Eventual Positivity of Hermitian Algebraic Functions and Associated Integral Operators∗

Quillen proved that repeated multiplication of the standard sesquilinear form to a positive Hermitian bihomogeneous polynomial eventually results in a sum of Hermitian squares, which was the first Hermitian analogue of Hilbert’s seventeenth problem in the nondegenerate case. Later Catlin-D’Angelo generalized this positivstellensatz of Quillen to the case of Hermitian algebraic functions on holomorphic line bundles over compact complex manifolds by proving the eventual positivity of an associated integral operator. The arguments of Catlin-D’Angelo involve subtle asymptotic estimates of the Bergman kernel. In this article, the authors give an elementary and geometric proof of the eventual positivity of this integral operator, thereby yielding another proof of the corresponding positivstellensatz.     

Validated quantitation method for a peptide in rat serum using liquid chromatography/high‐field asymmetric waveform ion mobility spectrometry

The analysis of peptides presents serious challenges for bioanalytical scientists including low total ion current and non‐selective fragmentation during tandem mass spectrometry (MS/MS). During method validation of a peptide in rat serum matrix some interferences could not be easily removed and thus prevented accurate and precise measurement. These problems associated with peptide quantitation were resolved by using FAIMS (high‐Field Asymmetric waveform Ion Mobility Spectrometry). This selectivity‐enhancing technique filters out matrix interferences, and the resulting pseudo‐selected reaction monitoring (pseudo‐SRM) chromatograms were nearly free from interferences. Control blank matrix samples contained an acceptable level of interference (only 7% signal as compared to the lower level of quantitation). Chromatographic peaks were easily, accurately and precisely integrated resulting in a validated liquid chromatography (LC)/FAIMS‐MS/MS method for the analysis of a peptide drug in rat serum according to United States Food and Drug Administration (US FDA) bioanalytical guidelines. These results confirm that new selectivity‐enhancing technologies aid the pharmaceutical industry in reliably producing acceptable pharmacokinetic data. Copyright © 2009 John Wiley & Sons, Ltd.     

Stimulated terahertz stokes emission of silicon crystals doped with antimony donors

Stimulated Stokes emission has been observed from silicon crystals doped by antimony donors when optically excited by radiation from a tunable infrared free electron laser. The photon energy of the emission is equal to the pump photon energy reduced by the energy of the intervalley transverse acoustic (TA) g phonon in silicon (approximately 2.92 THz). The emission frequency covers the range of 4.6-5.8 THz. The laser process occurs due to a resonant coupling of the 1s(E) and 1s(A1) donor states (separation approximately 2.97 THz) via the g-TA phonon, which conserves momentum and energy within a single impurity center.     

The Utilization of Low Frequency Raman Spectra of Gases for the Study of Molecules with Large Amplitude Vibration

The utilization of the Raman spectra of the low frequency bending mode for three quasi-linear molecules: disiloxane,(SiH3)2O;methylisocyanate,CH3NCO;and dimethylisocyanate,(CH3)2SiHNCO for observing the low frequency anharmonic bending vibration is demonstrated which is superior to the corresponding far infrared spectra.From the observed frequencies from the Raman spectra the potential function governing the heavy atom motion to linearity has been obtained from which the barrier has been determined.These experimental values are compared to the ab initio predicted values.Also low frequency Raman spectra of the ring puckering vibration of chlorocyclobutane,c-C4H7Cl,bromocyclobutane,c-C4H7Br,and aminocyclobutane,c-C4H7NH2,have been utilized to obtain the potential function governing the ring inversion for these molecules.The determined barriers to planarity are compared to those obtained from MP2(full) ab initio and density functional theory B3LYP calculations by utilizing a variety of basis sets.For all of these studies it is shown that the Raman spectra are superior to the infrared spectra for determining the frequencies of the excited state transitions.     

SELECTION OF TRAINING SAMPLES FOR MODEL UPDATING USING NEURAL NETWORKS

One unique feature of neural networks is that they have to be trained to function. In developing an iterative neural network technique for model updating of structures, it has been shown that the number of training samples required increases exponentially as the number of parameters to be updated increases. Training the neural network using these samples becomes a time-consuming task. In this study, we investigate the use of orthogonal arrays for the sample selection. A comparison between this orthogonal arrays method and four other methods is illustrated by two numerical examples. One is the update of the felxural rigidities of a simply supported beam and the other is the update of the material properties and the boundary conditions of a circular plate. The results indicate that the orthogonal arrays method can significantly reduce the number of training samples without affecting too much the accuracy of the neural network prediction.     

Conformational stability, r0 structural parameters, and vibrational assignments of mono-substituted cyclobutanes: fluorocyclobutane

