Certain Convolution Operators for Meromorphic Functions

Let (p N) be the class of functions analytic in 0 < |z| < 1. A convolution operator L_p(a, c) on p is introduced. This paper gives some sharp inequalities for f(z) satisfying Re{(1 – )z^pL_p(a, c) f(z) + z^pL_p(a + 1, c) f(z)} > , where 0, < 1, a > 0 and c 0, –1, –2,....AMS Subject Classification (1991) 30C45 30A10     

Nanoscale intrinsic heterogeneities in Ag-Ge-Se glasses and their correlation with physical properties

Ag-Ge-Se glass forming system is dominated by liquid immiscibility. Glasses in the Se-GeSe₂-Ag₂Se triangle may have different morphologies according to their composition. In this work inhomogeneous morphology is observed in Ag_x(Ge_ySe_1−y)_100−x bulk glasses with y = 0.20, 0.25 at.% fraction. Electron microscopy reveals that the scale of heterogeneity strongly depends on the sample composition. The physical properties of these glasses are also dependent on their composition and can be easily correlated to their morphology. Accordingly, the electric conductivity evolves from semiconducting to ionic conductivity whereas a percolation transition occurs in a narrow Ag concentration range.Mössbauer spectrometry let us to analyse the local order of these intrinsically heterogeneous glasses employing ⁵⁷Fe as a probe.     

Radiation attenuation and nuclear properties of high density concrete made with steel aggregates

Abstract

The fast neutron and gamma ray spectra measured behind different thickness of steel scrap concrete with density of 4 g/cm³ have been studied. The mix proportions by weight of this type of concrete were 1 cement: 6.89 steel scrap: 2.9 sand and 0.5 Water. Comparison with a standard ordinary concrete of density 2.3 g/cm³ have been carried out. The measurements were made using a collimated beam of both gamma rays and neutrons emitted from one of the horizontal channel of the Egyptian Research Reactor-1. A fast neutron and gamma ray spectrometer with a stilbene crystal was used to measure the spectra of fast neutrons and gamma rays. Pulse shape discrimination using the zero cross over technique was used to separate the photon pulses from the electron pulses. The equation due to Schmidt has been modified and applied for determining the neutron effective removal cross sections (～_R) for steel scrap, ordinary, hematite–serpentine, ilmenite–limonite and ilmenite concretes. This equation gives results which are in good agreement with the measured values. The derived empirical equation in a previous work to calculate the neutron integral flux behind different thicknesses of different types of concretes, gives good results for steel scrap concrete under investigation comparing with the corresponding experimental data. Total neutron macroscopic cross sections, linear attenuation coefficients for gamma rays and the half-value layers for both radiations at different energies have been obtained for steel scrap concrete and comparing with the corresponding values of ordinary concrete. The results show that steel scrap concrete is better than ordinary, hematite–serpentine, ilmenite–limonite and ilmenite concretes from the radiation shielding point of view.     

Prevention of blow-up by fast diffusion in chemotaxis

In this paper, we study a strongly coupled parabolic system with cross diffusion term which models chemotaxis. The diffusion coefficient goes to infinity when cell density tends to an allowable maximum value. Such ‘fast diffusion’ leads to global existence of solutions in bounded domains for any given initial data irrespective of the spatial dimension, which is usually the goal of many modifications to the classical Keller–Segel model. The key estimates that make this possible have been obtained by a technique that uses ideas from Moser's iterations.     

Construction of triangular DP surface and its application

In this paper, a new type of bivariate basis on a triangle is presented, which is constructed by extending the univariate NTP basis proposed by Delgado and Peña. Some algebraic properties and its recursive formulae are given. Then a new type of surfaces that is called triangular DP surface is defined, and its recursive evaluation algorithm is obtained. Also, in the case of low degree, its subdivision algorithm and degree elevation algorithm are derived. It is shown that this type of surfaces is obviously more advantageous than triangular Bézier surface, and hence extremely useful for geometric design, especially for the situation in which the surface needs to be evaluated quickly.     

High speed analysis of underivatized drugs by gas chromatography–mass spectrometry

The technique of choice for many types of forensic drug confirmations is gas chromatography/mass spectrometry (GC/MS). Significant amounts of analytical time can be involved in a GC/MS run. The use of a 0.1 mm i.d. fused silica capillary column with hydrogen carrier gas can significantly increase the speed of an analysis without sacrificing resolution. Nanogram levels of underivatized drugs, from amphetamine to strychnine, can be eluted in less than twelve minutes. The multitasking system permits data acquisition, while performing data reduction on the previous run.     

Fast analysis of doping agents in urine by ultra-high-pressure liquid chromatography–quadrupole time-of-flight mass spectrometry: I. Screening analysis

The general strategy to perform anti-doping analyses of urine samples starts with the screening for a wide range of compounds. This step should be fast, generic and able to detect any sample that may contain a prohibited substance while avoiding false negatives and reducing false positive results. The experiments presented in this work were based on ultra-high-pressure liquid chromatography coupled to hybrid quadrupole time-of-flight mass spectrometry. Thanks to the high sensitivity of the method, urine samples could be diluted 2-fold prior to injection. One hundred and three forbidden substances from various classes (such as stimulants, diuretics, narcotics, anti-estrogens) were analysed on a C₁₈ reversed-phase column in two gradients of 9 min (including two 3 min equilibration periods) for positive and negative electrospray ionisation and detected in the MS full scan mode. The automatic identification of analytes was based on retention time and mass accuracy, with an automated tool for peak picking. The method was validated according to the International Standard for Laboratories described in the World Anti-Doping Code and was selective enough to comply with the World Anti-Doping Agency recommendations. In addition, the matrix effect on MS response was measured on all investigated analytes spiked in urine samples. The limits of detection ranged from 1 to 500 ng/mL, allowing the identification of all tested compounds in urine. When a sample was reported positive during the screening, a fast additional pre-confirmatory step was performed to reduce the number of confirmatory analyses.     

A four-node discrete singular convolution for geometric transformation and its application to numerical solution of vibration problem of arbitrary straight-sided quadrilateral plates

A four-node discrete singular convolution (DSC) method is developed for free vibration analysis of arbitrary straight-sided quadrilateral plates. The straight-sided quadrilateral domain is mapped into a square domain in the computational space using a four-node element. By using the geometric transformation, the governing equations and boundary conditions of the plate are transformed from the physical domain into a square computational domain. Numerical examples illustrating the accuracy and convergence of the DSC method for skew, trapezoidal, rhombic and arbitrary quadrilateral plates are presented. The results obtained by DSC method were compared with those obtained by the other numerical methods.     

Asymptotic stability of traveling waves in a discrete convolution model for phase transitions

In a recent paper [P. Bates, A. Chmaj, A discrete convolution model for phase transition, Arch. Rational Mech. Anal. 150 (1999) 281-305], a discrete convolution model for Ising-like phase transition has been derived, and the existence, uniqueness of traveling waves and stability of stationary solution have been studied. This nonlocal model describes l₂-gradient flow for a Helmholts free energy functional with general range interaction. In this paper, by using the comparison principle and the squeezing technique, we prove that the traveling wavefronts with nonzero speed is globally asymptotic stable with phase shift.