Bounding the Bogoliubov coefficients

While over the last century or more considerable effort has been put into the problem of finding approximate solutions for wave equations in general, and quantum mechanical problems in particular, it appears that as yet relatively little work seems to have been put into the complementary problem of establishing rigourous bounds on the exact solutions. We have in mind either bounds on parametric amplification and the related quantum phenomenon of particle production (as encoded in the Bogoliubov coefficients), or bounds on transmission and reflection coefficients. Modifying and streamlining an approach developed by one of the present authors [M. Visser, Phys. Rev. A 59 (1999) 427-438, arXiv:quant-ph/9901030], we investigate this question by developing a formal but exact solution for the appropriate second-order linear ODE in terms of a time-ordered exponential of 2×2 matrices, then relating the Bogoliubov coefficients to certain invariants of this matrix. By bounding the matrix in an appropriate manner, we can thereby bound the Bogoliubov coefficients.     

The local ultraconvergence of high‐order finite element method for second‐order elliptic problems with constant coefficients over a rectangular partition

In this article, we will discuss the local ultraconvergence of high‐degree finite element method based on a rectangular partition for the second‐degree elliptic problem with constant coefficients in Ω ? ?² , u( y ) = 0 on ?Ω . Based on suitable regularity, ultraconvergence of the displacement of the extrapolated kth (k ≥ 3) degree finite element solution has been obtained by an extrapolation technique. Finally, numerical experiments are applied to demonstrate our theoretical findings.     

光催化材料反应系数测量新方法

本文提出光催化材料反应系数测量新方法-Mass transfer based(MTB)方法,该方法不同于传统方法中忽略传质影响,而是通过CFD计算考虑传质影响,这种改进无需传统方法所需反应控制过程也可准确测量光催化材料反应系数。利用该方法测量了光催化材料降解甲醛的反应系数,实验验证了其可行性。     

Rotational and rovibrational transitions in the a 1Δ2 and b 1Σ+0+ states of sulfur monoxide radical

ABSTRACT

Sulfur monoxide radical has widely been detected in outer space using ground-state spectroscopy. The a ¹Δ₂ and b ¹Σ⁺₀₊ states of this radical have low excitation energies, and they possibly exist in outer space. In this work, the potential energy curves and dipole moment functions of the two states were evaluated using the complete active space self- consistent field method, followed by the valence internally contracted multireference configuration interaction approach. The transition line positions, oscillator strengths, band transition dipole matrix elements, Einstein A coefficients, and Franck–Condon factors of all transitions were calculated for lower vibrational levels at rotational angular momentum quantum number J up to 150. The transition line positions calculated in this study are in good agreement with the experimental results. The rovibrational transition became noticeably weak at Δυ > 5. Comparing the results of a ¹Δ₂ and b ¹Σ⁺₀₊ states reported in this paper with the previous values, we conclude that these results are the most accurate and complete to date.     

Complications in the Use of the Taylor Dispersion Method for Ternary Diffusion Measurements: Methanol + Acetone + Water Mixtures

The Taylor dispersion technique is used to measure the ternary mutual diffusion coefficients of aqueous nonelectrolyte solutions at 25°C. The dispersion of the injected solutes is recorded by a differential refractometer and an ultraviolet-visible detector. The diffusion coefficients are calculated directly by fitting the theoretical dispersion equations to about six experimental curves simultaneously. If the ternary diffusion effects in the measured dispersion profiles are not confused by the inaccuracy of the experimental method or an unfavorable relative detector sensitivity, the diffusion coefficients are precise. For the system methanol + acetone + water, it is shown that the Taylor dispersion method is unsuitable for the determination of all the diffusion coefficients if the methanol mole fraction is less than 0.45 or the acetone mole fraction if more than 0.001.     

Calculating physical properties of organic compounds for environmental modeling from molecular structure

Mathematical models for predicting the transport and fate of pollutants in the environment require reactivity parameter values – that is the value of the physical and chemical constants that govern reactivity. Although empirical structure–activity relationships have been developed that allow estimation of some constants, such relationships are generally valid only within limited families of chemicals. The computer program, SPARC, uses computational algorithms based on fundamental chemical structure theory to estimate a large number of chemical reactivity parameters and physical properties for a wide range of organic molecules strictly from molecular structure. Resonance models were developed and calibrated using measured light absorption spectra, whereas electrostatic interaction models were developed using measured ionization pK_as in water. Solvation models (i.e., dispersion, induction, H-bonding, etc.) have been developed using various measured physical properties data. At the present time, SPARC’s physical property models can predict vapor pressure and heat of vaporization (as a function of temperature), boiling point (as a function of pressure), diffusion coefficient (as a function of pressure and temperature), activity coefficient, solubility, partition coefficient and chromatographic retention time as a function of solvent and temperature. This prediction capability crosses chemical family boundaries to cover a broad range of organic compounds.     

Improved Calcium Ion-Selective Electrode Based on a Neutral Carrier

Abstract

The performance of a liquid-membrane electrode using a synthetic, neutral carrier in o-nitro-phenyl-n-octyl-ether as membrane component in a PVC matrix, in the presence of sodium tetra-phenyl-borate, is described. Selectivities, working range, lifetime and anion interference are discussed. The electrode makes possible the measurement of calcium ion activities in the range 10^?1M to 10^?6M in unbuffered and in the range 10^?1M to 10^?8M in calcium buffered systems respectively. The selectivities of calcium over protons, magnesium, sodium and zinc are 25,000, 26,000, 2,800 and 7,100, respectively, and are far superior than those reported for other calcium sensors.     

基于标准差和平均差的权系数确定方法及其应用

本文以工业经济效益的综合评价为应用背景 ,提出了一种确定多指标决策权系数的新方法———标准差和平均差极大化方法。运用该方法进行多指标决策和评价 ,概念清楚、涵义明确 ,决策和评价结果准确、可信、不具有主观随意性     

Wavelet expansions and asymptotic behavior of distributions

We develop a distribution wavelet expansion theory for the space of highly time-frequency localized test functions over the real line S₀(R)⊂S(R) and its dual space , namely, the quotient of the space of tempered distributions modulo polynomials. We prove that the wavelet expansions of tempered distributions converge in . A characterization of boundedness and convergence in is obtained in terms of wavelet coefficients. Our results are then applied to study local and non-local asymptotic properties of Schwartz distributions via wavelet expansions. We provide Abelian and Tauberian type results relating the asymptotic behavior of tempered distributions with the asymptotics of wavelet coefficients.     

Differential operators in terms of Clebsch-Gordon (C-G) coefficients and the wave equation of massless tensor fields

The quantum theory of angular momentum affords a treatment of tensors and vectors in a spherical basis. By using this theory we define the tensor differential operators: divergence, curl and gradient which act on a tensor of any rank, in terms of C-G coefficients. With these definitions we obtain a matrix representation and useful properties for those operators. An interesting application of this formalism is to find the wave equation of a tensor of any rank in a linear theory. This provides a new common way to look at the wave equations associated with both Maxwell's equations and the Maxwell-like equations for the linearized Weyl curvature tensor in gravitoelectromagnetism describing gravitational radiation on a Minkowski spacetime background.