Existence theorems for boundary value problems in difference equations

In this research, we study linear difference equations with constant coefficients subject to boundary conditions. Necessary and/or sufficient conditions for the existence of a unique solution will be established. The proofs of the existence and uniqueness theorems are established by means of special types of determinants called Mosaic Vandermonde determinants.     

Elastic behavior of composites containing multi-layer coated particles with imperfect interface bonding conditions and application to size effects and mismatch in these composites

This paper proposes a procedure to deal with n-layered inclusion based composites with imperfect interfaces (which conditions consist of displacement or stress vector jumps) respecting spherical symmetry. For that purpose, “discontinuity matrices” have been introduced. These matrices have been derived for several classical interface-models and an asymptotic method has been used to determine some of them. A self-consistent condition based on a strain-energy equivalence in the case of inclusion-matrix type composite materials is restated for n-layered inclusions with imperfect interfaces and applied to get estimates of such composites materials. The remarkable feature of the presently self consistent approach is that it does not need any tedious algebra providing the attached interface models respect the spherical symmetry. The present Generalized Self Consistent Model (GSCM) is then used to study size effects and mismatch in composites reinforced by coated inclusions.     

A class of optimal iterative methods of inverting a linear bounded operator

A family of higher-order iterative methods for inverting a linear bounded operator in a Banach space is presented. This family depending on two integer parameters can be considered as hyperpower methods of [1]. A convergence Theorem is proved and an optimal class with respect to the efficiency index is determined . Several error bounds are derived and compared with those in the literature.     

m次幂等矩阵的等价条件

利用矩阵的秩和齐次线性方程组解空间的维数,给出了m(m≥2)次幂等矩阵的一些等价条件,推广了2,3次幂等矩阵的相应结果.此外,所获结果还给推广到了m次幂等线性变换中.     

On the inclusion of collisional correlations in quantum dynamics

We present a formalism to describe collisional correlations responsible for thermalization effects in finite quantum systems. The approach consists in a stochastic extension of time dependent mean field theory. Correlations are treated in time dependent perturbation theory and loss of coherence is assumed at some time intervals allowing a stochastic reduction of the correlated dynamics in terms of a stochastic ensemble of time dependent mean-fields. This theory was formulated long ago in terms of density matrices but never applied in practical cases because of its complexity. We propose here a reformulation of the theory in terms of wave functions and use a simplified 1D model of cluster and molecules allowing to test the theory in a schematic but realistic manner. We illustrate the performance in terms of several observables, in particular global moments of the density matrix and single particle entropy built on occupation numbers. The occupation numbers remain fixed in time dependent mean-field propagation and change when evaluating the correlations, then taking fractional values. They converge asymptotically towards Fermi distributions which is a clear indication of thermalization.     

SPECTRAL CHARACTERISTICS OF FREE AND LINKED PYRENE-TYPE CHROMOPHORES IN SOLUTION,POLYMER MATRICES,AND INTERPENETRATING NETWORKS

Monomers, 1-pyrenylmethyl methacrylate (PyMMA), 1-pyrenylbutyl methacrylate (PyBMA), 4-(1-pyrenyl)methoxymethyl styrene (PyMMS) and allyl-(1-pyrenylmehtyl) ether (PyMAE), with pyrene as chromophore, were prepared. Their spectral properties (absorption, emission and emission decay) in solution, and doped or bonded in polymer matrices and complex polymer systems as interpenetrating polymer networks (IPN), were investigated. Spectral properties of pyrene-containing monomers doped in polystyrene (PS), polymethylmethacrylate (PMMA), polyvinylchloride (PVC), polyethylene (PE) and grafted on PE as well as copolymerized in buthylmethacrylate-co-styrene copolymer (BMA-co-S) have been compared. Absorption and emission spectra of pyrene type probes in solution and in IPN matrices exhibit typical absorption of the pyrene moiety. For IPN with grafted probes on PE, the absorption is slightly shifted to red wavelength. For monomers, PyMMA, PyBMA and PyMAE grafted to PE, the shape of the emission spectrum depends on the wavelength of excitation. The ratio of intensity of the vibrational band, I₁/I₃, (I₁ peak at 377 nm and I₃ peak at 388 nm) has been a quite useful indicator of polarity of IPN. The relative quantum yields of fluorescence in IPN matrices are lower in comparison to polymer matrices of PE, PS, PMMA for all probes under study. The fluorescence life-times for bound and free probes have been in the range 100–200 ns, which is substiantialy shorter than for the parent pyrene chromophore under the same or similar condition. Grafted probes on PE alone, or as a part of IPN, exhibit substantially shorter life-time around 10 ns and decay is rather complex.     

