23,729 research outputs found
On Lerch's transcendent and the Gaussian random walk
Let be independent variables, each having a normal distribution
with negative mean and variance 1. We consider the partial sums
, with , and refer to the process as
the Gaussian random walk. We present explicit expressions for the mean and
variance of the maximum These expressions are in terms
of Taylor series about with coefficients that involve the Riemann
zeta function. Our results extend Kingman's first-order approximation [Proc.
Symp. on Congestion Theory (1965) 137--169] of the mean for .
We build upon the work of Chang and Peres [Ann. Probab. 25 (1997) 787--802],
and use Bateman's formulas on Lerch's transcendent and Euler--Maclaurin
summation as key ingredients.Comment: Published at http://dx.doi.org/10.1214/105051606000000781 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Mean-field scaling function of the universality class of absorbing phase transitions with a conserved field
We consider two mean-field like models which belong to the universality class
of absorbing phase transitions with a conserved field. In both cases we derive
analytically the order parameter as function of the control parameter and of an
external field conjugated to the order parameter. This allows us to calculate
the universal scaling function of the mean-field behavior. The obtained
universal function is in perfect agreement with recently obtained numerical
data of the corresponding five and six dimensional models, showing that four is
the upper critical dimension of this particular universality class.Comment: 8 pages, 2 figures, accepted for publication in J. Phys.
Miniature modular microwave end-to-end receiver
An end-to-end microwave receiver system contained in a single miniature hybrid package mounted on a single heatsink is presented. It includes an input end connected to a microwave receiver antenna and an output end which produces a digital count proportional to the amplitude of a signal of a selected microwave frequency band received at the antenna and corresponding to one of the water vapor absorption lines near frequencies of 20 GHz or 30 GHz. The hybrid package is on the order of several centimeters in length and a few centimeters in height and width. The package includes an L-shaped carrier having a base surface, a vertical wall extending up from the base surface and forming a corner therewith, and connection pins extending through the vertical wall. Modular blocks rest on the base surface against the vertical wall and support microwave monolithic integrated circuits on top surfaces thereof connected to the external connection pins. The modular blocks lie end-to-end on the base surface so as to be modularly removable by sliding along the base surface beneath the external connection pins away from the vertical wall
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