Decompositions of spaces of measures

Let M be the Banach space of sigma-additive complex-valued measures on an abstract measurable space. We prove that any closed, with respect to absolute continuity norm-closed, linear subspace L of M is complemented and describe the unique complement, projection onto L along which has norm 1. Using this fact we prove a decomposition theorem, which includes the Jordan decomposition theorem, the generalized Radon-Nikodym theorem and the decomposition of measures into decaying and non-decaying components as particular cases. We also prove an analog of the Jessen-Wintner purity theorem for our decompositions.

Extended spectral decompositions of the Renyi map

We present new general methods to obtain spectral decompositions of dynamical systems in rigged Hilbert spaces and investigate the existence of resonances and the completeness of the associated eigenfunctions. The results are illustrated explicitly for the simplest chaotic endomorphism, namely the Renyi map.

Fast Moving Window Algorithm for QR and Cholesky Decompositions

This paper proposes a fast moving window algorithm for QR and Cholesky decompositions by simultaneously applying data updating and downdating. The developed procedure is based on inner products and entails a similar downdating to that of the Chambers’ approach. For adding and deleting one row of data from the original matrix, a detailed analysis shows that the proposed algorithm outperforms existing ones in terms or computational efficiency, if the number of columns exceeds 7. For a large number of columns, the proposed algorithm is numerically superior compared to the traditional sequential technique.

New techniques for enhanced medial axis based decompositions in 2-D

New techniques are presented for using the medial axis to generate high quality decompositions for generating block-structured meshes with well-placed mesh singularities away from the surface boundaries. Established medial axis based meshing algorithms are highly effective for some geometries, but in general, they do not produce the most favourable decompositions, particularly when there are geometry concavities. This new approach uses both the topological and geometric information in the medial axis to establish a valid and effective arrangement of mesh singularities for any 2-D surface. It deals with concavities effectively and finds solutions that are most appropriate to the geometric shapes. Methods for directly constructing the corresponding decompositions are also put forward.

A study of thermal decompositions of an allylic hydroperoxide /|nby Thomas A. McCarrick. -- 260 St. Catharines [Ont.] : Dept. of Chemistry, Brock University,

The thermal decomposition of 2,3-di~ethy l - J-hydr operox y- 1 - butene , p r epared f rol") singl e t oxygen, has been studied i n three solvents over the tempe r a ture r ange from 1500e to l o00e and t!1e i 111 t ial ~oncentrfttl nn r Ange from O. 01 M to 0.2 M. Analys i s of the kine tic data ind ica te s i nduced homolysis as the n ost probRble mode of d e composition, g iving rise to a 3/2 f S order dependence upon hy d.roperoxide concent :r8.tl on . Experimental activation e nergies for the decomposition were f ound to be between 29.5 kcsl./raole and 30.0 k cal./mole .• \,iith log A factors between 11 . 3 and 12.3. Product studies were conducted in R variety of solvents a s well as in the pr esence of a variety of free r adical initiators . Investigation of the kinetic ch a in length indicated a chain length of about fifty. A degenerat i ve chain branching mechanism 1s proposed which predicts the multi t ude of products which Rre observed e xperimentally as well as giving activation energies and log A factors si~il a r to those found experimentally .

Dynamic Morse decompositions for semigroups of homeomorphisms and control systems

In this paper, we introduce the concept of dynamic Morse decomposition for an action of a semigroup of homeomorphisms. Conley has shown in [5, Sec. 7] that the concepts of Morse decomposition and dynamic Morse decompositions are equivalent for flows in metric spaces. Here, we show that a Morse decomposition for an action of a semigroup of homeomorphisms of a compact topological space is a dynamic Morse decomposition. We also define Morse decompositions and dynamic Morse decompositions for control systems on manifolds. Under certain condition, we show that the concept of dynamic Morse decomposition for control system is equivalent to the concept of Morse decomposition.