SPE–HPLC–MS/MS method for the trace analysis of tobacco‐specific N‐nitrosamines and 4‐(methylnitrosamino)‐1‐(3‐pyridyl)‐1‐butanol in rabbit plasma using tetraazacalix[2]arene[2]triazine‐modified silica as a sorbent

Tobacco‐specific N‐nitrosamines (TSNAs), including N′‐nitrosonornicotine, 4‐(methylnitrosamino)‐1‐(3‐pyridyl)‐1‐butanone, N′‐nitrosoanatabine, and N′‐nitrosoanabasine, have been implicated as a source of carcinogenicity in tobacco and cigarette smoke. We present a rapid and effective method comprising SPE based on tetraazacalix[2]arene[2]triazine‐modified silica as sorbent and analysis with HPLC–MS/MS for the determination of TSNAs and 4‐(methylnitrosamino)‐1‐(3‐pyridyl)‐1‐butanol (NNAL), a metabolite of 4‐(methylnitrosamino)‐1‐(3‐pyridyl)‐1‐butanone, in rabbit plasma. The linear dynamic ranges were 10–2000 pg/mL for NNAL and 4–2000 pg/mL for the four TSNAs with good correlation coefficients (>0.9965). The LODs were in the range of 0.9–3.7 pg/mL, and the LOQs were between 2.9 and 12.3 pg/mL. The accuracies of the method were also evaluated and found to be in the range of 90.1–113.3%. This method is promising to be applied to the preconcentration and determination of TSNAs and NNAL in smoke and human body fluids.     

Quantitative Determination of Octamethylcyclotetrasiloxane (D4) in Extracts of Biological Matrices by Gas Chromatography-Mass Spectrometry

Abstract

A method was developed and validated to measure octamethylcyclotetrasiloxane (D₄)^? quantitatively by gas chromatography-mass spectrometry (GC-MS) at low level in extracts of several biological matrices that include plasma, liver, lung, feces and fat from rats. The key to the successful determination lay in the use of extracts dried with anhydrous magnesium sulfate. This was necessary in view of the propensity of the methyl siloxane based GC-stationary phase to generate D₄ by its reaction with water present in the extracts. To enable quantiiation of D₄ at parts per billion (μg/L) levels, the base ion m/z 281 resulting from the loss of a methyl group from the parent molecule was selected for monitoring by SIM mode in GC-MS. The recovery of D₄ from any of the biological matrices was determined to be greater than 90% in three extractions. The D₄ response for the standards in GC-MS was linear (R² > 0.9900) and reproducible at concentrations ranging from 1—16,000 ng D₄/g solvent. Precision was less than 5%.     

Comparison of membrane assisted liquid–liquid microextraction devices applied to a series of volatile organic compounds in aqueous environmental matrices

An extraction device has been investigated for the separation and preconcentration of a series of volatile organic compounds (CHCl₃, CHCl₂Br, CHClBr₂ and CHBr₃) in aqueous matrices. The device consisted of a microporous membrane system utilising a hollow fibre tube filled with organic solvent directly immersed into the sample solution. The hollow fibre containing 160 µL organic solvent was immersed in a glass vial with 10 mL capacity, and the extraction took place through diffusive transport between the aqueous sample and the small amount of solvent. For validation of the method, some operational conditions, such as extraction solvent, temperature, stirring rate and separation time, were optimised. Limit of detection was at low ppb levels, with GC-MS analysis under selected ion monitoring (SIM), whereas enrichment factors between 22 and 35 were obtained. Good reproducibility with RSDs between 7.2% and 9.8% and large linear dynamic ranges with R ² between 0.996 and 0.998 were also achieved. In addition, the performance of the membrane assisted solvent extraction (MASE) system was compared with two existing configurations: a non-porous membrane separation device, as well as with a comparable microporous configuration. The comparison considered the extraction mechanism and the underlying transport processes. The application to real samples showed a good concordance with classical analytical methods.     

Ionic liquids as stationary phases in gas chromatography: Determination of chlorobenzenes in soils

The present research focuses on the evaluation of different ionic liquid (IL) stationary phases in gas chromatography. The different IL columns were evaluated in terms of peak resolution (R_s) and peak symmetry for the separation of the chlorobenzenes. The determination of chlorobenzenes in soil samples by means of the optimal IL stationary phase (SLB‐IL82) is proposed as an application. Soil pretreatment was based on a simplified quick, easy, cheap, effective, rugged, and safe extraction procedure and a large injection volume via a programed temperature vaporizer working in solvent vent mode. The retention time of the chlorobenzenes increased as the polarity of the IL column decreased. SLB‐IL82 is the stationary phase that provides the best values as regards R_s and asymmetry factor. Soil sample blanks were spiked with the analytes before subjecting the sample to the extraction process. The existence of a matrix effect was checked and the analytical characteristics of the method were determined in a fortified garden soil sample. The method provided good linearity, good repeatability and reproducibility values, and the LODs were in the 0.1–4.7 μg/kg range. Two fortified soil samples were applied to validate the proposed methodology.