SHARP ESTIMATES OF QUASI-CONVEX MAPPINGS OF TYPE B AND ORDER α

In this paper, we first establish several sharp inequalities of homogeneous expansion for biholomorphic quasi-convex mappings of type B and order α on the unit ball E in a complex Banach space X by applying the method and technique of complex analysis. Then, as the application of these sharp inequalities, we derive the sharp estimate of third homogeneous expansions for the above mappings defined on the unit polydisk U^n in C^n.

SHARP ESTIMATES OF ALL HOMOGENEOUS EXPANSIONS FOR A SUBCLASS OF QUASI-CONVEX MAPPINGS OF TYPE B AND ORDER α IN SEVERAL COMPLEX VARIABLES

In this article, first, the sharp estimates of all homogeneous expansions for a subclass of quasi-convex mappings of type B and order B on the unit ball in complex Ba- nach spaces are given. Second, the sharp estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in （in are also established. In particular, the sharp estimates of all homogeneous expansions for a subclass of quasi-convex mappings （include quasi-convex mappings of type A and quasi-convex mappings of type B） in several complex variables are get accordingly. Our results state that a weak version of the Bieber- bach conjecture for quasi-convex mappings of type B and order a in several complex variables is proved, and the derived conclusions are the generalization of the classical results in one complex variable.

THE SHARP ESTIMATE OF THE THIRD HOMOGENEOUS EXPANSION FOR A CLASS OF STARLIKE MAPPINGS OF ORDER α ON THE UNIT POLYDISK IN C^n

In this article, first, a sufficient condition for a starlike mapping of order a f（x） defined on the unit ball in a complex Banach space is given. Second, the sharp estimate of the third homogeneous expansion for f is established as well, where f（z） = （f1（z）, f2（z）,..., fn（z））＇ is a starlike mapping of order a or a normalized biholomorphic starlike mapping defined on the unit polydisk in Cn, and D2fk（0）（z2） /2i= zk（∑l=1^b akzzl）, k = 2t l=1 k = 1, 2,..., n. Our result states that the Bieberbaeh conjecture in several complex variables （the case of the third homogeneous expansion for starlike mappings of order α and biholomorphic starlike mappings） is partly proved.

AN INEQUALITY OF HOMOGENEOUS EXPANSION FOR BIHOLOMORPHIC QUASI-CONVEX MAPPINGS ON THE UNIT POLYDISK AND ITS APPLICATION

In this article,the authors obtain an inequality of homogeneous expansion for f,where f is a quasi-convex mapping(including quasi-convex mapping of type A and quasi-convex mapping of type B)defined on the open unit polydisk in C n .Meanwhile,the authors also investigate its application.

THE GROWTH THEOREM FOR QUASI-CONVEX MAPPINGS IN HILBERT SPACES

In this paper, the authors extend the definition of quasi-convex mappings and obtain the corresponding growth theorem-on the unit ball of a complex Hilbert space X.

FEKETE AND SZEG INEQUALITY FOR A SUBCLASS OF STARLIKE MAPPINGS OF ORDER αON THE BOUNDED STARLIKE CIRCULAR DOMAIN IN C^n

In this article, first, we establish the Fekete and Szego inequality for an interesting subclass of biholomorphic functions in the open unit disk U. Second, we generalize this result to the bounded starlike circular domain in Cn. The proofs of these results use some restrictive assumptions, which in the case of one complex variable are automatically satisfied.

A Remark on the Generalized Roper-Suffridge Extension Operator for Spirallike Mappings of Type β and Order α

Suppose f is a spirallike function of type β and order α on the unit disk D. Let Ωn,p1,p2,···,pn = {z = (z1,z2,··· ,zn) ∈ Cn : n: n j=1 |zj|pj < 1}, where 1 ≤ p1 ≤ 2,pj ≥1,j = 2,··· ,n, are real numbers. In this paper, we will prove that Φn,β2,γ2,···,βn,γn(f)(z) =(f(z1),(f(zz11 ))β2(f (z1))γ2z2,··· ,(f(zz11 ))βn(f (z1))γnzn) preserves spirallikeness of type βand order α on Ωn,p1,p2,···,pn.

