The Influence of Analyser Geometry Effects in Scanning Electron Microscope Voltage Contrast Measurements

A computer simulation model used to study specimen dependent and analyser geometry dependent effects is described in this paper. With this model, the influence of the specimen dependent effect on quantitative voltage contrast measurements can be isolated from the analyser geometry dependent effect. Linearization error voltages in quantitative voltage contrast measurements arising from the individual influences of the specimen dependent and analyser geometry dependent effects are presented. The results show that the error component due to very narrow analysers dominate the total linearization error. The same situation arises when the voltage measurement point on the specimen is very near to the edge of the analyser

An Anonymous Credit Card System

Credit cards have many important benefits; however, these same benefits often carry with them many privacy concerns. In particular, the need for users to be able to monitor their own transactions, as well as bank's need to justify its payment requests from cardholders, entitle the latter to maintain a detailed log of all transactions its credit card customers were involved in. A bank can thus build a profile of each cardholder even without the latter's consent. In this paper, we present a practical and accountable anonymous credit system based on ecash, with a privacy preserving mechanism for error correction and expense-reporting

Mathematics of Gravitational Lensing: Multiple Imaging and Magnification

The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds in the case of single and multiple lens planes. We discuss recent advances in the mathematics of stochastic lensing, discussing a general formula for the global expected number of minimum lensed images as well as asymptotic formulas for the probability densities of the microlensing random time delay functions, random lensing maps, and random shear, and an asymptotic expression for the global expected number of micro-minima. Multiple imaging in optical geometry and a spacetime setting are treated. We review global magnification relation results for model-dependent scenarios and cover recent developments on universal local magnification relations for higher order caustics.Comment: 25 pages, 4 figures. Invited review submitted for special issue of General Relativity and Gravitatio