关于非线性波动方程的爆破现象

通过引入一类“爆破因子K(u,ut）”,讨论了非线性波动方程分别具Newmann边界条件和Dirichlet边界条件时,混合问题对于常见的各种非线性情形及初值条件,解在有限时间内的爆破行为。     

The two-dimensional Coulomb gas on a sphere: Exact results

At the special value of the reduced inverse temperature=2, the equilibrium statistical mechanics of a two-dimensional Coulomb gas confined to the surface of a sphere is an exactly solvable problem, just as it was for the Coulomb gas in a plane. The thermodynamic quantities and all the correlation functions can be calculated. Use is made of an isomorphism between the classical Coulomb gas and the free Fermi field theory associated with the Dirac operator on the sphere.Laboratory associated with the Centre National de la Recherche Scientifique.     

Phase equilibria in the Ag4SSe-SnTe system

The phase diagram of the system Ag₄SSe-SnTe is studied by means of X-ray diffraction, differential thermal and metallographic analyses and measurements of the microhardness and the density of the material. This diagram is divided into two eutectic-type subdiagrams by the composition Ag₄SSe·2SnTe. The unit-cell parameters of the intermediate phases 3Ag₄SSe·SnTe (phase A) and -Ag₄SSe·2SnTe (phase B) are determined as follows: for phase A: a=0.7851 nm, b=0.7196 nm, c=0.6296 nm, =101.32°, =85.90°, =111.36°; for phase B: a=0.3662 nm, b=0.3303 nm, c=0.3343 nm, =90.74°, =108.94°, =91.91°. The phase Ag4SSe·2SnTe melts congruently at 615°C and a polymorphic transition of the phase takes place at T _- =110°C.This revised version was published online in November 2005 with corrections to the Cover Date.     

On the Interaction of Two Finite-Dimensional Quantum Systems

Interaction of quantum system S ^a described by the generalised × eigenvalue equation A| _s =E _s S ^a | _s (s=1,...,) with quantum system S ^b described by the generalised n×n eigenvalue equation B| _i = _i S ^b | _i (i=1,...,n) is considered. With the system S ^a is associated -dimensional space X ^a and with the system S ^b is associated an n-dimensional space X _n ^b that is orthogonal to X ^a . Combined system S is described by the generalised (+n)×(+n) eigenvalue equation [A+B+V]| _k = _k [S ^a +S ^b +P]| _k (k=1,...,n+) where operators V and P represent interaction between those two systems. All operators are Hermitian, while operators S ^a ,S ^b and S=S ^a +S ^b +P are, in addition, positive definite. It is shown that each eigenvalue _{k i} of the combined system is the eigenvalue of the × eigenvalue equation . Operator in this equation is expressed in terms of the eigenvalues _i of the system S ^b and in terms of matrix elements _s |V| _i and _s |P| _i where vectors | _s form a base in X ^a . Eigenstate | _k ^a of this equation is the projection of the eigenstate | _k of the combined system on the space X ^a . Projection | _k ^b of | _k on the space X _n ^b is given by | _k ^b =( _k S ^b –B)^–1(V– _k P})| _k ^a where ( _k S ^b –B)^–1 is inverse of ( _k S ^b –B) in X _n ^b . Hence, if the solution to the system S ^b is known, one can obtain all eigenvalues _{k i} } and all the corresponding eigenstates | _k of the combined system as a solution of the above × eigenvalue equation that refers to the system S ^a alone. Slightly more complicated expressions are obtained for the eigenvalues _{k i} } and the corresponding eigenstates, provided such eigenvalues and eigenstates exist.     

Phase equilibria in the Ag4SSe–As2Se3 system

The phase diagram of the system Ag₄SSe–As₂Se₃ is studied by means of X-ray diffraction, differential thermal analyses and measurements of the microhardness and the density of the materials. The unit-cell parameters of the intermediate phases 3Ag₄SSe·As₂Se₃ (phase A) and Ag₄SSe·2As₂Se₃ (phase B) are determined as follows for phase A: a=4.495 Å, b=3.990 Å, c=4.042 Å, α=89.05°, β=108.98°, γ=92.93°; for phase B: a=4.463 Å, b=4.136 Å, c=3.752 Å, α=118.60°, β=104.46°, γ=83.14°. The phase 3Ag₄SSe·As₂Se₃ and Ag₄SSe·2As₂Se₃ have a polymorphic transition α?β consequently at 105 and 120°C. The phase A melts incongruently at 390°C and phase B congruently at the same temperature.     

