On the index of finite determinacy of vector fields with resonances

In this paper we study normal forms for a class of germs of 1-resonant vector fields on R^n with mutually different eigenvalues which may admit extraneous resonance relations. We give an estimation on the index of finite determinacy from above as well as the essentially simplified polynomial normal forms for such vector fields. In the case that a vector field has a zero eigenvalue, the result leads to an interesting corollary, a linear dependence of the derivatives of the hyperbolic variables on the central variable.     

一类带有Holling Ⅱ类功能性反应和相互干扰及脉冲效应的捕食系统

A kind of predator-prey system of Holling typeⅡand interaction perturbation with impulsive effect is presented.By using Floquet theory and small amplitude perturbations skills,the locally asymptotical stability of prey-eradication periodic solution and the permanence of the system are discussed and the corresponding threshold conditions are given respectively.Finally,the existence of positive periodic solution is investigated by the bifurcation theory.     

The index problem for eigenvalues for coupled boundary conditions and Fulton’s conjecture

This paper deals with regular self-adjoint Sturm–Liouville problems with coupled boundary conditions. The spectrum of the problems can be either bounded from below, or unbounded from both below and above. We consider the following question: given an eigenvalue, how to determine its index or indices efficiently? Using results on the level surfaces of the nth eigenvalue and certain inequalities among eigenvalues, the determination is converted into that of the index of the same eigenvalue for an appropriate separated boundary condition and hence can be achieved in terms of the Prüfer angle. As an application of this complete solution of the index problem, we show that Fulton’s conjecture about such an index is true.     

Electrochemical properties of niosomes‐modified Au electrode and its interaction with 1‐anilino‐8‐naphthalene‐sulfonate

The gold electrode was modified by noisomes, prepared by sonicating the mixed solution of PEG 6000/Tween 80/Span 80/H₂O. Electrochemical cyclic voltammetry (CV) and impedance spectroscopy (EIS) were performed for characterizing the modification. The construction of multilayer films of octadecanethiol (ODT)‐niosomes had almost no pinholes, which elicited that niosomes‐coated electrode through ODT assembly was more effective immobilization compared to direct modification method. A large semicircle formation in the entire range of frequency indicated the complete electron‐transfer control for the redox reaction, implying a perfect blocking behavior. The Nyquist plot was consisting of two depressed semicircles after storage for 36 h in air, which implied a progressive and uniform construction manner, as expected for porous coatings. The modified electrode was used to investigate the interaction between 1‐anilino‐8‐naphthalene‐sulfonate (ANS) and noisomes. It was found that the low‐frequency semicircular arcs increase in diameter, indicating that the increase in the resistance R_p attributed mainly to the niosomes/solution interface. It was due to the binding of ANS to the niosomes‐modified electrode surface, exhibited against diffusing species through the pores. Copyright © 2009 John Wiley & Sons, Ltd.     

Equivalent Model, Error Analysis, and Design Steps of AGC Loop for MM-Wave Receiver

Automatic Gain Controlled (AGC) Loops are used in MM-Wave receiver in wide-ranging. In this paper, the equivalent model and loop equation of AGC Loop are built, the loop errors are analyzed and then the design steps of AGC Loop are given out.     

An X‐shaped π‐conjugated polymer comprising of fluorene units and anthracene units with high efficiency. Synthesis and optical and electrochemical properties

A new X‐shaped π‐conjugated monomer comprising of fluorene units and anthracene units was synthesized, and it was used to fabricate the new X‐shaped π‐conjugated polymers and investigate the properties of the new polymers. Using different molar ratios between such monomer and a fluorene monomer gave three polymers that showed higher absolute PL quantum yields than the linear polyfluorene (PF) in the solid state. After thermal annealing at 200 °C for 4 h, the linear PF showed an additional bathochromic emission at about 550 nm, whereas such red‐shifted emission was fully eliminated for the X‐shaped polymers. The electroluminescent devices based on the X‐shaped polymers with a configuration of ITO/PEDOT:PSS/polymer/LiF/Ca/Al displayed blue emission with low turn‐on voltage and high brightness. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 5616–5625, 2008     

相对平坦模的$\aleph$-积

设$M$是右$R$-模, $\aleph$是一个无穷基数. 称右$R$-模$N$是$\aleph$-$M$-凝聚的,如果对任意的$B/A\hookrightarrow mR$,其中设$M$是右$R$-模, $\aleph$是一个无穷基数. 称右$R$-模$N$是$\aleph$-$M$-凝聚的,如果对任意的$B/A\hookrightarrow mR$,其中设$M$是右$R$-模, $\aleph$是一个无穷基数. 称右$R$-模$N$是$\aleph$-$M$-凝聚的,如果对任意的$B/A\hookrightarrow mR$,其中设$M$是右$R$-模, $\aleph$是一个无穷基数. 称右$R$-模$N$是$\aleph$-$M$-凝聚的,如果对任意的$B/A\hookrightarrow mR$,其中$0\leq A相似文献   

Polyplatinayne/polyoxometalate composite Langmuir‐Blodgett films: Preparation,structural characterization,and potential optoelectronic applications

A new family of organometallic/inorganic composite Langmuir‐Blodgett (LB) films consisting of rigid‐rod polyplatinayne polymer ([Pt‐T(OMe‐Fl)T]_∞ or [Pt‐T(F‐Fl)T]_∞, where the triplet bonds are abbreviated by T, and fluorene ring by Fl) as the π‐conjugated organometallic molecule, polyoxometalate (POM, POM = K₃PMo₁₂O₄₀, H₃PW₁₂O₄₀, or H₆P₂W₁₈O₆₂) of the Keggin and Dawson structures as the inorganic component, and dimethyldioctadecylammonium bromide (DODA) or a mixture of octadecanoic acid (OA) and docosanoic acid (DA) as the auxiliary film‐forming agent were prepared and characterized by π–A isotherms, UV–Vis absorption spectra, photoluminescence spectra, atomic force microscopy imaging, scanning tunneling microscopy, and low‐angle X‐ray diffraction. Our experimental results indicate that steady, even, and ordered Langmuir and LB films are formed in pure water and polyoxometalate subphases. It was shown that the POM molecules are probably embedded inside the polyplatinayne molecules in the LB film structure and they can quench the luminescence of the Pt polyyne. These Pt‐polyyne based LB films display interesting electric conductivity behavior. [Pt‐T(OMe‐Fl)T]_∞/DODA/HPW₁₂ monolayer film shows a good electrical conductivity, and the tunneling current amounts to ±100 nA when the voltage is set at ±8 V. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 3193–3206, 2008     

Cyclization and halogenation of substituted o-allylphenols with diacetoxyiodobenzene in the presence of iodine or bromine

Substituted 2-halomethyl-2,3-dihydrobenzofurans were synthesized in one pot and in mild yield from substituted o-allylphenols with diacetoxyiodobenzene in the presence of 12 or Br2 in dry CH2Cl2 under reflux.