Coding theory plays an important role in efficient transmission of data over noisy communication channels. It consists of two steps; the first step is to encode the data to reduce its sensitivity to noise during transmission, and the second step is to decode the received data by detecting and correcting the noise induced errors. In this thesis an algebraic approach is used to develop efficient ...

instruction with the husband to send me word, if any graver symptoms make their appearance. 3 p.m.?Just, in the afternoon at 3 P.M. I was called again and I found her in tetanic fits (opisthotonos) lying on her head and heels, fits coming at. an interval of every five minutes. The power of deglutition partially impaired; pulse full and quick, 9G; temperature 101?. I gave her the following mixtu...

The concept of comprehensive Grobner bases was introduced by Weispfenning. Montes has proposed an efficient algorithm for computing these bases. But he has not explicitly used Buchberger's criteria in his algorithm. In this paper we prove that we can apply these criteria on Montes algorithm. We propose a modified version of Montes algorithm and evaluate its performance via some examples.

The theory of n-fold integer programming has been recently emerging as an important tool in parameterized complexity. The input to an n-fold integer program (IP) consists of parameter A, dimension n, and numerical data of binary encoding length L. It was known for some time that such programs can be solved in polynomial time using O(ng(A)L) arithmetic operations where g is an exponential functi...

Denote by H(t, q), t ≤ q, the incidence matrix (with respect to inclusion) of the t–sets versus the q–sets of the n–set {1, 2, . . . , n}. This matrix is considered as a linear map of Q–vector spaces Cq(n) −→ Ct(n), where Cs(n) is the Q–vector space having the s–sets as a basis (s ≤ n). As a basic tool, we introduce a connection of the vector spaces to a graded Q–algebra (which is at the same t...

In 1950 a class of generalized Petersen graphs was introduced by Coxeter and around 1970 popularized by Frucht, Graver and Watkins. The family of I-graphs mentioned in 1988 by Bouwer et al. represents a slight further albeit important generalization of the renowned Petersen graph. We show that each I-graph I(n, j, k) admits a unit-distance representation in the Euclidean plane. This implies tha...

These days our society is combating against a neurodegenerative disease called Alzheimer’s disease which is an age-related dementia. The concern has become graver as the disease may not be a necessary outcome in the oldest old and may even thrive in an age of thirties or forties. Alzheimer’s impairs a person’s cognitive ability and gradually leads to loss of bodily functions, making them depend...

the concept of comprehensive grobner bases was introduced by weispfenning. montes has proposed an efficient algorithm for computing these bases. but he has not explicitly used buchberger's criteria in his algorithm. in this paper we prove that we can apply these criteria on montes algorithm. we propose a modified version of montes algorithm and evaluate its performance via some examples.