Multiple vibrational excitations of H2O and D2O on Si(100)(2 × 1): A HREELS study

The HREELS (high-resolution electron energy-loss spectroscopy) spectra from H₂O and D₂O chemisorbed on the clean Si(100)(2 × 1) surface have been investigated in the energy region between about 500 and 1400 meV. For the first time, second overtones have been observed for a chemisorbed species. This observation is believed to be due to the enhancement of the O-H stretching fundamental and overtone modes because of the temporary formation of a negative ion that occurs when the incident electron is briefly trapped in a shape resonance. Additional multiple and combination modes are observed involving the resonance enhanced overtones as well as the fundamental modes. Furthermore, the dissociation energy of the hydroxyl group has been determined and found to be much larger than the actual energy needed to dissociate hydroxyl groups on the surface, indicating that the driving force for the observed atomic rearrangements is probably Si-O bond formation rather than O-H dissociation.     

Matchings in benzene chains

An explicit recurrence relation is derived for the matching polynomial of the general benzene chain B_n. A table is given for chains of length up to 6. Explicit formulae are then obtained for the first five coefficients of the matching polynomial of B_n. Finally, results are deduced for the number of perfect matchings and the number of matchings with two nodes.     

Decomposability of free Łukasiewicz implication algebras

?ukasiewicz implication algebras are {→,1}-subreducts of Wajsberg algebras (MV-algebras). They are the algebraic counterpart of Super-?ukasiewicz Implicational logics investigated in Komori, Nogoya Math J 72:127–133, 1978. The aim of this paper is to study the direct decomposability of free ?ukasiewicz implication algebras. We show that freely generated algebras are directly indecomposable. We also study the direct decomposability in free algebras of all its proper subvarieties and show that infinitely freely generated algebras are indecomposable, while finitely free generated algebras can be only decomposed into a direct product of two factors, one of which is the two-element implication algebra.     

When, how, and why prove theorems? A methodology for studying the perspective of geometry teachers

While every theorem has a proof in mathematics, in US geometry classrooms not every theorem is proved. How can one explain the practitioner’s perspective on which theorems deserve proof? Toward providing an account of the practical rationality with which practitioners handle the norm that every theorem has a proof we have designed a methodology that relies on representing classroom instruction using animations. We use those animations to trigger commentary from experienced practitioners. In this article we illustrate how we model instructional situations as systems of norms and how we create animated stories that represent a situation. We show how the study of those stories as prototypes of a basic model can help anticipate the response from practitioners as well as suggest issues to be considered in improving a model.     

Stability of closed timelike curves in the Gödel universe

We study, in some detail, the linear stability of closed timelike curves in the Gödel universe. We show that these curves are stable. We present a simple extension (deformation) of the Gödel metric that contains a class of closed timelike curves similar to the ones associated to the original metric. This extension correspond to the addition of matter whose energy-momentum tensor is analyzed. We find the conditions to have matter that satisfies the usual energy conditions. We study the stability of closed timelike curves in the presence of usual matter as well as in the presence of exotic matter (matter that does satisfy the above mentioned conditions). We find that the closed timelike curves in the Gödel universe with or without the inclusion of regular or exotic matter are stable under linear perturbations. We also find a sort of structural stability.     

Semi-Classical Limit for Radial Non-Linear Schrödinger Equation

We consider the nonlinear Schrödinger equation with superlinear and subcritical nonlinearity. Assuming that the potential is radially symmetric we find radial sign-changing solutions of the equation that concentrate in a ball, as the parameter goes to zero. We study the asymptotic profile of these highly oscillatory solutions, completely characterizing their behavior by means of an envelope function.Partially supported by FONDECYT Lineas Complementarias Grant 8000010.Partially Supported by FONDAP Matemáticas Aplicadas and FONDECYT Lineas Complementarias Grant 8000010.     

Accuracy and validity of stereology as a quantitative method for assessment of human temporal lobe volumes acquired by magnetic resonance imaging

The object of this study was to compare the accuracy and validity of stereology as a method for determining whole temporal lobe volume with the more established technique of semi-automated thresholding and tracing. Ten, fixed, post-mortem human brains, were imaged using a three dimensional (3D) acquisition protocol. The volume of the left temporal lobe, dissected from each brain, was determined by fluid displacement. Each volume was compared to measurements obtained from magnetic resonance images (MRI) of the post-mortem brain using each of the two segmentation methods. Post-acquisition processing was performed using MEASURE software. Three investigators performed each measurement three times using each method, yielding a total of 180 measurements. Stereology took, on average, half the time of thresholding/tracing. Using a clinically acceptable variation for 95% of repeat measures; both intra-observer and inter-observer variation were acceptable for each technique. However, validity, as demonstrated by graphs of agreement against water displacement showed that the "limits of agreement" using stereology were within the acceptable range, while those using the thresholding/tracing technique were not. Quantitative estimates of variation and a graphical representation of the limits of agreement show that stereology is at least as precise as the thresholding/tracing method but is superior in terms of speed and validity. This has broad implications for published estimates of brain region volumes in human diseases such as epilepsy, dementia and other neurodegenerative disorders.