Abstract In this paper we analyze the stability of problem performing a rational QZ step with shift that is an eigenvalue given regular pencil $$H-\lambda K$$ H - λ K in unreduced Hessenberg–Hessenberg form. exact arithmetic, backward m...

We study problems associated with an operator pencil, i.e., a pair of operators on Banach spaces. Two natural problems to consider are linear constrained differential equations and the description of the generalized spectrum. The main tool to tackle either of those problems is the reduction of the pencil. There are two kinds of natural reduction operations associated to a pencil, which are conj...

Let A(x) = A0 + x1A1 + · · · + xnAn be a linear matrix, or pencil, generated by given symmetric matrices A0, A1, . . . , An of size m with rational entries. The set of real vectors x such that the pencil is positive semidefinite is a convex semialgebraic set called spectrahedron, described by a linear matrix inequality (LMI). We design an exact algorithm that, up to genericity assumptions on th...

OBJECTIVE The purpose of this study was to determine whether writing tool type and angle of writing surface affect grasp. METHOD Fifty-one children 23 to 24 months of age who were typically developing drew with a primary marker, colored pencil, and small piece of crayon on a table and an easel. The marker and pencil were presented pointing left, right, and toward the child. The order of writi...

Many articles in the medical literature report some cases of foreign bodies introduced into the urogenital system. Most cases are related to psychiatric disorders, stories of drug addiction or the purpose of sexual stimulation. The urinary bladder seems to be an inaccessible site for the introduction of foreign bodies, particularly in the male; however, almost every conceivable object has been ...

Three techniques are proposed for more realistic image synthesis of transparent objects. The techniques simulate important phenomena due to refraction and/or reflection, such as focuses and dispersion. For efficient simulation of focuses and caustics, a method called grid-pencil tracing is proposed, based on the ideas of pencil tracing and backward ray tracing. An anti-aliasing filter is design...