ON THE OPERATIONS OF ALGEBROID FUNCTIONS

In this article, we first investigate the operational properties of algebroid functions. Then we prove two uniqueness theorems for algebroid functions.

THE NORMALITY OF ALGEBROID MULTIFUNCTIONS AND THEIR COEFFICIENT FUNCTIONS

In this paper, we investigate the normality relationship between algebroid multifunctions and their coefficient functions. We prove that the normality of a k-valued entire algebroid multifunctions family is equivalent to their coefficient functions in some conditions. Furthermore, we obtain some new normality criteria for algebroid multifunctions families based on these results. We also provide some examples to expound that some restricted conditions of our main results are necessary.

ALGEBROIDAL FUNCTION AND ITS DERIVED FUNCTION IN UNIT CIRCULAR DISC

In this article,the authors define the derived function of an algeboidal function in the unit disc,prove it is an algabriodal function,and study the order of algebroidal function and that of its derived function in unit circular disc.

NORMALITY CRITERIA FOR FAMILIES OF MEROMORPHIC ALGEBROID FUNCTIONS

By using the definition of Hausdorff distance, we prove some normality criteria for families of meromorphic algebroid functions. Some examples are given to complement the theory in this article.

BOREL RADIUS AND T-RADIUS OF THE ALGEBROIDAL FUNCTION IN THE UNIT DISC

Using Ahlfors’ theory of covering surface and a type-function,we confirm the existence theorem of a Borel radius and a T-radius for the algebroidal function dealing with multiple values in the unit disc,which briefly extend some results for the algebroidal functions in the complex plane

ON THE C.CHANG TYPE INEQUALITY OF ALGEBROID FUNCTIONS

In this paper,we investigate the growth relations between algebroid functions and their derivatives,and extend famous C.Chang inequality（see[1,4]）of meromorphic functions to algebroid functions.

THE BOREL DIRECTIONS OF ALGEBROIDAL FUNCTION AND ITS COEFFICIENT FUNCTIONS

In this article, the relationship between the Borel direction of algebroidal function and its coefficient functions is studied for the first time. To begin with, several theorems of algebroidal functions in unit disk are proved. By these theorems, some interesting conclusions are obtained.

ON THE SHARING VALUES OF ALGEBROID FUNCTIONS AND THEIR DERIVATIVES

In this paper, we define the shared value of an algebroid function and its derivative on its Riemann surface. By considering the relationship between the shared values and the branch points of algebroid functions and their derivatives, we obtain some uniqueness theorems of algebroid functions sharing values with their derivatives, which extend 3 IM shared values theorem of nonconstant meromorphic functions and their derivatives obtained by Mues-Steinmetz and Gundersen.

ON UNIQUENESS FOR ALGEBROID FUNCTIONS OF FINITE ORDER

Guided by Lo.Yang＇s method, we concern the question that how algebroid func- tions are determined by their multiple values and deficient values and we prove an at most 3v-valued theorem for algebroid functions. The results are complemented by an example for completeness.

Uniqueness Theorem of Algebroidal Functions in the Unit Disc

In this paper, the uniqueness of algebroidal functions in the unit disc is investigated. Suppose that W（z） and M（z） are v-valued and k-valued algebroidal functions in the unit disc, respectively. Let e^iθ be a b-cluster point of order co or order ρ（x） of the algebroidal function W（z） or M（z）. It is shown that if -↑E（aj, W（z）） = -↑E（aj,M（z）） holds in the domain {｜z｜ 〈 1}∩Ω（θ-δ,θ＋δ）, where b, aj （j = 1,…, 2v ＋ 2k ＋ 1） are complex constants, then W（z） = M（z）. The same results are obtained for the case that e^iθ is a Borel point of order co or order ρ（x） of the algebroidal function W（z） or M（z）.

GENERAL ALGEBROID FUNCTION AND ITS APPLICATION

In this paper, the authors introduce a kind of reducible algebroid functions, that is general algebroid functions and obtain two fundamental theorems of general algebroid functions. At last, as an application, we generalized a theorem of Li Guoping＇s.

THE INTEGRATION OF ALGEBROIDAL FUNCTIONS

In this paper, we introduce the integration of algebroidal functions on Riemann surfaces for the first time. Some properties of integration are obtained. By giving the defi- nition of residues and integral function element, we obtain the condition that the integral is independent of path. At last, we prove that the integral of an irreducible algebroidal function is also an irreducible algebroidal function if all the residues at critical points are zeros.

ON THE NEVANLINNA DIRECTION OF ALGEBROID FUNCTIONS

In this paper, we prove that for an algebroid function w（z）, the singular direction argz = φ0, satisfying that for arbitrary ε（0 〈 ε 〈 2/π） and any given α ∈ C^^,limr→＋∞ log τ/n（τ,φ0-ε,φ0＋ε,w=a）=＋∞ holds with at most; 2v possible exceptional values of a, is the Ncvanlinna direction of w（z）.