Common Fixed Point Result of Multivalued and Singlevalued Mappings in Partially Ordered Metric Space

In recent times the fixed point results in partially ordered metric spaces has greatly developed. In this paper we prove common fixed point results for multivalued and singlevalued mappings in partially ordered metric space. Our theorems generalized the theorem in [1] and extends the many more recent results in such spaces.

A Remark on the Generalized Roper-Suffridge Extension Operator for Almost Stalike Mappings of Order α

假定 f 是联合起来的磁盘 D 上的顺序的一个几乎星形的函数。在这份报纸，我们将证明那 n ， 2 ， 2 ，， n ， n (f)(z)=( f ( z1 )，( f ( z1 ) /z1 ) 2 (f'( z1 )) 2z2 ，，( f ( z1 ) /z1 ) n (f'( z11 )) nzn )“在 n 上保存顺序的几乎星形， p1 ， p2 ，， pn ={ z =( z1 ， z2 ，， zn )” Cn ：nj=1 | zj|pj 1 } 0 p11 2， pj 1， j = 2，， n，实数。

A SUBCLASS OF QUASI-CONVEX MAPPINGS ON A REINHARDT DOMAIN IN C^n

Let D p 1,p 2,⋯,p n={z∈C n:∑l=1 n|z l|p l<1},p l>1,l=1,2,⋯,n.In this article,we first establish the sharp estimates of the main coefficients for a subclass of quasi-convex mappings(including quasi-convex mappings of type A and quasi-convex mappings of type B)on D p 1,p 2,⋯,p n under some weak additional assumptions.Meanwhile,we also establish the sharp distortion theorems for the above mappings.The results that we obtain reduce to the corresponding classical results in one dimension.

THE INVARIANCE OF STRONG AND ALMOST SPIRALLIKE MAPPINGS OF TYPE β AND ORDER α

The invariance of strong and almost spirallike mappings of type β and order α is discussed in this paper. From the maximum modulus principle of holomorphic functions, we obtain that the generalized Roper-Suffridge operators preserve strong and almost spirallike-hess of type β and order α on the unit ball B^n in C^n and on bounded and complete Reinhardt domains. Therefore we obtain that the generalized Roper-Suffridge operators preserve strong spirllikeness of type β, strong and almost starlikeness of order α, strong starlikeness on the corresponding domains.Thus we can construct more subclasses of spirallike mappings in several complex variables.

ON REFINEMENT OF THE COEFFICIENT INEQUALITIES FOR A SUBCLASS OF QUASI-CONVEX MAPPINGS IN SEVERAL COMPLEX VARIABLES

Let K be the familiar class of normalized convex functions in the unit disk.In[14],Keogh and Merkes proved that for a function f(z)=z+∑k=2∞a k z k in the class K,|a 3−λa 22|≤max{13,|λ−1|},λ∈C.The above estimate is sharp for eachλ.In this article,we establish the corresponding inequality for a normalized convex function f on U such that z=0 is a zero of order k+1 of f(z)−z,and then we extend this result to higher dimensions.These results generalize some known results.

Some Fixed Point Results of Ciric-Type Contraction Mappings on Ordered <i>G</i>-Partial Metric Spaces

We introduce the concept of generalized quasi-contraction mappings in G-partial metric spaces and prove some fixed point results in ordered G-partial metric spaces. The results generalize and extend some recent results in literature.

ON THE SHARP GROWTH,COVERING THEOREMS FOR NORMALIZED BIHOLOMORPHIC MAPPINGS IN C^n

In this article, a normalized biholomorphic mapping f defined on bounded starlike circular domain in Cn is considered, where z = 0 is a zero of order k ＋ 1 of f（z） - z. The sharp growth, covering theorems for almost starlike mappings of order α and starlike mappings of order α are established. Meanwhile, the construction of the above mappings on bounded starlike circular domain in Cn is also discussed, it provides the extremal mappings for the growth, covering theorems of the above mappings.

