Definition and detection of data-based uniqueness in evaluating bilinear (two-way) chemical measurements

Multivariate curve resolution methods, frequently used in analyzing bilinear data sets, result in ambiguous decomposition in general. Implementing the adequate constraints may lead to reduce the so-called rotational ambiguity drastically, and in the most favorable cases to the unique solution. However, in some special cases, non-negativity constraint as minimal information of the system is a sufficient condition to resolve profiles uniquely. Although, several studies on exploring the uniqueness of the bilinear non-negatively constrained multivariate curve resolution methods have been made in the literature, it has still remained a mysterious question. In 1995, Manne published his profile-based theorems giving the necessary and sufficient conditions of the unique resolution. In this study, a new term, i.e., data-based uniqueness is defined and investigated in details, and a general procedure is suggested for detection of uniquely recovered profile(s) on the basis of data set structure in the abstract space. Close inspection of Borgen plots of these data sets leads to realize the comprehensive information of local rank, and these argumentations furnish a basis for data-based uniqueness theorem. The reported phenomenon and its exploration is a new stage (it can be said fundament) in understanding and describing the bilinear (matrix-type) chemical data in general.     

The Lamb-dip spectrum of methylcyanide: Precise rotational transition frequencies and improved ground-state rotational parameters

Methylcyanide, CH₃CN, is an important interstellar species, and therefore the accurate knowledge of precise rest frequencies for rotational transitions as well as ground-state rotational and hyperfine constants is needed. In this work the hyperfine structure of the millimeter- and submillimeter-wave spectra of CH₃CN has been further investigated. In addition, accurate THz measurements have been carried out for the first time. Consequently, the present investigation allowed us to provide the most accurate ground state rotational and hyperfine parameters known at the moment for CH₃C¹⁴N. To resolve the hyperfine structure of the rotational transitions observed, the Lamb-dip technique has been exploited. Both frequency-modulated and video-type detections have been employed.     

Rotational analysis ofA 1Π-X 1Σ+ bands of P14N and P15N: Perturbatio studies in theA 1Π state

The ultraviolet band systemsA ¹Π-X ¹Σ⁺ of P¹⁴N and P¹⁵N were excited in an electrodeless tube containing traces of phosphorus specpure nitrogen and neon using a microwave discharge (2450 MHz). Bands of the isotopic species, P¹⁵N, were obtained using¹⁵N₂ enriched to 95.5%. Rotational analyses of eleven bands of P¹⁴N and sixteen bands of P¹⁵N were carried out. Three perturbing statese ³Σ⁻,d ³Δ andb ³Π, arising from the lower valence configurations were identified from the observed perturbations in thev′=0–4 levels of theA ¹Π state. Deperturbation studies led to the determination of molecular constants of the perturbing states. Vibrational assignments of the perturbing states were made from isotope shift studies.     

Error estimates for Hermite interpolation on spheres

In this paper, we prove convergence rates for spherical spline Hermite interpolation on the sphere S^d−1 via an error estimate given in a technical report by Luo and Levesley. The functionals in the Hermite interpolation are either point evaluations of pseudodifferential operators or rotational differential operators, the desirable feature of these operators being that they map polynomials to polynomials. Convergence rates for certain derivatives are given in terms of maximum point separation.     

稀薄气体二维外部柱体绕流特性研究

本文采用直接模拟蒙特卡罗方法对稀薄气体二维外部柱体绕流问题进行了数值模拟。结果表明:外部绕流问题,在特定情况下会产生激波,激波的产生,不仅与气体的稀薄程度有关,还与来流马赫数有关。而气流与壁面之间的换热,随来流马赫数增加而增加,随气体稀薄程度增加而减小。     

Millimeter and submillimeter wave spectroscopic investigations into the rotation-tunneling spectrum of gGg ethylene glycol, HOCH2CH2OH

