On Growth of Meromorphic Solutions of Complex Functional Difference Equations

The main purpose of this paper is to investigate the growth order of the meromorphic solutions of complex functional difference equation of the form (∑λ∈I‍αλ(z)(∏ν=1n‍f(z+cν)lλ,ν))/(∑μ∈J‍βμ(z)(∏ν=1n‍f(z+cν)mμ,ν))=Q(z,f(p(z))), where I={λ=(lλ,1,lλ,2,…,lλ,n)∣lλ,ν∈ℕ⋃‍{0},  ν=1,2,…,n} and J={μ=(mμ,1,mμ,2,…,mμ,n)∣mμ,ν∈ℕ⋃‍{0},  ν=1,2,…,n} are two finite index sets, cν (ν=1,2,…,n) are distinct complex numbers, αλ(z) (λ∈I) and βμ(z) (μ∈J) are small functions relative to f(z), and Q(z,u) is a rational function in u with coefficients which are small functions of f(z), p(z)=pkzk+pk-1zk-1+⋯+p0∈ℂ[z] of degree k≥1. We also give some examples to show that our results are sharp

Meromorphic solutions of higher order Briot-Bouquet differential equations

For differential equations $P(y^{(k)},y)=0,$ where $P$ is a polynomial, we prove that all meromorphic solutions having at least one pole are elliptic functions, possibly degenerate

Comparative proteomic analysis of edible bird’s nest from different origins

Abstract Edible bird’s nest (EBN) mainly made of saliva that secreted by a variety of swiftlets is a kind of precious traditional Chinese medicine. EBNs from different biological and geographical origins exhibit varieties in morphology, material composition, nutritive value and commercial value. Here, we collected four different EBN samples from Huaiji, China (Grass EBN), Nha Trang, Vietnam (Imperial EBN) and East Kalimantan, Indonesia (White EBN and Feather EBN) respectively, and applied label-free quantitative MS-based proteomics technique to identify its protein composition. First, phylogenetic analysis was performed based on cytb gene to identify its biological origin. Second, a total of 37 proteins of EBNs were identified, among which there were six common proteins that detected in all samples and exhibited relatively higher content. Gene ontology analysis revealed the possible function of EBN proteins, and principal component analysis and hierarchical clustering analysis based on 37 proteins were performed to compare the difference of various EBNs. In summary, our study deciphered the common and characteristic protein components of EBNs of different origins and described their possible functions by GO enrichment analysis, which helps to establish an objective and reliable quality evaluation system