一类E-α-预不变拟凸性与数学规划（英文）

【目的】提出一类新的广义凸函数E-α-预不变拟凸函数,并研究它的性质和应用。【方法】由于E-α-预不变拟凸性是E-预不变凸性和α-预不变拟凸性的真推广,将E-预不变凸性和α-预不变拟凸性推广可以得到结果,并举例验证。【结果】首先,给出了E-α-不变凸集和E-α-预不变拟凸函数的定义,给出实例说明其存在性。然后,给出了E-α-预不变拟凸函数的几个重要性质,并借助条件A和条件C获得了E-α-预不变拟凸函数的等价刻画。最后,讨论了E-α-预不变拟凸性分别在无约束与约束多目标规划问题中的应用。【结论】研究了E-α--预不变拟凸函数的性质和应用。     

关于多目标规划问题绝对最优解、有效解、弱有效解间的关系

在较弱的条件下讨论了一类多目标向量规划问题(VP)的绝对最优解集、有效解集、弱有效解集(Rab,Rpa,Rwp)之间的关系,并在较弱的条件下对单目标向量规划问题(P)与多目标向量规划问题(VP)解的关系做进一步讨论.     

The first member of the eleven-vertex azadicarbaborane series, 1,6,9-NC2B8H13, and its N-alkyl derivatives

Reactions between closo-1,2-C(2)B(8)H(10) (1) and amines of general formulation R(1)R(2)NH (where R(1), R(2) = H, H; Me, H; t-Bu, H and Et, Et) resulted in a straightforward cluster expansion and formation of the 11-vertex arachno-azadicarbaboranes of the 1,1-R(1),R(2-)1,6,9-NC(2)B(8)H(11) (2) cluster constitution (where R(1), R(2) = H, H 2a; Me, H 2b; t-Bu, H 2c and Et, Et 2d) in yields 10-75%, depending on the nature of the amine used. The reactions are the first example of a direct closo to arachno transformation in the area of cluster-boron compounds. Compounds 2b and 2c were isolated in two isomeric forms anti- and syn- that differ in the positioning of the t-Bu substituent with respect to the bridging hydrogen site. Deprotonation of compounds 2 generally leads to removal of the bridging proton and formation of the [1,1-R(1),R(2-)1,6,9-NC(2)B(8)H(11)](-) (2-) anions that, in the case of the monoalkylated Me and t-Bu derivatives, adopt only an anti configuration. The structure of anti-2c was determined by X-ray diffraction analysis and the geometries of the parent compound and the corresponding syn and anti isomers were optimised at the RMP2/6-31G* level. The composition of all compounds is consistent with the results of mass spectrometry and multinuclear ((1)H and (11)B) spectroscopy complemented by two-dimensional [(11)B-(11)B]-COSY and (1)H{(11)B(selective)} NMR measurements. Experimental (11)B chemical shifts generally show acceptable agreement with theoretical values calculated by GIAO methods, in particular at GIAO-MP2/II, where possible.     

Macropolyhedral boron-containing cluster chemistry. The unique nido-five-vertex-<B2>-nido-ten-vertex conjuncto structure of [(eta5-C5Me5)2Rh2B11H15] via an unexpected cluster-dismantling

B16H20 and [RhCl2(eta5-C5Me5)]2 with tmnd give [(eta5-C5Me5)2Rh2B11H15], which has an unprecedented thirteen-vertex macropolyhedral cluster core based on a nido ten-vertex {MB9} subcluster and a nido five-vertex {MB4} subcluster fused with their open-face {B2} edges in common.     

半严格-（B,G）-半预不变凸函数的性质与应用研究

主要研究了半严格-（B,G）-半预不变凸函数的性质与应用,首先通过举例子来说明半严格-（B,G）-半预不变凸函数的存在性且区别于半严格-G-半预不变凸函数、G半预不变凸函数、半严格-G预不变凸函数与严格-（B,G）-半预不变凸函数;然后给出了半严格-（B,G）-半预不变凸性的一些基本性质;最后分别在无约束与不等式约束下,获得了两类半严格-（B,G）-半预不变凸规划问题解的最优性结果。     

