A set is a collection of items. To specify a set, the items are written as a list enclosed by braces, e.g. A = {1, 2, 4}. This means that A is the set containing the items 1, 2, and 4. There is no notion of order in the set listing, so {1, 2, 4} = {4, 1, 2} = {2, 4, 1}, etc. Also, there is no notion of duplicate items, so {1, 2, 1} = {1, 2} for example. The empty set is the set containing no it...

Definition Metasearch is to utilize multiple other search systems (called component search systems) to perform simultaneous search. A metasearch engine is a search system that enables metasearch. To perform a basic metasearch, a user query is sent to multiple existing search engines by the metasearch engine; when the search results returned from the search engines are received by the metasearch...

Sentence generation will be an integral part of future augmentative communication devices. By employing natural language processing techniques, we hope to enhance the speed, flexibility, and ease of use of current word-based systems. In this paper, we discuss the generation component of our “compansion” system, which expands compressed messages entered by the user into full English sentences. T...

Since its introduction in 1986 as a tool for imaging and creating three-dimensional micrographs with resolution down to the nanometer and angstrom scales, the scanning probe microscope (SPM) has increasingly been acclaimed as a quantitative probe of surface forces such as adhesion. The SPM is able to study these important parameters using a technique that measures forces on the probe as it appr...

1 Linear algebra 2 1.1 Inner product, norm, distance, and orthogonality . . . . . . . . . 2 1.2 Angle and inequality . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Vector projection . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Basics of matrices . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.5 Matrix multiplication . . . . . . . . . . . . . . . . . . . . . . . ....

The effect of lateral pressure on the wavelength response characteristics of a fiber Bragg grating embedded in a cylindrical package of silicone rubber has been investigated in this report. Due to high Poisson’s ratio (0.48) and low stiffness of silicone rubber, force applied in one direction will be efficiently transferred to the perpendicular direction also. A wavelength shift of more than 1 ...

One of the few research projects to have focused on NHS hospital chaplains reports widely divergent views regarding its service. On the one hand, chaplaincy is described as being ‘utterly essential’, a view supported by comments reporting that it is a discipline surfing along ‘on the crest a wave’. On the other hand, it has also been described as being ‘benignly superfluous’ and as a profession...

Abstract For the Schrödinger equation at fixed energy with a potential supported in a bounded domain we give formulas and equations for finding scattering data from the Dirichletto-Neumann map with nonzero background potential. For the case of zero background potential these results were obtained in [R.G.Novikov, Multidimensional inverse spectral problem for the equation −∆ψ + (v(x) − Eu(x))ψ =...