Hankel operators that commute with second-order differential operators

Suppose that Γ is a continuous and self-adjoint Hankel operator on L²(0,∞) with kernel ?(x+y) and that with a(0)=0. If a and b are both quadratic, hyperbolic or trigonometric functions, and ? satisfies a suitable form of Gauss's hypergeometric differential equation, or the confluent hypergeometric equation, then ΓL=LΓ. The paper catalogues the commuting pairs Γ and L, including important cases in random matrix theory. There are also results proving rapid decay of the singular numbers of Hankel integral operators with kernels that are analytic and of exponential decay in the right half-plane.     

Displacement Convexity for the Generalized Orthogonal Ensemble

Journal of Statistical Physics - The generalized orthogonal ensemble of n × n real symmetric matrices X has probability measure $\nu _n \left( {dX} \right) = Z_n^{ - 1} \exp \left\{ { -...     

Small coordination complexes as radiopharmaceuticals for cancer targeting

Transition Metal Chemistry -     

Hypoxia-targeting copper bis(selenosemicarbazone) complexes: comparison with their sulfur analogues

The first copper bis(selenosemicarbazone) complexes have been synthesized, using the ligands glyoxal bis(selenosemicarbazone), pyruvaldehyde bis(selenosemicarbazone), and 2,3-butanedione bis(selenosemicarbazone). Their spectroscopic properties indicate that they are structurally analogous to their well-known square-planar sulfur-containing counterparts, the copper bis(thiosemicarbazone) complexes. Spectroscopic comparison of the sulfur- and selenium-containing complexes provides insight into their electronic structure. The effects on spectroscopic and redox properties of replacing sulfur with selenium, and of successive addition of methyl groups to the ligand backbone, are rationalized in terms of their electronic structure using spin-unrestricted density functional calculations. These suggest that, like the sulfur analogues, the complexes have a very low-lying empty ligand-based pi-orbital immediately above the LUMO, while the LUMO itself has d(x2)-(y2) character (i.e., is the spin partner of the HOMO). Replacement of S by Se shifts the oxidation potentials much more than the reduction potentials, whereas alkylation of the ligand backbone shifts the reduction potentials more than the oxidation potentials. This suggests that oxidation and reduction involve spatially different orbitals, with the additional electron in the reduced species occupying the ligand-based pi-orbital rather than d(x2)-(y2). Density functional calculations on the putative singlet Cu(I)-reduced species suggest that this ligand pi-character could be brought about by distortion away from planarity during reduction, allowing the low-lying ligand pi-LUMO to mix into the d(x2)-(y2)-based HOMO. The analogy in the structure and reduction behavior between the sulfur- and selenium-containing complexes suggests that labeled with positron emitting isotopes of copper (Cu-60, Cu-62, Cu-64), the complexes warrant biological evaluation as radiopharmaceuticals for imaging of tissue perfusion and hypoxia.     

LeadScope: software for exploring large sets of screening data

Modern approaches to drug discovery have dramatically increased the speed and quantity of compounds that are made and tested for potential potency. The task of collecting, organizing, and assimilating this information is a major bottleneck in the discovery of new drugs. We have developed LeadScope a novel, interactive computer program for visualizing, browsing, and interpreting chemical and biological screening data that can assist pharmaceutical scientists in finding promising drug candidates. The software organizes the chemical data by structural features familiar to medicinal chemists. Graphs are used to summarize the data, and structural classes are highlighted that are statistically correlated with biological activity.     

Trithiacyclononane as a ligand for potential technetium and rhenium radiopharmaceuticals: synthesis of [M(9S3)(SC2H4SC2H4S)][BF4] (M = 99Tc, Re, 188Re) via C-S bond cleavage

Chemical or electrochemical reduction of the 1,4,7-trithiacyclononane (9S3) complexes [MII(9S3)2][BF4]2 (M = Re (3a) or Tc (3b)) results in instantaneous C-S bond cleavage to yield ethene and the stable MIII thiolate complexes [MIII(9S3)L][BF4] (M = Re (4a) or Tc (4b), L = SCH2CH2SCH2CH2S). Compounds 4 have been characterized by 1H NMR spectroscopy, and the pseudo-octahedral geometry of 4b has been confirmed by X-ray crystallography. Upon electrochemical reduction 4a loses ethene, while 4b can be reversibly reduced to [TcII(9S3)L], which is then further reduced to Tc(I) with loss of ethene. Successive ethene loss is observed in the mass spectra of compounds 3 and 4. The radiosynthesis of 4a with 188Re can be comfortably completed within 10 min starting with 188ReO4- from a 188W/188Re generator, with a radiochemical yield in excess of 90%, and thus represents a practical approach to the preparation of stable 188Re (and 99mTc) thioether complex derivatives/conjugates for clinical use. Crystal data: 4b, C10H20S6Tc, orthorhombic Pbca, a = 12.233(2) A, b = 14.341(2) A, c = 20.726(3) A, Z = 8.     

离心压缩机弯道最佳r/b值研究

本文将叶轮、无叶扩压器和弯道组合一起对弯道进行研究,充分考虑了叶轮出口的射流/尾迹结构对弯道进口气流的影响.通过对不同弯道半径r与流道宽度b的比值r/b条件下,数值研究其对离心压缩机基本级气动性能的影响.对弯道内部流动及r/b值变化与离心压缩机级的总体性能的变化关系进行详细的对比分析.研究结果表明:r/b值的变化对弯道出口气流角影响显著,并存在一个使级效率为最大值的最佳r/b值。壁面摩擦是引起弯道内部总压损失的主要因素。