We consider the problem of minimizing an indefinite quadratic function over the nonnegative orthant, or equivalently, the problem of deciding whether a symmetric matrix is copositive. We formulate the problem as a difference of convex functions (d.c.) problem. Using conjugate duality, we show that there is a one-to-one correspondence between their respective stationary points and minima. We the...

2. The Freudenthal theorem for symmetric spaces Our primary interest is in the classical compact groups; nevertheless, it is essential for our method to consider the larger family of compact symmetric spaces. A compact homogeneous Riemannian manifold M is called symmetric if it admits an 'inverse operation', i.e. if M admits an isometry, keeping a point P e M fixed, and whose differential at P ...

Two algorithms for constructing a class of compactly supported complex tight wavelet frames with conjugate symmetry are provided. Firstly, based on a given complex refinable function φ, an explicit formula for constructing complex tight wavelet frames is presented. If the given complex refinable function φ is compactly supported conjugate symmetric, then we prove that there exists a compactly s...

in this paper, we show that a matrix a in mn(c) that has n coneigenvectors, where coneigenvaluesassociated with them are distinct, is condiagonalizable. and also show that if allconeigenvalues of conjugate-normal matrix a be real, then it is symmetric.

In the present paper, we introduce two new subclasses P sc (λ, α) and Q sc (λ, α) of analytic functions with respect to 2k-symmetric conjugate points. Such results as integral representations, convolution conditions and coefficient inequalities for these classes are provided. 2000 Mathematics Subject Classification. Primary 30C45.