A Functional Analytic Approach to Perturbations of the Lorentz Gas

We present a functional analytic framework based on the spectrum of the transfer operator to study billiard maps associated with perturbations of the periodic Lorentz gas. We show that recently constructed Banach spaces for the billiard map of the classical Lorentz gas are flexible enough to admit a wide variety of perturbations, including: movements and deformations of scatterers; billiards subject to external forces; nonelastic reflections with kicks and slips at the boundaries of the scatterers; and random perturbations comprised of these and possibly other classes of maps. The spectra and spectral projections of the transfer operators are shown to vary continuously with such perturbations so that the spectral gap enjoyed by the classical billiard persists and important limit theorems follow.     

Approximations to fixed points of contraction semigroups in hilbert spaces

Sequences (or curves) are constructed to approximate common fixed points of a pair of nonex-pansive mappings (or contraction semigroups) in Hilbert spaces. The obtained results extend the previously known results from a single mapping to a family of mappings.     

A partially isochronous splitting algorithm for three-block separable convex minimization problems

During the last decade, the state-of-the-art alternating direction method of multipliers (ADMM) has successfully been used to solve many two-block separable convex minimization problems arising from several applied areas such as signal/image processing and statistical and machine learning. It however remains an interesting problem of how to implement ADMM to three-block separable convex minimization problems as required by the situation where many objective functions in the above-mentioned areas are actually more conveniently decomposed to the sum of three convex functions, due also to the observation that the straightforward extension of ADMM from the two-block case to the three-block case is apparently not convergent. In this paper, we shall introduce a new algorithm that is called a partially isochronous splitting algorithm (PISA) in order to implement ADMM for the three-block separable model. The main idea of our algorithm is to incorporate only one proximal term into the last subproblem of the extended ADMM so that the resulting algorithm maximally inherits the promising properties of ADMM. A remarkable superiority over the extended ADMM is that we can simultaneously solve two of the subproblems, thereby taking advantages of the separable structure and parallel architectures. Theoretically, we will establish the global convergence of our algorithm under standard conditions, and also the O(1/t) rate of convergence in both ergodic and nonergodic senses, where t is the iteration counter. The computational competitiveness of our algorithm is shown by numerical experiments on an application to the well-tested robust principal component analysis model.     

2,5-二(2-菲基)-[3,2-b]并二噻吩的合成、表征及在有机薄膜晶体管中的应用

本文合成了2,5-二(2-菲基)-[3,2-b]并二噻吩(PhTT), 表征了其基本的物理和化学性质, 制备了相应的有机薄膜晶体管.     

A new process for preparing dialdehyde by catalytic oxidation of cyclic olefins with aqueous hydrogen peroxide

A. novel peroxo-niobophosphate was synthesized for the first time and used as a catalyst in the oxidation reaction of cyclic olefins with aqueous hydrogen peroxide to prepare dialdehy-des. The catalyst was characterized by elemental analysis, thermographic analyses, IR, UV/vis, 31P NMR and XPS spectra as [ π-C5H5N(CH2 )13 CH3 ]2 [ Nb4O6 (O2 )2 (PO4 )2 ] ·6H2O (PTNP). It showed high selectivity to glutaraldehyde in the catalytic oxidation of cyclopentene with aqueous hydrogen peroxide in ethanol.     

Matrix approaches to approximate solutions of variational inequalities in Hilbert spaces

A matrix approach to approximating solutions of variational inequalities in Hilbert spaces is introduced. This approach uses two matrices: one for iteration process and the other for regularization. Ergodicity and convergence (both weak and strong) are studied. Our methods combine new or well-known iterative methods (such as the original Mann’s method) with regularized processes involved regular matrices in the sense of Toeplitz.     

Electrical Current in Sinai Billiards Under General Small Forces

The Lorentz gas of $\mathbb{Z}^{2}$ -periodic scatterers (or the so called Sinai billiards) can be used to model motion of electrons on a metal. We investigate the linear response for the system under various external forces (during both the flight and the collision). We give some characterizations under which the forced system is time-reversible, and derive an estimate of the electrical current generated by the forced system. Moreover, applying Pesin entropy formula and Young dimension formula, we get several characterizations of the non-equilibrium steady state of the forced system.     

Detection of mutant p53 using field-effect transistor biosensor

We assessed the abilities of wild p53 and mutant p53 proteins to interact with the consensus DNA-binding sequence using a MOSFET biosensor. This is the first report in which mutant p53 has been detected on the basis of DNA-protein interaction using a FET-type biosensor. In an effort to evaluate the performance of this protocol, we constructed the core domain of wild p53 and mutant p53 (R248W), which is DNA-binding-defective. After the immobilization of the cognate DNA to the sensing layer, wild p53 and mutant p53 were applied to the DNA-coated gate surface, and subsequently analyzed using a semiconductor analyzer. As a consequence, a significant up-shift in drain current was noted in response to wild p53, but not mutant p53, thereby indicating that sequence-specific DNA-protein interactions could be successfully monitored using a field-effect-based biosensor. These data also corresponded to the results obtained using surface plasmon resonance (SPR) measurements. Taken together, our results show that a FET-type biosensor might be promising for the monitoring of mutant p53 on the basis of its DNA-binding activity, providing us with very valuable insights into the monitoring for diseases, particularly those associated with DNA-protein binding events.     

Catalyst Control of Interfacial Welding Mechanical Properties of Vitrimers

Chinese Journal of Polymer Science - Interfacial welding of thermosetting polymers has been a challenge, but vitrimers with dynamic covalent networks open numerous opportunities for welding and...     

肖特基钙钛矿太阳电池结构设计与优化

有机-无机杂化钙钛矿材料有高吸收系数、低廉的制作成本以及较为简单的制备工艺,在近年来表现出良好的发展前景.本文采用wx-AMPS模拟软件对平面结构钙钛矿太阳电池和肖特基钙钛矿太阳电池进行建模仿真对比,从理论上分析无载流子传输层的肖特基钙钛矿太阳电池的优势.结果显示,器件两侧电极功函数和吸收层的能带分布是提高太阳电池效率的关键.在对电极使用Au(功函数为5.1 eV)的前提下,透明导电电极功函数为3.8 eV,可以得到肖特基钙钛矿太阳电池转换效率为17.93%.对器件模型吸收层进行优化,通过寻找合适的掺杂浓度,抑制缺陷密度,确定合适的厚度,可以获得理想的转换效率(20.01%),是平面异质结结构(理论转换效率31%)的63.84%.肖特基钙钛矿太阳电池在简单的器件结构下可以获得优异的光电性能,具有较好的应用潜力.