Finiteness and the falsification by fellow traveler property

We prove that groups enjoying the falsification by fellow traveler property are of type $F_3$, and have at most an exponential second order isoperimetric function.Comment: Appeared in 2002. I am putting all my past publications on arxi

Fundamental electrode kinetics

Report presents the fundamentals of electrode kinetics and the methods used in evaluating the characteristic parameters of rapid-charge transfer processes at electrode-electrolyte interfaces. The concept of electrode kinetics is outlined, followed by the principles underlying the experimental techniques for the investigation of electrode kinetics

A non-Hopfian almost convex group

In this article we prove that an "isometric multiple HNN-extension" of a group satisfying the falsification by fellow traveler property is almost convex. As a corollary, Wise's example of a CAT(0) non-Hopfian group is Almost convex.Comment: Appeared in 2004. I am putting all my past papers on arxi

On wild ramification in quaternion extensions

Quaternion extensions are often the smallest extensions to exhibit special properties. In the setting of the Hasse-Arf Theorem, for instance, quaternion extensions are used to illustrate the fact that upper ramification numbers need not be integers. These extensions play a similar role in Galois module structure. To better understand these examples, we catalog the ramification filtrations that are possible in totally ramified extensions of dyadic number fields. Interestingly, we find that the catalog depends, for sharp lower bounds, upon the refined ramification filtration, which is associated with the biquatratic subfield. Moreover these examples, as counter-examples to the conclusion of Hasse-Arf, occur only when the refined filtration is, in two different ways, extreme.Comment: 19 pages. This is an extensive revision of the earlier draf

On the Schr\"odinger equations with isotropic and anisotropic fourth-order dispersion

This paper deals with the Cauchy problem associated to the nonlinear fourth-order Schr\"odinger equation with isotropic and anisotropic mixed dispersion. This model is given by the equation $i\partial _{t}u+\epsilon \Delta u+\delta A u+\lambda|u|^\alpha u=0,$ $x\in \mathbb{R}^{n},$ $t\in \mathbb{R},$ where $A$ represents either the operator $\Delta^2$ (isotropic dispersion) or $\sum_{i=1}^d\partial_{x_ix_ix_ix_i},\ 1\leq d<n$ (anisotropic dispersion), and $\alpha, \epsilon, \lambda$ are given real parameters. We obtain local and global well-posedness results in spaces of initial data with low regularity, such as weak-$L^p$ spaces. Our analysis also includes the biharmonic and anisotropic biharmonic equation $(\epsilon=0)$ for which, the existence of self-similar solutions is obtained as consequence of his scaling invariance. In a second part, we investigate the vanishing second order dispersion limit in the framework of weak-$L^p$ spaces. We also analyze the convergence of the solutions for the nonlinear fourth-order Schr\"odinger equation $i\partial _{t}u+\epsilon \Delta u+\delta \Delta^2 u+\lambda|u|^\alpha u=0$, as $\epsilon$ goes to zero, in $H^2$-norm, to the solutions of the corresponding biharmonic equation $i\partial _{t}u+\delta \Delta^2 u+\lambda|u|^\alpha u=0$

Morphological instability, evolution, and scaling in strained epitaxial films: An amplitude equation analysis of the phase field crystal model

Morphological properties of strained epitaxial films are examined through a mesoscopic approach developed to incorporate both the film crystalline structure and standard continuum theory. Film surface profiles and properties, such as surface energy, liquid-solid miscibility gap and interface thickness, are determined as a function of misfit strains and film elastic modulus. We analyze the stress-driven instability of film surface morphology that leads to the formation of strained islands. We find a universal scaling relationship between the island size and misfit strain which shows a crossover from the well-known continuum elasticity result at the weak strain to a behavior governed by a "perfect" lattice relaxation condition. The strain at which the crossover occurs is shown to be a function of liquid-solid interfacial thickness, and an asymmetry between tensile and compressive strains is observed. The film instability is found to be accompanied by mode coupling of the complex amplitudes of the surface morphological profile, a factor associated with the crystalline nature of the strained film but absent in conventional continuum theory.Comment: 16 pages, 10 figures; to be published in Phys. Rev.

Patterns theory and geodesic automatic structure for a class of groups

We introduce a theory of "patterns" in order to study geodesics in a certain class of group presentations. Using patterns we show that there does not exist a geodesic automatic structure for certain group presentations, and that certain group presentations are almost convex.Comment: Appeared in 2003. I am putting all my past papers on arxi

Does correction for guessing reduce students' performance on multiple-choice examinations? Yes? No? Sometimes?

Multiple-choice (MC) examinations are becoming increasingly popular in higher education because they can be used effectively to assess breadth of knowledge in large cohorts of students. This present research investigated Psychology students' performance on, and experiences of, MC examinations with and without correction for guessing. In Study 1, data were collected from two cohorts of students across three Psychology MC examinations. The results revealed that students scored higher, and left fewer questions unanswered, when there was no correction for guessing. Furthermore, when the correction for guessing was removed from the theory MC examination, students who were told there was no correction for guessing did better than those told there was a correction. In addition, there was limited evidence of gender differences, with female students performing significantly better on one MC examination than males. In Study 2, a further set of first-year Psychology students reported their experiences of correction for guessing on open-book and closed-book MC examinations. Students reported feeling less anxious and more confident on the open-book MC examination. The findings of both of these studies have implications for instructors deciding whether or not correction for guessing is appropriate, and for the advice to be given to students preparing for MC examinations