Search results for "Operator"
showing 10 items of 1427 documents
Nonlinear Nonhomogeneous Robin Problems with Almost Critical and Partially Concave Reaction
2020
We consider a nonlinear Robin problem driven by a nonhomogeneous differential operator, with reaction which exhibits the competition of two Caratheodory terms. One is parametric, $$(p-1)$$-sublinear with a partially concave nonlinearity near zero. The other is $$(p-1)$$-superlinear and has almost critical growth. Exploiting the special geometry of the problem, we prove a bifurcation-type result, describing the changes in the set of positive solutions as the parameter $$\lambda >0$$ varies.
Determining a Random Schrödinger Operator : Both Potential and Source are Random
2020
We study an inverse scattering problem associated with a Schr\"odinger system where both the potential and source terms are random and unknown. The well-posedness of the forward scattering problem is first established in a proper sense. We then derive two unique recovery results in determining the rough strengths of the random source and the random potential, by using the corresponding far-field data. The first recovery result shows that a single realization of the passive scattering measurements uniquely recovers the rough strength of the random source. The second one shows that, by a single realization of the backscattering data, the rough strength of the random potential can be recovered…
On the inductive inference of recursive real-valued functions
1999
AbstractWe combine traditional studies of inductive inference and classical continuous mathematics to produce a study of learning real-valued functions. We consider two possible ways to model the learning by example of functions with domain and range the real numbers. The first approach considers functions as represented by computable analytic functions. The second considers arbitrary computable functions of recursive real numbers. In each case we find natural examples of learnable classes of functions and unlearnable classes of functions.
Local operators to detect regions of interest
1997
The performance of a visual system is strongly influenced by the information processing that is done in the early vision phase. The need exists to limit the computation on areas of interest to reduce the total amount of data and their redundancy. This paper describes a new method to drive the attention during the analysis of complex scenes. Two new local operators, based on the computation of local moments and symmetries, are combined to drive the selection. Experimental results on real data are also reported. © 1997 Elsevier Science B.V.
Exploring parallel capabilities of an innovative numerical method for recovering image velocity vectors field
2010
In this paper an efficient method devoted to estimate the velocity vectors field is investigated. The method is based on a quasi-interpolant operator and involves a large amount of computation. The operations characterizing the computational scheme are ideal for parallel processing because they are local, regular and repetitive. Therefore, the spatial parallelism of the process is studied to rapidly proceed in the computation on distributed multiprocessor systems. The process has shown to be synchronous, with good task balancing and requiring a small amount of data transfer.
On the Fučík spectrum of the p-Laplacian with no-flux boundary condition
2023
In this paper, we study the quasilinear elliptic problem \begin{align*} \begin{aligned} -\Delta_{p} u&= a\l(u^+\r)^{p-1}-b\l(u^-\r)^{p-1} \quad && \text{in } \Omega,\\ u & = \text{constant} &&\text{on } \partial\Omega,\\ 0&=\int_{\partial \Omega}\left|\nabla u\right|^{p-2}\nabla u\cdot \nu \,\diff \sigma,&& \end{aligned} \end{align*} where the operator is the $p$-Laplacian and the boundary condition is of type no-flux. In particular, we consider the Fu\v{c}\'{\i}k spectrum of the $p$-Laplacian with no-flux boundary condition which is defined as the set $\fucik$ of all pairs $(a,b)\in\R^2$ such that the problem above has a nontrivial solution. It turns out…
Explicit Characterization of Inclusions in Electrical Impedance Tomography
2001
In electrical impedance tomography one seeks to recover the spatial conductivity distribution inside a body from knowledge of the Neumann--Dirichlet map. In many practically relevant situations the conductivity is smooth apart from some inhomogeneities where the conductivity jumps to a higher or lower value. An explicit characterization of these inclusions is developed in this paper. To this end a class of dipole-like indicator functions is introduced, for which one has to check whether their boundary values are contained in the range of an operator determined by the measured Neumann--Dirichlet map. It is shown that this holds true if and only if the dipole singularity lies inside the inhom…
Uniqueness of solutions for some elliptic equations with a quadratic gradient term
2008
We study a comparison principle and uniqueness of positive solutions for the homogeneous Dirichlet boundary value problem associated to quasi-linear elliptic equations with lower order terms. A model example is given by −Δu + λ |∇u| 2 u r = f (x) ,λ , r >0. The main feature of these equations consists in having a quadratic gradient term in which singularities are allowed. The arguments employed here also work to deal with equations having lack of ellipticity or some dependence on u in the right hand side. Furthermore, they could be applied to obtain uniqueness results for nonlinear equations having the p-Laplacian operator as the principal part. Our results improve those already known, even…
On the structure of certain ultradistributions
2009
Let "o" be a nonempty open subset of the k-dimensional euclidean space Rk. In this paper we show that, if S is an ultradistribution in "o", belonging to a class of Roumieu type stable under differential operators, then there is a family f , 2 Nk 0, of elements of L1 loc("o") such that S is represented in the formP 2Nk 0 D"a"f "a". Some other results on the structure of certain ultradistributions of Roumieu type are also given.
Comparison of electron density properties in frozen and relaxed electronic distributions.
2003
Two kinds of electron densities for several small molecules (H(2), FH, CH(3)CH(3), CH(3)NH(2), CH(3)OH, and CH(3)F) have been generated for a wide range of bond distances. The first one, as the sum of the electron density of the isolated fragments, and the second one by optimizing the electron density at each given geometrical disposition. A number of properties of this two electronic distributions have been compared (position of the bond critical points, electron density, Laplacian, curvatures, and local energies). The differences, associated to the bond formation, are found to be very important for most of the cases.