Hom-Leibniz代数的广义导子

给出Hom-Leibniz代数L的广义导子代数GDer(L)、拟导子代数QDer(L)、型心C(L)、拟型心QC(L)及中心导子代数ZDer(L)的一些基本性质,并证明QDer(L)可以嵌入并成为一个更大的Hom-Leibniz代数的导子.

Hom-Leibniz超代数的广义导子

研究了Hom-Leibniz超代数L的广义导子及其性质,给出了Hom-李超代数的充要条件,证明了QDer(L)可以嵌入并成为一个更大的Hom-Leibniz超代数的导子.

Hom-Leibniz代数的直和

定义两个Hom-Leibniz代数(g,[,],α)和(h,[,],β)的直和(gh,[,],α+β),定义两个Hom-Leibniz代数(g,[,],α)和(h,[,],β)的同态Ф,讨论两个Hom-Leibniz代数(g,[,],α)和(h,[,],β)的线性映射Ф成为同态的充分必要条件.

On Algebroid Solutions of Generalized Complex Differential Equations

Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized complex algebraic differential equations and obtain some results.

Hom-Leibniz代数的导子

定义了Hom-Leibniz代数(g,[,],α)的αk-导子、内导子和导子扩张代数Der(g)g,并且证明了内导子adk(u)是一个αk+1-导子,导子集Der(g)是由各个αk-导子子集构成,导子集Der(g)按照通常括积的定义方法为李代数,导子扩张代数Der(g)g在适当的括积及线性运算αD下为Hom-Leibniz代数.

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.

Generalized Higher-Order Algebraic Differential Equations with Admissible Algebroid Solutions

Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized higher order algebraic differential equations.

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）.

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）.

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.

q-形变Witt超代数的Hom-Leibniz二上循环

将Lie超代数上的Leibniz二上循环推广到Hom-Lie超代数上,并确定了一类无限维Hom-Lie超代数q-形变Witt超代数上的Hom-Leibniz二上循环。

SEVERAL UNIQUENESS THEOREMS OF ALGEBROID FUNCTIONS ON ANNULI

In this paper, we discuss the uniqueness problem of algebroid functions on annull, we get several uniqueness theorems of algebroid functions on annuli, which extend the Nevanlinna value distribution theory for algebroid functions on annuli.