Multipeak solutions for an elliptic system of Fitzhugh-Nagumo type

We consider the Dirichlet problem for an elliptic system of FitzHugh-Nagumo type. We prove that the problem has solutions with arbitrary many sharp peaks near the boundary but not on the boundary. The work of the first author was partially supported by the ARC     

W_2~1[a,b]中的最佳逼近泛函及应用

1 引言 线性泛函的逼近问题有着十分广泛的应用背景,本文在具有再生核的W_2~1[a,b]空间中讨论线性泛函L(f)的形如 L_n(f)=sum from i=1 to n(i/1)w_if(x_i) (1)的逼近问题,其中{w_i}_1~n是待定系数,如果存在一组常数{w_i~x}_1~n使 L_n~x=sum from i=1 to n(i/1)w_i~xf(x_i) (2)满足||L—L_n~x||=inf||L—L_n||,则称L_n~x是L的最佳逼近,记 w_i E_n=L—L_n, E_n~3=L—L_n~x,则称E_n~x是最佳逼近误差泛函。 本文在§1中给出L_n~x的表达式及L_(n+1)~x与L_n~x之间的递推公式。并证明L_n~x的收敛性。§3中讨论了上L_n~x(f)在数值积分及常微分方程数值解中的应用,并给出数值算例。     

Fenestration operation in middle ear bone with pulsed infrared lasers: an in-vivo study

The feasibility of fenestration operation in middle ear bone with pulsed infrared laser is evaluated. Healthy male New Zealand rabbits in vivo are used in the experiment. Middle ear mastoid bone of animal model is completely exposed with conventional methods, and then a pulsed CO2 laser （10.6 μm） and an Er：YAG laser （2.94 μm） are used to perform the fenestration operation. Diamond drill is also used as a control group. The total operation time and light irradiation time are recorded and the opening efficiency is assessed. The morphological changes and thermal damage around the opening window on the middle ear bone are examined. It is shown that both laser systems are suitable for the fenestration operation in middle ear bone, and this no-touch technique has a lot of benefits compared with traditional methods. The bleeding during operation has an important effect on operation time and thermal injury and needs to be controlled efficiently in further study.     

Fountain theorem over cones and applications

In this paper, we establish fountain theorems over cones and apply it to the quasilinear elliptic problem{-pu = λ|u|q-2u + μ|u| γ-2 u, x ∈Ω,u = 0, x ∈Ω,(1)to show that problem (1) possesses infinitely many solutions, where 1 p N, 1 q p γ, ΩRN is a smooth bounded domain and λ, μ∈ R.     

Photophysical properties of pyridyloxy phthalocyanine encapsulated in nanoparticles

Two aluminum chloride phthalocyanines with pyridyloxy substitution at α/β positions were synthesized. Their structures were characterized by infrared spectroscopy, proton nuclear magnetic resonance as well as elemental analysis. Tetra-α(β)-(2-pyridyloxy) aluminum chloride phthalocyanines were encapsulated into a diblock copolymer methoxy-poly(ethylene glycol)-block-poly(L-lysine) through a cosolvent method. The morphologies and photophysical properties of phthalocyanines encapsulated in nanoparticles were studied by transmission electron microscope, ultraviolet-visible, and fluorescence spectroscopic methods. The photophysical properties of phthalocyanines encapsulated into nanoparticles exhibited substitution positions dependence. The phthalocyanines with substitution at α positions were found to be an excellent candidate for use as photosensitizers for treatment of cancer by photodynamic therapy.     

铝离子聚合物固态电解质

铝离子电池因其材料成本低、大倍率性能优异和循环寿命超长等优势,而被认为在大规模静态储能应用中具有广阔前景.目前的铝离子电池大部分采用离子液体、尿素和熔融盐等液态电解液,其在实际工程化应用当中存在电解液渗漏的风险.相对而言,全固态电池则可以避免电解液渗漏的问题,还具有因去除隔膜和简化封装所带来的电池整体能量密度提升的优点.但是,目前领域内少有关于全固态铝离子电池的研究.基于此,采用溶液浇筑法,以冠醚作为添加剂和配位基团、以聚乙二醇（PEO）作为基底,制备出无定型结构的聚合物固态铝离子电解质.其中,冠醚不仅作为配位基团与铝离子进行配位提高铝离子的稳定性,而且作为相容性高的添加剂降低聚合物结晶度,从而提高固态电解质的离子电导率.测试表明,制备出的18-6/PEO/Al（CF₃SO₃）₃体系聚合物固态铝离子电解质是非晶态为主的晶态与非晶态共存的薄膜,且具备很高的离子电导率（室温,5.5×10^-6 S/cm;100℃高温,1.86×10^-3 S/cm）和较宽的电化学稳定窗口（0~3 V）,这为全固态铝离子电池的研发奠定了基础.     

Constant boundary value problem for a quasilinear elliptic system

We study the constant boundary value problem for a class of quasilinear elliptic systems. The existence of a nonconstant solution is proved by discussing the minimization problem for the relaxed energy. As a by-product, we show that generally the Pohozaev identity does not hold for H¹-weak solutions.     

Junction‐Controlled Topological Polymerization

Methodology that enables the controlled synthesis of linear and branched polymers from an identical monomer will be a novel pathway for polymer synthesis and processing. Herein we first describe the control of one or both of the C(3)‐C(3′) and C(6)‐C(6′) coupling reactions of carbazolyl. In a second approach, an identical monomer containing two carbazolyls is polymerized using chemical and electrochemical oxidizers, leading to topologically controllable growth of linear polymers in weak oxidizer or of cross‐linked polymer chains in strong oxidizer, with satisfactory long chain propagation of step growth polymerization (M_n=6.0×10⁴ g mol^?1, M_w/M_n=2.3). This very simple polymerization with cheap reagents and low levels of waste has provided a flexible pathway for synthesis and processing of polymers.     

New solutions for nonlinear Schrödinger equations with critical nonlinearity

We consider the following nonlinear Schrödinger equations in Rn