Construction Techniques for Highly Accurate Quasi-Interpolation Operators

Under mild additional assumptions this paper constructs quasi-interpolants in the form

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with approximation order ℓ−1, where_h(x) is a linear combination of translatesψ(x−jh) of a functionψinC^ℓ( ). Thus the order of convergence of such operators can be pushed up to a limit that only depends on the smoothness of the functionψ. This approach can be generalized to the multivariate setting by using discrete convolutions with tensor products of odd-degreeB-splines.     

Comparison of Singer's Formant, Speaker's Ring, and LTA Spectrum Among Classical Singers and Untrained Normal Speakers

Many studies have described and analyzed the singer's formant. A similar phenomenon produced by trained speakers led some authors to examine the speaker's ring. If we consider these phenomena as resonance effects associated with vocal tract adjustments and training, can we hypothesize that trained singers can carry over their singing formant ability into speech, also obtaining a speaker's ring? Can we find similar differences for energy distribution in continuous speech? Forty classically trained singers and forty untrained normal speakers performed an all-voiced reading task and produced a sample of a sustained spoken vowel /a/. The singers were also requested to perform a sustained sung vowel /a/ at a comfortable pitch. The reading was analyzed by the long-term average spectrum (LTAS) method. The sustained vowels were analyzed through power spectrum analysis. The data suggest that singers show more energy concentration in the singer's formant/speaker's ring region in both sung and spoken vowels. The singers' spoken vowel energy in the speaker's ring area was found to be significantly larger than that of the untrained speakers. The LTAS showed similar findings suggesting that those differences also occur in continuous speech. This finding supports the value of further research on the effect of singing training on the resonance of the speaking voice.     

Ultra-Precise Mass Measurements Using the UW-PTMS

Based on the use of a single ion, isolated at the center of a cryogenically cooled Penning trap, an environment is produced which makes this mass spectrometer remarkably free of systematic errors. The most notable developments in our quest for an ultra-high accuracy instrument were (a) the compensation of the trapping potential, (b) the discovery that motional sidebands could manipulate radial energies, (c) the use of multiply-charged ions that could improve signal-to-noise, and (d) the use of an ultra-stable superconducting magnet/cryostat system with drift <0.010 ppb/h. The dominant systematic errors are associated with radial electric fields caused by image charges in the trap electrodes and with the rf-electrical drive field used to determine the harmonic axial resonance. To illustrate the potential of this improved spectrometer, the four-fold improved measurement of the proton's mass and the eight-fold improved measurement of oxygen's atomic mass will be described. This revised version was published online in July 2006 with corrections to the Cover Date.     

Gibbs Measures for Brownian Paths Under the Effect of an External and a Small Pair Potential

We consider Brownian motion in the presence of an external and a weakly coupled pair interaction potential and show that its stationary measure is a Gibbs measure. Uniqueness of the Gibbs measure for two cases is shown. Also the typical path behaviour, the degree of mixing and some further properties are derived. We use cluster expansion in the small coupling parameter.     

Cost minimization and the stochastic discount factor

It is shown that a cost function subject to internal costs of adjustment induces a stochastic discount factor (pricing kernel) that is a function of random output, input and output prices, existing capital stock, and investment. The only assumption on firm preferences is that they are increasing in current period consumption and future stochastic consumption. This ensures that the firm will always act to minimize current period cost of providing future consumption, and it is the first-order conditions for this cost minimization problem that generate the stochastic discount factor, which itself can be interpreted as the marginal variable cost of varying stochastic output. A cost-based pricing kernel is estimated using annual time-series data on macroeconomic variables and returns data for the S&P 500 and commercial paper.     

On the irrationality of factorial series II

In this paper we give irrationality results for numbers of the form where the numbers an behave like a geometric progression for a while. The method is elementary, not using differentiation or integration. In particular, we derive elementary proofs of the irrationality of π and em for Gaussian integers m≠0.     

Ab initio and semiempirical estimates of PN valence state interactions

Hartree-Fock wavefunctions for the valence states of PN arising from the lowest energy open shell configurations, 2π⁴7σ3π and 2π³7σ²3π, are generated and used in ab initio calculations of diagonal spin-orbit, off-diagonal spin-orbit, and rotation-electronic matrix elements. These results are compared with those from two semiempirical methods, one based on atomic orbital populations and the other dependent solely on atomic spin-orbit splittings. The latter method is found to be surprisingly successful in predicting the ³Δ spin-orbit constant for a series of isovalent molecules. Semiempirical estimates of the ³Δ and ³Π spin-orbit constants of AsN are given. The Hartree-Fock values of the a and b perturbation parameters are found to be 50 cm⁻¹ and 0.60 (unitless), respectively. A previously reported perturbation in the A¹Π-X¹Σ⁺ band system is shown to arise from a ³Σ^{− 1}Π spin-orbit interaction.     

The microwave spectrum,structure and nuclear quadrupole coupling constants for stibabenzene

The microwave spectrum of 121-SbC₅H₅, 123-SbC₅H₅, β-dideutero 121-SbC₅H₃D₂ and 123-SbC₅H₃D₂ has been assigned in the region 26.5–40.0 GHz. The respective rotational constants and uncertainties are: A = 4512.69 ± 0.42, B = 1738.00 ± 0.01, C = 1254.51 ± 0.01; A = 4512.84 ± 0.30, B = 1729.80 ± 0.01, C = 1250.22 ± 0.01; A = 4176.18 ± 0.33, B = 1660.94 ± 0.01, C = 1188.15 ± 0.01; A = 4176.60 ± 0.61, B = 1652.94 ± 0.03, C = 1184.03 ± 0.03 (in MHz units). The structure is found to be planar, C_2v in symmetry. The $\text{d(}\text{Sb-C}\text{) = 2.050 ± 0.005}\text{A}\text{?}$ and ∠CSbC = 92.9° ± 1.0°. The nuclear quadrupole coupling constants for the 121 and 123 antimony isotopes are χ_aa = 456.4 ± 4.1 MHz, η = 0.396 ± 0.008, and χ_aa = 583.00 ± 5.3 MHz, η = 0.399 ± 0.008, respectively. Several alternate techniques using the coupling constants as data support a σ-donating property for antimony.     

On risk minimizing portfolios under a Markovian regime-switching Black-Scholes economy

We consider a risk minimization problem in a continuous-time Markovian regime-switching financial model modulated by a continuous-time, observable and finite-state Markov chain whose states represent different market regimes. We adopt a particular form of convex risk measure, which includes the entropic risk measure as a particular case, as a measure of risk. The risk-minimization problem is formulated as a Markovian regime-switching version of a two-player, zero-sum stochastic differential game. One important feature of our model is to allow the flexibility of controlling both the diffusion process representing the financial risk and the Markov chain representing macro-economic risk. This is novel and interesting from both the perspectives of stochastic differential game and stochastic control. A verification theorem for the Hamilton-Jacobi-Bellman (HJB) solution of the game is provided and some particular cases are discussed.     

Path integral formulation of general diffusion processes

A method is given for the derivation of a path integral representation of the Green's function solutionP of equationsP/t=L P,L being some Liouville operator. The method is applied to general diffusion processes.Feynman's path integral representation of the Schrödinger equation and Stratonovich's path integral representation of multivariate Markovian processes are obtained as special cases if the metric of the general diffusion process is flat. For curved phase spaces our result is a nontrivial generalization and new. New applications e.g. to quantized motion in general relativity, to transport processes in inhomogeneous systems, or to nonlinear non-equilibrium thermodynamics are made possible. We expect applications to be fruitfull in all cases where (continuous) macroscopic transport processes in Riemann geometries have to be considered.