The limiting distributions of large heavy Wigner and arbitrary random matrices

A heavy Wigner matrix $X_N$ is defined similarly to a classical Wigner one. It is Hermitian, with independent sub-diagonal entries. The diagonal entries and the non-diagonal entries are identically distributed. Nevertheless, the moments of the entries of $\sqrt{N}{X}_N$ tend to infinity with N, as for matrices with truncated heavy tailed entries or adjacency matrices of sparse Erdös–Rényi graphs. Consider a family ${\mathbf{X}}_N$ of independent heavy Wigner matrices and an independent family ${\mathbf{Y}}_N$ of arbitrary random matrices with a bound condition and converging in ^?-distribution in the sense of free probability. We characterize the possible limiting joint ^?-distributions of $({\mathbf{X}}_N,{\mathbf{Y}}_N)$, giving explicit formulas for joint ^?-moments. We find that they depend on more than the ^?-distribution of ${\mathbf{Y}}_N$ and that in general ${\mathbf{X}}_N$ and ${\mathbf{Y}}_N$ are not asymptotically ^?-free. We use the traffic distributions and the associated notion of independence [21] to encode the information on ${\mathbf{Y}}_N$ and describe the limiting ^?-distribution of $({\mathbf{X}}_N,{\mathbf{Y}}_N)$. We develop this approach for related models and give recurrence relations for the limiting ^?-distribution of heavy Wigner and independent diagonal matrices.     

Sulfur monoxide transfer from peri-substituted trisulfide-2-oxides to dienes: substituent effects, mechanistic studies and application in thiophene synthesis

Three peri-substituted trisulfide-2-oxides are prepared by treatment of 1,8-naphthalene dithiols with thionyl chloride and pyridine. The 1,2,3-trithiane-2-oxide ring adopts a sofa conformation in the solid state, with a pseudoaxial oxygen and evidence of ring strain (peri-interaction). Heating the trisulfide-2-oxides in the presence of a diene results in formal sulfur monoxide (SO) transfer to form unsaturated cyclic sulfoxides, along with a recyclable 1,8-naphthalene disulfide. The presence of o-methoxy or o-tert-butyl substituents on the naphthalene ring lowers the temperature and increases the rate at which SO transfer occurs. Trapping experiments and kinetic studies are consistent with the generation of triplet SO, followed by in situ trapping by diene. Transfer of SO also occurs upon irradiation at room temperature, but yields of sulfoxide are lower. Dehydration of the sulfoxides under Pummerer conditions gives thiophenes, including the naturally occurring thioperillene. Two dienes form thiophenes directly under the SO transfer conditions. The methodology is applied in a formal synthesis of the antiplatelet medication Plavix.     

In search of a new class of stable nitroxide: synthesis and reactivity of a peri-substituted N,N-bissulfonylhydroxylamine

Acyclic bissulfonylnitroxides have never been isolated, and degrade through fragmentation. In an approach to stabilising a bissulfonylnitroxide radical, the cyclic, peri-substituted N,N-bissulfonylhydroxylamine, 2-hydroxynaphtho[1,8-de][1,3,2]dithiazine 1,1,3,3-tetraoxide (1), has been prepared by formal nitrogen insertion into the sulfur-sulfur bond of a sulfinylsulfone, naphtho[1,8-cd][1,2]dithiole 1,1,2-trioxide. The heterocyclic ring of 1 is shown to adopt a sofa conformation by X-ray crystallography, with a pseudo-axial hydroxyl group. N,N-Bissulfonylhydroxylamine 1 displays high thermal, photochemical and hydrolytic stability compared to acyclic systems. EPR analysis reveals formation of the corresponding bissulfonylnitroxide 2 upon oxidation of 1 with the Ce(IV) salts CAN and CTAN. Although 2 does not undergo fragmentation, it cannot be isolated, since hydrogen atom abstraction to reform 1 occurs in situ. The stability and reactivity of 1 and 2 are compared with the known cyclic benzo-fused N,N-bissulfonylhydroxylamine, N-hydroxy-O-benzenedisulfonimide (6), for which the X-ray data, and EPR of the corresponding nitroxide 10, are also reported for the first time.     

