Multisymplectic schemes for strongly coupled schrödinger system

In this paper, two semi-explicit multisymplectic schemes are derived for the strongly coupled schrödinger system. Based on the two new multisymplectic schemes, we obtain a multisymplectic composition scheme which improves the accuracy in time. The best merits of the present schemes are all implemented easily. Some numerical simulations are done for investigating nonlinear coupling and linear coupling. Numerical results indicate that the new multisymplectic composition scheme is effective.     

PHASE SEPARATION IN THE MELT OF POLYPROPYLENE–1-DECENE COPOLYMERS

A propylene homopolymer and three copolymers with 1-decene containing 1.82, 3.55, and 7.83 mol% of comonomer units, respectively, were prepared with metallocene catalyst and the phase behavior in the melt of these polymers was studied using simultaneous synchrotron small-angle x-ray scattering and differential scanning calorimetry. The results show that the phase behavior of the melt varies with comonomer content and the copolymers tend to be phase-separated with increasing comonomer content. The phase separation in the melt of the propylene–1-decene copolymers was further confirmed by the fitting of the experimental data with Teubner–Strey micro-emulsion model and a transition from the phase-separated melt to the disordered melt was observed. We tentatively attribute this phenomenon to the inhomogeneous intra-molecular composition distribution at high levels of comonomer and the incompatibility of propylene sequences with different lengths. Such a finding is consistent with the facts of multiple melting peaks and mixed γ and α crystal phases in the polymer solids. Since the phase behavior depends on temperature, the effect of annealing temperature, from which the copolymers were cooled, on the nonisothermal crystallization of the copolymers was also investigated. It is found that higher degree of phase separation accelerates the crystallization but reduces the crystallization enthalpy.     

Note on the Essential Norm of Composition Operators from HP（BN） to Hq（BN）

The authors give an upper bound of the essential norms of composition operators between Hardy spaces of the unit ball in terms of the counting function in the higher dimensional value distribution theory defined by Professor S.S.Chern.The sufcient condition for such operators to be bounded or compact is also given.     

Macro-Hybrid Variational Formulations of Constrained Boundary Value Problems

In the context of convex analysis, macro-hybrid variational formulations of constrained boundary value problems are presented. Monotone mixed variational inclusions are macro-hybridized on the basis of nonoverlapping domain decompositions, and corresponding three-field versions are derived. Then, for regularization purposes, augmented formulations are established via preconditioned exact penalizations and expressed in terms of proximation operators. Optimization interpretations are given for potential problems, recovering the classic two- and three-field augmented Lagrangian formulations. Furthermore, associated parallel two- and three-field proximal-point algorithms are discussed for numerical resolution of finite element discretizations. Applications to dual mixed variational formulations of problems from mechanics illustrate the theory.     

高光学质量氮化碳薄膜的制备和表征

氮化碳(graphitic carbon nitride,g-CN)作为一种非金属半导体材料已被广泛应用于多种能源相关领域研究中。目前由于制备高质量g-CN薄膜的困难,大大限制了其在实际器件上的应用。本文中,我们报道了一种可制备高光学质量gCN薄膜的方法:即由三聚氰胺先通过热聚合制备本体g-CN粉末,再由本体g-CN粉末经过气相沉积在ITO导电玻璃或钠钙玻璃基底上制备g-CN薄膜。扫描电子显微镜和原子力显微镜的测量结果表明在ITO玻璃基底上形成的g-CN薄膜形貌结构均一且致密,厚度约为300nm。扫描电镜能量色散能谱和X射线光电子能谱测量结果表明在ITO玻璃基底上制备的g-CN薄膜的化学组成与本体g-CN粉末的化学组成基本一致。同时,我们发现制备的g-CN薄膜和本体g-CN粉末一样在光照射下可以有效降解亚甲基蓝染料。此外,我们还测量了制备的g-CN薄膜的稳态吸收光谱、稳态荧光光谱、荧光寿命和价带谱,并运用吸收光谱和价带谱数据确定了其能带结构。     

Paramagnetic defects induced by ion implantation in oxide glasses

Radiation defects induced by ion bombardment of multicomponent oxide glasses of five compositions (phosphates and borosilicates) were investigated by means of electron paramagnetic resonance (EPR). The samples were implanted with N⁺, O⁺, Ar⁺, Mn⁺, Cu⁺ and Pb⁺ ions at energy E=150 keV at three different doses between 3×10¹⁵ and 10¹⁷ ions/cm². The broad anisotropic EPR spectra with principal g-values answering the relationship g_z>g_y>g_x˜g_e (g_e is g-factor of free electron) were observed for the samples of all five compositions. The g-values depend on glass composition. For example, g_z ranges from 2.016 to 2.057. Computer simulation shows that the spectra of many samples are superpositions of two spectra with g-values answering the mentioned relationship. These spectra are attributed to molecular O₂⁻ ions weakly coupled with glass network. In some samples narrow almost symmetric lines with g=2.0025±0.0005 were observed. The possible radiation defects responsible for this signal are discussed.     

Derivative-free characterizations of bounded composition operators between Lipschitz spaces

We prove that maps into if and only if belongs to . In the case β < 1, we give another two equivalent conditions. Supported by MNZŽS Serbia, Project No. ON144010.     

Composition of aromatic products in the catalytic degradation of the mixture of waste polystyrene and high-density polyethylene using spent FCC catalyst

In this chemical recycling process, spent FCC catalyst used had an advantage with an economical and environment aspect, such as a low catalyst price in liquid-phase reaction and a reuse of waste catalyst. The characteristics of oil product and its aromatic product distribution, as a function of reaction time in the reactor and also proportion of HDPE and PS in the mixture, were compared. Main products obtained were light hydrocarbons within the gasoline range that were mainly produced during initial reaction time. The formation of aromatic products such as styrene and ethylbenzene as major components depended appreciably on the reaction time, as well as the composition of HDPE and PS in the mixture used for degradation. For the distribution of C₉-C₁₂ alkylaromatic components as by-products, methylstyrene (C₁-styrene) and isopropylbenzene (C₃-benzene) components were the main products formed by β-scission and hydrogen transfer of PS, while the rest of alkylaromatic products showed very low fraction being 1% or less.     

Composition operators on Hardy spaces on Lavrentiev domains

For any simply connected domain , we prove that a Littlewood type inequality is necessary for boundedness of composition operators on , , whenever the symbols are finitely-valent. Moreover, the corresponding ``little-oh' condition is also necessary for the compactness. Nevertheless, it is shown that such an inequality is not sufficient for characterizing bounded composition operators even induced by univalent symbols. Furthermore, such inequality is no longer necessary if we drop the extra assumption on the symbol of being finitely-valent. In particular, this solves a question posed by Shapiro and Smith (2003). Finally, we show a striking link between the geometry of the underlying domain and the symbol inducing the composition operator in , and in this sense, we relate both facts characterizing bounded and compact composition operators whenever is a Lavrentiev domain.