Does Information Beget Information?

Using the language of mathematics, Professor Polk Wagner has recently argued that the impossibility of fully appropriating the value of information in a rightsholder leads to the surprising conclusion that expanding the degree of control of intellectual property rights will, in the long run, increase the sum total of information not subject to ownership claims and therefore available as part of the cultural and technological base on which new growth and development can occur. Indeed, he claims that open information will grow according to the formula for compound interest, where the interest rate is 100% plus or minus a factor z supposedly related to creation incentives. This article demonstrates that Professor Wagner’s mathematical analysis is simply wrong and does not lead to any of the conclusions he reaches concerning the growth of open information. It also shows both the difficulties and the dangers of the lay use of the language of mathematics in resolving complex social problems even if one does the math correctly

Criteria for \sigma-ampleness

In the noncommutative geometry of Artin, Van den Bergh, and others, the twisted homogeneous coordinate ring is one of the basic constructions. Such a ring is defined by a $\sigma$-ample divisor, where $\sigma$ is an automorphism of a projective scheme X. Many open questions regarding $\sigma$-ample divisors have remained. We derive a relatively simple necessary and sufficient condition for a divisor on X to be $\sigma$-ample. As a consequence, we show right and left $\sigma$-ampleness are equivalent and any associated noncommutative homogeneous coordinate ring must be noetherian and have finite, integral GK-dimension. We also characterize which automorphisms $\sigma$ yield a $\sigma$-ample divisor.Comment: 16 pages, LaTeX2e, to appear in J. of the AMS, minor errors corrected (esp. in 1.4 and 3.1), proofs simplifie

Fujita's Conjecture and Frobenius amplitude

We prove a version of Fujita's Conjecture in arbitrary characteristic, generalizing results of K.E. Smith. Our methods use the Frobenius morphism, but avoid tight closure theory. We also obtain versions of Fujita's Conjecture for coherent sheaves with certain ampleness properties.Comment: 8 pages. Erratum added to replace Lemma 2.

The flashing behavior of thunderstorms

Lightning flash distribution in thunderstorms - statistical analysi

A Range-Based GARCH Model for Forecasting Volatility

A new variant of the ARCH class of models for forecasting the conditional variance, to be called the Generalized AutoRegressive Conditional Heteroskedasticity Parkinson Range (GARCH-PARK-R) Model, is proposed. The GARCH-PARK-R model, utilizing the extreme values, is a good alternative to the Realized Volatility that requires a large amount of intra-daily data, which remain relatively costly and are not readily available. The estimates of the GARCH-PARK-R model are derived using the Quasi-Maximum Likelihood Estimation (QMLE). The results suggest that the GARCH-PARK-R model is a good middle ground between intra-daily models, such as the Realized Volatility and inter-daily models, such as the ARCH class. The forecasting performance of the models is evaluated using the daily Philippine Peso-U.S. Dollar exchange rate from January 1997 to December 2003.Volatility, Parkinson Range, GARCH-PARK-R, QMLE

Effect of engine, tank and propellant specific cost on single stage recoverable booster economics

Reusable first stages using hydrogen-oxygen, hydrogen-fluorine and kerosine-oxygen are compared with non-reusable stages using a solid in addition to the liquid combinations. The criterion used for comparison is the minimum specific cost of the "loaded and ready for launch" stage cost per unit of stage payload mass. A closed form relationship is used in which the empty stage mass without payload is taken to scale in part proportional to propellant mass, and in part to mass flow rate. The stage specific cost is proportional to specific cost of engine (or nozzle) tank and propellant. In the second part the hydrogen-oxygen combination is consiaered,in more detail. The sensitivity of the results to changes in various specific costs including that of refurbishing are described. Throughout, the stage velocity increments are compared in the 3000-6000 metres/second range with losses

The development of test methodology for testing glassy materials

The inherent brittleness of glass invariably leads to a large variability in strength data and a time dependence in strength (i.e., static fatigue). Loading rate plays a large role in strength values. Glass is found to be weaker when supporting loads over long periods as compared to glass which undergoes rapid loading. In this instance the purpose of rapid loading is to fail the glass before any significant crack growth occurs. However, a decrease in strength occurs with a decrease in loading rate, pursuant to substantial crack extension. These properties complicate the structural design allowable for the utilization of glass components in applications such as mirrors for the Space Telescope and AXAF for Spacelab and the space station