Differential Pulse Voltammetric Simultaneous Determination of Four Anti‐Inflammatory Drugs by Using Soft Modelling

An application of a partial least squares calibration method for the simultaneous voltammetric determination of indomethacin, acemethacin, piroxicam and tenoxicam is suggested. It was shown that it is possible to resolve complex mixtures of analytes even when they have strongly overlapped signals. In order to check the proposed method, statistical analysis of the results was performed by mean of hypothesis tests. The method developed was applied to the electrochemical reduction region of four anti‐inflammatory drugs and allowed the drugs to be quantified at concentrations between 0.52 and 4.09 μg mL^?1 for acemethacin, 0.44 and 3.50 μg mL^?1 for indomethacin, 0.43 and 3.40 μg mL^?1 for piroxicam, and 0.42 and 3.30 μg mL^?1 for tenoxicam with good results. The average absolute value of relative errors was 2.25%, 4.31%, 1.68% and 2.49%, respectively.     

Significance of Non-isothermal Kinetic Data. A statistical study

Arrhenius parameters values, in non-isothermal kinetic vaporisation processes for a series of compounds with related structures, have been calculated. This was made using a method of calculation that allows to find the most probable vaporisation mechanisms. According to this method DTG curves were compared with some theoretical ones reported in literature, whose shape results to be only a function of the mechanisms. In this way the choice of the mathematical functions which can be inserted in the kinetic equations, was influenced by the shape of the DTG plots and other thermal analysis signals thus allowing to choose the most probable mechanisms. The kinetic parameters derived from these mechanisms were compared, using statistical analysis, with those obtained from another method of calculation based on ‘a priori’ vaporisation mechanism chosen for the investigated liquid–gas transition. The standard deviations of the slope and of the intercept, together with the standard deviation and the square correlation coefficient (r ²) of the linear regression equations related to the mechanisms of the two methods were calculated. Student t-test, Fisher F-test, confidence intervals (c.i.) and residuals valueswere also given. Statistical analysis shows that the mechanisms obtained with the former method (diffusive and geometrical models) and the related Arrhenius parameters result to be more significant (in terms of probability) than the corresponding quantities of the latter for which a first-order model was chosen. This revised version was published online in August 2006 with corrections to the Cover Date.     

Water sorption and glass transition of freeze-dried camu-camu (myrciaria dubia (H.B.K.) Mc Vaugh) pulp

Differential scanning calorimetry (DSC) was used to determine phase transitions of freeze-dried camu-camu pulp in a wide range of moisture content. Samples were equilibrated at 25°C over saturated salt solutions in order to obtain water activities (a_w) between 0.11–0.90. Samples with a_w>0.90 were obtained by direct water addition. At the low and intermediate moisture content range, Gordon–Taylor model was able to predict the plasticizing effect of water. In samples, with a_w>0.90, the glass transition curve exhibited a discontinuity and T^’_g was practically constant (–58.8°C), representing the glass transition temperature of the maximally concentrated phase(T_g ).     

The temperature-composition phase diagram of the HgTe?HgI2 pseudobinary system on the HgTe rich side

The temperature-composition phase diagram of the HgTe? HgI₂ system was determined from 0 to 45 Mol-% HgI₂ between 25 and 670°C using Debye-Scherrer powder X-ray diffraction techniques and differential thermal analysis. Solid solutions of HgTe and HgI₂ with the cubic, zinc blende-type structure exist above 300°C, having a maximum solubility of 11.7 ± 0.8 Mol-% HgI₂ in HgTe at 501 ± 5°C. The known monoclinic compound Hg₃Te₂I₂ is formed by a peritectic reaction upon cooling at 501 ± 5°C, with the peritectic point at approximately 37 ± 4 Mol-% HgI₂.     

Volumetric and Refractive Index Behaviour of α-Amino Acids in Aqueous CTAB at Different Temperatures

Densities （ρ） and refractive indices （nD） of glycine （Gly）, DL-alanine （Ala）, DL-valine （Val） （0.02, 0.04, 0.06, 0.08, and 0.10 mol·L^-1） in 0.005 and 0.008 mol·L^-1 aqueous cetyltrimethylammonium bromide （CTAB） have been measured at 298.15, 303.15, 308.15, and 313.15 K. The density data have been utilized to calculate apparent molar volumes （φv）, partial molar volumes （φv^0）, at infinite dilution and partial molar volumes of transfer φv^0 （tr） of amino acids. The refractive index data have been used to calculate molar refractivity （Rr,） of amino acids in aqueous cetyltrimethylammonium bromide. It has been observed that φv^0 varies linearly with increasing number of carbon atoms in the alkyl chain of amino acids, and hence, was split to get contributions from the zwitterionic end groups （NH3^＋ COO^-） and methylene group （CH2） of the amino acids. The behaviour of these parameters has been used to investigate the solute-solute, solute-solvent interactions and the effect of cetyltrimethylammoniuln cation on these interactions,