Let I ⊆ R be an interval and let k : I2 → C be a reproducing kernel on I . We show that if k(x, y) is in the appropriate differentiability class, it satisfies a 2-parameter family of inequalities of which the diagonal dominance inequality for reproducing kernels is the 0th order case. We provide an application to integral operators: if k is a positive definite kernel on I (possibly unbounded) w...

Interval Markov Chains (IMC) are the base of a classic probabilistic specification theory by Larsen and Jonsson in 1991. They are also a popular abstraction for probabilistic systems. In this paper we study complexity of several problems for this abstraction, that stem from compositional modeling methodologies. In particular we close the complexity gap for thorough refinement of two IMCs and fo...

We consider linear control systems in a Hilbert space over an unbounded time interval of the form y′ α(t) = (A− αI)yα(t) +Bu(t), t ∈ (−∞, T ], with bounded control operator B, under appropriate stability assumptions on the operator A. We study how the space of states reachable at time T depends on the parameter α ≥ 0. We apply the results to study the dependence on α of the Cameron–Martin space...

Fourier spectral methods achieve exponential accuracy both on the approximation level and for solving partial differential equations (PDEs), if the solution is analytic. For linear PDEs with analytic but discontinuous solutions, Fourier spectral method produces poor pointwise accuracy, but still maintains exponential accuracy after post-processing [7]. In this paper, we develop a technique to r...

This paper is concerned with transparent boundary conditions for the one dimensional time–dependent Schrödinger equation. They are used to restrict the original PDE problem that is posed on an unbounded domain onto a finite interval in order to make this problem feasible for numerical simulations. The main focus of this article is on the appropriate discretization of such transparent boundary c...

in this study, a new and ecient approach is presented for numerical solution offredholm integro-dierential equations (fides) of the second kind on unbounded domainwith degenerate kernel based on operational matrices with respect to generalized laguerrepolynomials(glps). properties of these polynomials and operational matrices of integration,dierentiation are introduced and are ultilized to r...

This paper aims at establishing the existence of results for a nonstandard equilibrium problems $(EP_{N})$. The solutions of this inequality are discussed in a subset $K$ (either bounded or unbounded) of a Banach spaces $X$. Moreover, we enhance the main results by application of some differential inclusion.

Two eye-tracking experiments investigated processing of unbounded dependency constructions. Experiment 1 employed sentences like That’s the garage/pistol with which the heartless killer shot the man yesterday afternoon. Readers experienced greater processing difficulty in implausible sentences than in plausible sentences immediately after encountering the verb shot. This demonstrated that they ...

This paper discusses the in-domain feedback stabilization of reaction-diffusion PDEs with Robin boundary conditions in presence an uncertain time- and spatially-varying delay distributed actuation. The proposed control design strategy consists a constant-delay predictor designed based on known nominal value input is synthesized finite-dimensional truncated model capturing unstable modes origina...