On Tracial Operator Representations of Quantum Decoherence Functionals

A general `quantum history theory' can be characterised by the space of histories and by the space of decoherence functionals. In this note we consider the situation where the space of histories is given by the lattice of projection operators on an infinite dimensional Hilbert space $H$. We study operator representations for decoherence functionals on this space of histories. We first give necessary and sufficient conditions for a decoherence functional being representable by a trace class operator on $H \otimes H$, an infinite dimensional analogue of the Isham-Linden-Schreckenberg representation for finite dimensions. Since this excludes many decoherence functionals of physical interest, we then identify the large and physically important class of decoherence functionals which can be represented, canonically, by bounded operators on $H \otimes H$.Comment: 14 pages, LaTeX2

One Share/One Vote and the Market for Corporate Control

A corporation's securities provide the holder with particular claims on the firm's income stream and particular voting rights. These securities can be designed in various ways: one share of a particular class may have a claim to votes which is disproportionately larger or smaller than its claim to income. In this paper we analyze some of the forces which make it desirable to set up the corporation so that all securities have the same proportion of votes as their claim to income ("one share/one vote"). We show that security structure influences both the conditions under which a control change takes place and the terms on which it occurs. First, the allocation of voting rights to securities determines which securities a party must acquire in order to win control. Secondly, the assignment of income claims to the same securities determines the cost of acquiring these voting rights. We will show that it is in shareholders' interest to set the cost of acquiring control to be as large as possible, consistent with a control change occurring whenever this increases shareholder wealth. Under certain assumptions, one share/one vote best achieves this goal. We distinguish between two classes of benefits from control: private benefits and security benefits. The private benefits of control refer to benefits the current management or the acquirer obtain for themselves, but which the target security holders do not obtain. The security benefits refer to the total market value of the corporation's securities. The assignment of income claims to voting rights determines the extent 'to which an acquirer must face competition from parties who value the firm for its security benefits rather than its private benefits.

Code Usage Analysis System (CUAS)

A set of computer programs is offered to aid a user in evaluating performance of an application program. The system provides reports of subroutine usage, program errors, and segment loading which occurred during the execution of an application program. It is presented in support of the development and validation of the space vehicle dynamics project

Reverse engineering of CAD models via clustering and approximate implicitization

In applications like computer aided design, geometric models are often represented numerically as polynomial splines or NURBS, even when they originate from primitive geometry. For purposes such as redesign and isogeometric analysis, it is of interest to extract information about the underlying geometry through reverse engineering. In this work we develop a novel method to determine these primitive shapes by combining clustering analysis with approximate implicitization. The proposed method is automatic and can recover algebraic hypersurfaces of any degree in any dimension. In exact arithmetic, the algorithm returns exact results. All the required parameters, such as the implicit degree of the patches and the number of clusters of the model, are inferred using numerical approaches in order to obtain an algorithm that requires as little manual input as possible. The effectiveness, efficiency and robustness of the method are shown both in a theoretical analysis and in numerical examples implemented in Python