Characterization of the organization in shear layers via the Proper Orthogonal Decomposition

Experiments are performed in an incompressible plane turbulent mixing layer, using various hot wire rake configurations. From these experiments, the Proper Orthogonal Decomposition is applied for kernels where the space-time correlation tensor is evaluated over different spatial meshes and velocity components configurations. The resulting decompositions are then discussed in terms of characterization of the organization of the flow for various scalar or vectorial approaches of the POD. An incrtial range law is evidenced. The instantaneous contribution of the first modes of the POD to the organization of the flow is analyzed. A dynamical behavior for the organization of the flow is observed from the correlation between the first two modes contribution.     

The Newton modified barrier method for QP problems

The Modified Barrier Functions (MBF) have elements of both Classical Lagrangians (CL) and Classical Barrier Functions (CBF). The MBF methods find an unconstrained minimizer of some smooth barrier function in primal space and then update the Lagrange multipliers, while the barrier parameter either remains fixed or can be updated at each step. The numerical realization of the MBF method leads to the Newton MBF method, where the primal minimizer is found by using Newton's method. This minimizer is then used to update the Lagrange multipliers. In this paper, we examine the Newton MBF method for the Quadratic Programming (QP) problem. It will be shown that under standard second-order optimality conditions, there is a ball around the primal solution and a cut cone in the dual space such that for a set of Lagrange multipliers in this cut cone, the method converges quadratically to the primal minimizer from any point in the aforementioned ball, and continues, to do so after each Lagrange multiplier update. The Lagrange multipliers remain within the cut cone and converge linearly to their optimal values. Any point in this ball will be called a hot start. Starting at such a hot start, at mostO(In In ^-1) Newton steps are sufficient to perform the primal minimization which is necessary for the Lagrange multiplier update. Here, >0 is the desired accuracy. Because of the linear convergence of the Lagrange multipliers, this means that onlyO(In ^-1)O(In In ^-1) Newton steps are required to reach an -approximation to the solution from any hot start. In order to reach the hot start, one has to perform Newton steps, wherem characterizes the size of the problem andC>0 is the condition number of the QP problem. This condition number will be characterized explicitly in terms of key parameters of the QP problem, which in turn depend on the input data and the size of the problem.Partially supported by NASA Grant NAG3-1397 and National Science Foundation Grant DMS-9403218.     

Essential spectrum and -solutions of one-dimensional Schrödinger operators

In 1949, Hartman and Wintner showed that if the eigenvalue equations of a one-dimensional Schrödinger operator possess square integrable solutions, then the essential spectrum is nowhere dense. Furthermore, they conjectured that this statement could be improved and that under this condition the essential spectrum might always be void. This is shown to be false. It is proved that, on the contrary, every closed, nowhere dense set does occur as the essential spectrum of Schrödinger operators which satisfy the condition of existence of -solutions. The proof of this theorem is based on inverse spectral theory.

     

Repeat Space Theory Applied to Carbon Nanotubes and Related Molecular Networks. I

The present article is the first part of a series devoted to extending the Repeat Space Theory (RST) to apply to carbon nanotubes and related molecular networks. Four key problems are formulated whose affirmative solutions imply the formation of the initial investigative bridge between the research field of nanotubes and that of the additivity and other network problems studied and solved by using the RST. All of these four problems are solved affirmatively by using tools from the RST. The Piecewise Monotone Lemmas (PMLs) are cornerstones of the proof of the Fukui conjecture concerning the additivity problems of hydrocarbons. The solution of the fourth problem gives a generalized analytical formula of the pi-electron energy band curves of nanotube (a, b), with two new complex parameters c and d. These two parameters bring forth a broad class of analytic curves to which the PMLs and associated theoretical devices apply. Based on the above affirmative solutions of the problems, a central theorem in the RST, called the asymptotic linearity theorem (ALT) has been applied to nanotubes and monocyclic polyenes. Analytical formulae derived in this application of the ALT illuminate in a new global context (i) the conductivity of nanotubes and (ii) the aromaticity of monocyclic polyenes; moreover an analytical formula obtained by using the ALT provides a fresh insight into Hückel’s (4n+2) rule. The present article forms a foundation of the forthcoming articles in this series. The present series of articles is closely associated with the series of articles entitled ‘Proof of the Fukui conjecture via resolution of singularities and related methods’ published in the JOMC.     