Variable temperature (-55 to -100°C) studies of the infrared spectra (3500-400 cm(-1)) of fluorocyclobutane, c-C(4)H(7)F, dissolved in liquid xenon have been carried out as well as the infrared spectra of the gas. By utilizing eight pairs of conformers at 10 different temperatures, the enthalpy difference between the more stable equatorial conformer and the axial form has been determined to be 496±40 cm(-1) (5.93±0.48 kJ/mol). The percentage of the axial conformer present at ambient temperature is estimated to be 8±1%. The ab initio MP2(full) average predicted energy difference from a variety of basis sets is 732±47 cm(-1) (9.04±0.44 kJ/mol) and the average value of 602±20 cm(-1) from density functional theory predictions by the B3LYP method are significantly larger than the experimentally determined enthalpy value. By utilizing previously reported microwave rotational constants for the equatorial and axial conformers combined with ab initio MP2(full)/6-311+G(d,p) predicted structural values, adjusted r(0) parameters have been obtained. The determined heavy atom structural parameters for the equatorial [axial] conformer are: distances (?) C-F=1.383(3) [1.407(3)], C(α)-C(β)=1.543(3) [1.546(3)], C(β)-C(γ)=1.554(3) [1.554(3)] and angles (°) ∠C(α)C(β)C(γ)=85.0(5) [89.2(5)], ∠C(β)C(α)C(β)=89.3(5) [89.2(5)], ∠F-(C(β)C(α)C(β))=117.4(5) [109.2(5)] and a puckering angle of 37.4(5) [20.7(5)]. The conformational stabilities, harmonic force fields, infrared intensities, Raman activities, depolarization ratios and vibrational frequencies have been obtained for both conformers from MP2(full)/6-31G(d) ab initio calculations and compared to experimental values where available. The results are discussed and compared to the corresponding properties of some other monosubstituted cyclobutanes with halogen and pseudo-halogen substituents.     

Raman and infrared,microwave spectra,conformational stability,adjusted r0 structural parameters,and vibrational assignments of cyclopentylamine

Fourier transform microwave spectrum of cyclopentylamine, c–C₅H₉NH₂ has been recorded, and seven transitions have been assigned for the most abundant conformer, and the rotational constants have been determined: A = 4909.46(5), B = 3599.01(4), and C = 2932.94(4). From the determined microwave rotational constants and ab initio MP2(full)/6‐311 + G(d,p) predicted structural values, adjusted r₀ parameters are reported with distances (Å): rC_α–C_β = 1.529(3), rC_β–C_γ = 1.544(3), rC_γ–C_γ = 1.550(3), rC_α–N = 1.470(3), and angles (°) ∠CCN = 108.7(5), ∠C_βC_αC_β = 101.4(5), and τC_βC_αC_β′C_γ′ = 42.0(5). The infrared spectra (4000–220 cm⁻¹) of the gas have been recorded. Additionally, the variable temperature (−60 to −100 °C) Raman spectra of the sample dissolved in liquefied xenon was recorded from (3800–50 cm⁻¹). The four possible conformers have been identified, and their relative stabilities obtained with enthalpy difference relative to t‐Ax of 211 ± 21 cm⁻¹ for t‐Eq ≥ 227 ± 22 cm⁻¹ for g‐Eq ≥ 255 ± 25 cm⁻¹ for g‐Ax. The percentage of the four conformers is estimated to be 53% for the t‐Ax, 11 ± 1% for t‐Eq, 20 ± 2% for g‐Ax and 16 ± 2% for g‐Eq at ambient temperature. The conformational stabilities have been predicted from ab initio calculations by utilizing several different basis sets up to aug‐cc‐pVTZ from both MP2(full) and density functional theory calculations by the B3LYP method. Vibrational assignments have been provided for the observed bands for all four conformers, which are predicted by MP2(full)/6‐31G(d) ab initio calculations to predict harmonic force constants, wavenumbers, infrared intensities, Raman activities, and depolarization ratios for all of the conformers. The results are discussed and compared to the corresponding properties of some related molecules. Copyright © 2014 John Wiley & Sons, Ltd.     

Silicon donor and Stokes terahertz lasers

Two types of lasers based on hydrogen-like impurity-related transitions in bulk silicon operate at frequencies between 1 and 7 THz (wavelength range of 50-230 μm). These lasers operate under mid-infrared optical pumping of n-doped silicon crystals at low temperatures (<30 K). Dipole-allowed optical transitions between particular excited states of group-V substitutional donors are utilized in the first type of terahertz silicon lasers. These lasers have a gain ∼1-3 cm⁻¹ above the laser thresholds (>1 kW cm⁻²) and provide 10 ps-1 μs pulses with a few mW output power on discrete lines. Raman-type Stokes stimulated emission in the range 4.6-5.8 THz has been observed from silicon crystals doped by antimony and phosphorus donors when optically excited by radiation from a tunable infrared free electron laser. The scattering occurs on the 1s(E)→1s(A₁) donor electronic transition accompanied by an emission of the intervalley transverse acoustic g-phonon. The Stokes lasing has a peak power of a few tenths of a mW and a pulse width of a few ns. The Raman optical gain is about 7.4 cm GW⁻¹ and the optical threshold intensity is ∼100 kW cm⁻².     

Tail behaviour of credit loss distributions for general latent factor models

Using a limiting approach to portfolio credit risk, we obtain analytic expressions for the tail behavior of credit losses. To capture the co‐movements in defaults over time, we assume that defaults are triggered by a general, possibly non‐linear, factor model involving both systematic and idiosyncratic risk factors. The model encompasses default mechanisms in popular models of portfolio credit risk, such as CreditMetrics and CreditRisk⁺. We show how the tail characteristics of portfolio credit losses depend directly upon the factor model's functional form and the tail properties of the model's risk factors. In many cases the credit loss distribution has a polynomial (rather than exponential) tail. This feature is robust to changes in tail characteristics of the underlying risk factors. Finally, we show that the interaction between portfolio quality and credit loss tail behavior is strikingly different between the CreditMetrics and CreditRisk⁺ approach to modeling portfolio credit risk.