A note on minimum distance estimates

It is shown that minimum distance estimates enjoy the invariance property of maximum likelihood estimates. Supported under Grant No. 18-2773 of the American University of Beirut.     

Cooperative two-photon resonance fluorescence of a three-level atom

We have calculated the Green function describing the physical process where a three level atom interacts with a strong pump field as well as with a weak perturbing signal field in the limit of high photon densities. The theory is then used to describe the cooperative two-photon resonance fluorescence which occurs when the sum of the two atomic transition frequencies is nearly twice the frequency of the pump field. Our atomic system is equivalent to a two-level atom when the degeneracy of the ground state is removed by a Stark field. The excitation spectrum has been found to consist of new bands and sidebands which exist only in the presence of the Stark field. The resonance process which occurs when the Stark splitting is in the neighbourhood of the energy shift induced by the laser field has been discussed in detail.     

Unsolvability of binary forms

A property of a binary unit is obtained which is invariant in all number fields of fixed degree n, n ≥ 3. This property is then used to formulate a necessary condition for the solvability of a binary form.     

Resonance fluorescence spectrum of a three-level atom. II. Numerical results

Numerical computations are presented for the excitation spectra arising from the interaction between a three-level atom in the cascade configuration and a strong electromagnetic field whose frequency mode is initially populated. The excitation spectra are considered when the laser field is at resonance with the equally spaced levels of the atom as well as a function of the detunings. The physical process of optical amplification occurs without population inversion and it is more pronounced when the laser field is detuned than when it is at resonance. The shapes of the spectral lines for a number of side-bands are of the absorption-amplification type rather than that of the absorption one. In the presence of detunings as well as in the cooperative two-photon cascade process, the resulting spectra are far more complicated than those occuring at resonance. Results of numerical calculations for a wide range of Rabi frequencies and detunings are presented graphically.     

Performance optimisation of a new-generation orthogonal-acceleration quadrupole-time-of-flight mass spectrometer

Orthogonal-acceleration quadrupole time-of-flight (oa-QTOF) mass spectrometers, employed for accurate mass measurement, have been commercially available for well over a decade. A limitation of the early instruments of this type was the narrow ion abundance range over which accurate mass measurements could be made with a high degree of certainty. Recently, a new generation of oa-QTOF mass spectrometers has been developed and these allow accurate mass measurements to be recorded over a much greater range of ion abundances. This development has resulted from new ion detection technology and improved electronic stability or by accurate control of the number of ions reaching the detector. In this report we describe the results from experiments performed to evaluate the mass measurement performance of the Bruker micrOTOF-Q, a member of the new-generation oa-QTOFs. The relationship between mass accuracy and ion abundance has been extensively evaluated and mass measurement accuracy remained stable (+/-1.5 m m/z units) over approximately 3-4 orders of magnitude of ion abundance. The second feature of the Bruker micrOTOF-Q that was evaluated was the SigmaFit function of the software. This isotope pattern-matching algorithm provides an exact numerical comparison of the theoretical and measured isotope patterns as an additional identification tool to accurate mass measurement. The smaller the value, the closer the match between theoretical and measured isotope patterns. This information is then employed to reduce the number of potential elemental formulae produced from the mass measurements. A relationship between the SigmaFit value and ion abundance has been established. The results from the study for both mass accuracy and SigmaFit were employed to define the performance criteria for the micrOTOF-Q. This provided increased confidence in the selection of elemental formulae resulting from accurate mass measurements.     

Random sequential adsorption of line segments with a finite jamming limit

The traditional formulation for random sequential adsorption (RSA) of line segments onto a plane does not possess a jamming limit; there is always space for a 1D object on a 2D plane. We propose a qualitatively different RSA formulation for line segments which does lead to a finite jamming limit, 1.5707+/-0.0001 segments per square one segment on the side. To our knowledge, this is the first appearance of the number pi in the jamming limit of an RSA problem. This RSA formulation can be applied to adsorption of rigid, very high aspect ratio rods on a flat surface. These rods are not well modeled by the traditional RSA formulation. As an example of such a problem we describe the deposition of carbon nanotube-DNA hybrids on a surface and show that our theoretical formulation is consistent with experimental results.     

Observation of O-H...N scalar coupling across a hydrogen bond in nocathiacin I

We report here the observation of O-H...N hydrogen-bond (1h)J(N,OH) scalar coupling in a biologically active natural product. The intramolecular hydrogen bond between the threonine hydroxyl (Thr-OH) group and the thiazolyl nitrogen at the second thiazole ring (Thz-2) in nocathiacin I was directly detected by a 1H-15N HMBC NMR experiment. The magnitude of the scalar coupling constant (1h)J(N,OH) was accurately measured to be 1.8 +/- 0.1 Hz by a J-resolved 1H-15N HMBC experiment. By adding the O-H...N distance restraint, the 3D solution structure of nocathiacin I was refined. The structure refinement indicated that the distance between the Thr-3 hydroxyl hydrogen and the Thz-2 nitrogen is or= 0.23 A. The presence of an intramolecular hydrogen bond in nocathiacin I is further supported by a number of NMR parameters and additional NMR experiments. This observation provides valuable information for characterizing molecular conformations, and for studying structure-activity relationships.     

In-drop derivatisation liquid-phase microextraction assisted by ion-pairing transfer for the gas chromatographic determination of phenolic endocrine disruptors

A novel in-drop derivatisation liquid-phase microextraction procedure with an ion-pairing agent is developed and optimised for the extraction of endocrine-disrupting chemicals. The ethyl esters of the analytes were rapidly formed in the organic drop and analysed by gas chromatography. The effects of various parameters such as rate and time of agitation, ion-pairing agent and reactant concentration, pH and temperature were studied systematically to optimise the process and bring out the locale of reaction in the organic drop. A study of the mechanistic pathways of the overall procedure is attempted leading to interesting findings and delineating important points of the kinetics and mechanism. A mechanistic model is proposed on the basis of the theory of mass transfer with chemical reaction in two liquid phases. The O-ethoxycarbonyl derivatisation appears to take place in the bulk organic phase. The system provides insight into the first reported analytical case of single-drop extraction-preconcentration-derivatisation assisted by an ion-pairing transfer and has all of the interesting facets of chemical reaction in which the role of mass transfer comes into picture.The analytical features of the method are acceptable and the overall relative standard deviations of the intra-day repeatability (n = 5) and inter-day reproducibility were <3.9% and <5.4%, respectively, for gas chromatography-mass spectrometry analyses and <4.3% and <7.1% for gas chromatography-flame ionisation detection analyses. The method was applicable to urine and surface water samples. The LODs ranged between 0.2-1.3 ng mL⁻¹ and 8.5-26.5 ng mL⁻¹ for GC/MS and GC/FID analyses, respectively.     

Resonant generation of surface acoustic waves between moving and stationary piezoelectric crystals

The propagation of surface acoustic waves in a system composed of two piezoelectric crystals moving with respect to each other and separated by a vacuum gap is considered. The waves are localized on different sides of the gap and coupled only through the electrostatic interaction. It is shown that when the velocity of the relative motion of crystals is close to some value, there occurs a wave instability resulting in a resonant generation of these surface waves. The rate of growth of Bleustein-Gulyaev waves in piezoelectric crystals of 6mm symmetry class is determined analytically.