关于复正定矩阵的判定

研究了复矩阵的正定性 ,给出了复正定矩阵的一系列判定条件 ,获得了一些新的结果 ,改进并推广了著名的 Hadam ard不等式、Fejer定理及郭忠的结果 ,削弱了华罗庚不等式的条件 .     

Complex Hyperspherical Equations, Nodal-Partitioning, and First-Excited-State Theorems in ℝ n

Three problems related to the spherical quantum billiard in are considered. In the first, a compact form of the hyperspherical equations leads to their complex contracted representation. Employing these contracted equations, a proof is given of Courant's nodal-symmetry intersection theorem for diagonal eigenstates of spherical-like quantum billiards in . The second topic addresses the first-excited-state theorem for the spherical quantum billiard in . Wavefunctions for this system are given by the product form, ( )Z _q+()Y ⁽ⁿ⁾ , where is dimensionless displacement, is angular-momentum number, qis an integer function of dimension, Z() is either a spherical Bessel function (nodd) or a Bessel function of the first kind (neven) and represents (n– 1) independent angular components. Generalized spherical harmonics are written . It is found that the first excited state (i.e., the second eigenstate of the Laplacian) for the spherical quantum billiard in is n-fold degenerate and a first excited state for this quantum billiard exists which contains a nodal bisecting hypersurface of mirror symmetry. These findings establish the first-excited-state theorem for the spherical quantum billiard in . In a third study, an expression is derived for the dimension of the th irreducible representation (irrep) of the rotation group O(n) in by enumerating independent degenerate product eigenstates of the Laplacian.     

Optical functions of InGaP/GaAs epitaxial layers from 0.01 to 5.5 eV

In_0.49Ga_0.51P films, both undoped and doped n- and p-type (up to 10¹⁸ cm^-3), were grown lattice matched on GaAs substrates, with different miscut angles, by Metal-Organic Vapour Phase Epitaxy (MOVPE) at different temperatures. The shift of the fundamental gap E₀, caused by “ordering effect” was measured as a function of temperature by photoluminescence. The complex refractive index = n + ik and the dielectric function = ɛ ₁ + iɛ ₂ at room temperature were determined from 0.01 to 5.5 eV by using complementary data from fast-Fourier-transform far-infrared (FFT-FIR), dispersive, and ellipsometric spectroscopies. The effect of the native oxide was accounted for and the self-consistency of the optical functions was checked in the framework of the Kramers-Kronig causality relations. In the restrahlen region the dielectric function was well fitted by classical Lorentz oscillators; in the transparent region below E₀, the refractive index was modelled by a Sellmeier dispersion relation; in the interband region the dielectric function was well reproduced by analytical lineshapes associated to seven critical points. Thus parametrized analytical expressions were obtained for the optical functions all over the spectral range, without discontinuities, to be used in the modelling and characterization of multi-layer structures, also on opaque substrates. Received 13 December 2001 Published online 25 June 2002     

Hochschild Cohomologies of the Algebra of Smooth Functions

Based on the previously developed technique using the Laplace transformation of distributions with compact support, we calculate the Hochschild cohomologies of the algebra of smooth functions on a finite-dimensional real vector space with coefficients in the adjoint representation.     

Evolution in complex systems

What features characterize complex system dynamics? Power laws and scale invariance of fluctuations are often taken as the hallmarks of complexity, drawing on analogies with equilibrium critical phenomena. Here we argue that slow, directed dynamics, during which the system's properties change significantly, is fundamental. The underlying dynamics is related to a slow, decelerating but spasmodic release of an intrinsic strain or tension. Time series of a number of appropriate observables can be analyzed to confirm this effect. The strain arises from local frustration. As the strain is released through “quakes,” some system variable undergoes record statistics with accompanying log‐Poisson statistics for the quake event times. We demonstrate these phenomena via two very different systems: a model of magnetic relaxation in type II superconductors and the Tangled Nature model of evolutionary ecology and show how quantitative indications of aging can be found. © 2004 Wiley Periodicals, Inc. Complexity 10: 49–56, 2004     

Networks, Fields and Organizations: Micro-Dynamics, Scale and Cohesive Embeddings

