基于模糊值Choquet积分定义集函数的S性与PGP性

针对模糊测度空间上已建立的模糊值Choquet积分,将这种积分整体看成可测空间上取值于模糊数的集函数,当模糊测度满足一般S性和PGP性时,研究了这种模糊值集函数所保持的遗传性质.     

Normal coderivative for multifunctions and implicit function theorems

In the framework of the theory of normal coderivative for multifunctions, new implicit function theorems are obtained. The main tools of the proofs are the Ekeland variational principle, a nonsmooth version of Fermat's rule, a sum rule, and the differential estimate for marginal functions established by B.S. Mordukhovich and Y. Shao [B.S. Mordukhovich, Y. Shao, Nonsmooth sequential analysis in Asplund spaces, Trans. Amer. Math. Soc. 348 (1996) 1235-1280].     

Physicomechanical studies on the langmuir‐blodgett films of polythiophene containing mesogenic side chains

Liquid crystalline materials display unique properties, which can be exploited in various optoelectronic device applications. The Langmuir‐Blodgett (LB) film characteristics of polythiophene model compounds containing phenyl rings linked with azomethine, ester, and alkoxy functional groups poly‐4‐{[(E)‐thiophen‐3‐ylmethylidene]amino}phenyl 4‐alkyloxybenzoate (PTAPAB series) and poly‐4‐alkyloxy phenyl 4‐{[(E)‐thiophen‐3‐ylmethylidene]amino}benzoate (PAPTAB Series) were explored in this study. The AM1 optimized geometries of the aforementioned compounds showed that the films have different type of orientation in space because of the change in the linking functional group. The LB film characteristics were studied by applying the concepts of the failure mechanism in tensile failure. The compression‐expansion hysteresis cycle of the LB films at predetermined area per repeat unit was used to study the viscous, elastic, and plastic nature of the films. The results showed that in PAPTAB series compounds, the LB films were more flexible and took less surface energy than its PTAPAB series homologues, which formed into LB films of rigid nature. The LB films of PAPTAB series compounds were of more viscoplastic in nature. The studies suggested that PAPTAB series structures exhibited good thin film forming nature than its PTAPAB series homologues. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 173–182, 2009     

Synthesis and characterization of a series of diverse poly(2‐oxazoline)s

This article describes the synthesis and characterization of a variety of new poly(2‐oxazoline)s. With regard to functional polymers, 2‐oxazolines represent an interesting class of monomers because of the easy variation of the substituent in 2‐position. Starting from the corresponding nitriles, different 2‐oxazolines were obtained containing a diverse set of 2‐substituents, including thioether bonds ( M11 ), trifluoromethyl groups ( M8 , M10 ), and alkyl‐ or aryl groups ( M1 – M7 ). The subsequent polymerization of the majority of these monomers proceeded in a living manner, which was demonstrated by linear first‐order kinetics, a linear increase of molar mass with conversion, and relatively narrow molar mass distributions. In addition, selected thermal and surface properties of the polymers were studied utilizing DSC and contact‐angle measurements to determine the effects of different 2‐substituents on the macroscopic properties. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 3829–3838, 2009     

Weighted norm inequalities,off-diagonal estimates and elliptic operators. Part IV: Riesz transforms on manifolds and weights

This is the fourth article of our series. Here, we study weighted norm inequalities for the Riesz transform of the Laplace–Beltrami operator on Riemannian manifolds and of subelliptic sum of squares on Lie groups, under the doubling volume property and Gaussian upper bounds.      

q-Weighted log-concavity and q-product theorem on the normality of posets

We show that q-weighted log-concavity and the strict normalized matching property are preserved under the q-direct product over weighted posets. As consequences, two classes of weighted posets including the finite linear lattices are strictly q-weighted log-concave and strictly normal.     

