Electronic structures and ferroelectric properties of ABi2Ta2O9 (A=Ca, Sr, and Ba)

The electronic structures of ABi₂Ta₂O₉ (A=Ca, Sr, and Ba) were calculated by using first-principles under optimized structure. As the size of A-site cation decreases from that of Ba²⁺ to Ca²⁺, the band-gap between O 2p and Ta 5d increases from 2.0 to 2.9 eV, which responses to the stronger orbital hybridizations between Ta 5d and O 2p orbits favoring improvement of the ferroelectric property, decrease in leakage current, and increase in both spontaneous polarization and Curie temperature by the structural distortion. In contrast to CaBi₂Ta₂O₉ and SrBi₂Ta₂O₉, the hybridization between Ba 5p orbits and O 2p orbits in BaBi₂Ta₂O₉ has better structural stability.     

De Sitter空间中具有常均曲率的类空超曲面（Ⅱ）

设Ｍ＾ｎ是Ｄｅ Ｓｉｔｔｅｒ空间Ｓ１＾ｎ＋１中具有常数平均曲率且第二基本形式长度的平方为常数的完备类空超曲面，若Ｓ≤２（ｎ－１）＾１／２，则Ｍ＾ｎ是等参超曲面。     

Behaviors of the positive temperature coefficient of resistance of poly(styrene‐co‐n‐butylacrylate) filled with Ni‐plated core‐shell polymeric particles

Conductive composite films of poly(styrene‐co‐n‐butylacrylate) copolymers filled with low‐density, Ni‐plated core‐shell polymeric particles were prepared and their behaviors of positive temperature coefficient of resistance (PTCR) were investigated. When the conductive fillers in the composite film were loaded beyond the critical volume, 10 up to 25 vol %, composite films exhibited a unique electrical resistant transition behavior, which the electrical resistance rapidly increased by several orders of magnitude at the critical temperature. The PTCR transition temperature, in general, occurred before the glass transition temperature of polymer matrix. Further increased the conductive filler loading to 30 vol %, the overpacked conduction paths were formed in the entire composite and the PTCR effects became blurred. While the composite film treated with thermal cycle several times from room temperature up to 120 °C, the electrical resistivity increased accompanied with the shift of the PTCR transition to lower temperature. The reason might have been caused by the formed interfacial cracks within the composite film. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 322–329, 2007     

Side‐chain crystallization behavior of graft copolymers consisting of an amorphous main chain and crystalline side chains. II. Poly(n‐hexyl methacrylate)‐graft‐poly(ethylene glycol)

The phase behavior and crystallization of graft copolymers consisting of poly(n‐hexyl methacrylate) (PHMA) as an amorphous main chain and poly(ethylene glycol) (PEG) as crystallizable side chains (HMAx with 15 ≤ x ≤ 73, where x represents the weight percentage of PEG) were investigated. Small‐angle X‐ray scattering profiles measured above the melting temperature of PEG suggested that a microdomain structure with segregated PHMA and PEG domains was formed in HMA40 and HMA46. This phase behavior was qualitatively described by a calculated phase diagram based on the mean‐field theory. Because of the segregation of PEG into microdomains, the crystallization temperature of the PEG side chains in HMAx was higher than that in poly(methyl acrylate)‐graft‐poly(ethylene glycol) having a similar value of x, which was considered to be in a disordered state above the melting temperature. In HMAx with x ≤ 40, PEG crystallization was strongly restricted, probably because the PEG microdomains were isolated in the PHMA matrix. As a result, the growth of PEG spherulite was not observed because the PEG crystallization occurred after vitrification of the PHMA segregated domains. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 129–137, 2007     

Conservation Laws of K(m, n) and mK(m, n) Equations

Based on the rank analysis method, algorithmization idea, and symbolic computation, in this paper we have presented a method to construct the conservation laws for nonlinear evolution equations. The polynomial conservation laws for K (n 2, n) equations and mnK(m, n) equations are found by using of this approach and some new results have been obtained.     

“String” formulation of the dynamics of the forward interest rate curve

We propose a formulation of the term structure of interest rates in which the forward curve is seen as the deformation of a string. We derive the general condition that the partial differential equations governing the motion of such string must obey in order to account for the condition of absence of arbitrage opportunities. This condition takes a form similar to a fluctuation-dissipation theorem, albeit on the same quantity (the forward rate), linking the bias to the covariance of variation fluctuations. We provide the general structure of the models that obey this constraint in the framework of stochastic partial (possibly non-linear) differential equations. We derive the general solution for the pricing and hedging of interest rate derivatives within this framework, albeit for the linear case (we also provide in the appendix a simple and intuitive derivation of the standard European option problem). We also show how the “string” formulation simplifies into a standard N-factor model under a Galerkin approximation. Received: 30 January 1998 / Revised: 12 February 1998 / Accepted: 16 February 1998     

Electromagnetic field distribution on a rough gold thin film: An experimental study as a function of the gold thickness

The electromagnetic field distribution on an illuminated rough gold surface has been investigated by apertureless scanning near-field optical microscopy. The sample consists of an alumina substrate with a variable gold coverage ranging from 0 to 30 monolayers (ML). For such small thicknesses, the metal layer is not continuous but exhibits a certain roughness. We have studied the influence of this thickness on the electromagnetic field localization on the surface. For a gold coverage smaller than 10 equivalent monolayers, the electromagnetic field is almost uniform on the surface. For 10 and 14 ML, the field becomes inhomogeneous and isolated, localized peaks start to be visible. The width of the peaks is smaller than 50 nm. Above 14 ML, strong variations are apparent everywhere on the sample. Their amplitude tends to saturate beyond 24 ML. A complete statistical study of the sample (standard deviation, Fourier analysis) is performed.     

On the Exceptional Zeros of Rankin–Selberg L-Functions

The main objects of study in this article are two classes of Rankin–Selberg L-functions, namely L(s,f×g) and L(s, sym²(g)× sym²(g)), where f,g are newforms, holomorphic or of Maass type, on the upper half plane, and sym²(g) denotes the symmetric square lift of g to GL(3). We prove that in general, i.e., when these L-functions are not divisible by L-functions of quadratic characters (such divisibility happening rarely), they do not admit any LandauSiegel zeros. Such zeros, which are real and close to s=1, are highly mysterious and are not expected to occur. There are corollaries of our result, one of them being a strong lower bound for special value at s=1, which is of interest both geometrically and analytically. One also gets this way a good bound onthe norm of sym²(g).     

One-pot synthesis of an ionic half-sandwich complex of neodymium. Application to isoprene polymerisation catalysis

The reaction of one equivalent of Nd(BH₄)₃(THF)₃ with an half equivalent of dialkylmagnesium in the presence of a stoichiometric amount of pentamethylcyclopentadiene cleanly affords a new kind of half-sandwich of neodymium that is stable toward comproportionation. This strategy can be advantageously applied to generate in situ catalysts allowing the controlled polymerisation of isoprene.