In this paper, we discuss a spectral quadratic-SDP method for the iterative resolution of fixed-order H2 and H∞ design problems. These problems can be cast as regular SDP programs with additional nonlinear equality constraints. When the inequalities are absorbed into a Lagrangian function the problem reduces to solving a sequence of SDPs with quadratic objective function for which a spectral SD...

Following what is basically Kummer’s relatively neglected approach to non-unique factorization, we determine the structure of the irreducible factorizations of an element n in the ring of integers of a number field K. Consequently, we give a combinatorial expression for the number of irreducible factorizations of n in the ring. When K is quadratic, we show in certain cases how quadratic forms c...

Important progress made this year, both in theory and in experiment, helped solving the problem of 2σ–deviation from the unitarity of the first row elements in the CKM matrix. Today we have, |V us | 2 + |V ud | 2 + |V ub | 2 − 1 = −0.0008(13), −0.0010(13), or −0.0005(13), depending on whether the q 2-dependence of the relevant K ℓ3 form factor is considered as pole-like, linear or quadratic fun...

This paper investigates the relationship between instructional effectiveness of animated vs. static diagrams and levels of learner expertise in the task domain of transforming graphs of simple linear and quadratic functions. It was demonstrated on many occasions that instructional formats that are effective for low-knowledge learners could be ineffective, or even deleterious, for high-knowledge...

Abstract. We prove two related concentration inequalities concerning the number of rational points of hyperelliptic curves over subsets of a finite field. In particular, we investigate the probability of a large discrepancy between the numbers of quadratic residues and non-residues in the image of such subsets over uniformly random hyperelliptic curves of given degrees. We find a constant proba...

The University of Manitoba Sieve Unit is used to find several values of A (> 0) such that the quadratic polynomial x + x + A will have a large asymptotic density of prime values. The Hardy-Littlewood constants which characterize this density are also evaluated.

We give asymptotic formulas for the number of biquadratic extensions of Q that admit a quadratic extension which is a Galois extension of Q with a prescribed Galois group, for example, with a Galois group isomorphic to the quaternionic group. Our approach is based on a combination of the theory of quadratic equations with some analytic tools such as the Siegel–Walfisz theorem and the double osc...

In this paper, using a method of Luca and the author, we find all values x such that the quadratic polynomials x + 1, x + 4, x + 2 and x − 2 are 200-smooth and all values x such that the quadratic polynomial x − 4 is 100-smooth.

This paper constructs an asymptotically complete class of tests (i.e. for a test not within this class one can ...nd a test within the class that has better or equal asymptotical powerfunction) for testing one parametric restriction when the likelihoodfunction can asymptotically be approximated by a quadratic function: The coe¢cients of this quadratic form may be random variables, so that our r...

A new method for determining knots in parametric curve interpolation is presented. The determined knots have a quadratic polynomial precision in the sense that an interpolation scheme which reproduces quadratic polynomials would reproduce parametric quadratic polynomials if the new method is used to determine knots in the interpolation process. Testing results on the efficiency of the new metho...