Additive Maps Preserving the Star Partial Order on B(H)

Let B（H） be the C^＊-algebra of all bounded linear operators on a complex Hilbert space H. It is proved that an additive surjective map φ on B（H） preserving the star partial order in both directions if and only if one of the following assertions holds. （1） There exist a nonzero complex number a and two unitary operators U and V on H such that φ（X） = a UXV or φ（X） = α UX^＊ V for all X ∈B（H）. （2） There exist a nonzero a and two anti-unitary operators U and V on H such that φ（X） = αUXV or φ（X） = aUX^＊ Vfor all X∈ B（H）.

On Growth and Covering Theorem for Spiallike Mapping of Type β with Order α

在这份报纸，我们为 f (x)考虑生长和盖住的定理，在 f (x)是类型印射，顺序在统一复杂 Banach 空间的球 B 上定义的 spiallike 的地方，并且 x=0 也是为 f (x) -x.We 的零目 k+1 当时，评价是精确的 dicate =0 并且仍然给生长上面的界限和失真为辅助 mapping.This 结果的上面的界限包括知道的一些结果。

The Study for Some Subclasses of Biholomorphic Mappings by an Unified Method

让 Cn 是有 0 的一个围住的星形的圆形的领域。在这份报纸，我们上介绍 holomorphic mappings Mg 的一个班。让 f (z) 一局部地使 biholomorphic 印射在上正常化以便 J-1f (z) f (z) Mg 和 z=0 是 f (z) 的零顺序 k+1 - z。我们为 f (z) 获得生长和盖住的定理。作为推论，特别，我们统一并且概括许多已知的结果。而且鉴于推论的证明，在星形的 mappings 的子类之中的必要关系被显示出。

ORDERING CONTRACTION MAPPING PRINCIPLE AND APPLICATIONS

This paper establishes an ordering contraction mapping principle for increasing mapping in partial ordering metric spaces, and applies it to prove the existence and uniqueness of fixed point for some nonlinear operators controlled by a linear operator and phi-concave operator in a partial ordering Banach space. Therefore, this two results are unified.

改进粒子群优化滚珠丝杠进给系统BP神经网络PID控制策略研究

针对传统的BP神经网络PID(BP-PID)控制因其初始权值随机,导致系统的收敛速度较慢、控制前期会有较大误差和BP神经网络初始权值优化等问题,建立了滚珠丝杠进给系统伺服三环模型,设计了BP-PID控制器,提出了一种二阶振荡混沌映射粒子群算法(SCMPSO)优化滚珠丝杠进给系统BP-PID控制器。首先,混沌映射初始化粒子位置,使粒子均匀分布于空间,增加粒子解的多样性;随后,提出一种非线性余弦自适应惯性权重,以平衡算法的全局搜索能力和局部搜索能力;其次,在算法中引入二阶振荡环节,在面对突变多峰干扰时,能及时跳出局部最优解。研究结果表明:当加入外界干扰时,控制策略SCMPSO-BP-PID在正向进给时段的位移平均误差为0.013 mm,相比SAWPSO-BP-PID、LDWPSO-BP-PID、PSO-BP-PID这3种控制策略分别提升约45.8%、55.2%、61.7%;当加入阶跃响应时,SCMPSO-BP-PID的最大超调量仅为0.029,系统调节时间和峰值时间相比3种控制策略均有较大提升,具有较高的控制精度和稳定性。

关于Mapmaker/Exp遗传作图中标记分群和排序操作技术的讨论

Mapmaker/Exp(3.0)是国内外广泛使用的遗传连锁数据分析软件,在分子标记数量大时(多于500个)往往出现所绘制连锁图谱图距偏大的现象。本文从标记分群和标记排序两个遗传作图环节分析原因并概括出以下两个实施要点:(1)标记分群不应强求同一LOD值,对特殊的连锁群可试用不同LOD值;(2)在标记排序时,一次order命令后用ripple命令反复梳理有时并不能获得最佳排列顺序,而应多次使用order,每次order后用ripple反复梳理,经反复比较才能得出最佳排列顺序,必要时还须结合人工调整。通过大豆遗传作图实例比较了软件推荐思路2的通常用法和作者建议的新用法所构建的遗传图谱及相应QTL定位的差异,认为新用法具有更好的效果。