394,179 research outputs found
The Intuitive Logarithm
We introduce the intuitive method to select an analytic Abel function of an
analytic function f at a non-fixpoint. Due to the complexity of this method by
involving matrix inversion of increasing size there is little known about its
convergence.
We show its convergence in the simplest but still complicated case f(x)=bx.
We show that the obtained Abel function is, as expected, the logarithm to base
b, independent on its development point. As a by-product we obtain a new
polynomial approximation sequence for the logarithm to base b.Comment: 12 page
The ElGamal cryptosystem over circulant matrices
In this paper we study extensively the discrete logarithm problem in the
group of non-singular circulant matrices. The emphasis of this study was to
find the exact parameters for the group of circulant matrices for a secure
implementation. We tabulate these parameters. We also compare the discrete
logarithm problem in the group of circulant matrices with the discrete
logarithm problem in finite fields and with the discrete logarithm problem in
the group of rational points of an elliptic curve
Ultrametric Logarithm Laws, II
We prove positive characteristic versions of the logarithm laws of Sullivan
and Kleinbock-Margulis and obtain related results in Metric Diophantine
Approximation.Comment: submitted to Montasefte Fur Mathemati
Soft Gluons in Logarithmic Summations
We demonstrate that all the known single- and double-logarithm summations for
a parton distribution function can be unified in the Collins-Soper resummation
technique by applying soft approximations appropriate in different kinematic
regions to real gluon emissions. Neglecting the gluon longitudinal momentum, we
obtain the (double-logarithm) resummation for two-scale QCD processes,
and the Balitsky-Fadin-Kuraev-Lipatov (single-logarithm) equation for one-scale
processes. Neglecting the transverse momentum, we obtain the threshold
(double-logarithm) resummation for two-scale processes, and the
Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (single-logarithm) equation for
one-scale processes. If keeping the longitudinal and transverse momenta
simultaneously, we derive a unified resummation for large Bjorken variable ,
and a unified evolution equation appropriate for both intermediate and small
.Comment: 14 pages in Latex, 1 figure in postscript fil
Ultrametric Logarithm Laws I
We announce ultrametric analogues of the results of Kleinbock-Margulis for
shrinking target properties of semisimple group actions on symmetric spaces.
The main applications are S-arithmetic Diophantine approximation results and
logarithm laws for buildings, generalizing the work of Hersonsky-Paulin on
trees.Comment: This announcement has been completely revised to reflect many new
developments. Please direct all references to this NEW announcement. It is
now co-authored work. Submitted to Discrete and Continuous Dynamical System
Poisson noise induced switching in driven micromechanical resonators
We study Poisson-noise induced switching between coexisting vibrational
states in driven nonlinear micromechanical resonators. In contrast to Gaussian
noise induced switching, the measured logarithm of the switching rate is
proportional not to the reciprocal noise intensity, but to its logarithm, for
fixed pulse area. We also find that the switching rate logarithm varies as a
square root of the distance to the bifurcation point, instead of the
conventional scaling with exponent 3/2.Comment: accepted by PR
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