Vandermonde matrices on the circle: Spectral properties and conditioning

Summary We study Vandermonde matrices whose nodes are given by a Van der Corput sequence on the unit circle. Our primary interest is in the singular values of these matrices and the respective (spectral) condition numbers. Detailed information about multiplicities and eigenvectors, however, is also obtained. Two applications are given to the theory of polynomials.Dedicated to R. S. Varga on the occasion of his sixtieth birthdayResearch of A. C. supported by the Fundación Andes, Chile, and by the German Academic Exchange Service (DAAD), Federal Republic of GermanyResearch of W. G. supported, in part, by the National Science Foundation, USA, (Grant CCR-8704404)Research of S. R. supported by the Fondo Nacional de Desarollo Cientßfico y Tecnológico (FONDECYT), Chile, (Grant 237/89), by the Universidad Técnica F. Santa Marßa, Valparaßso, Chile, (Grant 89.12.06), and by the German Academic Exchange Service (DAAD), Federal Republic of Germany     

Calculating singular integrals as an ill-posed problem

Summary Applying numerical quadrature to singular integrals in a straightforward way leads to uncontrolled instability with respect to data errors. In this paper we describe how to control this instability.Dedicated to Professor G. Hämmerlin on the occasion of his 60th birthday.     

Partial differential equations with differential constraints

A geometric setting for constrained exterior differential systems on fibered manifolds with n-dimensional bases is proposed. Constraints given as submanifolds of jet bundles (locally defined by systems of first-order partial differential equations) are shown to carry a natural geometric structure, called the canonical distribution. Systems of second-order partial differential equations subjected to differential constraints are modeled as exterior differential systems defined on constraint submanifolds. As an important particular case, Lagrangian systems subjected to first-order differential constraints are considered. Different kinds of constraints are introduced and investigated (Lagrangian constraints, constraints adapted to the fibered structure, constraints arising from a (co)distribution, semi-holonomic constraints, holonomic constraints).     

Determination of Immunoglobulin G by a Hemin–Manganese(IV) Oxide-Labeled Enzyme-linked Immunosorbent Assay

An enzyme-linked immunosorbent assay (ELISA) is reported for human immunoglobulin G based on synthesized hemin–MnO₂ nanocomposite as the label. Enhanced sensitivity was obtained due to the increased catalytic activity of the hemin–MnO₂ nanocomposite toward 3,3′,5,5′-tetramethylbenzidine compared to hemin and MnO₂ alone. The synthesized hemin–MnO₂ nanocomposite was characterized by transmission electron microscopy and its catalytic activity to 3,3′,5,5′-tetramethylbenzidine was investigated by ultraviolet–visible absorption spectroscopy. After assembly of the sandwich-type immunoassay in the 96 wells of the plate the hemin–MnO₂-based label catalyzed 3,3′,5,5′-tetramethylbenzidine into blue compounds that were monitored by a plate reader. The absorbance increased with the concentration of human immunoglobulin G. The immunoassay displayed high sensitivity, a long linear dynamic range, and good selectivity for human immunoglobulin G. The immunoassay was also used for the determination of human immunoglobulin G in serum with favorable results. The developed assay combines the high throughput and low cost of ELISA with the simplicity of nanocomposite labeling and is suitable for application in clinical diagnosis.     

First- and second-order sensitivities of beams with respect to cross-sectional cracks

This paper deals with a variational formulation for the sensitivity problem of beam systems in the context of deformable solids with cracks. Natural frequencies are defined as state variables involved in the energy functional of the system, while the cracks length and position are treated as system parameters. The hierarchical equation system is formed and solved for the first and second derivatives of the natural frequency functions with respect to the cracks length and position. An analytical procedure for calculations of the second-order sensitivities of natural frequencies is proposed for the non-symmetrical equation system operator. Numerical algorithms are worked out and implemented computationally. Analytical and numerical aspects of the problem are discussed in detail through a number of illustrative results.The support of this work by the State Committee for Scientific Research (KBN) under Grant No. 4-050-0148/17-98-00 is gratefully acknowledged.     

Fructose-selective calorimetric biosensor in flow injection analysis

A highly selective, interference free biosensor for the measurement of fructose in real syrup samples was developed. The assay is based on the phosphorylation of d(−)fructose to fructose-6-phosphate by hexokinase and subsequent conversion of fructose-6-phosphate to fructose-1,6-biphosphate by fructose-6-phosphate-kinase. The heat liberated in the second reaction is monitored using an enzyme thermistor. The major advantages of this biosensor are rapid and selective measurement of fructose without the need to eliminate glucose and inexpensive FIA-based, mediator-free calorimetric measurement suitable for regular fructose analysis. This method was optimised for parameters, such as pH, ionic strength, interference, operational stability and shelf life. Good and reproducible linearity (0.5-6.0 mM) with a detection limit of 0.12 mM was obtained. Fructose determination in commercial syrup samples and spiked samples confirmed the reliability of this set-up and technique. The biosensor gave reproducible results with good overall stability for continuous measurements over a period of three months besides a useful shelf life of six months. The method could be used for routine fructose monitoring in food samples.     

