There are infinitely many limit points of the fractional parts of powers

Suppose that α > 1 is an algebraic number and ξ > 0 is a real number. We prove that the sequence of fractional partsξα ⁿ , n = 1, 2, 3, …, has infinitely many limit points except when α is a PV-number and ξ ∈ ℚ(α). For ξ = 1 and α being a rational non-integer number, this result was proved by Vijayaraghavan.     

On the distribution of the number of customers in the symmetric M/G/1 queue

We consider an M/G/1 queue with symmetric service discipline. The class of symmetric service disciplines contains, in particular, the preemptive last-come-first-served discipline and the processor-sharing discipline. It has been conjectured in Kella et al. [1] that the marginal distribution of the queue length at any time is identical for all symmetric disciplines if the queue starts empty. In this paper we show that this conjecture is true if service requirements have an Erlang distribution. We also show by a counterexample, involving the hyperexponential distribution, that the conjecture is generally not true. AMS Subject Classifications Primary—60K25; Secondary—90B22     

Effect of transverse object position on the reconstructed image of an aperture-limited in-line hologram

It is experimentally demonstrated that the image resolution from an in-line Fraunhofer hologram degrades appreciably when the centre of the diffraction pattern from a 5-bar resolution target is located asymmetrically in the hologram aperture. This effect is confirmed and analysed using calculated and experimentally measured images from holograms of a one-dimensional wire. Increasing asymmetry results in an increasing error in the measured linewidth, and a reduction of image resolution. A simple model based on average fringe contrast is used to predict this decrease in resolution with transverse object position.     

Electroencephalogram (EEG) time series classification: Applications in epilepsy

Epilepsy is among the most common brain disorders. Approximately 25–30% of epilepsy patients remain unresponsive to anti-epileptic drug treatment, which is the standard therapy for epilepsy. In this study, we apply optimization-based data mining techniques to classify the brain's normal and epilepsy activity using intracranial electroencephalogram (EEG), which is a tool for evaluating the physiological state of the brain. A statistical cross validation and support vector machines were implemented to classify the brain's normal and abnormal activities. The results of this study indicate that it may be possible to design and develop efficient seizure warning algorithms for diagnostic and therapeutic purposes. Research was partially supported by the Rutgers Research Council grant-202018, the NSF grants DBI-980821, CCF-0546574, IIS-0611998, and NIH grant R01-NS-39687-01A1.     

Characteristics of vinyl iodide microwave plasma etching of GaAs/AlGaAs and InP/InGaAs heterostructures

Vinyl iodide (C₂H₃I) microwave discharges with additions of H₂ and Ar are found to provide faster etch rates than conventional CH₄/H₂/Ar discharges for InP, InGaAs, GaAs, and AlGaAs. This is a result of the relatively high volatilities of indium, gallium, and aluminum iodide species. The etched features are smooth and anisotropic over a wide range of do self-biases (–150 to –350 V), process pressures (1–20mTorr), and microwave powers (150–500 W). The polymer that forms on the mask during the plasma exposure can be readily removed in O₂ discharges. Electron spectroscopy for chemical analysis (ESCA) showed that the etched surfaces are slightly deficient in the group V elements under most conditions, but changes to the optical properties of the semiconductors are minimal. No defects are visible by transmission electron microscopy (TEM) in GaAs or InP samples etched at dc biases –250 V.     

Oxidation of ferrocene and some substituted ferrocenes in the presence of horseradish peroxidase

The enzyme catalysed oxidation of ferrocene and some substituted ferrocenes to the corresponding ferricinium ions by hydrogen peroxide in the presence of native or immobilized horseradish peroxidase has been studied. Initial and maximum rates of oxidation have been determined. It was found that the oxidation was independent of the hydrogen peroxide concentration. The oxidation of ferrocene was effected also by horseradish peroxidase in a coupled system with glucose oxidase in the absence of any added hydrogen peroxide.     

Separation and identification of organic acid-coenzyme A thioesters using liquid chromatography/electrospray ionization-mass spectrometry

A method has been developed for the direct determination of coenzyme A (CoA) and organic acid-CoA thioesters in mixtures using directly combined liquid chromatography/electrospray ionization-mass spectrometry (LC/ESI-MS). Mixtures of CoA and organic acid-CoA thioesters were analyzed by LC/ESI-MS with detection of protonated molecular ions and characteristic fragment ions for each compound. The identities of the CoA-thioesters were established based on LC retention times and simultaneously recorded mass spectra. Monitoring of the CoA specific fragment ion at m/z 428 throughout the chromatogram provides a unique fingerprint for CoA content in the samples that corroborates the identification of organic acid-CoA thioesters in the mixtures. Furthermore, fragment ions arising from the ester linkage portion of the molecule allow unambiguous identification of the CoA esters in the samples. A second LC elution system was developed that allows the simultaneous separation and identification of 2-hydroxypropionyl-CoA (lactyl-CoA) and 3-hydroxypropionyl CoA (3HP-CoA), which have the same mass and identical MS fragmentation behavior. The utility of LC/ESI-MS employing this elution system is demonstrated by the determination of 3HP-CoA and lactyl-CoA (converted to CoA-thioesters from their corresponding free acids using CoA-transferase) in fermentation broths from Escherichia coli strains engineered for the production of 3-hydroxypropionic acid (3HP). External calibration employing a purified 3HP-CoA standard allowed indirect quantification of 3HP content in the broth with a precision of 1% (RSD). The feasibility of extending the method described above to perform LC/selected reaction monitoring-tandem mass spectrometry for direct determination of organic acid-CoA thioesters in cells was also demonstrated.     

Hybrid electron cyclotron resonance-radio-frequency plasma etching of III–V semiconductors in Cl2-based discharges. Part I: GaAs and related compounds

A systematic study has been performed of the dry etching characteristics of GaAs, Al_0.3Ga_0.7As, and GaSb in chlorine-based electron cyclotron resonance (ECR) discharges. The gas mixtures investigated were CCl₂F₂/O₂, CHCl₂F/O₂, and PCl₃. The etching rates of all three materials increase rapidly with applied RF power, while the addition of the microwave power at moderate levels (150 W) increases the etch rates by 20–80%. In the microwave discharges, the etch rates decrease with increasing pressure, but at 1 m Torr it is possible to obtain usable rates for self-bias voltages 100 V. Of the Freon-based mixtures, CHCl₂F provides the least degradation of optical (photoluminescence) and electrical (diode ideality factors and Schottky barrier heights) properties of GaAs as a result of dry etching. Smooth surface morphologies are obtained on all three materials provided the microwave power is limited to 200 W. Above this power, there is surface roughening evident with all of the gas mixtures investigated.     

Dry etching of InGaP and AlInP in CH4/H2/Ar

Electron cyclotron resonance (ECR) plasma etching with additional rf-biasing produces etch rates 2,500 A/min for InGaP and AlInP in CH₄/H₂/Ar. These rates are an order of magnitude or much higher than for reactive ion etching conditions (RIE) carried out in the same reactor. N₂ addition to CH₄/H₂/Ar can enhance the InGaP etch rates at low flow rates, while at higher concentrations it provides an etch-stop reaction. The InGaP and AlInP etched under ECR conditions have somewhat rougher morphologies and different stoichiometries up to 200 Å from the sur face relative to the RIE samples.