Search results for "Exponent"
showing 10 items of 896 documents
Fractal surfaces from simple arithmetic operations
2015
Fractal surfaces ('patchwork quilts') are shown to arise under most general circumstances involving simple bitwise operations between real numbers. A theory is presented for all deterministic bitwise operations on a finite alphabet. It is shown that these models give rise to a roughness exponent $H$ that shapes the resulting spatial patterns, larger values of the exponent leading to coarser surfaces.
KFAS : Exponential Family State Space Models in R
2017
State space modelling is an efficient and flexible method for statistical inference of a broad class of time series and other data. This paper describes an R package KFAS for state space modelling with the observations from an exponential family, namely Gaussian, Poisson, binomial, negative binomial and gamma distributions. After introducing the basic theory behind Gaussian and non-Gaussian state space models, an illustrative example of Poisson time series forecasting is provided. Finally, a comparison to alternative R packages suitable for non-Gaussian time series modelling is presented.
Using the Scaling Analysis to Characterize Financial Markets
2003
We empirically analyze the scaling properties of daily Foreign Exchange rates, Stock Market indices and Bond futures across different financial markets. We study the scaling behaviour of the time series by using a generalized Hurst exponent approach. We verify the robustness of this approach and we compare the results with the scaling properties in the frequency-domain. We find evidence of deviations from the pure Brownian motion behavior. We show that these deviations are associated with characteristics of the specific markets and they can be, therefore, used to distinguish the different degrees of development of the markets.
Single chain structure in thin polymer films: Corrections to Flory's and Silberberg's hypotheses
2005
Conformational properties of polymer melts confined between two hard structureless walls are investigated by Monte Carlo simulation of the bond-fluctuation model. Parallel and perpendicular components of chain extension, bond-bond correlation function and structure factor are computed and compared with recent theoretical approaches attempting to go beyond Flory's and Silberberg's hypotheses. We demonstrate that for ultrathin films where the thickness, $H$, is smaller than the excluded volume screening length (blob size), $\xi$, the chain size parallel to the walls diverges logarithmically, $R^2/2N \approx b^2 + c \log(N)$ with $c \sim 1/H$. The corresponding bond-bond correlation function d…
Persistence of temperature and precipitation: from local to global anomalies
2021
Using detrended fluctuation analysis (DFA) we find that all continents are persistent in temperature. The scaling exponents of the southern hemisphere (SH) continents, i.e., South America (0.77) and Oceania (0.72) are somewhat higher than scaling exponents of Europe (0.70), Asia (0.69) and North America (0.64), but the scaling of Africa is by far the highest (0.86). The reason for this is the location of Africa near the equator. The scaling exponents of the precipitation are much smaller, i.e. between 0.55 (Europe) and 0.68 (North America). The scaling exponent of Europe is near that of the random noise (0.5), while the other continents are slightly persistent in precipitation. We also show…
On differences and similarities in the analysis of Lorenz, Chen, and Lu systems
2015
Currently it is being actively discussed the question of the equivalence of various Lorenz-like systems and the possibility of universal consideration of their behavior (Algaba et al., 2013a,b, 2014b,c; Chen, 2013; Chen and Yang, 2013; Leonov, 2013a), in view of the possibility of reduction of such systems to the same form with the help of various transformations. In the present paper the differences and similarities in the analysis of the Lorenz, the Chen and the Lu systems are discussed. It is shown that the Chen and the Lu systems stimulate the development of new methods for the analysis of chaotic systems. Open problems are discussed.
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 …
A fully adaptive wavelet algorithm for parabolic partial differential equations
2001
We present a fully adaptive numerical scheme for the resolution of parabolic equations. It is based on wavelet approximations of functions and operators. Following the numerical analysis in the case of linear equations, we derive a numerical algorithm essentially based on convolution operators that can be efficiently implemented as soon as a natural condition on the space of approximation is satisfied. The algorithm is extended to semi-linear equations with time dependent (adapted) spaces of approximation. Numerical experiments deal with the heat equation as well as the Burgers equation.
A short proof of the self-improving regularity of quasiregular mappings
2005
. The theoryof quasiregular mappings is a central topic in modern analysis withimportant connections to a variety of topics as elliptic partial differen-tial equations, complex dynamics, differential geometry and calculus ofvariations [13] [10].A remarkable feature of quasiregular mappings is the self-improvingregularity. In 1957 [2], Bojarski proved that for planar quasiregularmappings, there exists an exponent
Robust fault detection filter design for a class of linear systems with mixed time-varying delays and nonlinear perturbations
2009
In this note, the problem of robust fault detection filter (RFDF) design for a class of linear systems subjected to some nonlinear perturbations and mixed neutral and discrete time-varying delays is investigated based on an H ∞ performance condition. By introducing a descriptor technique, using Lyapunov-Krasovskii functional and a suitable change of variables, new required sufficient conditions are established in terms of delay-dependent linear matrix inequalities (LMIs) to synthesize the residual generation scheme. Based on Luenberger type observers, the explicit expression of the filters is derived for the fault such that both asymptotic stability and a prescribed level of disturbance att…