Solution of the symmetric eigenproblem AX=lambda BX by delayed division

Delayed division is an iterative method for solving the linear eigenvalue problem AX = lambda BX for a limited number of small eigenvalues and their corresponding eigenvectors. The distinctive feature of the method is the reduction of the problem to an approximate triangular form by systematically dropping quadratic terms in the eigenvalue lambda. The report describes the pivoting strategy in the reduction and the method for preserving symmetry in submatrices at each reduction step. Along with the approximate triangular reduction, the report extends some techniques used in the method of inverse subspace iteration. Examples are included for problems of varying complexity

Holographic and ultrasonic detection of bond flaws in aluminum panels reinforced with boron-epoxy

An experimental investigation was made of the application of holographic interferometry to the nondestructive detection of unbonded areas (flaws) in bonded panels. Flaw detection results were compared with results obtained with an ultrasonic flaw detector. Holography, with panel deformation accomplished by a reduction in ambient pressure, is less sensitive for flaws beneath 5 and 10 plies of boron-epoxy than the ultrasonic method, though it does have its operational advantages. A process for the manufacture of bonded panels which incorporate known unbonded areas was also developed. The unbonded areas were formed without the use of foreign materials, which makes the method suitable for the construction of reference standards for bonded panels whenever needed for the proper setup of ultrasonic flaw-detection instruments

On affine rigidity

We define the notion of affine rigidity of a hypergraph and prove a variety of fundamental results for this notion. First, we show that affine rigidity can be determined by the rank of a specific matrix which implies that affine rigidity is a generic property of the hypergraph.Then we prove that if a graph is is $(d+1)$-vertex-connected, then it must be "generically neighborhood affinely rigid" in $d$-dimensional space. This implies that if a graph is $(d+1)$-vertex-connected then any generic framework of its squared graph must be universally rigid. Our results, and affine rigidity more generally, have natural applications in point registration and localization, as well as connections to manifold learning.Comment: Updated abstrac

Novel ring forming reactions for organic synthesis

Almost all biologically important molecules contain a ring in their structure. The first two sections of this manuscript deal with general methodology which will facilitate the construction of certain rings. The last part of this manuscript deals with the total synthesis of a natural product containing a tricyclic structure;Part I deals with the preparation of cyclic 1,2-aminoalcohols. Many important natural products contain this substructure. Several recent synthetic methods have been reported for the synthesis of 1,2-aminoalcohols, attesting to the high interest in this area and also to the need for additional methods. Part I deals with the cycloaddition of dienes with E-1-benzoyloxy-2-nitroethene. The nitro group is then reduced to yield the cyclic 1,2-aminoalcohols;Part II deals with the intramolecular cyclization of cyclic hemiketals with alkenes to yield bicyclic ketals. This reaction proceeds via an alkoxy radical. Many important natural products such as the ginkolides contain the bicyclic ketal moiety. Research is in progress on the application of this methodology to the total synthesis of these biologically important natural products;The last part of this manuscript deals with the total synthesis of a 9-hydroxy substituted iridoid, which was recently isolated from Gelsemium Sempervirens

Letter, 1978 December 3, from Thurston J. Dox to Eva Jessye

1 page, Dox was a Professor of Music for Hartwick College. Paradise Lost and Regained is mentioned. There are two copies of this letter; one has a note from Jessye