On pricing kernels, information and risk

We discuss the finding that cross-sectional characteristic based models have yielded portfolios with higher excess monthly returns but lower risk than their arbitrage pricing theory counterparts in an analysis of equity returns of stocks listed on the JSE. Under the assumption of general no-arbitrage conditions, we argue that evidence in favour of characteristic based pricing implies that information is more likely assimilated by means of nonlinear pricing kernels for the markets considered.Comment: 20 pages, 3 figures, 1 tabl

Coronal magnetic structure at a solar sector boundary

The persistent large-scale coronal magnetic structure associated with a sector boundary appears to consist of a magnetic arcade loop structure extending from one solar polar region to the other in approximately the North-South direction. This structure was inferred from computer coronal magnetic field maps for days on which a stable magnetic sector boundary was near central meridian, based on an interplanetary sector boundary observed to recur during much of 1968 and 1969

The Hale solar sector boundary

A Hale solar sector boundary is defined as the half (Northern Hemisphere or Southern Hemisphere) of a sector boundary in which the change of sector magnetic field polarity is the same as the change of polarity from a preceding spot to a following spot. Above a Hale sector boundary the green corona has maximum brightness, while above a non-Hale boundary the green corona has a minimum brightness. The Hale portion of a photospheric sector boundary tends to have maximum magnetic field strength, while the non-Hale portion has minimum field strength

Passive venting technique for shallow cavities

A device is introduced for reducing drag and store separation difficulties caused by shallow cavities on aircraft in supersonic flight consisting of a group of hollow pipes the same length as the cavity. The pipes are attached to the cavity floor so as to allow air to flow through the pipes. This device allows air to flow through the pipes opposite to the direction of flow outside the pipes. This results in reduced drag and improved store separation characteristics

The rotation of the Sun: Observations at Stanford

Daily observations of the photospheric rotation rate using the Doppler effect made at the Stanford Solar Observatory since May 1976 are analyzed. Results show that these observations show no daily or long period variations in the rotation rate that exceed the observational error of about one percent. The average rotation rate is the same as that of the sunspot and the large-scale magnetic field structures

The equatorial rotation velocity of the photosphere is measured to be the same as sunspots

The equatorial rotation rate of the photosphere was measured at effect data. It was found that scattered light has a large influence and must be taken into account properly. When this was done it was found that the rotation rate from Doppler shifts agreed very well with the rate found for sunspots. Short-term fluctuations in rotation rate (i.e. from day to day) were less than plus or minus 15 m/s and were thus within observational errors

Experimental cavity pressure distributions at supersonic speeds

An investigation was conducted to define pressure distributions for rectangular cavities over a range of free-stream Mach numbers and cavity dimensions. These pressure distributions together with schlieren photographs are used to define the critical values of cavity length-to-depth ratio that separate open type cavity flows from closed type cavity flows. For closed type cavity flow, the shear layer expands over the cavity leading edge and impinges on the cavity floor, whereas for open type cavity flow, the shear layer bridges the cavity. The tests were conducted by using a flat-plate model permitting the cavity length to be remotely varied from 0.5 to 12 in. Cavity depths and widths were varied from 0.5 to 2.5 in. The flat-plate boundary layer approaching the cavity was turbulent and had a thickness of approximately 0.2 in. at the cavity front face for the range of test Mach numbers from 1.5 to 2.86. Presented are a discussion of the results and a complete tabulation of the experimental data

Fast Mesh Refinement in Pseudospectral Optimal Control

Mesh refinement in pseudospectral (PS) optimal control is embarrassingly easy --- simply increase the order $N$ of the Lagrange interpolating polynomial and the mathematics of convergence automates the distribution of the grid points. Unfortunately, as $N$ increases, the condition number of the resulting linear algebra increases as $N^2$; hence, spectral efficiency and accuracy are lost in practice. In this paper, we advance Birkhoff interpolation concepts over an arbitrary grid to generate well-conditioned PS optimal control discretizations. We show that the condition number increases only as $\sqrt{N}$ in general, but is independent of $N$ for the special case of one of the boundary points being fixed. Hence, spectral accuracy and efficiency are maintained as $N$ increases. The effectiveness of the resulting fast mesh refinement strategy is demonstrated by using \underline{polynomials of over a thousandth order} to solve a low-thrust, long-duration orbit transfer problem.Comment: 27 pages, 12 figures, JGCD April 201

The sun's magnetic sector structure

The synoptic appearance of solar magnetic sectors is studied using 454 sector boundaries observed at earth during 1959-1973. The sectors are clearly visible in the photospheric magnetic field. Sector boundaries can be clearly identified as north-south running demarcation lines between regions of persistent magnetic polarity imbalances. These regions extend up to about 35 deg of latitude on both sides of the equator. They generally do not extend into the polar caps. The polar cap boundary can be identified as an east-west demarcation line marking the poleward limit of the sectors. The typical flux imbalance for a magnetic sector is about 4 x 10 to the 21st power Maxwells