Search results for "Exponential function"
showing 10 items of 173 documents
New Encodings of Pseudo-Boolean Constraints into CNF
2009
International audience; This paper answers affirmatively the open question of the existence of a polynomial size CNF encoding of pseudo-Boolean (PB) constraints such that generalized arc consistency (GAC) is maintained through unit propagation (UP). All previous encodings of PB constraints either did not allow UP to maintain GAC, or were of exponential size in the worst case. This paper presents an encoding that realizes both of the desired properties. From a theoretical point of view, this narrows the gap between the expressive power of clauses and the one of pseudo-Boolean constraints.
Towards saturation of the electron-capture delayed fission probability: The new isotopes $^{240}Es$ and $^{236}Bk$
2016
Abstract The new neutron-deficient nuclei 240 Es and 236 Bk were synthesised at the gas-filled recoil separator RITU. They were identified by their radioactive decay chains starting from 240 Es produced in the fusion–evaporation reaction 209 Bi( 34 S,3n) 240 Es. Half-lives of 6 ( 2 ) s and 22 − 6 + 13 s were obtained for 240 Es and 236 Bk, respectively. Two groups of α particles with energies E α = 8.19 ( 3 ) MeV and 8.09 ( 3 ) MeV were unambiguously assigned to 240 Es. Electron-capture delayed fission branches with probabilities of 0.16 ( 6 ) and 0.04 ( 2 ) were measured for 240 Es and 236 Bk, respectively. These new data show a continuation of the exponential increase of ECDF probabilitie…
Radiating and non-radiating sources in elasticity
2018
In this work, we study the inverse source problem of a fixed frequency for the Navier's equation. We investigate that nonradiating external forces. If the support of such a force has a convex or non-convex corner or edge on their boundary, the force must be vanishing there. The vanishing property at corners and edges holds also for sufficiently smooth transmission eigenfunctions in elasticity. The idea originates from the enclosure method: The energy identity and new type exponential solutions for the Navier's equation.
Right-jumps and pattern avoiding permutations
2015
We study the iteration of the process "a particle jumps to the right" in permutations. We prove that the set of permutations obtained in this model after a given number of iterations from the identity is a class of pattern avoiding permutations. We characterize the elements of the basis of this class and we enumerate these "forbidden minimal patterns" by giving their bivariate exponential generating function: we achieve this via a catalytic variable, the number of left-to-right maxima. We show that this generating function is a D-finite function satisfying a nice differential equation of order~2. We give some congruence properties for the coefficients of this generating function, and we sho…
Exponential sums related to Maass forms
2019
We estimate short exponential sums weighted by the Fourier coefficients of a Maass form. This requires working out a certain transformation formula for non-linear exponential sums, which is of independent interest. We also discuss how the results depend on the growth of the Fourier coefficients in question. As a byproduct of these considerations, we can slightly extend the range of validity of a short exponential sum estimate for holomorphic cusp forms. The short estimates allow us to reduce smoothing errors. In particular, we prove an analogue of an approximate functional equation previously proven for holomorphic cusp form coefficients. As an application of these, we remove the logarithm …
Repetition times for Gibbsian sources
1999
In this paper we consider the class of stochastic stationary sources induced by one-dimensional Gibbs states, with Holder continuous potentials. We show that the time elapsed before the source repeats its first n symbols, when suitably renormalized, converges in law either to a log-normal distribution or to a finite mixture of exponential random variables. In the first case we also prove a large deviation result.
Floquet theory: exponential perturbative treatment
2001
We develop a Magnus expansion well suited for Floquet theory of linear ordinary differential equations with periodic coefficients. We build up a recursive scheme to obtain the terms in the new expansion and give an explicit sufficient condition for its convergence. The method and formulae are applied to an illustrative example from quantum mechanics.
Order statistics-based parametric classification for multi-dimensional distributions
2013
Traditionally, in the field of Pattern Recognition (PR), the moments of the class-conditional densities of the respective classes have been used to perform classification. However, the use of phenomena that utilized the properties of the Order Statistics (OS) were not reported. Recently, in [10,8], we proposed a new paradigm named CMOS, Classification by the Moments of Order Statistics, which specifically used these quantifiers. It is fascinating that CMOS is essentially ''anti''-Bayesian in its nature because the classification is performed in a counter-intuitive manner, i.e., by comparing the testing sample to a few samples distant from the mean, as opposed to the Bayesian approach in whi…
On the fractional probabilistic Taylor's and mean value theorems
2016
In order to develop certain fractional probabilistic analogues of Taylor's theorem and mean value theorem, we introduce the nth-order fractional equilibrium distribution in terms of the Weyl fractional integral and investigate its main properties. Specifically, we show a characterization result by which the nth-order fractional equilibrium distribution is identical to the starting distribution if and only if it is exponential. The nth-order fractional equilibrium density is then used to prove a fractional probabilistic Taylor's theorem based on derivatives of Riemann-Liouville type. A fractional analogue of the probabilistic mean value theorem is thus developed for pairs of nonnegative rand…
Stochastic dynamical modelling of spot freight rates
2014
Based on empirical analysis of the Capesize and Panamax indices, we propose different continuous-time stochastic processes to model their dynamics. The models go beyond the standard geometric Brownian motion, and incorporate observed effects like heavy-tailed returns, stochastic volatility and memory. In particular, we suggest stochastic dynamics based on exponential Levy processes with normal inverse Gaussian distributed logarithmic returns. The Barndorff-Nielsen and Shephard stochastic volatility model is shown to capture time-varying volatility in the data. Finally, continuous-time autoregressive processes provide a class of models sufficiently rich to incorporate short-term persistence …