level at 30 Hz and 2-5 dB below Wenz's sea state zero level through the wind-dominated portion of the spectrum. The basin's geographical isolation and the rigorous measurement and analysis methodologies employed make this two-decade-old data set a reasonable and justified proxy for pre-industrial era ocean noise levels in the 20 Hz to 20 kHz frequency band.     

Enhancement of high harmonics generated by field steering of electrons in a two-color orthogonally polarized laser field

We demonstrate enhancement by 1 order of magnitude of the high-order harmonics generated in argon by combining a fundamental field at 1300 nm (10(14) W cm(-2)) and its orthogonally polarized second harmonic at 650 nm (2 × 10(13) W cm(-2)) and by controlling the relative phase between them. This extends earlier work by ensuring that the main effect is the combined field steering the electron trajectory with negligible contribution from multiphoton effects compared to the previous schemes with 800/400 nm fields. We access a broad energy range of harmonics (from 20 eV to 80 eV) at a low laser intensity (far below the ionization saturation limit) and observe deep modulation of the harmonic yield with a period of π in the relative phase. Strong field theoretical analysis reveals that this is principally due to the steering of the recolliding electron wave packet by the two-color field. Our modeling also shows that the atto chirp can be controlled, leading to production of shorter pulses.     

The four-block Adamjan-Arov-Krein problem

This paper is concerned with the mixed sensitivity H^∞ design in the most general, i.e., the four-block, case. This problem involves in a crucial manner the so-called four-block operator Γ, the norm of which is the achievable feedback tolerance. Our objective in this paper is to provide an interpretation for all singular values of Γ. These singular values are given an Adamjan-Arov-Krein interpretation in terms of the L^∞ distance of an L^∞ function to H^∞(l). Intuitively, the singular values of Γ are the various tolerance levels that can be achieved if we allow a various number of unstable poles in the closed loop. We finally provide an upper bound on the number of singular values.     

Ab initio calculations on SF2 and its low-lying cationic states: anharmonic Franck-Condon simulation of the UV photoelectron spectrum of SF2

Geometry optimization calculations were carried out on the (approximate)X(1)A(1) state of SF2 and the (approximate)X(2)B(1), (approximate)A(2)A(1), (approximate)B(2)B(2), (approximate)C(2)B(2), (approximate)D(2)A(1), and (approximate)E(2)A(2) states of SF2(+) employing the restricted-spin coupled-cluster single-double plus perturbative triple excitation [RCCSD(T)] method and basis sets of up to the augmented correlation-consistent polarized quintuple-zeta [aug-cc-pV(5+d)Z] quality. Effects of core electron (S 2s(2)2p(6) and F 1s(2) electrons) correlation and basis set extension to the complete basis set limit on the computed minimum-energy geometries and relative electronic energies (adiabatic and vertical ionization energies) were investigated. RCCSD(T) potential energy functions (PEFs) were calculated for the (approximate)X(1)A(1) state of SF2 and the low-lying states of SF2(+) listed above employing the aug-cc-pV(5+d)Z and aug-cc-pV5Z basis sets for S and F, respectively. Anharmonic vibrational wave functions of these neutral and cationic states of SF2, and Franck-Condon (FC) factors of the lowest four one-electron allowed neutral photoionizations were computed employing the RCCSD(T) PEFs. Calculated FC factors with allowance for Duschinsky rotation and anharmonicity were used to simulate the first four photoelectron bands of SF2. The agreement between the simulated and observed first bands in the He I photoelectron spectrum reported by de Leeuw et al. [Chem. Phys. 34, 287 (1978)] is excellent. Our calculations largely support assignments made by de Leeuw et al. on the higher ionization energy bands of SF2.     

Excited-state electron-transfer quenching by a series of water photoreduction mediators

Rate constants k_q for the quenching of the excited state of Ru(bipy)₃²⁺ by a series of viologen salts having different redox potential E_{$\text{1}\text{2}$} have been determined in deaerated aqueous solutions at pH = 5 by laser flash photolysis. The k_q values are found to decrease with increasing —E_{$\text{1}\text{2}$} and to correlate with the reaction free-energy change ΔG. Such a correlation is shown to be consistent with the Rehm—Weller model for electron-transfer reactions.     

Synthesis of substituted 5-diethoxymethyl-5-ethyloxazolidines

Mixtures of stereoisomeric 2-diethoxymethyl-5-ethyloxazolidines with one of the stereoisomeric forms predominating were obtained by the reaction of 2-ethyl-2-formyloxirane diethyl acetal with alkyl-substituted Schiff bases in ethanol solution.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 7, 985–988, July, 1987.     

Detailed analysis of α,ω-bis(4-hydroxybutyl) poly(dimethylsiloxane) using GPC-MALDI TOF mass spectrometry

In this study the prepolymer alpha,omega-bis(4-hydroxybutyl) poly(dimethylsiloxane), used in the formulation of oxygen permeable films, is evaluated by gel permeation chromatography (GPC) combined with matrix assisted laser desorption ionization (MALDI) time of flight (TOF) mass spectrometry (MS). Two unexpected mass distributions are observed in the mass spectra. Reaction schemes for the formation of these distributions are proposed. A solution phase trimethylsilane end group modification was performed on the prepolymer to determine whether the unexpected mass distributions occur as impurities from synthesis or as artifacts from the MS process. Evaluation of the TMS modified prepolymer indicates the unexpected mass distributions indeed occur as impurities from the synthetic procedure. Average molecular weight values are determined by traditional GPC, direct MALDI-TOF MS, and GPC-MALDI-TOF MS methods and the results are compared.