On the convexity of numerical range in quaternionic hilbert spaces

Let A be a bounded linear operator in a quaternionic Hilberi space (H,(·,·)). The numerical range of A is defined to be the set W (A)={( Au, u): u ε H, (u,u) = 1}. Quite different from the complex caseW (A) may not be convex. In this note the author proves that W (A) is convex if and only if R ∩ W (A) = {Req : q ε W(A)}. where R is the real field and Re q denotes the real part of the quaternion q. For a normal operator A in a finite dimensional space H, the author gives a characterization on the convexity of W(A) in terms of ihe eigenvalues of A and also proves that the generalized numerical range of A is convex if and only if A is Hermitian.     

Unusual iron(II) and cobalt(II) complexes derived from monodentate arylamido ligands

The coordination chemistry of the N-substituted arylamido ligands [N(R)(C6H3R'2-2,6)] [R = SiMe3, R' = Me (L1); R = CH2But, R' = Pri (L2)] toward FeII and CoII ions was studied. The monoamido complexes [M(L1)(Cl)(tmeda)] [M = Fe (1), Co (2)] react readily with MeLi, affording the mononuclear, paramagnetic iron(II) and cobalt(II) methyl-arylamido complexes [M(L1)(Me)(tmeda)] [M = Fe (3), Co (4)]. Treatment of 2:1 [Li(L2)(THF)2]/FeCl2 affords the unusual two-coordinate iron(II) bis(arylamide) [Fe(L2)2] (5).     

Distinctive features and challenges in catenane chemistry

From being an aesthetic molecular object to a building block for the construction of molecular machines, catenanes and related mechanically interlocked molecules (MIMs) continue to attract immense interest in many research areas. Catenane chemistry is closely tied to that of rotaxanes and knots, and involves concepts like mechanical bonds, chemical topology and co-conformation that are unique to these molecules. Yet, because of their different topological structures and mechanical bond properties, there are some fundamental differences between the chemistry of catenanes and that of rotaxanes and knots although the boundary is sometimes blurred. Clearly distinguishing these differences, in aspects of bonding, structure, synthesis and properties, between catenanes and other MIMs is therefore of fundamental importance to understand their chemistry and explore the new opportunities from mechanical bonds.

Catenane chemistry is closely associated with that of rotaxane and knot, and this perspective highlights their similarities and differences in various aspects including synthesis, structure and properties.     

A Combined Experimental and Theoretical Study of the Versatile Reactivity of an Oxocerium(IV) Complex: Concerted Versus Reductive Addition

A combined experimental and theoretical investigation on the cerium(IV) oxo complex [(L_OEt)₂Ce(=O)(H₂O)] ⋅ MeC(O)NH₂ ( 1 ; L_OEt⁻=[Co(η⁵-C₅H₅){P(O)(OEt)₂}₃]⁻) demonstrates that the intermediate spin-state nature of the ground state of the cerium complex is responsible for the versatility of its reactivity towards small molecules such as CO, CO₂, SO₂, and NO. CASSCF calculations together with magnetic susceptibility measurements indicate that the ground state of the cerium complex is of multiconfigurational character and comprised of 74 % of Ce^IV and 26 % of Ce^III. The latter is found to be responsible for its reductive addition behavior towards CO, SO₂, and NO. This is the first report to date on the influence of the multiconfigurational ground state on the reactivity of a metal–oxo complex.     

Quantitative determination of glucose in blood plasma by homonuclear proton decoupled water attenuation transverse relaxation Carr-Purcell-Meiboom-Gill (WATR-HDCPMG) NMR spectroscopy

Glucose in 5% D₂O/95% H₂O solution was successfully determined quantitatively by measurements of the ¹H NMR peak height (intensity) of the single peaks at δ(¹H) = 5.22 and 4.64 ppm corresponding to the α-D and the β-D-glucose spectrum, respectively. The single peaks were obtained from decoupling of the high field part of the AX spectrum of the α-D- or the β-D-glucose by incorporation of time shared homonuclear decoupling in the WATR-CPMG method (WATR-HDCPMG) without re-attenuation of the water peak. The method was applied to the determination of total glucose in blood plasma from human subjects undergoing oral glucose tolerance test (OGTT) in the teaching hospital. The results compared favorably with those obtained from the standard glucose oxidase method obtained in a hospital pathology laboratory. The accuracy of the results obtained using the WATR-HDCPMG method was within 3.5% of the glucose oxidation method. Received: 5 January 1998 / Revised: 23 February 1998 / Accepted: 26 February 1998     

Some inequalities for the rational power of a nonnegative definite matrix

In this note the author gives a simple proof of the following fact: Let r and s be two positive rational numbers such that r ? s and let A and B be two n × n non-negative definite Hermitian matrices such that A^r ? B^r. Then A^S ? B^s.     

过渡金属核磁共振谱

以数种过渡金属的核磁共振研究介绍了有关技术在近年的发展;内容集中于如何从图谱取得化学信息。讨论分为固体谱与液体谱两部分,固体谱会着重谱线的分析,液体谱则集中对有关化学位移的理论解释。     

Dynamic combinatorial donor-acceptor catenanes in water: access to unconventional and unexpected structures

We describe here the assembly of new types of donor-acceptor [2]catenanes from dynamic combinatorial libraries (DCL) in water. These new catenanes contain both the donor and acceptor components in at least one of the interlocked rings, thereby possessing unusual and unexpected DAAD or DADD stacking sequences of the π units in their structures. The efficiency of the catenane assembly process can be enhanced by manipulating the DCL equilibrium in a variety of ways: adding a guest, changing the building block stoichiometries, or increasing the library concentration or the ionic strength of the solvent. The formation of catenanes and their constitutions are found to be dependent on subtle differences in the geometry, dimension, and flexibility of the donor building blocks.