EQCM Study of the Couple Thallium(I)/Thallium Amalgam at a Thin Film Mercury Electrode

EQCM and voltammetric data show that thallium(I) ions, which are adsorbed in the region of the positive surface charge, most probably, in the form of the ionic pairs, are not reduced. In this potential region, thallium(I) ions are reduced directly from the solution. At more negative potentials, the previously adsorbed stable ionic pairs slowly undergo transition into the less stable form. From this form, thallium(I) ions can be reduced or desorbed into the solution. The process is best described by a model of one electron, i.e., full charge transfer.     

Peculiarities of Adsorption of Some Polar Substances from Vapor Phase on a Microporous Clay Adsorbent

The adsorption of polar organic substances (methanol, pyridine, and acetonitrile) and water was studied from the vapor phase on microporous adsorbent prepared by the substitution of polyhydroxyaluminum ions for the sodium ions of natural montmorillonite clay. The differential isosteric heats of adsorption of these substances were calculated and analyzed in a wide range of fillings.     

The existence of Thom classes

In this paper we consider the category of unstable modules over the Steenrod algebra. We prove the existence of finite primary decompositions in this category. Moreover, we prove the existence of Thom classes in noetherian unstable modules, i.e., elements that generate cyclic unstable submodules that are closed under the action of the Steenrod algebra. This in turn leads to the proof of the prime filtration theorem in the category of noetherian unstable modules. As an application we present a proof of the Landweber-Stong conjecture (now a theorem by D. Bourguiba and S. Zarati) that does not make use of the classification of injectives.     

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     

Carousels,Zindler curves and the floating body problem

A carousel is a dynamical system that describes the movement of an equilateral linkage in which the midpoint of each rod travels parallel to it. They are closely related to the floating body problem. We prove, using the work of Auerbach, that any figure that floats in equilibrium in every position is drawn by a carousel. Of special interest are such figures with rational perimetral density of the floating chords, which are then drawn by carousels. In particular, we prove that for some perimetral densities the only such figure is the circle, as the problem suggests.     

Reform Teaching Strategies Used by Student Teachers

The purposes of this study were to observe the teaching practices occurring in student teachers' science and mathematics K‐12 classrooms, compare the student teachers' perceptions of their teaching with what was actually occurring in their classrooms, and determine which college faculty members and courses these student teachers felt contributed to the teaching methods they used. Data on each student teacher were gathered via field notes of three classes, an observation protocol completed after each lesson, and an interview. Composites were written for each of the students. The total data set of all composites was examined to see if any patterns generalizable to the whole were evident. Differences between and among grade levels and content areas surfaced and are discussed.     

Gauss Algebras

A special class of associative algebras is introduced and studied. A criteria of semisimplicity for suitable category of modules is obtained.     

Some Problems of Harmonic Analysis on Reductive Groups

An algebraic approach to harmonic analysis on reductive Lie groups is proposed. The case of complex semisimple Lie groups is considered in details. Some problems for real reductive Lie groups are discussed.