On proximality with Banach density one

Let (X,T)$(X,T)$ be a topological dynamical system. A pair of points (x,y)∈X²$(x,y)\in X^2$ is called Banach proximal if for any ε>0$\epsilon >0$, the set {n∈_Z+:d(Tⁿx,Tⁿy)<ε}$\{n\in {\mathbb{Z}}_{+}:d(T^{n}x,T^{n}y)<\epsilon \}$ has Banach density one. We study the structure of the Banach proximal relation. A useful tool is the notion of the support of a topological dynamical system. We show that a dynamical system is strongly proximal if and only if every pair in X²$X^2$ is Banach proximal. A subset S of X is Banach scrambled if every two distinct points in S form a Banach proximal pair but not asymptotic. We construct a dynamical system with the whole space being a Banach scrambled set. Even though the Banach proximal relation of the full shift is of first category, it has a dense Mycielski invariant Banach scrambled set. We also show that for an interval map it is Li–Yorke chaotic if and only if it has a Cantor Banach scrambled set.     

基于密度泛函理论的DBDS与DBS对铜绕组腐蚀性能对比研究

二苄基二硫醚(DBDS)与二苄基硫醚(DBS)是变压器内部主要腐蚀性硫化物,能腐蚀铜绕组,破坏变压器的安全运行.为从微观层面探究两者腐蚀性能的差异,基于密度泛函理论(DFT)对DBDS与DBS的腐蚀性能进行对比研究.计算了DBDS/Cu(110)吸附模型与DBS/Cu(110)吸附模型的功函变化,发现DBDS/Cu(110)的功函变化ΔΦ_1(-0.388 eV)绝对值要小于DBS/Cu(110)功函变化ΔΦ_2(-1.118 eV)绝对值,说明DBS更易吸附Cu(110)表面;DBDS在Cu(110)表面的吸附能E_(ads1)为8.571 eV,DBS在Cu(110)表面吸附能E_(ads2)为6.077 eV,表明两者都不能自发吸附,需要从外界吸热才能吸附,且DBS从外界获取能量更少,更容易吸附.同时比较了DBDS分子与DBS分子前线轨道分布以及HOMO轨道与LUMO轨道能量差,计算了DBDS分子与DBS分子的电负性,结果表明:DBDS电负性大小为3.132 eV,DBS电负性大小为3.100 eV,两者基本相等.而DBDS前线轨道能量差(2.610 eV)明显小于DBS前线轨道能量差(3.610 eV), DBDS优化前后的S-S键长分别为2.033?和3.057?,说明DBDS更容易与Cu发生反应.以上模拟结果说明,DBS更易吸附于Cu,而DBDS更易与Cu发生反应.     

Notes on the Lightlike Hypersurfaces Along Spacelike Submanifolds

Ukrainian Mathematical Journal - In connection with the method of construction of lightlike hypersurfaces along spacelike submanifolds, we present a relation between the second fundamental form of...     

Implementation of a novel two-attractor grid multi-scroll chaotic system

This paper proposed a method of generating two attractors in a novel grid multi-scroll chaotic system.Based on a newly generated three-dimensional system,a two-attractor grid multi-scroll attractor system can be generated by adding two triangular waves and a sign function.Some basic dynamical properties,such as equilibrium points,bifurcations,and phase diagrams,were studied.Furthermore,the system was experimentally confirmed by an electronic circuit.The circuit simulation results and numerical simulation results verified the feasibility of this method.     

一类高次系统极限环的存在与唯一性

本文对系统dxdt=-y(1-ax2n)(1-bx2n) δx-lx4n 1dydt=x2n-1(1-cx2n)(1-bx2n)进行定性分析,得出其极限环的存在性,不存在性及唯一性的一系列充分条件.     

ON THE SINGULAR DIRECTIONS OF VALUE DISTRIBUTION OF HOLOMORPHIC CURVES IN P^n（C）

This article proves the existence of singular directions of value distribution theory for some transcendental holomorphic curves in the n-dimensional complex projective space Pn(C). An example is given to complement these results.     

