Search results for "UNIQUE"
showing 10 items of 268 documents
Newton algorithm for Hamiltonian characterization in quantum control
2014
We propose a Newton algorithm to characterize the Hamiltonian of a quantum system interacting with a given laser field. The algorithm is based on the assumption that the evolution operator of the system is perfectly known at a fixed time. The computational scheme uses the Crank-Nicholson approximation to explicitly determine the derivatives of the propagator with respect to the Hamiltonians of the system. In order to globalize this algorithm, we use a continuation method that improves its convergence properties. This technique is applied to a two-level quantum system and to a molecular one with a double-well potential. The numerical tests show that accurate estimates of the unknown paramete…
Existence, uniqueness and Malliavin differentiability of Lévy-driven BSDEs with locally Lipschitz driver
2019
We investigate conditions for solvability and Malliavin differentiability of backward stochastic differential equations driven by a L\'evy process. In particular, we are interested in generators which satisfy a locally Lipschitz condition in the $Z$ and $U$ variable. This includes settings of linear, quadratic and exponential growths in those variables. Extending an idea of Cheridito and Nam to the jump setting and applying comparison theorems for L\'evy-driven BSDEs, we show existence, uniqueness, boundedness and Malliavin differentiability of a solution. The pivotal assumption to obtain these results is a boundedness condition on the terminal value $\xi$ and its Malliavin derivative $D\xi…
A class of stochastic differential equations with non-Lipschitzian coefficients: pathwise uniqueness and no explosion
2003
Abstract A new result for the pathwise uniqueness of solutions of stochastic differential equations with non-Lipschitzian coefficients is established. Furthermore, we prove that the solution has no explosion under the growth ξlogξ. To cite this article: S. Fang, T. Zhang, C. R. Acad. Sci. Paris, Ser. I 337 (2003).
Fuzzy Stochastic Integral Equations Driven by Martingales
2011
Exploiting the properties of set-valued stochastic trajectory integrals we consider a notion of fuzzy stochastic Lebesgue–Stieltjes trajectory integral and a notion of fuzzy stochastic trajectory integral with respect to martingale. Then we use these integrals in a formulation of fuzzy stochastic integral equations. We investigate the existence and uniqueness of solution to such the equations.
THE MINIMIZING TOTAL VARIATION FLOW WITH MEASURE INITIAL CONDITIONS
2004
In this paper we obtain existence and uniqueness of solutions for the Cauchy problem for the minimizing total variation flow when the initial condition is a Radon measure in ℝN. We study limit solutions obtained by weakly approximating the initial measure μ by functions in L1(ℝN). We are able to characterize limit solutions when the initial condition μ=h+μs, where h∈L1(ℝN)∩L∞(ℝN), and μs=αℋk⌊ S,α≥0,k is an integer and S is a k-dimensional manifold with bounded curvatures. In case k<N-1 we prove that the singular part of the solution does not move, it remains equal to μs for all t≥0. In particular, u(t)=δ0 when u(0)=δ0. In case k=N-1 we prove that the singular part of the limit solution …
Existence, nonexistence and uniqueness of positive solutions for nonlinear eigenvalue problems
2017
We study the existence of positive solutions for perturbations of the classical eigenvalue problem for the Dirichlet $p-$Laplacian. We consider three cases. In the first the perturbation is $(p-1)-$sublinear near $+\infty$, while in the second the perturbation is $(p-1)-$superlinear near $+\infty$ and in the third we do not require asymptotic condition at $+\infty$. Using variational methods together with truncation and comparison techniques, we show that for $\lambda\in (0, \widehat{\lambda}_1)$ -$\lambda>0$ is the parameter and $\widehat{\lambda}_1$ being the principal eigenvalue of $\left(-\Delta_p, W^{1, p}_0(\Omega)\right)$ -we have positive solutions, while for $\lambda\geq \widehat{\…
Resonant neumann equations with indefinite linear part
2015
We consider aseminonlinear Neumann problem driven by the $p$-Laplacian plus an indefinite and unbounded potential. The reaction of the problem is resonant at $\pm \infty$ with respect to the higher parts of the spectrum. Using critical point theory, truncation and perturbation techniques, Morse theory and the reduction method, we prove two multiplicity theorems. One produces three nontrivial smooth solutions and the second four nontrivial smooth solutions.
Notice of Violation of IEEE Publication Principles: Enhanced P2P Services Providing Multimedia Content
2006
[This paper has been withdrawn by the publisher]Traditional peer-to-peer (P2P) services provide only basic searching facilities, based on unique identifiers or small sets of keywords. Unfortunately, this approach is very inadequate and inefficient when a huge amount of multimedia resources is shared. In this paper, we present an original image and video sharing system, in which a user is able to interactively search interesting resources by means of content-based image and video retrieval techniques. In order to limit the network traffic cost, maximizing the usefulness of each peer contacted in the query process, we also propose the adoption of an adaptive overlay routing algorithm, exploit…
On a stochastic disease model with vaccination
2006
We propose a stochastic disease model where vaccination is included and such that the immunity isn’t permanent. The existence, uniqueness and positivity of the solution and the stability of disease free equilibrium is studied. The numerical simulation is done.
Spectral approach to D-bar problems
2017
We present the first numerical approach to D-bar problems having spectral convergence for real analytic, rapidly decreasing potentials. The proposed method starts from a formulation of the problem in terms of an integral equation that is numerically solved with Fourier techniques. The singular integrand is regularized analytically. The resulting integral equation is approximated via a discrete system that is solved with Krylov methods. As an example, the D-bar problem for the Davey-Stewartson II equations is considered. The result is used to test direct numerical solutions of the PDE.© 2017 Wiley Periodicals, Inc.