Carath\'eodory's Theorem and moduli of local connectivity

We give a constructive proof of the Carath\'eodory Theorem by means of the concept of a modulus of local connectivity and the extremal distance of the separating curves of an annulus

Analytical and test equipment: A compilation

A compilation is presented of innovations in testing and measuring technology for both the laboratory and industry. Topics discussed include spectrometers, radiometers, and descriptions of analytical and test equipment in several areas including thermodynamics, fluid flow, electronics, and materials testing

User's manual for the ALS base heating prediction code, volume 2

The Advanced Launch System (ALS) Base Heating Prediction Code is based on a generalization of first principles in the prediction of plume induced base convective heating and plume radiation. It should be considered to be an approximate method for evaluating trends as a function of configuration variables because the processes being modeled are too complex to allow an accurate generalization. The convective methodology is based upon generalizing trends from four nozzle configurations, so an extension to use the code with strap-on boosters, multiple nozzle sizes, and variations in the propellants and chamber pressure histories cannot be precisely treated. The plume radiation is more amenable to precise computer prediction, but simplified assumptions are required to model the various aspects of the candidate configurations. Perhaps the most difficult area to characterize is the variation of radiation with altitude. The theory in the radiation predictions is described in more detail. This report is intended to familiarize a user with the interface operation and options, to summarize the limitations and restrictions of the code, and to provide information to assist in installing the code

Electronic Components Subsystems and Equipment: a Compilation

Developments in electronic components, subsystems, and equipment are summarized. Topics discussed include integrated circuit components and techniques, circuit components and techniques, and cables and connectors

Defections From The Inner Circle: Social Exchange, Reciprocity, And The Diffusion Of Board Independence In Us Corporations

This study seeks to reconcile traditional sociological views of the corporate board as an instrument of elite cohesion with recent evidence of greater board activism and control over top management. We propose that CEO-directors may typically support fellow CEOs by impeding increased board control over management but that CEO-directors may also foster this change if they have experienced it in their own corporation. Drawing on social exchange theory, we develop and test the argument that these CEO-directors may experience a reversal in the basis for generalized social exchange with other top managers from one of deference and support to one of independence and control. Using data from a large sample of major U.S. corporations over a recent ten-year period, we show (1) how CEO-directors ''defect'' from the network of mutually supportive corporate leaders, (2) how defections have diffused across organizations and over time, and (3) how this has contributed to increased board control, as measured by changes in board structure, diversification strategy, and contingent compensation. We also provide evidence that a social exchange perspective can explain the diffusion of these changes better than more conventional perspectives on network diffusion that emphasize imitation or learning.Business Administratio

Some new results on decidability for elementary algebra and geometry

We carry out a systematic study of decidability for theories of (a) real vector spaces, inner product spaces, and Hilbert spaces and (b) normed spaces, Banach spaces and metric spaces, all formalised using a 2-sorted first-order language. The theories for list (a) turn out to be decidable while the theories for list (b) are not even arithmetical: the theory of 2-dimensional Banach spaces, for example, has the same many-one degree as the set of truths of second-order arithmetic. We find that the purely universal and purely existential fragments of the theory of normed spaces are decidable, as is the AE fragment of the theory of metric spaces. These results are sharp of their type: reductions of Hilbert's 10th problem show that the EA fragments for metric and normed spaces and the AE fragment for normed spaces are all undecidable.Comment: 79 pages, 9 figures. v2: Numerous minor improvements; neater proofs of Theorems 8 and 29; v3: fixed subscripts in proof of Lemma 3

Efficient Solving of Quantified Inequality Constraints over the Real Numbers

Let a quantified inequality constraint over the reals be a formula in the first-order predicate language over the structure of the real numbers, where the allowed predicate symbols are $\leq$ and $<$. Solving such constraints is an undecidable problem when allowing function symbols such $\sin$ or $\cos$. In the paper we give an algorithm that terminates with a solution for all, except for very special, pathological inputs. We ensure the practical efficiency of this algorithm by employing constraint programming techniques