An efficient numerical scheme is described for the solution of certain types of nonlinear hyperbolic equations with an integral constraint which are used to model the Gunn effect in semiconductors with impurity capture. We analyze the stability and convergence properties of the scheme and present the results of numerical simulations. Depending on the value of the parameters defining the problem...

An optimal stochastic control problem is considered for systems with unbounded controls satisfying an integral constraint. It is shown that there exists an optimal control within the class of generalized controls leading to impulse actions. Applying an approach of time transformation, developed recently for deterministic systems, the original control problem is shown to be equivalent to an opti...

Given a time-delay system, we are interested in nding new robust stability conditions for the system. We apply the integral quadratic constraint approach to obtain two results which allow us to test the robust stability using the linear matrix inequality technique. Both results give an estimate of the maximum time-delay which preserves robust stability. The rst result is simpler to apply while ...

General covariance in quantum gravity is seen once one integrates over all possible metrics. In recent years topological field theories have given us a different route to general covariance without integrating over all possible metrics. Here we argue that Einstein quantum gravity may be viewed of as a topological field theory as long as a certain constraint from the path integral measure is sat...

In this paper, we derive an integral quadratic constraint (IQC) that proves stability of a spatially invariant array of systems. The IQC involves only the expression of a local system (unit) in the array, and is equivalent to a scaled small gain condition in a transformed version of the local unit. This IQC is used to develop a method based on the DK iteration to design decentralized controller...

Evolution of power spectrum is studied for non-Gaussian models of structure formation. We generalize the dark-matter-approach to these models and find that the evolved spectrum at weakly nonlinear regime is mainly determined by a simple integral of the dark-matter-halo mass function in this approach. We also study the change of the nonlinear spectrum within the current observational constraint ...

The current study identifies locality as a near-universal property of phonological input-output mappings that describe processes with local triggers and presents a learning algorithm which uses locality as an inductive principle to generalize such mappings from finite data. Input-output (or UR-SR) mappings like the one in (1) are integral to both the rewrite rules of Sound Pattern of English (C...

in this paper, we present an efficient method for determining the solution of the stochastic second kind volterra integral equations (svie) by using the taylor expansion method. this method transforms the svie to a linear stochastic ordinary differential equation which needs specified boundary conditions. for determining boundary conditions, we use the integration technique. this technique give...

We prove the analyticity of smooth critical points for generalized integral Menger curvature energies $\mathrm{intM}^{(p,2)}$, with $p \in (\tfrac 73, \tfrac 83)$, subject to a fixed length constraint. This implies, together already well-known regularity results, that finite-energy, $C^1$-curves $\gamma: \mathbb{R}/\mathbb{Z} \to \mathbb{R}^n$ $\mathrm{intM}^{(p,2)}$ constraint are not only $C^...

The paper investigates the problem of adaptive finite-time robust stabilization for a set high-order uncertain nonlinear systems in presence asymmetric output constraint, dynamic uncertainty and complicated external disturbances. Via effectively integrating artful Barrier Lyapunov Function (BLF) conjunction with continuous control armed serial integral functions consisting embedded sign operati...