On the Areas of Cyclic and Semicyclic Polygons

We investigate the ``generalized Heron polynomial'' that relates the squared area of an n-gon inscribed in a circle to the squares of its side lengths. For a (2m+1)-gon or (2m+2)-gon, we express it as the defining polynomial of a certain variety derived from the variety of binary (2m-1)-forms having m-1 double roots. Thus we obtain explicit formulas for the areas of cyclic heptagons and octagons, and illuminate some mysterious features of Robbins' formulas for the areas of cyclic pentagons and hexagons. We also introduce a companion family of polynomials that relate the squared area of an n-gon inscribed in a circle, one of whose sides is a diameter, to the squared lengths of the other sides. By similar algebraic techniques we obtain explicit formulas for these polynomials for all n <= 7.Comment: 22 page

Carrier-interference ratios for frequency sharing between frequency-modulated amplitude-modulated-vestigial-sideband television systems

For just perceptible interference, an FM television signal interfering with another FM television signal must have an average signal power that is 26 to 37 db less than the wanted signal power. For an AM-VSB television signal interfering with an FM television signal, the AM-VSB television's sync peak average power must be 18 to 31 db below the FM television signal's average power. Also, when an FM television signal interferes with an AM-VSB signal, the average signal power of the FM signal should be 56 to 59 db below the sync peak average power of the AM-VSB television signal. The range of power ratios occur as a result of different TV scenes used in the tests and different FM-signal frequency deviations used. All tests were performed using 525 line, system M, color-television signals

An overview of the fundamental aerodynamics branch's research activities in wing leading-edge vortex flows at supersonic speeds

For the past 3 years, a research program pertaining to the study of wing leading edge vortices at supersonic speeds has been conducted in the Fundamental Aerodynamics Branch of the High-Speed Aerodynamics Division at the Langley Research Center. The purpose of the research is to provide an understanding of the factors governing the formation and the control of wing leading-edge vortices and to evaluate the use of these vortices for improving supersonic aerodynamic performance. The studies include both experimental and theoretical investigations and focus primarily on planform, thickness and camber effects for delta wings. An overview of this research activity is presented

Phenomenological Consequences of the Constrained Exceptional Supersymmetric Standard Model

The Exceptional Supersymmetric Standard Model (E$_6$SSM) provides a low energy alternative to the MSSM, with an extra gauged U(1)$_N$ symmetry, solving the $\mu$-problem of the MSSM. Inspired by the possible embedding into an E$_6$ GUT, the matter content fills three generations of E$_6$ multiplets, thus predicting exciting exotic matter such as diquarks or leptoquarks. We present predictions from a constrained version of the model (cE$_6$SSM), with a universal scalar mass $m_0$, trilinear mass $A$ and gaugino mass $M_{1/2}$. We reveal a large volume of the cE$_6$SSM parameter space where the correct breakdown of the gauge symmetry is achieved and all experimental constraints satisfied. We predict a hierarchical particle spectrum with heavy scalars and light gauginos, while the new exotic matter can be light or heavy depending on parameters. We present representative cE$_6$SSM scenarios, demonstrating that there could be light exotic particles, like leptoquarks and a U(1)$_N$ Z' boson, with spectacular signals at the LHC.Comment: Contribution to the proceedings of SUSY 09, Boston, USA, June 2009, 4 page

Frequency response calibration of recess-mounted pressure transducers

A technique is described for measuring the frequency response of pressure transducers mounted inside a model, where a narrow pipette leads to an orifice at the surface. An acoustic driver is mounted to a small chamber which has an opening at the opposite end with an O-ring seal to place over the orifice. A 3.18 mm (1/8 inch) reference microphone is mounted to one side of the chamber. The acoustic driver receives an input of white noise, and the transducer and reference microphone outputs are compared to obtain the frequency response of the pressure transducer. Selected results are presented in the form of power spectra for both the transducer and the reference, as well as the amplitude variation and phase shift between the two signals as a function of frequency. The effect of pipette length and the use of this technique for identifying both blocked orifices and faulty transducers are described

Chemical Bonding Technology: Direct Investigation of Interfacial Bonds

This is the third Flat-Plate Solar Array (FSA) Project document reporting on chemical bonding technology for terrestrial photovoltaic (PV) modules. The impetus for this work originated in the late 1970s when PV modules employing silicone encapsulation materials were undergoing delamination during outdoor exposure. At that time, manufacturers were not employing adhesion promoters and, hence, module interfaces in common with the silicone materials were only in physical contact and therefore easily prone to separation if, for example, water were to penetrate to the interfaces. Delamination with silicone materials virtually vanished when adhesion promoters, recommended by silicone manufacturers, were used. The activities related to the direct investigation of chemically bonded interfaces are described

Families of classical subgroup separable superintegrable systems

We describe a method for determining a complete set of integrals for a classical Hamiltonian that separates in orthogonal subgroup coordinates. As examples, we use it to determine complete sets of integrals, polynomial in the momenta, for some families of generalized oscillator and Kepler-Coulomb systems, hence demonstrating their superintegrability. The latter generalizes recent results of Verrier and Evans, and Rodriguez, Tempesta and Winternitz. Another example is given of a superintegrable system on a non-conformally flat space.Comment: 9 page