Results 1 to 10 of about 2,173 (163)

Improved Lebesgue Indicator-Based Evolutionary Algorithm: Reducing Hypervolume Computations

Mathematics, 2021
One of the major limitations of evolutionary algorithms based on the Lebesgue measure for multi-objective optimization is the computational cost required to approximate the Pareto front of a problem.
Saúl Zapotecas-Martínez, Abel García-Nájera, Adriana Menchaca-Méndez   +2 more
doaj   +1 more source

The spectrality of symmetric additive measures

Comptes Rendus. Mathématique, 2023
Let $\rho $ be a symmetric measure of Lebesgue type, i.e., \begin{equation*} \rho =\frac{1}{2}(\mu \times \delta _0+\delta _0\times \mu ), \end{equation*} where the component measure $\mu $ is the Lebesgue measure supported on $[t, t+1]$ for $t\in ...
Ai, Wen-Hui, Lu, Zheng-Yi, Zhou, Ting
doaj   +1 more source

A Generalization of the Hausdorff Dimension Theorem for Deterministic Fractals

Mathematics, 2021
How many fractals exist in nature or the virtual world? In this paper, we partially answer the second question using Mandelbrot’s fundamental definition of fractals and their quantities of the Hausdorff dimension and Lebesgue measure.
Mohsen Soltanifar
doaj   +1 more source

A Subtle Symmetry of Lebesgue’s Measure [PDF]

Journal of Theoretical Probability, 2017
To appear in Journal of Theoretical ...
Uludag, Muhammed, Ayral, Hakan
openaire   +5 more sources

On Soft Lebesgue Measure

Journal of Uncertain Systems, 2020
In this article, we introduce the concept of soft intervals, soft ordering and sequences of soft real numbers and study their properties and some interesting results. Also the notion of soft Lebesgue measure on the soft real numbers has been introduced.
Sujay Goldar, Subhasis Ray
openaire   +2 more sources

Dirichlet-Neumann problem for the partial differential equations with deviation over the space argument

Karpatsʹkì Matematičnì Publìkacìï, 2021
Dirichlet-Neumann problem for the typeless high order partial differential equation with deviating over the space argument is studied in the domain, which is the Cartesian product of the segment $(0,T)$ and the unit circle $\Omega=\mathbb R/(2\pi \mathbb
P.Ya. Pukach, S.M. Repetylo, M.M. Symotiuk, M.I. Vovk   +3 more
doaj   +1 more source

Lebesgue Points of Besov and Triebel–Lizorkin Spaces with Generalized Smoothness

Mathematics, 2021
In this article, the authors study the Lebesgue point of functions from Hajłasz–Sobolev, Besov, and Triebel–Lizorkin spaces with generalized smoothness on doubling metric measure spaces and prove that the exceptional sets of their Lebesgue points have ...
Ziwei Li, Dachun Yang, Wen Yuan
doaj   +1 more source

Neutrosophic Non-Newtonian and Geometric Measures: A Consistent Analytical Framework [PDF]

Neutrosophic Sets and Systems
The neutrosophic measure is a generalization of the classical measure in situations when the space contains some indeterminacy. In this paper, we introduce the concept of the Neutrosophic Geometric Measure, we also provide some results, and examples ...
Amer Darweesh, Kamel Al-Khaled, Mohammed Shakhatreh, Mahmood Shareef Ajeel, Nermin Abo Hasan   +4 more
doaj   +1 more source

Conformable Fractional Martingales and Some Convergence Theorems

Mathematics, 2021
In this paper, we define conformable Lebesgue measure and conformable fractional countable martingales. Some convergence theorems are proved.
Ma’mon Abu Hammad
doaj   +1 more source

The Second Generalization of the Hausdorff Dimension Theorem for Random Fractals

Mathematics, 2022
In this paper, we present a second partial solution for the problem of cardinality calculation of the set of fractals for its subcategory of the random virtual ones.
Mohsen Soltanifar
doaj   +1 more source