Parameter estimation of ordinary differential equations

This paper addresses the development of a new algorithm forparameter estimation of ordinary differential equations. Here,we show that (1) the simultaneous approach combined with orthogonalcyclic reduction can be used to reduce the estimation problemto an optimization problem subject to a fixed number of equalityconstraints without the need for structural information to devisea stable embedding in the case of non-trivial dichotomy and(2) the Newton approximation of the Hessian information of theLagrangian function of the estimation problem should be usedin cases where hypothesized models are incorrect or only a limitedamount of sample data is available. A new algorithm is proposedwhich includes the use of the sequential quadratic programming(SQP) Gauss–Newton approximation but also encompassesthe SQP Newton approximation along with tests of when to usethis approximation. This composite approach relaxes the restrictionson the SQP Gauss–Newton approximation that the hypothesizedmodel should be correct and the sample data set large enough.This new algorithm has been tested on two standard problems.     

A new method for estimating bounds of eigenvalues

A new method for estimating the bounds of eigenvalues is presented. In order to show that the method proposed is as effective as Qiu's, an undamping spring-mass system with 5 nodes and 5 degrees of freedom is given. To illustrate that the present method can be applied to structures which cannot be treated by non-negative decomposition, a plane frame with 202 nodes and 357 beam elements is given. The results show that the present method is effective for estimating the bounds of eigenvalues and is more common than Qiu's. Project supported by the National Natural Science Foundation (No. 19872028) and the Mechanical Technology Development Foundation of China.     

A characteristic nonoverlapping domain decomposition method for multidimensional convection‐diffusion equations

We develop a quasi‐two‐level, coarse‐mesh‐free characteristic nonoverlapping domain decomposition method for unsteady‐state convection‐diffusion partial differential equations in multidimensional spaces. The development of the domain decomposition method is carried out by utilizing an additive Schwarz domain decomposition preconditioner, by using an Eulerian‐Lagrangian method for convection‐diffusion equations and by delicately choosing appropriate interface conditions that fully respect and utilize the hyperbolic nature of the governing equations. Numerical experiments are presented to illustrate the method. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005     

First enantiospecific synthesis of (+)-β-herbertenol

The first enantiospecific synthesis of (+)-β-herbertenol, from naturally occurring R-(+)-citronellal, employing Taber's diazo decomposition protocol as the key step, is described.     

More on regular linear spaces

We extend the enumeration of regular linear spaces in 1 to at most 19 points. In addition, one of the 5 missing cases in the previous list is settled. The number of regular linear spaces of type (15|2¹⁵,3³⁰) is 10,177,328. © 2005 Wiley Periodicals, Inc. J Combin Designs.     

Preparation and Thermal Decomposition of Synthetic Bayerite

The formation process of bayerite, from an aqueous solution of sodium aluminate through enforced decomposition of aluminate ions by introducing CO₂ gas and aging with mechanical stirring, was investigated by pH measurements of the mother solution during preparation reaction and characterization of precipitates obtained at various stages of preparation. An amorphous precipitate, produced initially by the reaction of introduced CO₂, transformed to bayerite via pseudoboehmite during aging. It was found that the crystalline particle size and morphology of the crystallized bayerite change depending systematically on the preparation conditions. The reaction pathway of the thermal decomposition of the synthesized bayerite was investigated by using thermoanalytical techniques. This revised version was published online in July 2006 with corrections to the Cover Date.     

Spectral Decomposition of Intracellular Complex Fluorescent Signals Using Multiwavelength Phase Modulation Lifetime Determination

Lifetime-based spectral decomposition using a frequency-domain phase/modulation technique has been developed on our UV confocal microspectrofluorimeter prototype. Examples of such an application are first given in the case of complex mixtures of three overlapping fluorescent components in solution. Preliminary results concerning cellular potential application are also reported in the case of Snarf-1 pH sensor. Limits and perspectives of such an approach at the subcellular level are discussed in view of future improvement.     

Synthesis of 2,6-Disubstituted Fluorenones

Various 2,6-disubstituted fluorenones 1a-1g were synthesized by the dry salt decomposition of 5,4′ -disubstituted 2-diazoniobenzophenone tetrafluoroborates 8a-8g via Pschorr cyclization in reasonable yields.     

Quantitative analysis of triazine herbicides in environmental samples by using high performance liquid chromatography and diode array detection combined with second-order calibration based on an alternating penalty trilinear decomposition algorithm

A novel application of second-order calibration method based on an alternating penalty trilinear decomposition (APTLD) algorithm is presented to treat the data from high performance liquid chromatography-diode array detection (HPLC-DAD). The method makes it possible to accurately and reliably analyze atrazine (ATR), ametryn (AME) and prometryne (PRO) contents in soil, river sediment and wastewater samples. Satisfactory results are obtained although the elution and spectral profiles of the analytes are heavily overlapped with the background in environmental samples. The obtained average recoveries for ATR, AME and PRO are 99.7 ± 1.5, 98.4 ± 4.7 and 97.0 ± 4.4% in soil samples, 100.1 ± 3.2, 100.7 ± 3.4 and 96.4 ± 3.8% in river sediment samples, and 100.1 ± 3.5, 101.8 ± 4.2 and 101.4 ± 3.6% in wastewater samples, respectively. Furthermore, the accuracy and precision of the proposed method are evaluated with the elliptical joint confidence region (EJCR) test. It lights a new avenue to determine quantitatively herbicides in environmental samples with a simple pretreatment procedure and provides the scientific basis for an improved environment management through a better understanding of the wastewater-soil-river sediment system as a whole.     

About the Stokes decomposition theorem of waves

The Stokes decomposition theorem deals with the electrical field of a light beam. The theorem asserts that a beam can be viewed as the sum of two differently polarized parts. This result was recently discussed for light in the frame of the unified theory of coherence. We study the general case of an electromagnetic wave which can be in radio, radar, communications, or light. We assume stationary components with any power spectrum and finite or infinite bandwidth. We show that an accurate definition of polarization and unpolarization is a key parameter which rules the set of solutions of the problem. When dealing with a “strong definition” of unpolarization, the problem is treated in the frame of stationary processes and linear invariant filters. When dealing with a “weak definition”, solutions are given by elementary properties of bidimensional random variables.