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This is a set of notes for the first two chapters of an Abstract Algebra course, following the Hungerford textbook table of contents.
One notable feature is the use of a couple of commands that allow one to show only definitions, or only the examples, etc., and another command that allows one to format examples for making handouts.

Since their adaptation from a tool of computer science to one of linguistics, continuations have been applied to a wide variety of natural language phenomena. Here we expand upon these efforts to give an account of the class of phrases known as ``weak definites:'' nominals that appear with a definite article but do not set up an individual discourse referent. We draw upon Aguilar-Guevara and Zwarts' formalization of weak definites (2010) as reference to kinds to develop two operators that can be applied within the continuation-based grammar presented by Barker & Shan (2013) to produce weak readings.

This example shows how to create citations in footnotes using biblatex. Biblatex automatically formats references and citations, much like BibTeX, but biblatex is more robust and more powerful. You can (almost certainly) use your existing .bib databases with biblatex, it comes with a wide variety of styles built in, and it's much easier to write your own custom styles.
In this example, we use the verbose-ibid style to generate footnotes with automatic “ibid.” abbreviations. For a full list of styles, see the user guide in the biblatex manual.

Compressive Sensing is a Signal Processing technique, which gave a break through in 2004. The main idea of CS is, by exploiting the sparsity nature of the signal (in any domain), we can reconstruct the signal from very fewer samples than required by Shannon-Nyquist sampling theorem. Reconstructing a sparse signal from fewer samples is equivalent to solving a under-determined system with sparsity constraints. Least square solution to such a problem yield poor `results because sparse signals cannot be well approximated to a least norm solution. Instead we use l1 norm(convex) to solve this problem which is the best approximation to the exact solution given by l0 norm(non-convex). In this paper we plan to discuss three applications of CS in estimation theory. They are, CS based reliable Channel estimation assuming sparsity in the channel is known for TDS-OFDM systems[1]. Indoor location estimation from received signal strength (RSS) where CS is used to reconstruct the radio map from RSS measurements[2]. Identifying that subspace in which the signal of interest lies using ML estimation, assuming signal lies in a union of subspaces which is a standard sparsity assumption according to CS theory[3]. Index terms : Compressive Sensing, Indoor positioning, fingerprinting, radio map, Maximum likelihood estimation, union of linear subspaces, subspace recovery.