On Subspaces and Quotients of Banach Spaces C(K, X)

 We study the relation of to the subspaces and quotients of Banach spaces of continuous vector-valued functions , where K is an arbitrary dispersed compact set. More precisely, we prove that every infinite dimensional closed subspace of totally incomparable to X contains a copy of complemented in . This is a natural continuation of results of Cembranos-Freniche and Lotz-Peck-Porta. We also improve our result when K is homeomorphic to an interval of ordinals. Next we show that complemented subspaces (resp., quotients) of which contain no copy of are isomorphic to complemented subspaces (resp., quotients) of some finite sum of X. As a consequence, we prove that every infinite dimensional quotient of which is quotient incomparable to X, contains a complemented copy of . Finally we present some more geometric properties of spaces. Received 8 November 2000; in revised form 7 December 2001     

Non-trivial simple poles at negative integers and mass concentration at singularity

Let (X,0) be the germ of a normal space of dimension n+1 and let f be the germ at 0 of a holomorphic function on X. Assume both X and f have an isolated singularity at 0. Denote by J the image of the restriction map , where F is the Milnor fibre of f at 0. We prove that the canonical Hermitian form on , given by poles of order at in the meromorphic extension of , passes to the quotient by J and is non-degenerate on . We show that any non-zero element in J produces a “mass concentration” at the singularity which is related to a simple pole concentrated at for (in a non-na?ve sense). We conclude with an application to the asymptotic expansion of oscillatory integrals , for , when . Received: 28 May 2001 / Published online: 26 April 2002     

Recent developments in the statistical processing of textual data

Statisticians are accustomed to processing numerical, ordinal or nominal data. In many circumstances, such as socio-economic, epidemiologic sample surveys and documentary data bases, this data is juxtaposed with textual data (for example, responses to open questions in surveys). This article presents a series of language-independent procedures based upon applying multivariate techniques (such as correspondence analysis and clustering) to sets of generalized lexical profiles. The generalized lexical profile of a text is a vector whose components are the frequencies of each word (graphical form) or ‘repeated segment’ (sequence of words appearing with a significant frequency in the text). The processing of such large (and often sparse) vectors and matrices requires special algorithms. The main outputs are the following: (1) printouts of the characteristic words and characteristic responses for each category of respondent (these categories are generally derived from available nominal variables); (2) graphical displays of the proximities between words or segments and categories of respondents; (3) when analysing a combination of several texts: graphical displays of proximities between words or segments and each text, or between words or segments and groupings of texts. The systematic use of ‘repeated segments’ provides a valuable help in interpreting the results from a semantic point of view.     

A class of proper priors for Bayesian simultaneous prediction of independent Poisson observables

Simultaneous prediction and parameter inference for the independent Poisson observables model are considered. A class of proper prior distributions for Poisson means is introduced. Bayesian predictive densities and estimators based on priors in the introduced class dominate the Bayesian predictive density and estimator based on the Jeffreys prior under Kullback-Leibler loss.     

A comparative XPS and UPS study of VOx layers on mineral TiO2(001)‐anatase supports

Four vanadium oxide layers on mineral TiO₂(001)‐anatase supports with different thickness (3–33 Å) were prepared with reactive d.c. magnetron sputtering and were extensively studied with photoelectron spectroscopy. Al Kα radiation and 150 eV synchrotron radiation were used as excitation sources. The evolution of the 2p, 3s and 3p core level line shapes of V and Ti as a function of the vanadium oxide thickness was studied, as well as the O1s and O2s core lines and the valence band. All the V2p spectra of the deposited vanadium oxide layers consist of at least 60% V⁵⁺, the rest being V⁴⁺. The V3p region is complicated by multiplet splitting, which prevents the determination of the vanadium oxidation state. The V3p multiplet splitting is different for the two excitation energies. No reduction of the titania support surface due to the vanadium oxide deposition was observed. Copyright © 2006 John Wiley & Sons, Ltd.     

