On the validity of the inverse conjecture in classical density functional theory

It is shown that the basic assumptions of the classical density functional approach are rigorously correct forH-stable systems in the grand canonical ensemble. Moreover, it is established that the set of all single-particle densities is convex. These results are derived by providing necessary and sufficient conditions for the solution of the classical inverse problem for single-particle densities. Analogous results are obtained for the solution of the higher-order correlation inverse problem, and the ramifications of these results for the validity of two-body decomposition of forces are discussed.Research supported in part by the National Science Foundation under grants PHY-8116101 A01 (J.T.C.), PHY-8301493 (L.C.) and PHY-8203669 (J.T.C. and L.C.).     

广义投影型的超线性收敛算法

该文利用矩阵分解与广义投影等技巧，给出了求解线性约束的非线性规划的一个广义投影型的超线性收敛算法，不需要δ－主动约束与每一步反复计算投影矩阵，避免了计算的数值不稳定性，利用矩阵求逆的递推公式，计算简便，由于采用了非精确搜索，算法实用可行，文中证明了算法具有收敛性及超线性的收敛速度．     

Synthesis,characterization, and thermal studies of cardanol-based polyphosphate esters

Polyphosphate esters were synthesized from derivatives of cardanol phosphorodichloridateates and dihydric phenols by interfacial polycondensation using a phase transfer catalyst. The polymers were characterized by IR, ¹H-, ¹³C-, and ³¹P-NMR spectroscopy, and GPC. The thermal stability and thermal degradation kinetics of the polymers were determined by thermogravimetry. The flammability of the polymers was evaluated by limiting oxygen index values. © 1993 John Wiley & Sons, Inc.     

Solvation effect in thermal decomposition of 2,2′-azoisobutyronitrile

The solvation effect in the thermal decomposition of a radical initiator (AIBN) in monomer–solvent mixtures is discussed. Equations were derived which comprise the initiator decomposition constant as a function of the monomer mole fraction for chosen types of solvation. In addition, equations were deduced presenting the concentrations and partial relative decomposition rates for the solvated initiator species as a function of the monomer mole fraction. The equations obtained were compared to the experimental literature data and possible dependences of decomposition constants on monomer concentration were simulated for various solvated species. The simulated relationships were found to be straight lines, curves of saturated type (possessing a plateau), S-shaped curves, and maximum or minimum curves. © 1995 John Wiley & Sons, Inc.     

STUDIES OF THE MOBILITY OF SURFACE CARBON FORMED BY THE DECOMPOSITION OF METHANE ON SUPPORTED TRANSITION METAL CATALYSTS

IntroductionInformationonrelativereactiviticsofsuffocccarbonfromthcdecompositionofmethaneontransitionmetalcataIystspla}.simportantruleinourunderstandingthenatllreofeffcctiveutiliZaionofmethane.Asignificantamountofdataonthissubjecthavealread}'bccnaccumulatcd.Itx"asdiscovercdthatrcactiviticsofthesuffocecarbonstrongl}'dependonthcstructuralparameters-suchasthctyPcofsuffocecarbon.thestrengthofsurfacecarbon-metalinteractionsandthetendencyoftransformationamongthemll'2].0fspecialsarcthatthenatureofth…     

The thermal decomposition of NaHCO3

New EGA findings revealed that the small endothermal event preceding that of the main decomposition of commercial NaHCO₃ involves the simultaneous evolution of water and CO₂. At very high sensitivity, EGA experiments evidenced that the above (limited) evolution of gases also took place from the recrystallized material for which thermal methods gave no indication of endotherms.Careful reexamination of previous DSC results indicated that for one kind of recrystallized material a very small endotherm had been neglected. Renewed experiments revealed that this endotherm can be enhanced if the samples are prepared by crushing and sieving in a wet atmosphere. Parallel FT-IR experiments on commercial and recrystallized materials demonstrated the presence of carbonate in samples that had previously been taken just beyond the first small endotherm; this confirmed the EGA results. SEM experiments showed that surface texture changes take place when samples are heated to temperatures just above that of the preliminary endotherm. On the basis of these new findings, the interpretation previously given to the small endotherm is revised and detailed knowledge is gained on the mechanism of decomposition of NaHCO₃.The authors express their gratitude to Dr. Stephen B. Warrington (Thermal Analysis Consultancy Service, Leeds Metropolitan University) for having communicated the EGA results that led to the present report. The authors also feel indebted to Dr. Mario Paolieri of the Centro Interdipartimentale per la Microscopia Elettronica e la Microanalisi (M.E.M.A.) for his help in performing and interpreting the SEM experiments, and to Mr. Paolo Parri for his careful preparation of the illustrative material. Financial support from the University of Florence (ex 60% MURST) is greatly appreciated.     

Quasi-monotone mappings on θn-continua

A continuous function f from a continuum X onto a continuum Y is quasi-monotone if, for every subcontinuum M of Y with nonvoid interior, f^-1(M) has a finite number of components each of which is mapped onto M by f. A θ_n-continuum is one that no subcontinuum separates into more than n components. It is known that if f is quasi-monotone and X is a θ₁-continuum, then Y is a θ₁-continuum or a θ₂-continuum that is irreducible between two points. Examples are given to show that this cannot be generalized to a θ_n-continuum and n + 1 points for any n >1, but it is proved that if f is quasi-monotone and X is a θ_n-continuum, then Y is a θ_n-continuum or a θ_n+1-continuum that is the union of n + 2 continua H,S₁,S₂,…,S_n+1, whe for each i, S_i is the closure of a component of Y H, S_i is irreducible from some point P_i to H, and H is irreducible about its boundary. Some theorems and examples are given concerning the preservation of decomposition elements by a quasi-monotone map defined on a θ_n-continuum that admits a monotone, upper-semicontinuous decomposition onto a finite graph.     

Approximated Bayes and empirical Bayes confidence intervals—The known variance case

In this paper hierarchical Bayes and empirical Bayes results are used to obtain confidence intervals of the population means in the case of real problems. This is achieved by approximating the posterior distribution with a Pearson distribution. In the first example hierarchical Bayes confidence intervals for the Efron and Morris (1975, J. Amer. Statist. Assoc., 70, 311–319) baseball data are obtained. The same methods are used in the second example to obtain confidence intervals of treatment effects as well as the difference between treatment effects in an analysis of variance experiment. In the third example hierarchical Bayes intervals of treatment effects are obtained and compared with normal approximations in the unequal variance case.Financially supported by the CSIR and the University of the Orange Free State, Central Research Fund.     

Asymptotically optimal sequential estimation of regular functionals of several distributions based on generalized U-statistics

For the several sample problem, a vector of estimable parameters is considered. For a fixed total sample size, a multistage (sequential) procedure based on generalized U-statistics is developed for choosing a partition of this sample size into individual sample size for which the generalized variance of the estimator of the parameter vector is asymptotically minimized.     

On the Explicit Determination of the Polar Decomposition in n-Dimensional Vector Spaces

A method for the explicit determination of the polar decomposition (and the related problem of finding tensor square roots) when the underlying vector space dimension n is arbitrary (but finite), is proposed. The method uses the spectral resolution, and avoids the determination of eigenvectors when the tensor is invertible. For any given dimension n, an appropriately constructed van der Monde matrix is shown to play a key role in the construction of each of the component matrices (and their inverses) in the polar decomposition.