Related papers: Complex-order Derivative and Integral Filters and …
Over the last decade, it has been demonstrated that many systems in science and engineering can be modeled more accurately by fractional-order than integer-order derivatives, and many methods are developed to solve the problem of fractional…
We introduce complex order fractional derivatives in models that describe viscoelastic materials. This can not be carried out unrestrictedly, and therefore we derive, for the first time, real valued compatibility constraints, as well as…
Derivatives and integration operators are well-studied examples of linear operators that commute with scaling up to a fixed multiplicative factor; i.e., they are scale-invariant. Fractional order derivatives (integration operators) also…
The fractional integrals and fractional derivatives problem is tackled by using the operator approach. The definition domain E of operators is causal functions.Many properties of fractional integrals are given. Fractional derivatives…
Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…
In this paper, we study an unconventional but practically meaningful reversibility problem of commonly used image filters. We broadly define filters as operations to smooth images or to produce layers via global or local algorithms. And we…
A natural consequence of the fractional calculus is its extension to a matrix order of differentiation and integration. A matrix-order derivative definition and a matrix-order integration arise from the generalization of the gamma function…
The Riemann-Liouville formula for fractional derivatives and integrals (differintegration) is used to derive formulae for matrix order derivatives and integrals. That is, the parameter for integration and differentiation is allowed to…
When Fourier series are employed to solve partial differential equations, low-pass filters can be used to regularize divergent series that may appear. In this paper we show that the linear low-pass filters defined in a previous paper can be…
We introduce a notion of fractional (noninteger order) derivative on an arbitrary nonempty closed subset of the real numbers (on a time scale). Main properties of the new operator are proved and several illustrative examples given.
Fractional order derivatives and integrals (differintegrals) are viewed from a frequency-domain perspective using the formalism of Riesz, providing a computational tool as well as a way to interpret the operations in the frequency domain.…
By approximating posterior distributions with weighted samples, particle filters (PFs) provide an efficient mechanism for solving non-linear sequential state estimation problems. While the effectiveness of particle filters has been…
Integral transformations are used to estimate high order derivatives of various special functions. Applications are given to numerical integration, where estimates of high order derivatives of the integrand are needed to achieve bounds on…
Deep learning; it is often used in dividing processes on images in the biomedical field. In recent years, it has been observed that there is an increase in the division procedures performed on prostate images using deep learning compared to…
Complex systems are composed of a large number of simple components connected to each other in the form of a network. It is shown that, for some network configurations, the equivalent dynamic behavior of the system is governed by an…
For a complex number s, the s-order integral of function f fulfilling some conditions is defined as action of an operator, noted J^s, on f. The definition of the operator J^s is given firstly for the case of complex number s with positive…
In recent years, deep neural network is introduced in recommender systems to solve the collaborative filtering problem, which has achieved immense success on computer vision, speech recognition and natural language processing. On one hand,…
We present new examples of complexes of differential operators of order $k$ (any given positive integer) that satisfy div-curl and/or $L^1$-duality estimates.
Distortion is widely existed in the images captured by popular wide-angle cameras and fisheye cameras. Despite the long history of distortion rectification, accurately estimating the distortion parameters from a single distorted image is…
In this work, we propose to extend an approach to calculate at any order $(n)$, the functional derivative of the diffracted field with respect to the permittivity-contrast function. These derivatives obtained for different orders are used…