Uncertainty of the Thermal Conductivity Measurement Using the Transient Hot Wire Method

This work deals with uncertainty analysis of the thermal conductivity measurement using the transient hot wire method. The characterization is made from a sample of low-density, polyethylene BRALEN SA 200-22. The utilized experimental data are obtained from the test measurements performed on the air at room temperature. The sources of measurement errors are analyzed and the uncertainty of the measured value of the thermal conductivity is evaluated. The analysis shows that in the present case the uncertainty of the thermal conductivity measurement is about ±3.3% for 68% confidence level.This revised version was published online in November 2005 with corrections to the Cover Date.     

Rapid determination of panaxynol in a traditional Chinese medicine of Saposhnikovia divaricata by pressurized hot water extraction followed by liquid-phase microextraction and gas chromatography-mass spectrometry

Panaxynol is a bioactive component in traditional Chinese medicines (TCMs), such as Saposhnikovia divaricata and Panax ginseng. In the work, two solvent-free sample techniques of pressurized hot water extraction (PHWE) and headspace liquid-phase microextraction (HS-LPME) were combined and developed for the determination of panaxynol in a TCM of S. divaricata. Panaxynol in the TCM samples from different growing areas was extracted by PHWE in dynamic mode, followed by extraction and concentration with HS-LPME and analysis with gas chromatography-mass spectrometry (GC-MS). The PHWE and HS-LPME parameters were optimized and the method validations were studied. Panaxynol in S. divaricata from four different growing areas was quantitatively analyzed by internal standard method. These results have shown that PHWE-LPME-GC-MS is a simple, rapid, efficient and low-cost method for the determination of panaxynol in TCMs and is a potential tool for TCM quality assessment.     

Proof of the Fukui conjecture via resolution of singularities and related methods. II $$^{\star}$$

The present article is a direct continuation of the first part of this series. We reduce a proof of the Fukui conjecture (concerning the additivity problem of the zero-point vibrational energies of hydrocarbons) to that of a proposition related to the theory of algebraic curves, so that we can focus on the key mechanism of the additivity phenomena. Namely, by establishing what is called the Basic Piecewise Monotone Theorem (BPMT), we reduce a proof of the Fukui conjecture to that of a proposition, called the Local Analyticity Proposition, Version 1 (LAP1), which admits a proof via resolution of singularities. By LAP1, the essential part of the mechanism of the asymptotic linearity phenomena is extracted and is elucidated by using tools from the mathematical theory of algebraic curves, whose language is of vital importance in analyzing the crux of the additivity mechanism. Dedicated to the memory of Prof. Kenichi Fukui (1918–1998).     

Application of Hot Press Sintering to Na2O-B2O3-SiO2 Gels Containing Quantum Dots for Lowering of Densification Temperature

Na₂O-B₂O₃-SiO₂ (NBS) gels containing a large amount of CdS quantum-dots (10 wt%) were densified using the hot press (HP) sintering method. By HP treatment, full-densification temperature could be lowered by about 40°C than that of the normal non-pressing (NP) heat treatment. Exciton absorption of CdS quantum-dots in HP-sample showed a large blue shift compared with that in the NP sample, and the size-distribution of CdS dots remained very sharp, with a mean particle diameter d = 3.66 nm and a standard deviation of = 0.72. HP pressure had a large effect on the reduction of sintering temperature and time, resulting in the suppression of the aggregation and growth of CdS quantum-dots in NBS glasses.     

Multiple polypeptide forms observed in two-dimensional gels of Methylococcus capsulatus (Bath) polypeptides are generated during the separation procedure

We have examined two-dimensional electrophoresis (2-DE) gel maps of polypeptides from the Gram-negative bacterium Methylococcus capsulatus (Bath) and found the same widespread trains of spots as often reported in 2-DE gels of polypeptides of other Gram-negative bacteria. Some of the trains of polypeptides, both from the outer membrane and soluble protein fraction, were shown to be generated during the separation procedure of 2-DE, and not by covalent post-translational modifications. The trains were found to be regenerated when rerunning individual polypeptide spots. The polypeptides analysed giving this type of trains were all found to be classified as stable polypeptides according to the instability index of Guruprasad et al. (Protein Eng. 1990, 4, 155-161). The phenomenon most likely reflects conformational equilibria of polypeptides arising from the experimental conditions used, and is a clear drawback of the standard 2-DE procedure, making the gel picture unnecessarily complex to analyse.