Crystallization behavior and electroactive properties of PVDF,P(VDF-TrFE) and their blend films

PVDF, poly(vinylidene fluoride), as a semi-crystalline polymer, has interesting electroactive properties but usual melt and solution processing techniques result in its thermodynamically favored non-polar α-phase. By comparison, poly(vinylidene fluoride-trifluoroethylene) P(VDF-TrFE), PT for short, directly crystallizes in the polar β-phase under the same conditions as PVDF. In this study, blend thin films comprising PVDF and P(VDF-TrFE) were prepared by solvent casting method. The difference in the crystallization behavior is comprehensively investigated between the polymers: PVDF, P(VDF-TrFE), and the resulting blend films. It is found that replacement of the fluoride atom in TrFE monomer induces a strong steric hindrance that may alter the crystallization process to become more favorable for nucleation of the PVDF β-phase. To figure out the effect of TrFE content on the crystallization behavior and electroactive properties, films with different blend ratios of PVDF and P(VDF-TrFE) were prepared. We found that the PVDF films exhibit higher crystallization activation energy (ΔE) as PT content increases. The atomic force microscopy (AFM) in the piezoresponse force microscopy (PFM) mode illustrated that P5T5 films with equal contents of PVDF and P(VDF-TrFE) induced the highest d₃₃ values.     

Asymptotics for the Tail Probability of Random Sums with a Heavy-Tailed Random Number and Extended Negatively Dependent Summands

Let {X,X_k:k≥1} be a sequence of extended negatively dependent random variables with a common distribution F satisfying EX 0.Let r be a nonnegative integer-valued random variable,independent of {X,X_k:k≥1}.In this paper,the authors obtain the necessary and sufficient conditions for the random sums S_r =(?)X_n to have a consistently varying tail when the random number t has a heavier tail than the summands,i.e.,(P(Xx))/(P(r x))→0as x→∞     

The t-coefficient method II: A new series expansion formula of theta function products and its implications

By means of Jacobi?s triple product identity and the t  -coefficient method, we establish a general series expansion formula with five free parameters for the product of arbitrary two Jacobi theta functions. It embodies the triple, quintuple, sextuple and septuple theta function product identities and the generalized Schröter formula. As further applications, we also set up a series expansion formula for the product of three theta functions. It not only generalizes Ewell?s and Chen–Chen–Huang?s octuple product identities, but also contains three cubic theta function identities due to Farkas–Kra and Ramanujan respectively and the Macdonald identity for the root system _A2$A_2$ as special cases. In the meantime, many other new identities including a new short expression of the triple theta series of Andrews are also presented.     

On the tangent space to the BMO-Teichmüller space

In a previous paper [31] we established the complex analytic manifold theory of the BMO-Teichmüller space. In this paper we identify the function space which is the tangent space to the BMO-Teichmüller space.     

On simple modules over conformal Galilei algebras

We study irreducible representations of two classes of conformal Galilei algebras in 1-spatial dimension. We construct a functor which transforms simple modules with nonzero central charge over the Heisenberg subalgebra into simple modules over the conformal Galilei algebras. This can be viewed as an analogue of oscillator representations. We use oscillator representations to describe the structure of simple highest weight modules over conformal Galilei algebras. We classify simple weight modules with finite dimensional weight spaces over finite dimensional Heisenberg algebras and use this classification and properties of oscillator representations to classify simple weight modules with finite dimensional weight spaces over conformal Galilei algebras.     

On angles in Teichmüller spaces

We discuss the existence of the angle between two curves in Teichmüller spaces and show that, in any infinite dimensional Teichmüller space, there exist infinitely many geodesic triangles each of which has the same three vertices and satisfies the property that its three sides have the same and arbitrarily given length while its three angles are equal to any given three possibly different numbers from 0 to $\pi $ . This implies that the sum of three angles of a geodesic triangle may be equal to any given number from 0 to $3\pi $ in an infinite dimensional Teichmüller space.     

A super hierarchy of coupled derivative nonlinear Schrödinger equations and conservation laws

By solving the zero-curvature equation associated with a 3 × 3 matrix spectral problem, a super hierarchy of coupled derivative nonlinear Schrödinger equations is proposed. The corresponding super bi-Hamiltonian structures are established by means of the super trace identity. Then, we derive infinite conservation laws of the super coupled derivative nonlinear Schrödinger equation with the aid of spectral parameter expansions.     

Combinatorial constructions for optimal 2-D optical orthogonal codes with AM-OPPTS property

We develop a new one-to-one correspondence between a two-dimensional (m × n, k, ρ) optical orthogonal code (2-D (m × n, k, ρ)-OOC) with AM-OPPTS (at most one-pulse per time slot) property and a certain combinatorial subject, called an n-cyclic holey packing of type m ⁿ . By this link, an upper bound on the size of a 2-D (m × n, k, ρ)-OOC with AM-OPPTS property is derived. Afterwards, we employ combinatorial methods to construct infinitely many 2-D (m × n, k, 1)-OOCs with AM-OPPTS property, whose existence was previously unknown. All these constructions meet the upper bounds with equality and are thus optimal.     

非线性脉冲差分方程解的稳定性

应用不等式估值法讨论了非线性脉冲时滞差分方程解的性质,并得到它的解的一致稳定性的一些充分条件.     

弱闭T(N)-模的预零化子的等距映射

本文刻划了弱闭T(N)-模的预零化子间的等距映射.设u,W分别为由左连续序同态N→~N和N→~N所确定的弱闭T(N)-模, u(?),W(?)分别为u,W的预零化子,Φ为由u(?)到W(?)上的线性等距映射.若(0)*=(0)#=(0),dim(0)+≠1且min{dim(H(?)~H),dim(He(?)^H)}≥2,则存在酉算子Ui,Vi(i=1,2),使得Φ(A)=U1AV*1或Φ(A)=U2A*V2*.