Results 1 to 10 of about 52,088 (229)

An Extension of the 1-Dim Lebesgue Integral of a Product of Two Functions

Mathematics, 2023
In this paper, our main aim is to present a reasonable extension of the 1-dim Lebesgue integral of the product of two functions, in case this Lebesgue integral does not exist (i.e., the integrals of its negative and positive parts are both ∞).
Clara Carlota, António Ornelas
doaj   +1 more source

Inequalities in Riemann–Lebesgue Integrability

Mathematics, 2023
In this paper, we prove some inequalities for Riemann–Lebesgue integrable functions when the considered integration is obtained via a non-additive measure, including the reverse Hölder inequality and the reverse Minkowski inequality.
Anca Croitoru, Alina Gavriluţ, Alina Iosif, Anna Rita Sambucini   +3 more
doaj   +1 more source

FUNGSI ELEMEN KELAS STUMMEL MODULUS TERBATAS TETAPI BUKAN ELEMEN DARI KELAS STUMMEL

Barekeng, 2021
In the paper [1], it was given a function which belongs to the bounded Stummel modulus classes but not in Stummel classes. The given proof of this function properties in that paper was not obvious and very concise.
Nicky Kurnia Tumalun
doaj   +1 more source

Data-driven Probabilistic Static Security Assessment for Power System Operation Using High-order Moments

Journal of Modern Power Systems and Clean Energy, 2021
In this letter, a new formulation of Lebesgue integration is used to evaluate the probabilistic static security of power system operation with uncertain renewable energy generation.
Guanzhong Wang, Zhiyi Li, Feng Zhang, Ping Ju, Hao Wu, Changsen Feng   +5 more
doaj   +1 more source

Approximation of the Hilbert transform in the Lebesgue spaces

Journal of Numerical Analysis and Approximation Theory, 2023
The Hilbert transform plays an important role in the theory and practice of signal processing operations in continuous system theory because of its relevance to such problems as envelope detection and demodulation, as well as its use in relating the ...
Rashid Aliev, Lale Alizade
doaj   +1 more source

Formulation of scale transformation in a stochastic data assimilation framework [PDF]

Nonlinear Processes in Geophysics, 2017
Understanding the errors caused by spatial-scale transformation in Earth observations and simulations requires a rigorous definition of scale. These errors are also an important component of representativeness errors in data assimilation.
F. Liu, F. Liu, X. Li, X. Li, X. Li
doaj   +1 more source

A direct integral pseudospectral method for solving a class of infinite-horizon optimal control problems using Gegenbauer polynomials and certain parametric maps

AIMS Mathematics, 2023
We present a novel direct integral pseudospectral (PS) method (a direct IPS method) for solving a class of continuous-time infinite-horizon optimal control problems (IHOCs).
Kareem T. Elgindy, Hareth M. Refat
doaj   +1 more source

A note on Kurzweil-Henstock's anticipating non-stochastic integral [PDF]

Mathematica Bohemica
Motivated by the study of anticipating stochastic integrals using Kurzweil-Henstock approach, we use anticipating interval-point pairs (with the tag as the right-end point of the interval) in studying non-stochastic integral, which we call the Kurzweil ...
Yu Xin Ng, Tin Lam Toh
doaj   +1 more source

Homogeneous Banach Spaces as Banach Convolution Modules over M(G)

Mathematics, 2022
This paper is supposed to form a keystone towards a new and alternative approach to Fourier analysis over LCA (locally compact Abelian) groups G.
Hans Georg Feichtinger
doaj   +1 more source

Representation of maxitive measures: an overview [PDF]

, 2015
Idempotent integration is an analogue of Lebesgue integration where $\sigma$-maxitive measures replace $\sigma$-additive measures. In addition to reviewing and unifying several Radon--Nikodym like theorems proven in the literature for the idempotent ...
Poncet, Paul
core   +1 more source