In this paper we study multivariate polynomial functions in complex variables and the corresponding associated symmetric tensor representations. The focus is on finding conditions under which such complex polynomials/tensors always take real values. We introduce the notion of symmetric conjugate forms and general conjugate forms, and present characteristic conditions for such complex polynomial...

In [10, 18] the transformation technique has been proposed to store k-dimensional intervals { which serve as bounding boxes for arbitrary geometric objects in many applications { as 2k-dimensional points in a point access structure. Unfortunately the transformation technique has two pitfalls: (1) The transformation leads to a skew distribution of the 2k-dimensional image points. (2) Processing ...

The theory of conjugate points in the calculus of variations is reconsidered with a perspective emphasizing the connection to finite-dimensional optimization. The object of central importance is the spectrum of the second-variation operator, analogous to the eigenvalues of the Hessian matrix in finite dimensions. With a few basic properties of this spectrum, one can gain a new perspective on th...

Background: The dosimetric performance of Eclipse 6.5 three dimensional treatment planning system (3DTPS) is evaluated by comparing the calculated and measured dose in two dimensions following the guide lines of American Association for Physicists in Medicine Task Group 53. Materials and Methods: The calculations were performed by the 3DTPS for symmetric as well as asymmetric fields for standar...

Let (M, g) be a complete Riemannian manifold with no conjugate points and f : (M, g) → (B, gB) a principal G-bundle, where G is a Lie group acting by isometries and B the smooth quotient with gB the Riemannian submersion metric. We obtain a characterization of conjugate point-free quotients (B, gB) in terms of symplectic reduction and a canonical pseudo-Riemannian metric on the tangent bundle T...