On the uniform perfectness of the boundary of multiply connected wandering domains

We investigate in which cases the boundary of a multiply connected wandering domain of an entire function is uniformly perfect. We give a general criterion implying that it is not uniformly perfect. This criterion applies in particular to examples of multiply connected wandering domains given by Baker. We also provide examples of infinitely connected wandering domains whose boundary is uniformly perfect.Comment: 19 page

On multiply-connected Fatou components in iteration of meromorphic functions

AbstractLet f:C↦Cˆ be a transcendental meromorphic function with at most finitely many poles. We mainly investigated the existence of the Baker wandering domains of f(z) and proved, among others, that if f(z) has a Baker wandering domain U, then for all sufficiently large n, fn(U) contains a round annulus whose module tends to infinity as n→∞ and so for some 0<d<1,Mc(r,a,f)d⩽mc(r,a,f),r∈G, where G is a set of positive numbers with infinite logarithmic measure. Therefore, we give out several criterion conditions for non-existence of the Baker wandering domains

The limit set of iterations of entire functions on wandering domains

We first establish any continuum without interiors can be a limit set of iterations of an entire function on an oscillating wandering domain, and hence arise as a component of Julia sets. Recently, Luka Boc Thaler showed that every bounded connected regular open set, whose closure has a connected complement, is an oscillating or an escaping wandering domain of some entire function. A natural question is: What kind of domains can be realized as a periodic domain of some entire function? In this paper, we construct a sequence of entire functions whose invariant Fatou components can be approached to a regular domain

Effect of Taoren-Quyu decoction on endometriosis in rats

Purpose: To study the effect of traditional Chinese Medicine formula Taoren-Quyu decoction (TQD) on endometriosis. Method: Fifty female Wistar rats were randomly separated into five groups (10 rats/group): normal control, model (untreated) group, positive control (danazol), 200 mg/kg/day (low dose) or 400 mg/kg/day (high dose). All rats were prepared into endometriosis except for normal control rats. TDQ groups rats were orally administered of TQD for 5 weeks. After treatment, the rats were sacrificed by cervical dislocation. The number of total endometriotic lesions were counted. Serum levels of cancer antigen 125 (CA-125), interleukin 13 (IL-13), interleukin 18 (IL-18) and peritoneal fluid tumor necrosis factoralpha (TNF-α) were measured by ELISA kits. Result: Compared with control rats, TQD reduced the number of total endometriotic lesions significantly (12.7 ± 1.2, p &lt; 0.01), as well as serum levels of CA-125 (6.4 ± 1.2 U/mL), IL-18 (118.6 ± 7.4 pg/mL), IL13 (6.3 ± 0.8 pg/mL) and peritoneal fluid TNF-α (231.5 ± 11.7 pg/mL) (p &lt; 0.01). Conclusion: The results reveal that TQD exerts anti-endometriotic effect in rats by inhibiting inflammatory factors. Therefore, TQD has potentials for use in the treatment of endometriosis

Revisit spin effects induced by thermal vorticity

We revisit the spin effects induced by thermal vorticity by calculating them directly from the spin-dependent distribution functions. For the spin-1/2 particles, we give the polarization up to the first order of thermal vorticity and compare it with the usual result calculated from the spin vector. For the spin-1 particles, we give the spin alignment in terms of thermal vorticity. Although the spin alignment receives only second-order contribution from thermal vorticity, we find that some non-diagonal elements in spin density matrix can receive first order contribution. We also find that the spin effects for both Dirac and vector particles will receive extra contribution when the spin direction is associated with the particle's momentum.Comment: 23 pages, no figure