Magnetic resonance imaging in hemophilic children: value of gradient echo and contrast-enhanced imaging

The purpose of this study was to determine the value of Gradient Echo imaging for the evaluation of cartilage (3D fatsat) and blood products (2D Hemoflash), and the use of contrast enhanced SE imaging for the evaluation of synovial changes, in comparison to the clinical evaluation of children with hemophilia A. We investigated 21 joints in 16 patients with evidence of hemophilia A (mean age 11.3+/-2.1 years). In all patients, clinical examination, plain film radiographs, and MR evaluation were performed magnetic resonance imaging (MRI) was performed by using sagittal T1 SE and T2 SE images, as well as 3D fatsat GE and 2D GE images. Axial and sagittal T1 weighted SE images were obtained before and after contrast application. Findings from the clinical examination and MR imaging, regarding the evaluation of blood, synovia, and cartilage were compared. Clinical examination revealed evidence of a bleeding episode in 12 joints (57.1%), whereas MRI revealed evidence of blood or blood products in 15 joints (71.4%). Clinical investigations, including bleeding scores, pain scores, and physical examination scores did not correlate with MR findings. Due to the MR findings in 6 of 16 patients, therapeutic management was changed from on demand to prophylactic therapy. MR imaging with gradient echo and contrast-enhanced sequences is more sensitive than clinical examination for the detection of blood products in children with hemophilia. Its ability to demonstrate potentially early stages of cartilage or synovial alterations might assist in therapy planning. Clinical scores might underestimate effects of hemophilia.     

Synthesis,Structure, and Electrochemical Properties of Sterically Protected Molybdenum Trihydride Redox Pairs: A Paramagnetic “Stretched” Dihydrogen Complex?

Complexes [MoCp(#)(PMe(3))(2)H(3)] (Cp(#)=1,2,4-C(5)H(2)tBu(3), 2 a; C(5)HiPr(4), 2 b) have been synthesized from the corresponding compounds [MoCp(#)Cl(4)] (1 a, 1 b) and fully characterized, including by X-ray crystallography and by a neutron diffraction study for 2 a. Protonation of 2 a led to complex [Mo(1,2,4-C(5)H(2)tBu(3))(PMe(3))(2)H(4)](+) (3 a) in THF and to [Mo(1,2,4-C(5)H(2)tBu(3))(PMe(3))(2)(MeCN)H(2)](+) (4 a) in MeCN. Complex 4 b analogously derives from protonation of 2 b in MeCN, whereas the tetrahydride complex 3 b is unstable. One-electron oxidation of 2 a and 2 b by [FeCp(2)]PF(6) produces the EPR-active 17-electron complexes 2 a(+) and 2 b(+). The former is thermally more stable than the latter and could be crystallographically characterized as the PF(6) (-) salt by X-ray diffraction, providing evidence for the presence of a stretched dihydrogen ligand (H...H=1.36(6) angstroms). Controlled thermal decomposition of 2 a(+) yielded the product of H(2) elimination, the 15-electron monohydride complex [Mo(1,2,4-C(5)H(2)tBu(3))(PMe(3))(2)H]PF(6) (5 a), which was characterized by X-ray crystallography and by EPR spectroscopy at liquid He temperature. The compound establishes an equilibrium with the solvent adduct in THF. An electrochemical study by cyclic voltammetry provides further evidence for a rapid H(2) elimination process from the 17-electron complexes. In contrast to the previously investigated [MoCp*(dppe)H(3)](+) system (dppe=1,2-bis(diphenylphosphino)ethane; Cp*=pentamethylcyclopentadienyl), the decomposition of 2 a(+) by H(2) substitution with a solvent molecule appears to follow a dissociative pathway in MeCN.     

