We use conference matrices to define an action of the complex numbers on the real Euclidean vector space R. In certain cases, the lattice D n becomes a module over a ring of quadratic integers. We can then obtain new unimodular lattices, essentially by multiplying the lattice D n by a non-principal ideal in this ring. We show that lattices constructed via quadratic residue codes, including the ...

We propose two types, namely Type-I and Type-II, quantum stabilizer codes using quadratic residue sets of prime modulus given by the form p = 4n ± 1. The proposed Type-I stabilizer codes are of cyclic structure and code length N = p. They are constructed based on multi-weight circulant matrix generated from idempotent polynomial, which is obtained from a quadratic residue set. The proposed Type...

We consider three parametric relaxations of the 0-1 quadratic programming problem. These relaxations are to: quadratic maximization over simple box constraints, quadratic maximization over the sphere, and the maximum eigenvalue of a bordered matrix. When minimized over the parameter, each of the relaxations provides an upper bound on the original discrete problem. Moreover, these bounds are eec...

In this paper piecewise quadratic stability of closed-loop affine Takagi-Sugeno (ATS) fuzzy systems with linear state-space submodels in the consequent of rules is addressed. The control law is assumed in the form of Parallel Distributed Compensation (PDC). Stability analysis of the closed-loop system is based on piecewise quadratic Lyapunov functions. This technique reduces conservatism of cla...

With the proved efficacy on solving linear time-varying matrix or vector equations, Zhang neural network (ZNN) could be generalized and developed for the online minimization of time-varying quadratic functions. The minimum of a time-varying quadratic function can be reached exactly and rapidly by using Zhang neural network, as compared with conventional gradient-based neural networks (GNN). Com...

This paper presents an improved lower bound and an approximation algorithm based on spectral decomposition for the binary constrained quadratic programming problem. To decompose spectrally the quadratic matrix in the objective function, we construct a low rank problem that provides a lower bound. Then an approximation algorithm for the binary quadratic programming problem together with a worst ...