Behavior and surface energies of polybenzoxazines formed by polymerization with argon,oxygen, and hydrogen plasmas

Polybenzoxazine (PBZZ) thin films can be fabricated by the plasma‐polymerization technique with, as the energy source, plasmas of argon, oxygen, or hydrogen atoms and ions. When benzoxazine (BZZ) films are polymerized through the use of high‐energy argon atoms, electronegative oxygen atoms, or excited hydrogen atoms, the PBZZ films that form possess different properties and morphologies in their surfaces. High‐energy argon atoms provide a thermodynamic factor to initiate the ring‐opening polymerization of BZZ and result in the polymer surface having a grid‐like structure. The ring‐opening polymerization of the BZZ film that is initiated by cationic species such as oxygen atoms in plasma, is propagated around nodule structures to form the PBZZ. The excited hydrogen atom plasma initiates both polymerization and decomposition reactions simultaneously in the BZZ film and results in the formation of a porous structure on the PBZZ surface. We evaluated the surface energies of the PBZZ films polymerized by the action of these three plasmas by measuring the contact angles of diiodomethane and water droplets. The surface roughness of the films range from 0.5 to 26 nm, depending on the type of carrier gas and the plasma‐polymerization time. By estimating changes in thickness, we found that the PBZZ film synthesized by the oxygen plasma‐polymerization process undergoes the slowest rate of etching in CF₄ plasma. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4063–4074, 2004     

Bio‐based nanocomposites from functionalized plant oils and layered silicate

Some discovery work was done on the synthesis of clay nanocomposites based on renewable plant oils. Functionalized triglycerides, such as acrylated epoxidized soybean oil, maleinized acrylated epoxidized soybean oil, and soybean oil pentaerythritol maleates, combined with styrene were used as the polymer matrix. The miscibility of these monomers and clay organomodifier was assessed by solubility parameters. The formation of nanocomposites was confirmed by both X‐ray data and transmission electron microscopy. The morphology showed a mix of intercalated and partially exfoliated sheets. The flexural modulus increased 30% at only 4 vol % clay content, but there was no significant effect on flexural strength, glass‐transition temperature, and thermal stability. Property enhancement was related to the degree of exfoliation that depends on both the polarity and flexibility of the monomers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1441–1450, 2004     

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.