In India and across the globe, liver disease is a serious area of concern in medicine. Therefore, it becomes essential to use classification algorithms for assessing the disease in order to improve the efficiency of medical diagnosis which eventually leads to appropriate and timely treatment. The study accordingly implemented various classification algorithms including linear discriminant analy...

Here the first sum is taken over the finite set of orbits of SL2(Z) on the set QD of all positive definite binary quadratic forms of discriminant −D, z is the (orbit of the) unique root in the upper half plane, and u(z) is half the order of the stabilizer. The internal sum in the second expression is over the primitive positive definite binary quadratic forms of discriminant −d and zd is a root...

Identification of functional motifs in a DNA sequence is fundamentally a statistical pattern recognition problem. Discriminant analysis is widely used for solving such problems. This paper will review two basic parametric methods: LDA (linear discriminant analysis) and QDA (quadratic discriminant analysis). Their usage in recognition of splice sites and exons in the human genome will be demonst...

Among the values of a binary quadratic form, there are many twins of fixed distance. This is shown in quantitative form. For quadratic forms of discriminant −4 or 8 a corresponding result is obtained for triplets.

We consider some properties of indefinite binary quadratic forms F (x, y) = ax +bxy−y of discriminant ∆ = b +4a, and quadratic ideals I = [a, b−√∆ ]. AMS Mathematics Subject Classification (2000): 11E04, 11E12, 11E16

We are now going to take a decisive step forward by proving the Main Theorem on which primes p are represented by the principal quadratic form qD(x, y) of discriminant D < 0, when D is a fundamental discriminant, i.e., the discriminant of the full ring of integers of Q( √ D). Of course, to solve our original problem of representation of primes by x + ny for arbitrary n, we need to look also at ...