Search results for "Exponential function"
showing 10 items of 173 documents
MUTUAL INDUCTANCE FOR AN EXPLICITLY FINITE NUMBER OF TURNS
2011
Non coaxial mutual inductance calculations, based on a Bessel function formulation, are presented for coils modelled by an explicitly flnite number of circular turns. The mutual inductance of two such turns can be expressed as an integral of a product of three Bessel functions and an exponential factor, and it is shown that the exponential factors can be analytically summed as a simple geometric progression, or other related sums. This allows the mutual inductance of two thin solenoids to be expressed as an integral of a single analytical expression. Sample numerical results are given for some representative cases and the approach to the limit where the turns are considered to be smeared ou…
Self-stabilizing Balls & Bins in Batches
2016
A fundamental problem in distributed computing is the distribution of requests to a set of uniform servers without a centralized controller. Classically, such problems are modelled as static balls into bins processes, where m balls (tasks) are to be distributed to n bins (servers). In a seminal work, [Azar et al.; JoC'99] proposed the sequential strategy Greedy[d] for n = m. When thrown, a ball queries the load of d random bins and is allocated to a least loaded of these. [Azar et al.; JoC'99] showed that d=2 yields an exponential improvement compared to d=1. [Berenbrink et al.; JoC'06] extended this to m ⇒ n, showing that the maximal load difference is independent of m for d=2 (in contrast…
Sharp generalized Trudinger inequalities via truncation
2006
Abstract We prove that the generalized Trudinger inequalities into exponential and double exponential Orlicz spaces improve to inequalities on Orlicz–Lorentz spaces provided they are stable under truncation.
Method for Computing Scattering Matrices
2021
Chapter 4 presents statement and justification of a method for approximate computing a waveguide scattering matrix. As an approximation to a row of such a matrix, a minimizer of a quadratic functional is suggested. To construct the functional, one has to solve a boundary value problem in a bounded domain obtained by cutting off the cylindrical ends of the waveguide at distance R. The minimizer tends to the scattering matrix row at exponential rate as R increases to infinity.
Estimating rainfall erosivity by aggregated drop size distributions
2016
Rainfall erosivity is defined as the potential of the rain to cause erosion, and it can be represented by rainfall kinetic power. At first in this paper, the raindrop size distributions (DSD) measured by an optical disdrometer located at Palermo in the period June 2006–March 2014 and aggregated for intensity classes, are presented. Then an analysis of raindrop size characteristics is carried out, and the reliability of Ulbrich's distribution, using both the maximum likelihood and momentum estimate parameter methods, is tested. The raindrop size measurements are used to determine the experimental rainfall kinetic power values, which are compared with the ones calculated by a theoretically de…
Higher order Peregrine breathers solutions to the NLS equation
2015
The solutions to the one dimensional focusing nonlinear Schrödinger equation (NLS) can be written as a product of an exponential depending on t by a quotient of two polynomials of degree N (N + 1) in x and t. These solutions depend on 2N − 2 parameters : when all these parameters are equal to 0, we obtain the famous Peregrine breathers which we call PN breathers. Between all quasi-rational solutions of the rank N fixed by the condition that its absolute value tends to 1 at infinity and its highest maximum is located at the point (x = 0, t = 0), the PN breather is distinguished by the fact that PN (0, 0) = 2N + 1. We construct Peregrine breathers of the rank N explicitly for N ≤ 11. We give …
Hierarchy of solutions to the NLS equation and multi-rogue waves.
2014
The solutions to the one dimensional focusing nonlinear Schrödinger equation (NLS) are given in terms of determinants. The orders of these determinants are arbitrarily equal to 2N for any nonnegative integer $N$ and generate a hierarchy of solutions which can be written as a product of an exponential depending on t by a quotient of two polynomials of degree N(N+1) in x and t. These solutions depend on 2N-2 parameters and can be seen as deformations with 2N-2 parameters of the Peregrine breather P_{N} : when all these parameters are equal to 0, we recover the P_{N} breather whose the maximum of the module is equal to 2N+1. Several conjectures about the structure of the solutions are given.
Exponential synchronization of master-slave neural networks with time-delays
2009
This paper establishes an exponential H ∞ synchronization method for a class of master and slave neural networks (MSNNs) with mixed time-delays, where the delays comprise different neutral, discrete and distributed time-delays and the class covers the Lipschitz-type nonlinearity case. By introducing a novel discretized Lyapunov-Krasovskii functional in order to minimize the conservatism in the stability problem of the system and also using some free weighting matrices, new delay-dependent sufficient conditions are derived for designing a delayed state-feedback control as a synchronization law in terms of linear matrix inequalities (LMIs). The controller guarantees the exponential H ∞ synchr…
Six Matrix Adjustment Problems Solved by Some Fundamental Theorems on Biproportion
2011
After defining biproportion (or RAS) rigorously, we recall two fundamental theorems: unicity of biproportion (any biproportional algorithm leads to the same solution than biproportion, which turns biproportion into a mathematical tool as indisputable than proportion), ineffectiveness of separability (premultiplying or post multiplying the initial matrix by a diagonal matrix does not change the biproportional solution) and its corollary (it is equivalent to do a separable modification of the initial matrix or to do a proportional change of each biproportional factors). We then apply these theorems to show immediately that: i) no difficulties are encountered when solving the biproportional pr…
Step-by-step integration for fractional operators
2018
Abstract In this paper, an approach based on the definition of the Riemann–Liouville fractional operators is proposed in order to provide a different discretisation technique as alternative to the Grunwald–Letnikov operators. The proposed Riemann–Liouville discretisation consists of performing step-by-step integration based upon the discretisation of the function f(t). It has been shown that, as f(t) is discretised as stepwise or piecewise function, the Riemann–Liouville fractional integral and derivative are governing by operators very similar to the Grunwald–Letnikov operators. In order to show the accuracy and capabilities of the proposed Riemann–Liouville discretisation technique and th…