Numerical modelling of bubbly flows with and without heat and mass transfer

In this paper, modelling gas–liquid bubbly flows is achieved by the introduction of a population balance equation combined with the three-dimensional two-fluid model. For gas–liquid bubbly flows without heat and mass transfer, an average bubble number density transport equation has been incorporated in the commercial code CFX5.7 to better describe the temporal and spatial evolution of the geometrical structure of the gas bubbles. The coalescence and breakage effects of the gas bubbles are modelled according to the coalescence by the random collisions driven by turbulence and wake entrainment while for bubble breakage by the impact of turbulent eddies. Local radial distributions of the void fraction, interfacial area concentration, bubble Sauter mean diameter, and gas and liquid velocities, are compared against experimental data in a vertical pipe flow. Satisfactory agreements for the local distributions are achieved between the predictions and measurements. For gas–liquid bubbly flows with heat and mass transfer, boiling flows at subcooled conditions are considered. Based on the formulation of the MUSIG (multiple-size-group) boiling model and a model considering the forces acting on departing bubbles at the heated surface implemented in the computer code CFX4.4, comparison of model predictions against local measurements is made for the void fraction, bubble Sauter mean diameter, interfacial area concentration, and gas and liquid velocities covering a range of different mass and heat fluxes and inlet subcooling temperatures. Good agreement is achieved with the local radial void fraction, bubble Sauter mean diameter, interfacial area concentration and liquid velocity profiles against measurements. However, significant weakness of the model is evidenced in the prediction of the vapour velocity. Work is in progress through the consideration of additional momentum equations or developing an algebraic slip model to account for the effects of bubble separation.     

Optimization of microcrystalline silicon thin film solar cell isolation processing parameters using ultraviolet laser

This study used ultraviolet laser to perform the microcrystalline silicon thin film solar cell isolation scribing process, and applied the Taguchi method and an L₁₈ orthogonal array to plan the experiment. The isolation scribing materials included ZnO:Al, AZO transparent conductive film with a thickness of 200 nm, microcrystalline silicon thin film at 38% crystallinity and of thickness of 500 nm, and the aluminum back contact layer with a thickness of 300 nm. The main objective was to ensure the success of isolation scribing. After laser scribing isolation, using the minimum scribing line width, the flattest trough bottom, and the minimum processing edge surface bumps as the quality characteristics, this study performed main effect analysis and applied the ANOVA (analysis of variance) theory of the Taguchi method to identify the single quality optimal parameter. It then employed the hierarchical structure of the AHP (analytic hierarchy process) theory to establish the positive contrast matrix. After consistency verification, global weight calculation, and priority sequencing, the optimal multi-attribute parameters were obtained. Finally, the experimental results were verified by a Taguchi confirmation experiment and confidence interval calculation. The minimum scribing line width of AZO (200 nm) was 45.6 μm, the minimum scribing line width of the microcrystalline silicon (at 38% crystallinity) was 50.63 μm and the minimum line width of the aluminum thin film (300 nm) was 30.96 μm. The confirmation experiment results were within the 95% confidence interval, verifying that using ultraviolet laser in the isolation scribing process for microcrystalline silicon thin film solar cell has high reproducibility.     

Theoretical study on instantaneous linewidth of Fourier-domain mode-locked fiber lasers

We have numerically simulated the operation of the Fourier-domain mode-locked (FDML) fiber laser based on the wavelength reconstruction method instead of numerical solving the nonlinear Schrödinger equation. We studied the influences of the filter bandwidth and the relative time delay caused by the fiber chromatic dispersion on the instantaneous linewidth of the FDML fiber laser. The results show that the instantaneous linewidth broadens as the filter bandwidth and the relative time delay increase. When the filter has the bandwidth of 0.02 nm, the narrowest and broadest instantaneous linewidths are 0.024 and 0.042 nm, respectively. We give an understanding for the oscillation of the instantaneous linewidth of FDML. The presented result can be used to evaluate the performance achievable in the FDML fiber lasers.     

Error estimates for space–time discontinuous Galerkin formulation based on proper orthogonal decomposition

In this study, proper orthogonal decomposition (POD) method is applied to diffusion–convection–reaction equation, which is discretized using space–time discontinuous Galerkin (dG) method. We provide estimates for POD truncation error in dG-energy norm, dG-elliptic projection, and space–time projection. Using these new estimates, we analyze the error between the dG and the POD solution, and the error between the exact and the POD solution. Numerical results, which are consistent with theoretical convergence rates, are presented.