Double degeneration on second-order breather solutions of Maxwell–Bloch equation

The breather solutions of the Maxwell–Bloch equations in a two-level resonant system associated with the self-induced transparency phenomenon are constructed by the Darboux transformation. After constructing the formulas of the second-order breather solutions, the double degeneration and hybrid solutions are studied by the analytical form as well as figures. Our results might be helpful in such application or prevention of the rogue waves from breather solution interactions and degeneration in the nonlinear optical systems associated with the Maxwell–Bloch equations.     

含噻唑、硫醚结构的1,2,4-三唑类化合物的合成及生物活性

以三氟乙酰乙酸乙酯、磺酰氯、水合肼、异硫氰酸苯酯、碘代芳烃、氯乙酸等为原料,设计、合成了7种新型的含噻唑环、硫醚和三氟甲基的1,2,4-三氮唑类化合物,通过¹H NMR、¹³C NMR、¹⁹F NMR和MS等技术手段对新化合物进行了结构表征。 杀菌活性测试表明,化合物6b、6d和6g在浓度为100 mg/L时对纹枯病菌(Rhizoctoniasolani)的抑制率分别为91%、92%和93%。     

Global stability of a class of delay differential systems

This paper is concerned with a class of systems of delay differential equations which are defined on the nonnegative function space. Under proper conditions, we employ a novel proof to establish several criteria of the global stability of positive equilibrium. Moreover, we give two examples to illustrate our main results.     

Existence and uniqueness of periodic solutions for forced Rayleigh-type equations

In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of T-periodic solutions for a kind of forced Rayleigh equation of the form

x^″+f(x^′(t))+g(t,x(t))=e(t).     

Multiple positive solutions for a semilinear elliptic equation with critical Sobolev exponent

In this paper, we study a class of semilinear elliptic equations with Hardy potential and critical Sobolev exponent. By means of the Ekeland variational principle and Mountain Pass theorem, multiple positive solutions are obtained.     

New Exact Solutions of （1 ＋ 1）-Dimensional Coupled Integrable Dispersionless System

This paper applies the exp-function method, which was originally proposed to find new exact travelling wave solutions of nonlinear evolution equations, to the Riccati equation, and some exact solutions of this equation are obtained. Based on the Riccati equation and its exact solutions, we find new and more generalvariable separation solutions with two arbitrary functions of (1+1)-dimensional coupled integrable dispersionless system. As some special examples, some new solutions can degenerate into variable separation solutions reported in open literatures. By choosing suitably two independent variables p(x) and q(t) inour solutions, the annihilation phenomena of the flat-basin soliton, arch-basin soliton, and flat-top soliton are discussed.     

基于萘基块新型开链冠醚的合成及晶体结构研究

以3,6-二溴-2,7-二羟基萘为起始原料,经与2-溴-N-苯基乙酰胺醚化,再用硼氢化钠和三氟化硼乙醚还原得基于萘基块新型的开链冠醚,两步总收率为96%.利用单晶X衍射研究其结构,晶体为三斜晶系,P-1空间群,a=9.588(3),b=10.898(3),c=13.060(4),α=103.190(4)°,β=93.953(4)°,γ=115.622(5)°,V=1176.0(6)3,Z=2,Dc=1.571 g/cm3,λ=0.71075 nm,μ(Mo Kα)=3.472 mm-1,Mr=353.22,F(000)=560.在晶体结构中,分子中的一个N—H基团与另外一分子形成双分叉氢键N—H…Br和N—H…O,进而组装成二聚体.这些中心对称的二聚体进一步通过C—H…π相互作用叠加成二维层状结构平行于(110)面.     

Vibrational Spectroscopic Study of （E）-3-（4-fluorophenyl）-N-[4-（phenylamino） quinazoline-7-yl] Acrylamide

Geometry optimization and subsequent harmonic vibration calculations of prior synthesized (E)-3-(4-fluorophenyl)-N-[4-(phenyl-amino) quinazoline-7-yl] acrylamide were carried out by DFT/B3LYP method with both 6-31G and 6-311G basis sets.The Infrared (IR) spectrum of the title compound was recorded in the field of 400-4000 cm 1 and then assigned.The correlation analyses between the scaled theoretical vibration frequencies and the experimental ones indicate that there exist good linearity relationships since the correlation coefficients R 2 are larger than 0.999.The intramolecular interactions existed in the title molecule were confirmed by the Atoms in molecules (AIM) method,and their influences on the absorption frequency were also investigated.     

向量组线性相关程度的研究

利用向量组的格拉姆矩阵,给出了欧氏空间中衡量向量组线性相关程度的一个特征量．