Uniqueness Theorem of Algebroidal Function in the Unit Disc

In this paper, discussed are the problems about uniqueness of algebroidal functions in the unit disc with share-values in a sector domain instead of the whole disk. Results are obtained extending some uniqueness theorems of meromorphic functions.

THE UNIQUENESS FOR ALGEBROID FUNCTIONS OF FINITE ORDER

In this article,we discuss,by Nevanlinna theory,the influence of multiple values and deficiencies on the uniqueness problem of algebroid functions.We get several uniqueness theorems of algebroid functions which include an at most 3v-valued theorem.These results extend the existing achievements of some scholars.

THE GROWTH AND BOREL POINTS OF RANDOM ALGEBROID FUNCTIONS IN THE UNIT DISC

In this paper,we construct k-valued random analytic algebroid functions for the first time.By combining the properties of random series,we study the growth and Bor el points of random analytic algebroid functions in the unit disc and obtain some interesting theorems.

Branched Polyamines Functionalized with Proposed Reaction Pathways Based on ¹H-NMR, Atomic Absorption and IR Spectroscopies

Three novel branched polyamines N,N,N’,N’-tetrakis-[3((pyridine-2-methyl)-amine) propyl]-1,4- butanediamine (1), N,N,N’,N’-tetrakis-[N-((2-methylpyridine)ethyl)propanamide]ethylenediamine (2) and N,N,N’,N’-tetrakis-[3((2-hidroxibenziliden)-amine)propyl]-1,4-butanediamine (3), were synthesized starting from 2-pyridinecarboxaldeyde with DAB-Am-4 for 1, PAMAM G0 for 2 and from salicylaldehyde with DAB-Am-4 for 3. The pathway reactions have been proposed by 1H-NMR, IR and Atomic Absorption Spectroscopy. The optimal reaction time was set by IR spectroscopy following aldehyde? peak modification. 1 and 2 were obtained as both hydrochlorides and as free amines and 3 only as free imine. These polyamines were characterized by UV-Vis, IR, 1H-NMR and 13C-NMR and Mass Spectrometry.

ON ALGEBROID FUNCTIONS IN A SUBDOMAIN OF THE COMPLEX PLANE

This paper discusses some basic properties of algebroid functions in a subdomain of the complex plane and some similar results (to those in the whole complex plane) and a new situation are showed.

Functional microbiomics reveals branched-chain amino acids depletion for alleviation of insulin resistance by berberine

Increased circulating branched-chain amino acids(BCAAs)have been involved in the pathogenesis of obesity and insulin resistance.However,evidence relating berberine(BBR),gut microbiota,BCAAs,and insulin resis⁃tance is limited.Here,we showed that BBR could effectively rectify steatohepatitis and glucose intolerance in high-fat diet(HFD)-fed mice.BBR reorganized gut microbiota populations under both the normal chow diet(NCD)and HFD.Particu⁃larly,BBR noticeably decreased the relative abundance of BCAA-producing bacteria,including order Clostridiales;fami⁃lies Streptococcaceae,Clostridiaceae,and Prevotellaceae;and genera Streptococcus and Prevotella.Compared with the HFD group,predictive metagenomics indicated a reduction in the proportion of gut microbiota genes involved in BCAA biosynthesis but the enrichment genes for BCAA degradation and transport by BBR treatment.Accordingly,the elevated serum BCAAs of HFD group were significantly decreased by BBR.Furthermore,the Western blotting results implied that BBR could promote the BCAA catabolism in the liver and epididymal white adipose tissues of HFD-fed mice by acti⁃vation of the multienzyme branched-chain α-ketoacid dehydrogenase complex,whereas by inhibition of the phosphoryla⁃tion state of BCKDHA(E1α subunit)and branched-chain α-ketoacid dehydrogenase kinase.The ex vivo assay further confirmed that BBR could increase BCAA catabolism in both AML12 hepatocytes and 3T3-L1 adipocytes.Finally,data from healthy subjects and diabetics confirmed that BBR could improve glycemic control and modulate circulating BCAAs.Besides,functional microbiomics integrated high-throughput microbial genomics,metabolomics and molecular biotechnology has also been successfully applied to reveal the anti-obesity mechanism of hydroxysafflor yellow A.

高校书院学生社区功能型党支部建设研究

深入推动学生社区党建工作发展,是高校强化党的领导、提升人才培养质量的内在要求。书院学生社区是推动人才培养模式改革的重要形式,在“双院”教育格局、育人空间共同体、多学科融合等方面为功能型党支部建设提供可能性。建设学生社区功能型党支部是落实立德树人根本任务的重要举措、增强学生党建活力的有效载体、强化学生思想政治教育的必然要求。在具体路径上,要坚持全面从严治党的基本要求,同时规范组织建构、明确功能定位、完善制度文件。