The Periods of States for Markov Chains in a Random Environment

The periods of states for Markov chains in a random environment are introduced and some properties about periods are investigated. An open problem (Orey, 1991; Problem 1.3.3) is studied under the assumption that states have periods.     

一维线性非共轭石墨烯基(CH2)n分子链的电子输运

一维非共轭烷烃链虽不具富电子或少电子特征,但常存在于单分子器件或多肽、蛋白质等生物分子中,对电子传输产生重要影响.为理解这类物质的电子输运特征,本研究设计了一维线性非共轭(CH2)n分子结模型,并利用密度泛函理论结合非平衡态格林函数的方法,对(CH2)n(n=1-12)线性分子链与两个石墨烯电极耦合而成的分子结进行了第一性原理计算.结果表明,CH2分子链随着n值的变化,其电导值表现出明显的奇偶振荡现象,并且随着链长的增加呈指数级的衰减,这一结果与实验研究取得了很好的一致性,为理解和设计性能更加优良的单分子器件提供了重要理论依据.     

TBOR-shaped electro-optic modulator with dual output based on double-layer graphene

We proposed an electro-optic modulator with two-bus one-ring (TBOR) structure to improve the extinction ratio and reduce insert loss. It has a dual output compared with one-bus one-ring structure. In addition, double-layer graphene makes it possible for the modulation in the visible to mid-infrared wavelength range. It shows that this new electro-optic modulator can present two switching states well with low insertion loss, high absorption and high extinction ratio. At $\lambda =1550\text{ nm}$, when the switching states are based on the chemical potential, ${\mu }_{\mathrm{c}}=0.38\text{ eV}$ and ${\mu }_{\mathrm{c}}=0.4\text{ eV}$, the insertion losses of both output ports are less than 2 dB, the absorption of the output port coupled via a micro-ring reaches 45 dB and the extinction ratio reaches 14 dB. When the refractive index of the dielectric material is 4.2, the applied voltage will be less than 1.2 V, thus can be used in low-voltage CMOS technology.     

Rapid and Scalable Access to Sequence-Controlled DHDM Multiblock Copolymers by FLP Polymerization

An immortal N-(diphenylphosphanyl)-1,3-diisopropyl-4,5-dimethyl-1,3-dihydro-2H-imidazol-2-imine/diisobutyl (2,6-di-tert-butyl-4-methylphenoxy) aluminum (P(NIⁱPr)Ph₂/(BHT)AlⁱBu₂)-based frustrated Lewis pair (FLP) polymerization strategy is presented for rapid and scalable synthesis of the sequence-controlled multiblock copolymers at room temperature. Without addition of extra initiator or catalyst and complex synthetic procedure, this method enabled a tripentacontablock copolymer (n=53, k=4, dp_n=50) to be achieved with the highest reported block number (n=53) and molecular weight (M_n=310 kg mol⁻¹) within 30 min. More importantly, this FLP polymerization strategy provided access to the multiblock copolymers with tailored properties by precisely adjusting the monomer sequence and block numbers.     

Conversion of Methanol to Aromatic-Rich Gasoline over High-Efficiency Bifunctional Catalysts: Green Synthesis of GaZSM-5 Zeolites via Dry-Gel Conversion Strategy

Russian Journal of Applied Chemistry - Nanoscale ZSM-5 (AlZ5-D) and Ga-substituted ZSM-5 zeolites ((Al,Ga)Z5-D and GaZ5-D) were synthesized by a green dry-gel conversion strategy. For comparison,...     

Exact controllability for some degenerate wave equations

In this paper, we study one-dimensional linear degenerate wave equations with a distributed controller. We establish observability inequalities for degenerate wave equation by multiplier method. We also deduce the exact controllability for degenerate wave equation by Hilbert uniqueness method when the control acts on the nondegenerate boundary. Moreover, an explicit expression for the controllability time is given.     

Nanocomposite hydrogel consisting of Na‐montmorillonite with enhanced mechanical properties

A new kind of nanocomposite (NC) hydrogel with Na‐montmorillonite (MMT) is presented in this article. The NC hydrogels were synthesized by free radical copolymerization of acrylamide and (3‐acrylamidopropyl) trimethylammonium chloride (ATC) in the presence of MMT and N,N′‐methylene‐bis‐acrylamide used as chemical cross‐linker. Due to the cation‐exchange reaction between MMT and ATC (cationic monomer) during the synthesis of NC hydrogels, MMT platelets were considered chemical “plane” cross‐linkers, different from “point” cross‐linkers. With increasing amount of MMT, the crosslinking degree enhanced, causing a decrease of the swelling degree at equilibrium. Investigations of mechanical properties indicated that NC hydrogels exhibited enhanced strength and toughness, which resulted from chemical interaction between exfoliated MMT platelets and polymer chains in hydrogels. Dynamic shear measurements showed that both storage modulus and loss modulus increased with increasing MMT content. The idea described here provided a new route to prepare hydrogels with high mechanical properties by using alternative natural Na‐MMT. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1020–1026