On a Two-Variable Class of Bernstein–Szegő Measures

The one-variable Bernstein–Szegő theory for orthogonal polynomials on the real line is extended to a class of two-variable measures. The polynomials orthonormal in the total degree ordering and the lexicographical ordering are constructed and their recurrence coefficients discussed.      

Near holomorphy of some automorphic forms at critical points

Oblatum 1-IV-1989 &; 27-IX-1989     

Performance of lateral vorticity probe in a turbulent wake

A useful experimental check of the accuracy of measured lateral vorticity components is provided by comparing the vorticity-velocity cross products with the lateral derivative of the Reynolds shear stress. The check has been carried out in the self-preserving turbulent wake of a cylinder.     

Vorticity characteristics of the turbulent intermediate wake

Measurements of the lateral components _j (j=2 and 3) of the vorticity fluctuation vector have been made, using a vorticity probe consisting of two X-wires, in the intermediate wake of a circular cylinder. The effect of the spatial resolution of the probe on the measurement of _j has been studied. As the spatial resolution impairs, the variance and flatness factor of _j decrease whereas the skewness of _j increases. Reasonably accurate values of _j ² can be obtained by applying spectral corrections for the spatial resolution effect.Near the beginning of the intermediate wake, the variance of ₂ is larger than that of ₃ due to the significant contribution from ribs which connect consecutive spanwise roll vortices. This difference decreases with downstream distance. Also, the presence of the rolls is reflected by a local extremum in the skewness of ₃ on each side of the wake centerline. The magnitude of the extremum decreases with downstream distance.The support of the Australian Research Council is gratefully acknowledged.     

Effect of different initial conditions on a turbulent round free jet

Velocity measurements were made in two jet flows, the first exiting from a smooth contraction nozzle and the second from a long pipe with a fully developed pipe flow profile. The Reynolds number, based on nozzle diameter and exit bulk velocity, was the same (䏪,000) in each flow. The smooth contraction jet flow developed much more rapidly and approached self-preservation more rapidly than the pipe jet. These differences were associated with differences in the turbulence structure in both the near and far fields between the two jets. Throughout the shear layer for x<3d, the peak in the v spectrum occurred at a lower frequency in the pipe jet than in the contraction jet. For x́d, the peaks in the two jets appeared to be nearly at the same frequency. In the pipe jet, the near-field distributions of f(r) and g(r), the longitudinal and transverse velocity correlation functions, differed significantly from the contraction jet. The integral length scale L_u was greater in the pipe jet, whereas L_v was smaller. In the far field, the distributions of f(r) and g(r) were nearly similar in the two flows. The larger initial shear layer thickness of the pipe jet produced a dimensionally lower frequency instability, resulting in longer wavelength structures, which developed and paired at larger downstream distances. The regular vortex formation and pairing were disrupted in the shear layer of the pipe jet. The streamwise vortices, which enhance entrainment and turbulent mixing, were absent in the shear layer of the pipe jet. The formation of large-scale structures should occur much farther downstream in the pipe jet than in the contraction jet.     

The effect of Reynolds number on a turbulent far-wake

The turbulent far-waked generated by a circular cylinder is investigated for two values (1350 and 4600) of the Reynolds number Re _θ (based on the free stream velocity and the momentum thickness). Two arrays of sixteen X-wires, eight in the (x,?y)-plane and eight in the (x,?z)-plane, are used to capture the main features of the large-scale motion in two orthogonal planes. Both the magnitude of the measured Reynolds stresses and the size of the two-point velocity and vorticity correlation contours increase with Reynolds number. The probability density function and spectra of the velocity signals also exhibit differences with Re _θ. A comparison of centerline turbulence intensities with those in the literature suggests that the Reynolds number dependence may disappear for Re _θ?5000.     

A Highly Versatile Catalyst System for the Cross‐Coupling of Aryl Chlorides and Amines

The syntheses of 2‐(di‐tert‐butylphosphino)‐N,N‐dimethylaniline ( L1 , 71 %) and 2‐(di‐1‐adamantylphosphino)‐N,N‐dimethylaniline ( L2 , 74 %), and their application in Buchwald–Hartwig amination, are reported. In combination with [Pd(allyl)Cl]₂ or [Pd(cinnamyl)Cl]₂, these structurally simple and air‐stable P,N ligands enable the cross‐coupling of aryl and heteroaryl chlorides, including those bearing as substituents enolizable ketones, ethers, esters, carboxylic acids, phenols, alcohols, olefins, amides, and halogens, to a diverse range of amine and related substrates that includes primary alkyl‐ and arylamines, cyclic and acyclic secondary amines, N? H imines, hydrazones, lithium amide, and ammonia. In many cases, the reactions can be performed at low catalyst loadings (0.5–0.02 mol % Pd) with excellent functional group tolerance and chemoselectivity. Examples of cross‐coupling reactions involving 1,4‐bromochlorobenzene and iodobenzene are also reported. Under similar conditions, inferior catalytic performance was achieved when using Pd(OAc)₂, PdCl₂, [PdCl₂(cod)] (cod=1,5‐cyclooctadiene), [PdCl₂(MeCN)₂], or [Pd₂(dba)₃] (dba=dibenzylideneacetone) in combination with L1 or L2 , or by use of [Pd(allyl)Cl]₂ or [Pd(cinnamyl)Cl]₂ with variants of L1 and L2 bearing less basic or less sterically demanding substituents on phosphorus or lacking an ortho‐dimethylamino fragment. Given current limitations associated with established ligand classes with regard to maintaining high activity across the diverse possible range of C? N coupling applications, L1 and L2 represent unusually versatile ligand systems for the cross‐coupling of aryl chlorides and amines.     

