Search results for " Operator"

Introducing ARTMO's Machine-Learning Classification Algorithms Toolbox: Application to Plant-Type Detection in a Semi-Steppe Iranian Landscape.

2022

Accurate plant-type (PT) detection forms an important basis for sustainable land management maintaining biodiversity and ecosystem services. In this sense, Sentinel-2 satellite images of the Copernicus program offer spatial, spectral, temporal, and radiometric characteristics with great potential for mapping and monitoring PTs. In addition, the selection of a best-performing algorithm needs to be considered for obtaining PT classification as accurate as possible . To date, no freely downloadable toolbox exists that brings the diversity of the latest supervised machine-learning classification algorithms (MLCAs) together into a single intuitive user-friendly graphical user interface (GUI). To…

Elliptic problems involving the 1–Laplacian and a singular lower order term

2018

Two theorems of N. Wiener for solutions of quasilinear elliptic equations

1985

Relatively little is known about boundary behavior of solutions of quasilinear elliptic partial differential equations as compared to that of harmonic functions. In this paper two results, which in the harmonic case are due to N. Wiener, are generalized to a nonlinear situation. Suppose that G is a bounded domain in R n. We consider functions u: G--~R which are free extremals of the variational integral

Bounded solutions to the 1-Laplacian equation with a critical gradient term

2012

Fundamental isomorphism theorems for quantum groups

2017

The lattice of subgroups of a group is the subject of numerous results revolving around the central theme of decomposing the group into "chunks" (subquotients) that can then be compared to one another in various ways. Examples of results in this class would be the Noether isomorphism theorems, Zassenhaus' butterfly lemma, the Schreier refinement theorem for subnormal series of subgroups, the Dedekind modularity law, and last but not least the Jordan-H\"older theorem. We discuss analogues of the above-mentioned results in the context of locally compact quantum groups and linearly reductive quantum groups. The nature of the two cases is different: the former is operator algebraic and the latt…

Kurzweil-Henstock type integral in fourier analysis on compact zero-dimensional group

2009

Abstract A Kurzweil-Henstock type integral defined on a zero-dimensional compact abelian group is studied and used to obtain a generalization of some results related to the problem of recovering, by generalized Fourier formulae, the coefficients of convergent series with respect to the characters of such a group.

Modified Operators Interpolating at Endpoints

2021

Some classical operators (e.g., Bernstein) preserve the affine functions and consequently interpolate at the endpoints. Other classical operators (e.g., Bernstein–Durrmeyer) have been modified in order to preserve the affine functions. We propose a simpler modification with the effect that the new operators interpolate at endpoints although they do not preserve the affine functions. We investigate the properties of these modified operators and obtain results concerning iterates and their limits, Voronovskaja-type results and estimates of several differences.

Removable singularities for div v=f in weighted Lebesgue spaces

2018

International audience; Let $w\in L^1_{loc}(\R^n)$ be apositive weight. Assuming that a doubling condition and an $L^1$ Poincar\'e inequality on balls for the measure $w(x)dx$, as well as a growth condition on $w$, we prove that the compact subsets of $\R^n$ which are removable for the distributional divergence in $L^{\infty}_{1/w}$ are exactly those with vanishing weighted Hausdorff measure. We also give such a characterization for $L^p_{1/w}$, $1<p<+\infty$, in terms of capacity. This generalizes results due to Phuc and Torres, Silhavy and the first author.

The Existence of Solutions for Local Dirichlet (r(u),s(u))-Problems

2022

In this paper, we consider local Dirichlet problems driven by the (r(u),s(u))-Laplacian operator in the principal part. We prove the existence of nontrivial weak solutions in the case where the variable exponents r,s are real continuous functions and we have dependence on the solution u. The main contributions of this article are obtained in respect of: (i) Carathéodory nonlinearity satisfying standard regularity and polynomial growth assumptions, where in this case, we use geometrical and compactness conditions to establish the existence of the solution to a regularized problem via variational methods and the critical point theory; and (ii) Sobolev nonlinearity, somehow related to the spac…

Non-hermitian operator modelling of basic cancer cell dynamics

2018

We propose a dynamical system of tumor cells proliferation based on operatorial methods. The approach we propose is quantum-like: we use ladder and number operators to describe healthy and tumor cells birth and death, and the evolution is ruled by a non-hermitian Hamiltonian which includes, in a non reversible way, the basic biological mechanisms we consider for the system. We show that this approach is rather efficient in describing some processes of the cells. We further add some medical treatment, described by adding a suitable term in the Hamiltonian, which controls and limits the growth of tumor cells, and we propose an optimal approach to stop, and reverse, this growth.