The rotation-tunneling spectrum of the second most stable gGg^′ conformer of ethylene glycol (1,2-ethanediol) in its ground vibrational state has been studied in selected regions between 77 and 579 GHz. Compared to the study of the more stable aGg^′ conformer, a much larger frequency range was studied, resulting in a much extended frequency list covering similar quantum numbers, J?55 and K_a?19. While the input data were reproduced within experimental uncertainties up to moderately high values of J and K_a larger residuals remain at higher quantum numbers. The severe mixing of the states caused by the Coriolis interaction between the two tunneling substates is suggested to provide a considerable part of the explanation. In addition, a Coriolis interaction of the gGg^′ ground vibrational state with an excited state of the aGg^′ conformer may also contribute. Relative intensities of closely spaced lines have been investigated to determine the signs of the Coriolis constants between the two tunneling substates relative to the dipole moment components and to estimate the magnitudes of the dipole moment components and the energy difference between the gGg^′ and the aGg^′ conformers. Results of ab initio calculations on the total dipole moment and the vibrational spectrum were needed for these estimates. The current analysis is limited to transitions with quantum numbers J?40 and K_a?6 plus those having J?22 and K_a?17 which could be reproduced within experimental uncertainties. The results are aimed at aiding radioastronomers to search for gGg^′ ethylene glycol in comets and in interstellar space.     

Stagnation flow on a cylinder with partial slip--an exact solution of the Navier-Stokes equations

The stagnation slip flow on an axially moving cylinder is studied.The Navier–Stokes and energy equations reduce to nonlinearordinary differential equations under a similarity transform.For large slip, the flow field decays exponentially into potentialflow. The heat transfer can be expressed as an incomplete gammafunction. In general, the heat transfer increases with slip,Prandtl number and Reynolds number.     

有限长FGM圆筒的热/机应力的解析解

利用微分方程的级数求解方法,分析了两端简支的有限长功能梯度圆筒的轴对称稳态热弹性问题,推导出了稳态温度场与应力场的解析解。分析中采用指数函数模型来描述FGM圆筒中材料性能在厚度方向的连续变化,同时忽略温度对材料性能的影响。另外,论文以金属钼和多铝红柱石制成的功能梯度圆筒为例,给出了稳态温度场和应力场的数值结果。     

Polarization transforming properties of Dove prisms

We analyze the polarization changes introduced by a rotated Dove prism on the linearly polarized light, using the Jones calculus and the exact ray trace analysis. The state of polarization changes from the linear to a mildly elliptical one when a plane wave front passes through a rotated Dove prism: its semi-major axis is nearly parallel to the input plane of polarization, for any angle of prism rotation. The interferogram contrast remains high for all shearing angles in spite of polarization changes when the Dove prism is incorporated into a rotational shearing interferometer. These results are confirmed experimentally.     

Ground state parameters of BiH3 from infrared and millimeter-wave spectra: ground state and equilibrium structures

Unstable, short-lived BiH₃ has been synthesized and investigated by rotational spectroscopy in the range 158 (J=1-0) to 1280 GHz (J=8-7). Quadrupole and spin-rotation hyperfine structures (eQq=584.676(96) MHz), and the A₁A₂ splitting of the K=3 ground state level, have been resolved. By merging the pure rotational data with 1764 ground state combination differences obtained from the analysis of high resolution Fourier transform infrared spectra of the ν₁-ν₄ bands [J. Mol. Spectrosc. (2004) (in press)] spanning J and K values up to 16 and 14, respectively, with 0?ΔK?9, the ground state rotational and centrifugal distortion constants up to octic and sextic terms for reductions A and B, respectively, have been determined. Of the reductions of the ground state rovibrational Hamiltonian, reduction B including ε rather than h₃ as off-diagonal element is clearly favored. An experimental r₀ structure of the very-near spherical oblate symmetric top BiH₃, r(BiH)=178.82 pm and α(HBiH)=90.320°, has been deduced from the rotational constants B₀=2.64160172(18) and C₀=2.6010403(31) cm⁻¹. The derived experimental r_e structure, r_e(BiH)=177.834(50) pm and α_e(HBiH)=90.321(10)°, was determined. This is in excellent agreement with the most recent ab initio structure, r_e(BiH)=177.84 pm, and α_e(HBiH)=90.12°.