Forms Equivalent to Curvatures

Equivalent Forms of Multistep Formulas

For uniform meshes it is shown that any linear fc-step formula can be formulated so that only k values need to be saved between steps. By saving additional m values it is possible to construct local polynomial approximations of degree k + m — 1, which can be used as predictor formulas. Different polynomial bases lead to different equivalent forms of multistep formulas. In particular, local mono...

Quadratic Integer Programming: Complexity and Equivalent Forms

Applications of quadratic D-forms to generalized quadratic forms

In this paper, we study generalized quadratic forms over a division algebra with involution of the first kind in characteristic two. For this, we associate to every generalized quadratic from a quadratic form on its underlying vector space. It is shown that this form determines the isotropy behavior and the isometry class of generalized quadratic forms.

Equivalent forms of the Bessis-Moussa-Villani conjecture

The BMV conjecture for traces, which states that Tr exp(A−λB) is the Laplace transform of a positive measure, is shown to be equivalent to two other statements: (i) The polynomial λ 7→ Tr (A+λB)p has only non-negative coefficients for all A,B ≥ 0, p ∈ N and (ii) λ 7→ Tr (A + λB)−p is the Laplace transform of a positive measure for A,B ≥ 0, p > 0. An intriguing conjecture [1], which is more than...

Inequalities for Generalized Normalized Δ-casorati Curvatures of Slant Submanifolds in Quaternionic Space Forms

In this paper we prove two sharp inequalities involving the normalized scalar curvature and the generalized normalized δ-Casorati curvatures for slant submanifolds in quaternionic space forms. We also characterize those submanifolds for which the equality cases hold. These results are a generalization of some recent results concerning the Casorati curvature for a slant submanifold in a quaterni...