Precise mass measurement of a double-stranded 500 base-pair (309 kDa) polymerase chain reaction product by negative ion electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry

Electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI-FTICRMS) has been used to determine the mass of a double-stranded 500 base-pair (bp) polymerase chain reaction (PCR) product with an average theoretical mass of the blunt-ended (i.e. unadenylated) species of 308 859.35 Da. The PCR product was generated from the linearized bacteriophage Lambda genome which is a double-stranded template. Utilization of ethanol precipitation in tandem with a rapid microdialysis step to purify and desalt the PCR product was crucial to obtain a precise mass measurement. The PCR product (0.8 pmol/μL) was electrosprayed from a solution containing 75% acetonitrile, 25 mM piperidine, and 25 mM imidazole and was infused at a rate of 200 nL/min. The average molecular mass and the corresponding precision were determined using the charge-states ranging from 172 to 235 net negative charges. The experimental mass and corresponding precision (reported as the 95% confidence interval of the mean) was 309 406 +/- 27 Da (87 ppm). The mass accuracy was compromised due to the fact that the PCR generates multiple products when using Taq polymerase due to the non-template directed 3'-adenylation. This results in a mixture of three PCR products with nearly identical mass (i.e. blunt-ended, mono-adenylated and di-adenylated) with unknown relative abundances that were not resolved in the spectrum. Thus, the experimental mass will be a weighted average of the three species which, under our experimental conditions, reflects a nearly equal concentration of the mono- and di-adenylated species. This report demonstrates that precise mass measurements of PCR products up to 309 kDa (500 bp) can be routinely obtained by ESI-FTICR requiring low femtomole amounts. Copyright 1999 John Wiley & Sons, Ltd.     

A new type of luminescent alkynyl Au4Cu2 cluster

Changes in the optical properties of an alkynyldigold(I) complex upon reaction with Cu(I) are associated with a complicated structural change to form an unusual Au4Cu2 cluster with metallophilic interactions as well as pi-alkyne coordination.     

The norm of polynomials in large random and deterministic matrices

Let ${{\bf X}_N =(X_1^{(N)}, \ldots, X_p^{(N)})}$ be a family of N × N independent, normalized random matrices from the Gaussian Unitary Ensemble. We state sufficient conditions on matrices ${{\bf Y}_N =(Y_1^{(N)}, \ldots, Y_q^{(N)})}$ , possibly random but independent of X _N , for which the operator norm of ${P({\bf X}_N, {\bf Y}_N, {\bf Y}_N^*)}$ converges almost surely for all polynomials P. Limits are described by operator norms of objects from free probability theory. Taking advantage of the choice of the matrices Y _N and of the polynomials P, we get for a large class of matrices the ??no eigenvalues outside a neighborhood of the limiting spectrum?? phenomena. We give examples of diagonal matrices Y _N for which the convergence holds. Convergence of the operator norm is shown to hold for block matrices, even with rectangular Gaussian blocks, a situation including non-white Wishart matrices and some matrices encountered in MIMO systems.     

Rapid access to polycyclic indolines related to the stephacidin alkaloids using a radical cascade

A new and very rapid access to indoline intermediates useful for the synthesis of alkaloids related to the stephacidins has been established using a radical cascade process initiated from a sulphur-substituted diketopiperazine.     

Photo- and Electrochemical Dual-Responsive Iridium Probe for Saccharide Detection

Dual detection systems are of interest for rapid, accurate data collection in sensing systems and in vitro testing. We introduce an Ir^III complex with a boronic acid receptor site attached to the 2-phenylpyridine ligand as an ideal probe with photo- and electrochemical signals that is sensitive to monosaccharide binding in aqueous solution. The complex displays orange luminescence at 618 nm, which is reduced by 70 and 40 % upon binding of fructose and glucose, respectively. The electro-chemiluminescent signal of the complex also shows a direct response to monosaccharide binding. The Ir^III complex shows the same response upon incorporation into hydrogel matrices as in solution, thus demonstrating the potential of its integration into a device, as a nontoxic, simple-to-use tool to observe sugar binding over physiologically relevant pH ranges and saccharide concentrations. Moreover, the complex's luminescence is responsive to monosaccharide presence in cancer cells.