Limiting Behavior of Travelling Waves for the Modified Degasperis-Procesi Equation

Using an improved qualitative method which combines characteristics of several methods, we classify all travelling wave solutions of the modified Degasperis-Procesi equation in specified regions of the parametric space. Besides some popular exotic solutions including peaked waves, and looped and cusped waves, this equation also admits some very particular waves, such as fractal-like waves, double stumpons, double kinked waves, and butterfly-like waves. The last three types of solutions have not been reported in the literature. Furthermore, we give the limiting behavior of all periodic solutions as the parameters trend to some special values

Melnikov’s Criteria and Chaos Analysis in the Nonlinear Schrödinger Equation with Kerr Law Nonlinearity

The dynamics of the nonlinear Schrödinger equation with Kerr law nonlinearity with two perturbation terms are investigated. By using Melnikov method, the threshold values of chaotic motion under periodic perturbation are given. Moreover we also study the effects of the parameters of system on dynamical behaviors by using numerical simulation. The numerical simulations, including bifurcation diagram of fixed points, chaos threshold diagram of system in three-dimensional space, maximum Lyapunov exponent, and phase portraits, are also plotted to illustrate theoretical analysis and to expose the complex dynamical behaviors. In particular, we observe that the system can leave chaotic region to periodic motion by adjusting controller e, amplitude d1, and frequency ω2 of external forcing which can be considered a control strategy, and when the frequenciesy ω2 and ω1 approach the maximum frequency of disturbance, the system turmoil intensifies and control intensity increases

Synthesis, structure and photophysical properties of NIR aza-BODIPYs with -F/-N-3/NH2 groups at 1,7-positions

International audienceWith 4-fluorostyrene as the starting material, symmetric/asymmetric fluorine-containing aza-difluor-oboradiaza-s-indacenes (aza-BODIPYs) 3-6 at 1/7-position were successfully prepared. NaN3 undertook nucleophilic aromatic substitution via replacement of F atoms of 4 to form the N-3/NH2-containing aza-BODIPYs 9 and 10. The solid-state structure of aza-BODIPY 4 was confirmed by single crystal X-ray analysis, the F-Cph bond distance of which was found to be shorter than those of the reported fluoride. These aza-BODIPYs absorb and emit in the NIR region. Surprisingly, although the withdrawing group was introduced at 1/7 positions of 3-6, the effect of the fluorine atoms to the photophysical properties is trifling. However, 9 and 10 with N-3/NH2 groups resulted in a remarkable bathochromic shift. Aza-BODIPY 10 could be also used as a turn-on fluorescent probe for pH value. Moreover, the main photo physical data are well supported and explained by cLR-PCM(CHCI3)-M06-2X/6-311 + G(2d,p)/SOS-CIS(D) calculations

Yiqihuoxuejiedu Formula Restrains Vascular Remodeling by Reducing the Inflammation Reaction and Cx43 Expression in the Adventitia after Balloon Injury

Vascular remodeling is closely related to hypertension, atherosclerosis, and restenosis after PCI. Considerable evidence indicates that the activation and proliferation of adventitial fibroblasts play key roles in vessel injury. The inflammatory response and high expression of connexins contribute to adventitial remodeling. Therefore, reducing inflammation reaction and connexins expression in adventitia may become a new target to prevent vascular remodeling. Yiqihuoxuejiedu formula, composed of TCM therapeutic principle of supplementing qi, activating blood and detoxification, can inhibit restenosis after intimal injury. To further investigate the effect of Yiqihuoxuejiedu formula on inflammation and connexins, we established a carotid artery injury model. In model rats, hyperplasia in the intima was mild but obvious in the adventitia; CRP heightened; expressions of MCP-1, CD68, and Cx43 increased. Yiqihuoxuejiedu formula relieved intimal hyperplasia and adventitial area, obviously diminished the expressions of CD68 and Cx43 in the adventitia, and reduced CRP but did not lower MCP-1. These results indicated that Yiqihuoxuejiedu formula inhibited vascular remodeling especially adventitial hyperplasia by reducing the inflammation reaction including lowering macrophages infiltration and systemic nonspecific inflammatory response and also restraining gap junction connexins leading to less communication among cells. This study provides new ideas and methods for the prevention and treatment of vascular remodeling