We introduce a new method for the calculation of bounds on the eigenvalues of Hessian matrices of twice continuously differentiable functions. Eigenvalue bounds of Hessian matrices arise in a number of notoriously difficult tasks in computational chemical engineering. For example, Hessian matrix eigenvalue bounds are used in global nonlinear optimization, global convexity/concavity analysis in ...

A choice test revealed that Hessian fly, Mayetiola destructor (Say) (Diptera: Cecidomyiidae), adults deposited approximately 3 times more eggs on wheat (Triticum spp.), seedlings than on barley (Hordeum spp.) or rice, Oryza sativa L., seedlings. On a barley seedling, 49.4% of eggs were deposited on either the abaxial leaf surface or the coleoptile and first leaf sheath (C&FLS), where newly hatc...

In this paper, we consider a class of connected oriented (with respect to Z/p) closed G-manifolds with a non-empty finite fixed point set, each of which is G-equivariantly formal, where G = Z/p and p is an odd prime. Using localization theorem and equivariant index, we give an explicit description of the mod p equivariant cohomology ring of such a G-manifold in terms of algebra. This makes ...

We consider a family of damped quasi-Newton methods for solving unconstrained optimization problems. This family resembles that of Broyden with line searches, except that the change in gradients is replaced by a certain hybrid vector before updating the current Hessian approximation. This damped technique modifies the Hessian approximations so that they are maintained sufficiently positive defi...

here, a finsler manifold $(m,f)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. certain subspaces of the tangent spaces of $m$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. it is shown that if the dimension of foliation is constant, then the distribution is involutive a...