EPR study of RLi2O.V2O5, RNa2O.V2O5, RCaO.V2O5, and RBaO.V2O5 modified vanadate glass systems

Experimental EPR spectra in several modified vanadate glass systems reveal hyperfine structure (hfs) lines whose widths vary with the molar ratio of modifier to vanadium pentoxide, R. In the RNa₂O.V₂O₅ system, for example, hfs lines show no resolution at low R values (near 0.1); by contrast, these lines exhibit dramatic narrowing as R approaches 0.5. In the model proposed here, this narrowing is due to an increase in hopping time for small polarons associated with V⁴⁺ ions in these systems. Increases in polaron hopping times are accompanied by increases in electron spin-spin relaxation times T₂'s, and, an associated narrowing of EPR linewidths. Experiments confirm that spectral widths are limited by electron T₂'s due to the fact that EPR linewidths do not vary with temperature down to 4.2 K. Resolved spectra in RNa₂O.V₂O₅ at R = 0.5 reveal a hyperfine coupling parameter of 0.0177 ± 0.0008 T, corresponding to an upper-limit polaron hopping frequency of 487 ± 20 MHz. By similar analyses, the systems of RCaO.V₂O₅, RBaO.V₂O₅, and RLi₂O.V₂O₅ exhibit comparable polaron hopping frequencies limits of 480 ± 20 MHz, 469 ± 20 MHz, and 468 ± 20 MHz, respectively, when R is near 1.0. In addition to the relaxation effects discussed here, results of modeling of resolved spectra to obtain hyperfine coupling constants A_|| and A_┴, and g_┴ values g_|| and g_┴ are presented and discussed.     

15N216O在1650-3450 cm-1的高分辨红外光谱

采用傅里叶变换红外光谱仪记录了富含¹⁵N₂¹⁶O同位素的一氧化二氮样品在1650-3450 cm^-1波段的高分辨振转光谱,得到了该同位素分子超过7300吸收谱线位置的实验值,经分析实验精确度好于5.0×10^-4 cm^-1. 基于有效哈密顿量模型预测和带带转动分析,确定了所有吸收线的归属;获得了29个新吸收带的振转光谱参数,并优化了其他44个吸收带的光谱参数值. 并且发现有效哈     

Detection and analysis of new bands of O3 by CRDS between 6500 and 7300 cm

The absorption spectrum of the ¹⁶O₃ isotopologue of ozone has been recorded in the 7000-7920 cm⁻¹ region by high sensitivity CW-Cavity Ring Down Spectroscopy. This report is devoted to the analyses of the 7065-7300 cm⁻¹ region dominated by the ν₁ + 2ν₂ + 5ν₃ and ν₁ + 5ν₂ + 3ν₃ A-type bands at 7130.8 and 7286.8 cm⁻¹ respectively. 289 transitions were assigned to the ν₁ + 2ν₂ + 5ν₃ band. The corresponding line positions were modeled with an effective Hamiltonian involving Coriolis resonance interactions between the (1 2 5) upper state and the (4 4 0), (0 2 6) and (6 1 0) dark states, and an anharmonic resonance interaction with the (2 0 5) state. The very strong interaction (up to 50% mixing of the wavefunctions) between the (1 2 5) and (6 1 0) states leads to the observation of two extra lines of the 6ν₁ + ν₂ band due to a resonance intensity transfer. 213 transitions of the ν₁ + 5ν₂ + 3ν₃ band were assigned and modeled taking into account a Coriolis resonance interaction with the (3 6 0) state.We take the opportunity of the present work to report the analysis of the very weak 4ν₂ + 4ν₃ B-type band at 6506.1 cm⁻¹ which was assigned from previously recorded CRDS spectra. 286 transitions were modeled using the effective Hamiltonian approach.The dipole transition moment parameters of the three analyzed bands were determined by a least-squares fit to the measured line intensities. For the three studied band systems, the effective Hamiltonian and transition moment operator parameters were used to generate line lists provided as Supplementary Materials.     

Photoemission intensity oscillations in the valence bands of C70 film

We have measured and analyzed the photoemission spectra (PES) of a C₇₀ film in the photon energy region from 13.4 eV to 98.4 eV. The photoelectron intensities of two C 2p π-derived features (denoted by A and B) oscillate regularly in the whole energy region with some fine structures below ∼30 eV. To obtain the detailed information of the oscillations, we have developed a sophisticated but practical procedure for intensity calculation. The procedure consists of two core concepts. The first is ascribing the PES features to their corresponding molecular orbitals with the help of density functional calculations. The second is a background subtraction algorithm. With this procedure, we obtained the oscillating behavior for individual features (A and B), which is by and large consistent with the predictions based on the spherical symmetric approximation although C₇₀ has the ellipsoidal shape. Owing to the solid state effect, the oscillating amplitudes of the A/B intensity ratios are smaller than those of gas phase C₇₀, but an orbital shift reported recently was not observed on our sample. The oscillating curve of a deeper feature, which consists of both σ and π states, are also reported.