Generalizations of ?wierczkowski’s lemma and the arity gap of finite functions

?wierczkowski’s lemma-as it is usually formulated-asserts that if f:Aⁿ→A is an operation on a finite set A, n≥4, and every operation obtained from f by identifying a pair of variables is a projection, then f is a semiprojection. We generalize this lemma in various ways. First, it is extended to B-valued functions on A instead of operations on A and to essentially at most unary functions instead of projections. Then we characterize the arity gap of functions of small arities in terms of quasi-arity, which in turn provides a further generalization of ?wierczkowski’s lemma. Moreover, we explicitly classify all pseudo-Boolean functions according to their arity gap. Finally, we present a general characterization of the arity gaps of B-valued functions on arbitrary finite sets A.     

Poly(vinylpyrrolidone)‐based films grown on copper surfaces

The influence of molecular weight and the amount of the poly(vinylpyrrolidone) (PVP) on the growth of poly(vinylpyrrolidone)–based films on copper surfaces was studied by electrochemical, infrared and electronic spectroscopy, and thermogravimetric methods. Complex polymer/metal ions were deposited onto a copper surface, as the result of the electrochemically generated reaction of copper cations with PVP and SCN^?, in sulfuric acid media. Spontaneous film growth on copper surfaces was generated and characterized as a Cu(II)/PVP/SCN^? complex. Infrared spectra and thermal gravimetric curves of the films generated at + 0.7 V were compared with the chemically synthesized complex, and show the same patterns. The oxidation process can be described as: Cu(0)→Cu(I) and Cu(I)→Cu(II), and the copper complex formed at more positive potentials was characterized as Cu(II)/PVP/SCN^?, with copper bonded to the oxygen atom of PVP and thiocyanate ligand N‐linked. This study focuses on the complex formation on a copper surface in acid media and its characterization through electrochemical and spontaneously generated reactions. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2206–2214, 2009     

Structure–property relationship of photoactive liquid crystalline polyethers containing benzylidene moiety

A series of main chain photoactive liquid crystalline polyethers, containing rigid bisbenzylidene photoactive mesogen and flexible methylene spacers, were synthesized by polycondensation of bisbenzylidene diols and dibromoalkanes. The polyethers were characterized with ¹H NMR, gel permeation chromatography (GPC), differential scanning calorimeter (DSC), thermo gravimetric analyzer (TGA), and polarized light optical microscopy. The individual and combined effects of spacer length and number of methoxy substituents on mesogenic and photoactive properties were investigated. Both first order and second order transition temperatures decreased with increased spacer length and the number of substituents. The combined effect of spacers and substituents drastically reduced the transition temperatures. All monomers and polymers showed mainly the smectic mesophase. In a few cases, nematic droplets along with the smectic phase were observed. The width of the liquid crystalline phase reduced with an increasing number of methoxy substituents on mesogenic unit. Variation of spacer length has a negligible effect on photocycloaddition. However, steric hinderance caused by the substituents decreased the photoactivity as the number of substituents increased. Total energies of crosslinked dimers calculated from modeling studies supported the above findings. Intermolecular photocycloaddition was also confirmed by photoviscosity measurement. The refractive index change was found to be in the range of 0.017–0.031. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 2143–2155, 2009     

Testing monotonicity over graph products

We consider the problem of monotonicity testing over graph products. Monotonicity testing is one of the central problems studied in the field of property testing. We present a testing approach that enables us to use known monotonicity testers for given graphs G₁, G₂, to test monotonicity over their product G₁ × G₂. Such an approach of reducing monotonicity testing over a graph product to monotonicity testing over the original graphs, has been previously used in the special case of monotonicity testing over [n]^d for a limited type of testers; in this article, we show that this approach can be applied to allow modular design of testers in many interesting cases: this approach works whenever the functions are boolean, and also in certain cases for functions with a general range. We demonstrate the usefulness of our results by showing how a careful use of this approach improves the query complexity of known testers. Specifically, based on our results, we provide a new analysis for the known tester for [n]^d which significantly improves its query complexity analysis in the low‐dimensional case. For example, when d = O(1), we reduce the best known query complexity from O(log ²n/ε) to O(log n/ε). © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008