Development of fast screening methods for the analysis of veterinary drug residues in milk by liquid chromatography-triple quadrupole mass spectrometry

Two rapid multi-residue screening methods for the determination of 21 veterinary drugs in milk by ultra-high-performance liquid chromatography-tandem mass spectrometry (UHPLC-MS/MS) have been developed and compared. For both methods, veterinary drugs were extracted from milk samples using a rapid extraction procedure based on the modification of the well-known QuEChERS (Quick, Easy, Cheap, Effective, Rugged, and Safe) method, and no further clean-up steps were necessary. One screening method was based on the selection of a characteristic neutral loss or product ion of the various families of compounds, whereas another one was based on the choice of a selected reaction monitoring (SRM) for each compound. These methods were compared with regards to false negatives, cut-off values and the unreliability region. The total run time for both methods was 3 min, allowing quick selection of samples that contained veterinary drugs. Non-negative samples were re-analyzed by the UHPLC-MS/MS confirmation/quantification method, which consisted in the monitoring of two SRM for each compound. The methods were validated according to international guides. The proposed analytical methods allow for the identification and confirmation of the target veterinary drugs at trace levels employing quick analysis time.     

Application of a quick,easy, cheap,effective, rugged and safe-based method for the simultaneous extraction of chlorophenols,alkylphenols, nitrophenols and cresols in agricultural soils,analyzed by using gas chromatography–triple quadrupole-mass spectrometry/mass spectrometry

Due to the different physico-chemical properties of phenols, the development of a methodology for the simultaneous extraction and determination of phenolic compounds belonging to several families, such as chlorophenols (CPs), alkylphenols (APs), nitrophenols (NTPs) and cresols is difficult. This study shows the development and validation of a method for the analysis of 13 phenolic compounds (including CPs, APs, NTPs and cresols) in agricultural soils. For this purpose, a quick, easy, cheap, effective, rugged and safe (QuEChERS)-based procedure was developed, validated and applied to the analysis of real samples. A derivatization step prior to the final determination by gas chromatography (GC) coupled to a triple quadrupole analyzer operating in tandem mass spectrometry (QqQ-MS/MS) was performed by using acetic acid anhydride (AAA) and pyridine (Py). The optimized procedure was validated, obtaining average extraction recoveries in the range 69–103% (10 μg kg⁻¹), 65–98% (50 μg kg⁻¹), 76–112% (100 μg kg⁻¹) and 76–112% (300 μg kg⁻¹), with precision values (expressed as relative standard deviation, RSD) ≤ 22% (except for 4-chlorophenol) involving intra-day and inter-day studies. Furthermore, 15 real soil samples were analyzed by the proposed method in order to assess its applicability. Some phenolic compounds (e.g. 2,4,6-trichlorophenol or 4-tert-octylphenol) were found in the samples at trace levels (<10 μg kg⁻¹).     

Dysregulation of chemo-cytokine production in schizophrenic patients versus healthy controls

Background  

The exact cause of schizophrenia is not known, although several aetiological theories have been proposed for the disease, including developmental or neurodegenerative processes, neurotransmitter abnormalities, viral infection and immune dysfunction or autoimmune mechanisms. Growing evidence suggests that specific cytokines and chemokines play a role in signalling the brain to produce neurochemical, neuroendocrine, neuroimmune and behavioural changes. A relationship between inflammation and schizophrenia was supported by abnormal cytokines production, abnormal concentrations of cytokines and cytokine receptors in the blood and cerebrospinal fluid in schizophrenia. Since the neuropathology of schizophrenia has recently been reported to be closely associated with microglial activation we aimed to determined whether spontaneous or LPS-induced peripheral blood mononuclear cell chemokines and cytokines production is dysregulated in schizophrenic patients compared to healthy subjects. We enrolled 51 untreated first-episode schizophrenics (SC) and 40 healthy subjects (HC) and the levels of MCP-1, MIP-1α, IL-8, IL-18, IFN-γ and RANTES were determined by Elisa method in cell-free supernatants of PBMC cultures.