Log-likelihood ratio test for detecting transient change

The limit behaviour of scan statistics in a form of maxima of moving sum processes with changing window size for detecting a transient change is studied. Approximate critical values obtained from tail behaviour of the limit variables that are maxima of some locally homogeneous Gaussian fields are compared with critical values obtained by simulation.     

On the folding of plates which buckle before and beyond the elastic limit

Simply supported rectangular elasto-plastic plates which are uniformly compressed buckle either before or beyond the elastic limit. Consequently, the post critical behaviour, the position of first membrane yield and folding mode differ significantly whether buckling happens before or beyond the elastic limit. A distinct folding-line perpendicular to the loading direction develops only for plates which buckle beyond the elastic limit. This article analysis the post-buckling behaviour and the folding mode of uniformly compressed plates and points out the correlation to the folding mode of axially crushed profiles. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A martingale approach to directed polymers in a random environment

The diffusive behavior for a system of directed polymers in a random environment was first rigorously discussed by Imbrie and Spencer, and then by Bolthausen. By means of some basic properties of martingales we extend some results due to Imbrie and Spencer concerning the asymptotic behaviour of the mean square displacement. We also obtain a Wiener process behaviour with probability one for this system. Bolthausen already used some martingale limit theorems to prove a central limit theorem for this system.Partly supported by AvH Foundation.     

Asymptotics of best Sobolev constants on thin manifolds

We study the asymptotic behaviour of best Sobolev constants on a compact manifold with boundary that we contract in k directions or to a point. We find in the limit best Sobolev constants for weighted Sobolev spaces of the limit manifold.     

Jet profile solutions of the Falkner-Skan equation

New solutions of the Falkner-Skan equation are presented which display jet-like behaviour. Within non-uniform flow the parameter range over which the new solutions exist is bounded by a singular limit. The limit is shown to be closely related to the well-known plane jet similarity solution.     

Asymptotic behaviour of a sequence of neumann problems

We study the limit behaviour of a sequence of Nuemann problems on fractured and perforated domains, allowing for largely arbitrary fracture—perforation patterns.     

Functional limits of empirical distributions in crossing theory

We present a functional limit theorem for the empirical level-crossing behaviour of a stationary Gaussian process. This leads to the well-known Slepian model process for a Gaussian process after an upcrossing of a prescribed level as a weak limit in C-space for an empirically defined finite set of functions.We also stress the importance of choosing a suitable topology by giving some natural examples of continuous and non-continuous functionals.     

Separation of Scales and Almost-Periodic Effects in the Asymptotic Behaviour of Perforated Periodic Media

We study the asymptotic behaviour of highly oscillating functionals in finely perforated domains, when the periods of the oscillation and of the perforation may be at different scales. We highlight two types of regimes: in the first one we have separation of scales and the two process superimpose. In the second one the scales interact in a periodic or almost-periodic fashion; as a consequence we may not have a unique limit behaviour.     

Markovian master equations. II

We prove some theorems on the behaviour of solutions of master equations in the weak coupling limit, obtaining an exponential decay law under more general conditions than in an earlier paper. As well as applying the theory to a new type of example, we analyse some previously unstudied aspects of the dissipative behaviour.     

Behaviour of weak solutions of compressible Navier-Stokes equations for isothermal fluids with a nonlinear stress tensor

The aim of this paper is to study the behaviour of a weak solution to Navier-Stokes equations for isothermal fluids with a nonlinear stress tensor for time going to infinity. In an analogous way as in [18], we construct a suitable function which approximates the density for time going to infinity. Using properties of this function, we can prove the strong convergence of the density to its limit state. The behaviour of the velocity field and kinetic energy is mentioned as well.     

Asymptotic properties of minimax solutions of Isaacs-Bellman equations in differential games with fast and slow motions

Sufficient conditions under which the solutions of the Cauchy problem for singularly-perturbed Hamilton-Jacobi equations will converge to a limit are established. The results are used to investigate the asymptotic behaviour of the value function of a differential game involving fast and slow motions.     

Limit behaviour of optimal control problems governed by elliptic boundary value problems with equivalued surface

In this paper, we discuss the limit behaviour of optimal control problems governed by elliptic boundary value problems with equivalued surface when the equivalued surface boundary shrinks to a fixed point on the outer boundary of a bounded domain.     

Some minimal bimolecular mass-action systems with limit cycles

We discuss three examples of bimolecular mass-action systems with three species, due to Feinberg, Berner, Heinrich, and Wilhelm. Each system has a unique positive equilibrium which is unstable for certain rate constants and then exhibits stable limit cycles, but no chaotic behaviour. For some rate constants in the Feinberg–Berner system, a stable equilibrium, an unstabe limit cycle, and a stable limit cycle coexist. All three networks are minimal in some sense.By way of homogenising these three examples, we construct bimolecular mass-conserving mass-action systems with four species that admit a stable limit cycle. The homogenised Feinberg–Berner system and the homogenised Wilhelm–Heinrich system admit the coexistence of a stable equilibrium, an unstable limit cycle, and a stable limit cycle.     

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??The local limit theorems for the minimum of a random walk with Markovian increments is given, with using Presman's factorization theory. This result implies the asymptotic behaviour of the survival probability for a critical branching process in Markovian depended random environment.     

Limit behaviour of solutions to boundary value problem with equivalued surface

In this paper, we discuss the limit behaviour of solutions to boundary value problem with equivalued surface with m inner holes and give a different proof from that of Li Ta-tsien et al. (1998).     

Fractal analysis of spiral trajectories of some planar vector fields

We study box dimension, Minkowski content and Minkowski measurability of nonrectifiable, smooth spiral trajectories of some dynamical systems in the plane. From this point of view we consider a standard model of Hopf-Takens bifurcation and study the behaviour of trajectories near singular points and limit cycles.     

Low-frequency asymptotics for dissipative Maxwell's equations in bounded domains

Consider a bounded domain Ω surrounded by a perfect conductor and containing a conducting cavity D. The behaviour of the solutions of the time harmonic Maxwell problem as frequency tends to 0 is analysed in this situation. Necessary and sufficient conditions on the excitations are given which guarantee the existence of a limit. This limit turns out to be the solution of some static problem.     

On a limit class of approximation spaces

We describe the behaviour under interpolation of a limit class of approximation spaces. We characterize them as extrapolation spaces. Moreover, we study the boundedness of certain operators on these spaces. As an application, we derive several results on Macaev operator ideals.     

On conditions for regularity of solutions for a piecewise linear system

We study a piecewise linear system approximating the behaviour of a switched DC/DC converter. We give conditions for a unique limit cycle in our different cases and give examples of complicated phenomena that might occur. The stability of a state space trajectory controlled converter is addressed.