Social action is situated in fields that are simultaneously composed of interpersonal ties and relations among organizations, which are both usefully characterized as social networks. We introduce a novel approach to distinguishing different network macro-structures in terms of cohesive subsets and their overlaps. We develop a vocabulary that relates different forms of network cohesion to field properties as opposed to organizational constraints on ties and structures. We illustrate differences in probabilistic attachment processes in network evolution that link on the one hand to organizational constraints versus field properties and to cohesive network topologies on the other. This allows us to identify a set of important new micro-macro linkages between local behavior in networks and global network properties. The analytic strategy thus puts in place a methodology for Predictive Social Cohesion theory to be developed and tested in the context of informal and formal organizations and organizational fields. We also show how organizations and fields combine at different scales of cohesive depth and cohesive breadth. Operational measures and results are illustrated for three organizational examples, and analysis of these cases suggests that different structures of cohesive subsets and overlaps may be predictive in organizational contexts and similarly for the larger fields in which they are embedded. Useful predictions may also be based on feedback from level of cohesion in the larger field back to organizations, conditioned on the level of multiconnectivity to the field.     

三元混配铂(Ⅱ)配合物的稳定性和分子内芳环堆积效应研究

用 pH电位滴定法测定了铂 (Ⅱ )与核苷酸NTP (NTP为腺苷 5′ 三磷酸和尿苷 5′ 三磷酸 )和另一芳环系列配体ArL形成的三元混配配合物Pt(ArL) (NTP) n -(ArL =Phen ,Bpy和Trp ;n =2或 3)在水溶液中的稳定常数 (I=0 .1mol/L ,KNO3 ;2 5℃ ) .用ΔlogKPt比较了二元和三元混配配合物的稳定性差异 ,认为三元混配配合物稳定性的增加可归因于π 酸与π 碱之间的合作效应和分子内芳环配体的堆积作用     

氟喹诺酮类抗菌药物与过渡金属离子Cr3+, Mn2+和Fe3+形成配合物配位位置的研究

通过1D ¹H NMR, ¹³C NMR和1H自旋-晶格弛豫时间T₁对氟喹诺酮类抗菌药物与过渡金属离子Cr³⁺, Mn²⁺和Fe³⁺形成配合物的位置进行了研究, 合成了固体配合物对其进行了元素分析. 实验结果表明过渡金属离子Cr³⁺, Mn²⁺和Fe³⁺与氟喹诺酮类抗菌药物形成1∶2的配合物, 并确定了配位位置.     

水杨醛缩二乙基三胺铜配合物的合成与结构分析

合成了水杨醛缩二乙基三胺 (配体 L,2 - [(N- Salicylideneamino) ethyl]amine)与 Cu( )形成的配合物[Cu L(H2 O) ]Cl,通过元素分析、红外光谱、X射线单晶衍射进行了结构分析。配合物为单斜晶系 ,空间群P2 (1) / c,晶体学结构数据 ,a=0 .912 3(5 ) nm,b=1.382 1(7) nm,c=1.0 82 9(5 ) nm,β=10 1.712 (7)°,V=1.336 9(11) nm3 ,Z=4 ,Dcalcd=1.6 0 6 mg/ m3 ,F(0 0 0 ) =6 6 8,R1=0 .0 377,w R2 =0 .10 18。结构分析表明 ,配合物通过氢键形成二聚结构     

二正丁基锡三齿酰腙Schiff碱配合物的合成和红外光谱研究

合成了 4种三齿酰腙Schiff碱配体H2 L [H2 L1 :C6 H5C(O)NHN =CHC6 H4OH 2 ,H2 L2 :C6 H5C(O)NHN =CHC6 H3(OH) 2 2 ,4,H2 L3:NC5H4C(O)NHN =CHC6 H4OH 2 ,H2 L4:NC5H4C(O)NHN =CHC6 H3(OH) 2 2 ,4]和它们的二正丁基锡新型配合物 (n Bu) 2 SnL ,通过元素分析确定了这些配合物的组成 ,并对配合物在 4 0 0 0～ 40 0cm- 1范围内的主要红外光谱吸收峰进行了归属和讨论 ,推测出配合物可能的分子结构。