Determination of nickel in alloys and plant leaves with salicylaldehyde 3-oxobutanoylhydrazone by spectrophotometry.

A simple and highly sensitive reagent of salicylaldehyde 3-oxobutanoylhydrazone (salicylaldehyde acetoacetic acid hydrazone, SAAH) was synthesized and studied for the spectrophotometric determination of nickel in detail. In the pH range 6, which greatly increased the selectivity, nickel reacted with SAAH to form a 1:1 yellow complex, having a sensitive absorption peak at 405 nm. Under the optimal conditions, Beer's law was obeyed over the range from 0.0117 to 0.1174 microg cm(-3). The apparent molar absorptivity was 3.025 x 10(5) dm3 mol(-1) cm(-1). The detection limit and the variation coefficient were found to be 1.752 ng cm(-3) and 1.0%, respectively. The method has been applied to the quantitative determination of nickel in different alloys and leaves.     

Extractive spectrophotometric determination of Cobalt(II) in synthetic and pharmaceutical samples using Cyanex 923.

Cyanex 923 has been proposed as a sensitive analytical reagent for the direct extractive spectrophotometric determination of cobalt(II). Cobalt(II) forms a blue-colored complex with Cyanex 923 in the organic phase. The maximum absorbance of the complex is measured at 635 nm. Beer's law was obeyed in the range 58.9 - 589.0 microg of cobalt. The molar absorptivitiy and Sandell's sensitivity of the complex was calculated to be 6.79 x 10920 l mol(-1) cm(-1) and 0.088 microg cm(-2), respectively. The nature of the extracted species was found to be Co(SCN)2 x 2S. An excellent linearity with a correlation coefficient value of 0.999 was obtained for the Co(II)-Cyanex 923 complex. Stability and regeneration of the reagent (Cyanex 923) for reuse is the main advantage of the present method. The method was successfully applied to the determination of cobalt in synthetic mixtures and pharmaceutical samples was found to give values close to the actual ones. Standard alloy samples, such as high-speed tool BCS 484 and 485, have been tested for the determination of cobalt for the purpose of validating the present method. The results of the proposed method are comparable with atomic absorption spectrometry and were found to be in good agreement.     

On division rings with algebraic commutators of bounded degree

We shall answer several questions concerning additive or multiplicative commutators in a division ring which are algebraic of bounded degree over its center.     

Seizure warning algorithm based on optimization and nonlinear dynamics

There is growing evidence that temporal lobe seizures are preceded by a preictal transition, characterized by a gradual dynamical change from asymptomatic interictal state to seizure. We herein report the first prospective analysis of the online automated algorithm for detecting the preictal transition in ongoing EEG signals. Such, the algorithm constitutes a seizure warning system. The algorithm estimates STL_max, a measure of the order or disorder of the signal, of EEG signals recorded from individual electrode sites. The optimization techniques were employed to select critical brain electrode sites that exhibit the preictal transition for the warning of epileptic seizures. Specifically, a quadratically constrained quadratic 0-1 programming problem is formulated to identify critical electrode sites. The automated seizure warning algorithm was tested in continuous, long-term EEG recordings obtained from 5 patients with temporal lobe epilepsy. For individual patient, we use the first half of seizures to train the parameter settings, which is evaluated by ROC (Receiver Operating Characteristic) curve analysis. With the best parameter setting, the algorithm applied to all cases predicted an average of 91.7% of seizures with an average false prediction rate of 0.196 per hour. These results indicate that it may be possible to develop automated seizure warning devices for diagnostic and therapeutic purposes.Mathematics Subject Classification (1991):20E28, 20G40, 20C20     

On Einstein four-manifolds with <Emphasis Type="Italic">S</Emphasis><Superscript>1</Superscript>-actions

We study closed Einstein 4-manifolds which admit S¹ actions of a certain type, i.e., warped products. In particular, we classify them up to isometry when the fixed point of the S¹ action satisfies certain natural geometric conditions. The proof uses the Bochner-Weitzenböck formula for 1-forms and the theory of minimal surfaces in 3-manifolds.in final form: 22 January 2003     

Kinetic Models for Chemotaxis and their Drift-Diffusion Limits

Kinetic models for chemotaxis, nonlinearly coupled to a Poisson equation for the chemo-attractant density, are considered. Under suitable assumptions on the turning kernel (including models introduced by Othmer, Dunbar and Alt), convergence in the macroscopic limit to a drift-diffusion model is proven. The drift-diffusion models derived in this way include the classical Keller-Segel model. Furthermore, sufficient conditions for kinetic models are given such that finite-time-blow-up does not occur. Examples are given satisfying these conditions, whereas the macroscopic limit problem is known to exhibit finite-time-blow-up. The main analytical tools are entropy techniques for the macroscopic limit as well as results from potential theory for the control of the chemo-attractant density.Present address: Centro de Matemática e Aplicações Fundamentais, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003, Lisboa, Portugal     

Bounded Positive Solutions of Schrödinger Equations in Two-Dimensional Exterior Domains

We prove under quite general assumptions the existence of a bounded positive solution to the semilinear Schrödinger equation in a two-dimensional exterior domain.     

On a Definitizable Analog of the Trigonometric Moment Problem Generating an Indefinite Toeplitz Form

We prove the existence of an integro-polynomial representation for a sequence of numbers such that there exists a difference operator mapping this sequence to a sequence that generates the solvable trigonometric moment problem. A similar result related to the power moment problem was given in [12].     

Pseudorandom properties of prime factors

In this paper we study some pseudo-random properties related to the prime factors of integers. We prove some results concerning the well distribution of the greatest prime factor modulo 4, and give some computational insight on the correlations, which seem to be beyond reach of proof.