例析高等数学背景下的高考数学试题

高等数学是大学理工科及部分文科专业开设的一门非常重要的基础课程,它对培养学生的理性思维、创新意识、解决实际问题的能力等基本素质起着重要的作用;以近几年出现的高考试题为例,探讨高等数学中的有关知识在解题中的应用．     

关于Lipsehitz严格伪压缩映象的带误差的Ishikawa型迭代程序

设K是任意实Banach空间X中的闭凸子集,T：K→K是Lipschitz严格伪压缩映象,在没有假设∑n=0^∞ αnβn〈∞之下,本文证明了由xa＋1=（1-αn）xn＋αnTyn＋un与yn=（1-βn）xn＋βnTxn＋vn,任意n∈N,生成的带误差的Ishikawa迭代序列强收敛到T的唯一不动点,并给出了更为一般的收敛率估计：若un=vn=0,任意n∈N,则有｜｜xn＋1-x^＊｜｜≤（1-γn）｜｜xn-x^＊｜｜≤…≤∏j=0^n（1-γj）｜｜x0-x^＊｜｜,其中{γn}是（0,1）中的序列,满足γn≥1/1＋kmin（ε,η-ε）αn。所得结果改进和推广了最新的一些结果。     

The [2,5,12-C3B8H15]- anion, the first representative of the eleven-vertex hypho family of tricarbaboranes

In one synthetic step from the readily available 9-Me(2)SCH(2)-nido-7,8-C(2)B(9)H(11) (compound 1), the first representative of the eleven-vertex hypho family of tricarbaboranes, [2,5,12-C(3)B(8)H(15)][X] (X=[NMe4]+ or [PPh4]+) (compound 2), has been isolated in 32% yield and structurally characterised by single-crystal X-ray diffraction, multi-nuclear NMR spectroscopy, mass spectrometry, and computational methods. Both [NMe4]+ or [PPh4]+ salts of anion 2 were found to undergo degradative conversion to the [hypho-6,7-C(2)B(6)H(13)]- anion (anion 3) in alkaline medium. The [PPh4]+ salt of anion 2 converted quantitatively to the [6-CH3-arachno-5,10-C(2)B(8)H(12)]- anion (anion 4) if passed through a silica column or to the neutral 5-CH3-arachno-6,9-C(2)B(8)H(13) (compound 5) on treatment of its [NMe4]+ salt with dilute HCl. Moreover, the reaction of compound 2 with [RhCl2(C(5)Me(5))]2 afforded the eleven-vertex ruthenadicarbaborane [1-C(5)Me(5)-4-CH(3)-closo-1,2,3-RhC(2)B(8)H(9)] (compound 8). All these reactions resulted in an extrusion of one of the cluster carbon atoms into an exoskeletal position.     

Lipschitz增生算子方程逼近解的带误差的Ishikawa迭代序列

设X是一实Banach空间,T∶X→X是Lipschitz连续的增生算子,在没有假设∑∞n=0αnβn<∞之下,本文证明了由xn 1=(1-αn)xn αn(f-Tyn) un以yn=(1-βn)xn βn(f-Txn) vn,n≥0产生的带误差的Ishikawa迭代序列强收敛到方程x Tx=f的唯一解,并给出了更为一般的收敛率估计:若un=vn=0,n≥0,则有‖xn 1-x*‖≤(1-αn)‖xn-x*‖≤…≤∏in=0(1-αj)‖xn-x*‖,其中{αn}是(0,1)中的序列,满足γn≥4ηL(L 1)αn,n≥0。     

α-D-半预不变凸映射与最优化

【目的】提出了一类新的向量值映射,即α-D-半预不变凸映射,研究了此类映射的判定定理、性质以及该类映射在优化问题中的应用。【方法】理论推导并举例进行验证,利用向量值映射的半连续性获得α-D-半预不变凸型映射的相关结论。【结果】首先给出了α-D-半预不变凸映射的定义,并用实例说明了α-D-半预不变凸映射的存在性;然后获得了α-D-半预不变凸映射的判定定理和两个性质;最后讨论了α-D-半严格半预不变凸映射在向量优化问题中的应用,并举例说明所得结果的正确性。【结论】α-D-半预不变凸映射在一定程度上丰富了广义凸向量值映射及最优化理论的研究。