Fluorinated,crosslinkable terpolymers based on vinylidene fluoride and bearing sulfonic acid side groups for fuel‐cell membranes

The radical terpolymerization of 8‐bromo‐1H,1H,2H‐perfluorooct‐1‐ene with vinylidene fluoride (VDF) and perfluoro(4‐methyl‐3,6‐dioxaoct‐7‐ene) sulfonyl fluoride is presented. Changing the feed compositions of these three fluorinated comonomers enabled us to obtain different random‐type poly[vinylidene fluoride‐ter‐perfluoro(4‐methyl‐3,6‐dioxaoct‐7‐ene) sulfonyl fluoride‐ter‐8‐bromo‐1H,1H,2H‐perfluorooct‐1‐ene] terpolymers containing various sulfonyl fluoride and brominated side groups. Yields higher than 70% were reached in all cases. The hydrolysis of the sulfonyl fluoride group into the ? SO₃Li function in the presence of lithium carbonate was quantitatively achieved without the content of VDF being affected, and so dehydrofluorination of the VDF base unit was avoided. These original terpolymers were then crosslinked via dangling bromine atoms in the presence of a peroxide/triallyl isocyanurate system, which produced films insoluble in organic solvents such as acetone and dimethylformamide (which totally dissolved uncured terpolymers). The acidification of ? SO₃Li into the ? SO₃H function enabled protonic membranes to be obtained. The thermal stabilities of the crosslinked materials were higher than those of the uncured terpolymers, and their electrochemical performances were investigated. According to the contents of the sulfonic acid side functions, the ion‐exchange capacities ranged from 0.6 to 1.5 mequiv of H⁺/g, whereas the water uptake and conductivities ranged from 5–26% (±11%) and from 0.5 to 6.0 mS/cm, respectively. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4566–4578, 2006     

Farkas-type results for fractional programming problems

Considering a constrained fractional programming problem, within the present paper we present some necessary and sufficient conditions, which ensure that the optimal objective value of the considered problem is greater than or equal to a given real constant. The desired results are obtained using the Fenchel–Lagrange duality approach applied to an optimization problem with convex or difference of convex (DC) objective functions and finitely many convex constraints. These are obtained from the initial fractional programming problem using an idea due to Dinkelbach. We also show that our general results encompass as special cases some recently obtained Farkas-type results.     

Permanence and stability of a predator–prey system with stage structure for predator

A stage-structured predator–prey system with delays for prey and predator, respectively, is proposed and analyzed. Mathematical analysis of the model equations with regard to boundedness of solutions, permanence and stability are analyzed. Some sufficient conditions which guarantee the permanence of the system and the global asymptotic stability of the boundary and positive equilibrium, respectively, are obtained.     

Colossal magnetoresistance manganites: A new approach

Manganites of the LA_1−x Ca _x MnO₃ family show a variety of new and poorly understood electronic, magnetic and structural effects. Here we outline a new approach recently proposed by us, where we argue that due to strong Jahn-Teller (JT) coupling with phonons the twofold degeneratee _g states at the Mn sites dynamically reorganize themselves into localised, JT polaronsl with exponentially small inter-site hopping, and band-like, nonpolaronic statesb, leading to anew 2-band model for manganites which includes strong Coulomb and Hund’s couplings. We also discuss some results from a dynamical mean-field theory treatment of the model which explains quantitatively a wide variety of experimental results, including insulator-metal transitions and CMR, in terms of the influence of physical conditions on the relative energies and occupation of thel andb states. We argue that this microscopic coexistence of the two types of electronic states, and their relative occupation and spatial correlation is the key to manganite physics. Dedicated to Professor C N R Rao on his 70th birthday     

傅里叶变换红外光谱固体制样技术

通过对溴化钾与纳米固体超强酸样品的比例进行了探讨 ,得出制样时溴化钾与样品比例范围为1∶ 0 .0 0 1— 1∶ 0 .0 2 9,其最佳比例范围为 1∶ 0 .0 0 98— 1∶ 0 .0 1 5 ,并且应用于其他固体样品的测定 ,结果基本一致。同时得出 ,固体样品的最少检测量为 2 .0× 1 0 -5g