67,287 research outputs found
Binomial coefficients, Catalan numbers and Lucas quotients
Let be an odd prime and let be integers with and . In this paper we determine
mod for ; for example,
where is the Jacobi symbol, and is the Lucas
sequence given by , and for
. As an application, we determine modulo for any integer , where denotes the
Catalan number . We also pose some related conjectures.Comment: 24 pages. Correct few typo
Achieving Effective Innovation Based On TRIZ Technological Evolution
Organised by: Cranfield UniversityThis paper outlines the conception of effective innovation and discusses the method to achieve it. Effective
Innovation is constrained on the path of technological evolution so that the corresponding path must be
detected before conceptual design of the product. The process of products technological evolution is a
technical developing process that the products approach to Ideal Final Result (IFR). During the process, the
sustaining innovation and disruptive innovation carry on alternately. By researching and forecasting potential
techniques using TRIZ technological evolution theory, the effective innovation can be achieved finally.Mori Seiki – The Machine Tool Compan
Current-Induced Effective Magnetic Fields in Co/Cu/Co Nanopillars
We present a method to measure the effective field contribution to
spin-transfer-induced interactions between the magnetic layers in a trilayer
nanostructure, which enables spin-current effects to be distinguished from the
usual charge-current-induced magnetic fields. This technique is demonstrated on
submicron Co/Cu/Co nanopillars. The hysteresis loop of one of the magnetic
layers in the trilayer is measured as a function of current while the direction
of magnetization of the other layer is kept fixed, first in one direction and
then in the opposite direction. These measurements show a current-dependent
shift of the hysteresis loop which, based on the symmetry of the magnetic
response, we associate with spin-transfer. The observed loop-shift with applied
current at room temperature is reduced in measurements at 4.2 K. We interprete
these results both in terms of a spin-current dependent effective activation
barrier for magnetization reversal and a spin-current dependent effective
magnetic field. From data at 4.2 K we estimate the magnitude of the
spin-transfer induced effective field to be Oe
cm/A, about a factor of 5 less than the spin-transfer torque.Comment: 6 pages, 4 figure
Current Induced Excitations in Cu/Co/Cu Single Ferromagnetic Layer Nanopillars
Current-induced magnetic excitations in Cu/Co/Cu single layer nanopillars
(~50 nm in diameter) have been studied experimentally as a function of Co layer
thickness at low temperatures for large applied fields perpendicular to the
layers. For asymmetric junctions current induced excitations are observed at
high current densities for only one polarity of the current and are absent at
the same current densities in symmetric junctions. These observations confirm
recent predictions of spin-transfer torque induced spin wave excitations in
single layer junctions with a strong asymmetry in the spin accumulation in the
leads.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let
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