this paper presents a framework for long term transmission expansion planning in competitive, electricity markets. transmission lines and phase shifters are taken into account as expansion options. maximization of the network users' benefits, with satisfying security constraints are considered as the criterion for transmission expansion planning. the elements of the objective function are the...

Abelian class group Cl(D) of imaginary quadratic order with odd squarefree discriminant D is used in public key cryptosystems, based on discrete logarithm problem in class group and in cryptosystems, based on isogenies of elliptic curves. Discrete logarithm problem in Cl(D) is hard if #Cl(D) is prime or has large prime divisor. But no algorithms for generating such D are known. We propose proba...

this paper presents a simplifiedlagrangian multiplier based algorithm to solve the fixed head hydrothermalscheduling problem. in fixed head hydrothermal scheduling problem, waterdischarge rate is modeled as quadratic function of hydropower generation andfuel cost is modeled as quadratic function of thermal power generation. thepower output of each hydro unit varies with the rate of water discha...

A lot of methods have been used in the past for the prediction of failure business like Discriminant analysis, Logit analysis, Quadratic Function etc. Although some of these methods lead to models with a satisfactory ability to discriminate between healthy and bankrupt, they endure some limitations, often due to the unrealistic assumption of statistical hypotheses. This is why we have undertake...

Decision making problems, according to their nature, the policy of the decision maker, and the overall objective of the decision, may require the choice of an alternative solution, the ranking of the alternatives from the best to the worst ones or the assignment of the considered alternatives into predefined homogeneous classes. This last type of decision problem is referred to as classificatio...

We develop a framework for computing with rational approximations to real numbers in number theoretic computations. We use that framework to analyze the approximate evaluation of the value L(1;) where L(s;) is the L-function of the quadratic order of discriminant .

An algorithm is given to efficiently compute, for large discriminant, L-functions of characters on the class group of a complex quadratic field. This is an analog in conductor aspect of the Odlyzko-Schönhage algorithm to compute the Riemann zeta function. Examples are included for about 21000L-functions with conductor near 10. The data shows good agreement with a symplectic random matrix model.

Let d be the discriminant of an imaginary quadratic field. Let a, b, c be integers such that b − 4ac = d, a > 0, gcd(a, b, c) = 1. The value of |η ( (b + √ d)/2a ) | is determined explicitly, where η(z) is Dedekind’s eta function η(z) = e ∞ ∏ m=1 (1− e) ( im(z) > 0 ) .

2 Classification of One-Dimensional Data 2 2.1 Linear Discriminant Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.1.1 Building the LDA Classifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.1.2 Results of One-Dimensional LDA Classification . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Quadratic Discriminant Analysis . . . . . ....