The catalogues and mid-infrared environment of Interstellar OH Masers

Data for a number of OH maser lines have been collected from surveys. The posi- tions are compared to recent mid-infrared (MIR) surveys such as Spitzer-GLIMPSE and WISE, restricting the comparison to point sources. The colors and intensities of the IR sources are compared. There are many 18 cm OH masers, but far fewer in lines arising from higher energy levels. We also make a comparison with the 5 cm Class II methanol masers. We have divided the results into 3 subsamples: those associated with OH masers only, those associated with OH masers and Class II methanol masers, and those only associated with Class II methanol masers. There are no obvious dif- ferences in the color-color or color-magnitude results for the GLIMPSE point sources. However, according to the results from the WISE 22 {\mu}m survey, the sources associ- ated with OH masers are brighter than those associated with methanol masers. We interpret the presence of OH and methanol masers mark the locations of regions where stars are forming. The OH masers are located on the borders of sharp features found in the IR. These are referred to as bubbles. If the OH masers mark the positions of protostars, the result provides indirect evidence for triggered star formation caused by the expansion of the bubbles.Comment: 23 pages (11 pages online only), 12 figures, Accepted. Monthly Notices of the Royal Astronomical Society,201

Averaging approach to cyclicity of Hopf bifurcation in planar linear-quadratic polynomial discontinuous differential systems

Agraïments: The first author is supported by NSFC grant #11471228. The third author is supported by NSFC grants #11231001, #11221101.It is well known that the cyclicity of a Hopf bifurcation in continuous quadratic polynomial differential systems in \R^2 is 3. In contrast here we consider discontinuous differential systems in \R^2 defined in two half--planes separated by a straight line. In one half plane we have a general linear center at the origin of \R^2, and in the other a general quadratic polynomial differential system having a focus or a center at the origin of \R^2. Using averaging theory, we prove that the cyclicity of a Hopf bifurcation for such discontinuous differential systems is at least 5. Our computations show that only one of the averaged functions of fifth order can produce 5 limit cycles and there are no more limit cycles up to sixth order averaged function

Linearizability conditions of quasi-cubic systems

In this paper we study the linearizability problem of the two-dimensional complex quasi-cubic system $\dot{z}=z+(zw)^{d}(a_{30}z^{3}+a_{21}z^{2}w+a_{12}zw^2+a_{03}w^{3}),~\dot{w}=-w-(zw)^{d}(b_{30}w^{3}+b_{21}w^{2}z+b_{12}wz^2+b_{03}z^{3})$, where $z, w, a_{ij}, b_{ij}\in \mathbb{C}$ and $d$ is a real number. We find a transformation to change the quasi-cubic system into an equivalent quintic system and then obtain the necessary and sufficient linearizability conditions by the Darboux linearization method or by proving the existence of linearizing transformations

Cyclicity of (1,3)-switching FF type equilibria

Hilbert's 16th Problem suggests a concern to the cyclicity of planar polynomial differential systems, but it is known that a key step to the answer is finding the cyclicity of center-focus equilibria of polynomial differential systems (even of order 2 or 3). Correspondingly, the same question for polynomial discontinuous differential systems is also interesting. Recently, it was proved that the cyclicity of (1, 2)-switching FF type equilibria is at least 5. In this paper we prove that the cyclicity of (1, 3)-switching FF type equilibria with homogeneous cubic nonlinearities is at least 3

Research Progress on Integrated Traditional Chinese and Western Medicine in the Treatment of Post-Cholecystectomy Syndrome

Laparoscopic cholecystectomy (LC) is a highly accepted treatment at this stage, with the increasing incidence of biliary tract disease and the development of endoscopic technique in recent years However, some patients after cholecystectomy still have symptoms similar to preoperative symptoms, such as abdominal pain, diarrhea, indigestion and so on. This series of syndromes has become a common clinical problem at present.This article reviews the research progress of etiology, pathogenesis, diagnosis and treatment of post-cholecystectomy syndrome by reading related literatures

Restricted independence in displacement function for better estimation of cyclicity

Agraïments: The author is partially supported by NSFC grant #11471228 (X. Chen), NSFC grant # 11501083 (Z. Wang), and NSFC grants # 11231001 and # 11221101 (W. Zhang).Since the independence of focal values is a sufficient condition to give a number of limit cycles arising from a center-focus equilibrium, in this paper we consider a restricted independence to a parametric curve, which gives a method not only to increase the lower bound for the cyclicity of the center-focus equilibrium but also to be available when those focal values are not independent. We apply the method to a nondegenerate cubic center-focus variety and prove that the cyclicity reaches its an upper bound