Detection of variable frequency signals using a fast chirp transform

The detection of signals with varying frequency is important in many areas of physics and astrophysics. The current work was motivated by a desire to detect gravitational waves from the binary inspiral of neutron stars and black holes, a topic of significant interest for the new generation of interferometric gravitational wave detectors such as LIGO. However, this work has significant generality beyond gravitational wave signal detection. We define a Fast Chirp Transform (FCT) analogous to the Fast Fourier Transform (FFT). Use of the FCT provides a simple and powerful formalism for detection of signals with variable frequency just as Fourier transform techniques provide a formalism for the detection of signals of constant frequency. In particular, use of the FCT can alleviate the requirement of generating complicated families of filter functions typically required in the conventional matched filtering process. We briefly discuss the application of the FCT to several signal detection problems of current interest

Laurent inversion

There are well-understood methods, going back to Givental and Hori--Vafa, that to a Fano toric complete intersection X associate a Laurent polynomial f that corresponds to X under mirror symmetry. We describe a technique for inverting this process, constructing the toric complete intersection X directly from its Laurent polynomial mirror f. We use this technique to construct a new four-dimensional Fano manifold

Research in particles and fields

Research activities in Cosmic Rays Gamma Rays, and Astrophysical Plasmas are covered The investigation of the astrophysical aspects of cosmic rays and gamma rays and of the radiation and electromagnetic field environment of the Earth and other planets are studied. These investigations are carried ut by means of energetic particle and photon detector systems flown on spacecraft and balloons. The emphasis is on precision measurements with high resolution in charge mass and energy. An extensive bibliography is given

Research in particles and fields

The astrophysical aspects of cosmic rays and gamma rays and the radiation and electromagnetic field environment of the Earth and other planets are investigated. These investigations are carried out by means of energetic particle and photon detector systems flown on spacecraft and balloons. Particle astrophysics is directed toward the investigation of galactic, solar, interplanetary, and planetary energetic particles and plasmas. The emphasis is on precision measurements with high resolution in charge, mass, and energy. Gamma ray research is directed toward the investigation of galactic, extragalactic, and solar gamma rays with spectrometers of high angular resolution and moderate energy resolution carried on spacecraft and balloons

Research in particles and fields

Research activities in Cosmic Rays, Gamma Rays, and Astrophysical Plasmas supported under NASA Grant NGR 05-002-160 are discussed. The report is divided into sections which describe the activities, followed by a bibliography. This group's research program is directed toward the investigation of the astrophysical aspects of cosmic rays and gamma rays and of the radiation and electromagnetic field environment of the Earth and other planets. These investigations are carried out by means of energetic particle and photon detector systems flown on spacecraft and balloons

Research in cosmic and gamma ray astrophysics

Research activities in cosmic rays, gamma rays, and astrophysical plasmas are covered. The activities are divided into sections and described, followed by a bibliography. The astrophysical aspects of cosmic rays, gamma rays, and of the radiation and electromagnetic field environment of the Earth and other planets are investigated. These investigations are performed by means of energetic particle and photon detector systems flown on spacecraft and balloons

Research in particle and gamma-ray astrophysics

Research activities in cosmic rays, gamma rays, and astrophysical plasmas are covered. Each activity is described, followed by a bibliography. The research program is directed toward the investigation of the astrophysical aspects of cosmic rays and gamma rays and of the radiation and electromagnetic field environment of the earth and other planets. These investigations were performed by means of energetic particle and photon detector systems flown on spacecraft and balloons

Research in particles and fields

Discussed are the research activities in Cosmic Rays, Gamma Rays, and Astrophysical Plasmas supported under NASA Grant NGR 05-002-160. The report is divided into sections which describe the activities, followed by a bibliography. This research program is directed toward the investigation of the astrophysical aspects of cosmic rays and gamma rays and of the radiation and electromagnetic field environment of the Earth and other planets. These investigations are carried out by means of energetic particle and photon detector systems flown on spacecraft and balloons