Investigation of the chemical state of copper in Cu/SiO2 composite films by x-ray photoelectron spectroscopy

The concentration and chemical state of copper in the subsurface region of Cu/SiO₂ composite films obtained by simultaneous magnetron sputtering from two sources (Cu and SiO₂) are determined by x-ray photoelectron spectroscopy (XPS). It is established that copper in the as-grown film is primarily in the form of unoxidized atoms dispersed in a SiO₂ matrix. Annealing of the film results in practically no oxidation, but about 70% of the copper atoms condense into metallic clusters with sizes below 10 Å in the subsurface region and about 50 Å in the bulk of the film. The changes in the binding energy of core electrons, and especially in the energies of Auger electrons, are so large in this situation that photoelectron and Auger spectroscopy are efficient methods for monitoring the chemical state of this composite material.     

Student-Invented Numeration Systems: Pattern-Analysis and Mathematical Understanding

Thirteen fifth graders were given an assignment to invent their own numeration systems, following a unit on bases and a look at early events in the history of numbers. The task presented options that required the students to make decisions (such as whether to use a base, which base to use, design of symbols, etc.), and build a rationale for the elements of their system. Analyses of patterns embedded in their invented systems provided an assessment of student understanding of numeration. The progression of more and less complex thinking related to the student's choice of a base other than 10, consistency of logic throughout the system in words and symbols, rationale for change, and perception of real life examples that would change if the system was adopted. The invention task is presented as another way to make connections.     

Spin effects in instanton models

Nonperturbative nolocal structure of QCD vacuum is well described by instanton model. Specific helicity and flavor structure of zero modes of quarks, in instanton field allows simultaneously to explain some important features of low-and high-energy hadron phenomemology. The basic characteristics of hadron spectrum, partonic sum rules, heavyquark potential etc within the instanton liquid model are briefly discussed.     

Some remarks on metaplectic cusp forms and the correspondences of Shimura and Waldspurger

The simple relation between representations of the covering groups of SL₂ and GL₂ makes it possible to fuse and extend the recent metaplectic results of Shimura, Waldspurger, Flicker, and ourselves. By giving a new (purely local andL-function theoretic) treatment of the Waldspurger-Shintani correspondence, we also simplify some of Waldspurger’s original results.     

A New Distribution Function for Risk Analysis

This paper presents an alternative to the beta continuous probability distribution for risk analysis. Particular attention has been given to two major applications of distributions, namely project management risk and critical path analysis (PERT). In conjunction with the beta, the triangular and normal distributions are frequently employed in order to give sufficient robustness to risk analysis. The beta distribution, as used in PERT, has a major theoretical implementation flaw. The new distribution was developed to give a possible alternative method of assessing risk. It is shown that the requirement to estimate the most pessimistic variate may be replaced by the probability to exceed the mode. Proposals for other simplifications in risk analysis are discussed. Practical means to validate the most appropriate distributions for risk analysis are outlined, and a cost-data case study is included.     

Existence and Stability for Spherical Crystals Growing in a Supersaturated Solution

We consider the growth of a spherical crystal in a supersaturatedsolution. In the first part, existence and uniqueness resultsfor radially symmetric growth are obtained, provided that thesupersaturation is not too large; conversely, when the far-fieldsupersaturation exceeds a critical value, it is shown that theradially symmetric solution ceases to exist in finite time.In the second part, we examine the linear stability of a radiallysymmetric similarity solution (in which the radius grows ast?) to shape perturbations. The results are compared with previousquasi-static analyses, and, in particular, the critical radiusat which the crystal becomes unstable is found to be largerfor small supersaturations, but smaller for large supersaturations,than those predicted by the quasi-static analysis