Crystal Structure and Third-Order Nonlinear Optical Properties Study of Tetraphenylporphyrin and Its Nickle Complex at Wavelength 532 nm and 1064 nm

Tetraphenylporphyrin (TPP) and its nickel(II) (NiTPP) complex have been synthesized, their crystal structures have been determined by means of X-ray single crystal diffraction. The TPP possesses good planarity in the porphyrin core, while in the complex the planarity disappeared. The central nickel(II) ion coordinates with four nitrogen atoms, which constructed a distorted square environment. Their third-order nonlinear optical properties have been studied using Z-scan technique at wavelength 532 nm and 1064 nm in picosecond (ps) domain. At 532 nm nonlinear absorption were observed, TPP shows two-photon absorption (TPA) combined with saturable absorption (SA), while NiTPP shows SA. At 1064 nm nonlinear refraction were observed, the molecular second hyperpolarizability γ of the NiTPP was about 1.4 times larger than that of the TPP.     

Pricing range notes within Wishart affine models

We provide analytic pricing formulas for Fixed and Floating Range Accrual Notes within the multifactor Wishart affine framework which extends significantly the standard affine model. Using estimates for three short rate models, two of which are based on the Wishart process whilst the third one belongs to the standard affine framework, we price these structured products using the FFT methodology. Thanks to the Wishart tractability the hedge ratios are also easily computed. As the models are estimated on the same dataset, our results illustrate how the fit discrepancies (meaning differences in the likelihood functions) between models translate in terms of derivatives pricing errors, and we show that the models can produce different price evolutions for the Range Accrual Notes. The differences can be substantial and underline the importance of model risk both from a static and a dynamic perspective. These results are confirmed by an analysis performed at the hedge ratios level.     

Effect of hydrogen dimers on the electronic structure of graphene

We investigate the effect of hydrogen dimers on the electronic structure of graphene. Using Greenʼs function and the T-matrix approach, we calculate the local density of states of graphene with single hydrogen dimer, as well as the quasiparticle spectral function of graphene with a finite concentration of randomly distributed hydrogen dimers. Our results show that the effect of dimer adsorption is dramatically different from that of monomer adsorption previously studied, and strongly depends on the configuration of the dimer. The features of the plotted spectral function of graphene are relevant to the band gap opening and the metal–insulator transition.     

From curing kinetics to network structure: A novel approach to the modeling of the network buildup of epoxy–anhydride thermosets

The curing kinetics and network buildup during curing of epoxy–anhydride formulations using tertiary amines as initiators are reviewed in this work. A mechanism‐based kinetic and structural model has been defined, showing better prediction capabilities than previous living polymerization and simple regeneration models. The curing kinetics have been analyzed using differential scanning calorimetry (DSC), and the gelation during curing has been determined by combined thermomechanical analysis and DSC. The effect of initiator content and epoxy equivalent weight are taken into account. The network buildup has been modeled using a stochastic network buildup model based on the random combination of primary chains generated by the kinetic model. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 61–75     

Formation of polyketone particle structure by hexafluoroisopropanol solvent evaporation and effects of plasticizer addition

Few solvents are capable of dissolving polyketones (PKs). 1,1,1,3,3,3‐Hexafluoro‐2‐propanol (hexafluoroisopropanol, HFIP) is a better solvent than trifluoroethanol and m‐cresol. When HFIP was evaporated from a PK/HFIP solution, a porous cast‐film with a microparticle structure was formed because the isotactic PKs adopted a helical conformation, and convection during evaporation of the high polarity and low‐boiling‐point HFIP caused aggregation and rolling of the polymer molecules. The addition of plasticizer suppressed particle formation, improving the surface structure and mechanical properties of the film. In particular, the dielectric properties of the film improved significantly. This will enable PKs, which are rigid insulating materials, to be used as dielectric materials, broadening their range of applications. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 887–892     

Korn inequality for a thin rod with rounded ends

We consider an elastic rod with rounded ends and diameter proportional to a small parameter h > 0. The roundness of the ends is described by an exponent m ∈ (0,1). We derive for the rod an asymptotically sharp Korn inequality with a special weighted anisotropic norm. Weight factors with m‐dependent powers of h appear both in the anisotropic norm and the Korn inequality itself, and we discover three critical values m = 1 ∕ 4, m = 1 ∕ 2 and m = 3 ∕ 4 at which these exponents are crucially changed. Copyright © 2014 John Wiley & Sons, Ltd.     

Operators on Soft Inner Product Spaces

In the present paper, self-adjoint operator and completely continuous operator on soft inner product spaces have been introduced and some basic properties of such operators are studied.     

面向变厚度柔性轧制工艺的帽型梁横向冲击吸能优化设计

作为汽车主要吸能构件的帽型梁的吸能提升设计是备受关注的问题.研究表明,通过优化薄壁结构的厚度可有效提升吸能性能,但复杂的厚度分布造成制造困难.针对可实现厚度调控的工艺,发展易制造的结构设计方法极为必要.本文基于变厚度柔性轧制工艺(variable gauge rolling, VGR)可实现厚度调控的特点,发展建立帽型梁横向冲击吸能优化设计方法.基于变厚度柔性轧制工艺生产的柔性轧制板(tailor rolled blanks, TRB)的特点,将受横向冲击的帽型薄壁梁设计成沿轴线分段变厚度、分段间设梯度过渡段的结构形式,通过调整各段厚度、分段位置和过渡层梯度变化规律,实现性能的优化.以应变能密度分布均匀为优化准则、基于混合元胞自动机(hybird cellular automata, HCA)方法构建优化模型和求解方法,并在迭代过程中施加满足轧制约束的过滤函数,使结构满足轧制工艺要求.其中,轧制约束的过滤函数由粒子群算法自动寻找.基于本文方法,具体设计了柔性轧制帽型梁横向冲击吸能最优的分段位置、各段厚度及过渡段厚度的梯度过渡方式,设计结果验证了方法的有效性.