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 explicitly construct a large class of symmetric Boolean functions on 2k variables with algebraic immunity not less than d, where integer k is given arbitrarily and d is a given suffix of k in binary representation. If let d = k, our constructed functions achieve the maximum algebraic immunity. Remarkably, 22 k⌋+2 symmetric Boolean functions on 2k variables with maximum algebra...

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.

The Mullineux involution is a relevant map that appears in the study of modular representations symmetric group and alternating group. fixed points this are certain partitions particular interest. It known cardinality set these self-Mullineux equal to distinguished subset self-conjugate partitions. In work, we give an explicit bijection between two families terms symbol.

We propose an adaptation of the Feasible Direction Interior Points Algorithm (FDIPA) J. Herskovits, for solving large-scale linear programs. At each step, solution two systems with same coefficient matrix is determined. This step involves a significant computational effort. Reducing time is, therefore, way to improve performance method. The be solved are associated definite positive symmetric m...

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.