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Starting an abstract or introduction with "This paper concerns" or "In this paper" often means that results are going to be stated out of context. Writing for Computer Science 32 X In this paper we describe a new programming language with matrix manipulation operators . / Most numerical computation is dedicated to manipulation of matrices, but matrix operations are difficult to implement efficiently in current high-level programming languages. In this paper we describe a new programming language with matrix manipulation operators.
This was discovered 2000 years ago by the Greeks. The problem arises in squares with sides of unit length. The length of the diagonals of these squares is irrational. This discovery was a serious blow to the Greek mathematicians . / The Greeks discovered 2000 years ago that the system of rational num bers is incomplete. The problem is that some quantities, such as the length of the diagonal of a square with unit sides, are irrational. This discovery was a serious blow to the Greek mathematicians.
Limited-Memory Huff man Coding for Databases of Textual and Numeric Data" is awkward, but it is superior to "Huffman Coding for Databases", which is far too general. " is excessive, not to mention uninformative. The more interesting the title, however, the more likely that the text underneath it will be read. The title is the only part of your paper that most people see; if the title does not reflect the paper's contents, the paper will not be read by the right readership. Titles and section headings do not have to be complete sentences; indeed, such titles can look rather odd.