36,402 research outputs found
Computer modeling of multiple-channel input signals and intermodulation losses caused by nonlinear traveling wave tube amplifiers
The multiple channel input signal to a soft limiter amplifier as a traveling wave tube is represented as a finite, linear sum of Gaussian functions in the frequency domain. Linear regression is used to fit the channel shapes to a least squares residual error. Distortions in output signal, namely intermodulation products, are produced by the nonlinear gain characteristic of the amplifier and constitute the principal noise analyzed in this study. The signal to noise ratios are calculated for various input powers from saturation to 10 dB below saturation for two specific distributions of channels. A criterion for the truncation of the series expansion of the nonlinear transfer characteristic is given. It is found that he signal to noise ratios are very sensitive to the coefficients used in this expansion. Improper or incorrect truncation of the series leads to ambiguous results in the signal to noise ratios
Proof of a modular relation between 1-, 2- and 3-loop Feynman diagrams on a torus
The coefficients of the higher-derivative terms in the low energy expansion
of genus-one graviton Type II superstring scattering amplitudes are determined
by integrating sums of non-holomorphic modular functions over the complex
structure modulus of a torus. In the case of the four-graviton amplitude, each
of these modular functions is a multiple sum associated with a Feynman diagram
for a free massless scalar field on the torus. The lines in each diagram join
pairs of vertex insertion points and the number of lines defines its weight
, which corresponds to its order in the low energy expansion. Previous
results concerning the low energy expansion of the genus-one four-graviton
amplitude led to a number of conjectured relations between modular functions of
a given , but different numbers of loops . In this paper we shall
prove the simplest of these conjectured relations, namely the one that arises
at weight and expresses the three-loop modular function in terms of
modular functions with one and two loops. As a byproduct, we prove three
intriguing new holomorphic modular identities.Comment: 38 pages, 9 figures, in version 2: Appendix D added and corrections
made in section
On Hilbert's construction of positive polynomials
In 1888, Hilbert described how to find real polynomials in more than one
variable which take only non-negative values but are not a sum of squares of
polynomials. His construction was so restrictive that no explicit examples
appeared until the late 1960s. We revisit and generalize Hilbert's construction
and present many such polynomials
On the structure of large N cancellations in baryon chiral perturbation theory
We show how to compute loop graphs in heavy baryon chiral perturbation theory
including the full functional dependence on the ratio of the Delta--nucleon
mass difference to the pion mass, while at the same time automatically
incorporating the 1/N cancellations that follow from the large-N spin-flavor
symmetry of baryons in QCD. The one-loop renormalization of the baryon axial
vector current is studied to demonstrate the procedure. A new cancellation is
identified in the one-loop contribution to the baryon axial vector current. We
show that loop corrections to the axial vector currents are exceptionally
sensitive to deviations of the ratios of baryon-pion axial couplings from SU(6)
values
Analysis of existing mathematics textbooks for use in secondary schools.
Thesis (Ed.M.)--Boston University
Thesis (M.A.)--Boston Universit
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