in this paper, the variational iteration method proposed by ji-huan he is applied to solve both linear and nonlinear schrodinger equations. the main property of the method is in its flexibility and ability to solve linear and nonlinear equations accurately and conveniently. in this method, general lagrange multipliers are introduced to construct correction functionals to the problems. the multi...

A renewal theorem is obtained for stationary sequences of the form ~,=~( . . . , Xn_ ~, X,, X,+I , ...), where X,, n~Z, are i.i.d.r.v.s, valued in a Polish space. This class of processes is sufficiently broad to encompass functionals of recurrent Markov chains, functionals of stationary Gaussian processes, and functionals of one-dimensional Gibbs states. The theorem is proved by a new coupling ...

The continuous functionals were independently introduced by Kleene [6] and Kreisel [7]. Kleenes motivation was to isolate a subclass of the total functionals of pure, finite type closed under S1-S9-computations (Kleene [5]) which could be described using countable information. He defined his functionals via the associates and the idea is that an associate for a functional Ψ contains sufficient ...

Small-molecule binding in metal-organic frameworks (MOFs) can be accurately studied both experimentally and computationally, provided the proper tools are employed. Herein, we compare and contrast properties associated with guest binding by means of density functional theory (DFT) calculations using nine different functionals for the M2(dobdc) (dobdc4- = 2,5-dioxido,1,4-benzenedicarboxylate) se...

We report how closely the Kohn-Sham highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) eigenvalues of 11 density functional theory (DFT) functionals, respectively, correspond to the negative ionization potentials (-IPs) and electron affinities (EAs) of a test set of molecules. We also report how accurately the HOMO-LUMO gaps of these methods predict the low...

We formulate a noncommutative generalization of the Ricci flow theory in the framework of spectral action approach to noncommutative geometry. Grisha Perelman’s functionals are generated as commutative versions of certain spectral functionals defined by nonholonomic Dirac operators and corresponding spectral triples. We derive the formulas for spectral averaged energy and entropy functionals an...

Discontinuous Lyapunov functionals appeared to be very efficient for sampled-data systems (Fridman, 2010; Naghshtabrizi, Hespanha, & Teel, 2008). In the present paper, new discontinuous Lyapunov functionals are introduced for sampled-data control in the presence of a constant input delay. The construction of these functionals is based on the vector extension of Wirtinger’s inequality. These fun...

In earlier works, the gauge theorem was proved for additive functionals of Brownian motion of the form f ~o q(Bs)ds, where q is a function in the Kato class. Subsequently, the theorem was extended to additive functionals with Revuz measures/ t in the Kato class. We prove that the gauge theorem holds for a large class of additive functionals of zero energy which are, in general, of unbounded var...

We characterize the functionals which are Mosco-limits, in the L2(Ω) topology, of some sequence of functionals of the kind Fn(u) := ∫ Ω αn(x)|∇u(x)| dx , where Ω is a bounded domain of RN (N ≥ 3). It is known that this family of functionals is included in the closed set of Dirichlet forms. Here, we prove that the set of Dirichlet forms is actually the closure of the set of diffusion functionals...

In this paper we introduce the concept of q coherent pair of linear functionals. We prove that if ðu0; u1Þ is a q coherent pair of linear functionals, then at least one of them has to be a q classical linear functional. Moreover, we present the classification of all q coherent pairs of positive definite linear functionals when u0 or u1 is either the little q Jacobi linear functional or the litt...