Maximum Entropy Probability Density Principle in Probabilistic Investigations of Dynamic Systems

In this study, we consider a method for investigating the stochastic response of a nonlinear dynamical system affected by a random seismic process. We present the solution of the probability density of a single/multiple-degree of freedom (SDOF/MDOF) system with several statically stable equilibrium states and with possible jumps of the snap-through type. The system is a Hamiltonian system with weak damping excited by a system of non-stationary Gaussian white noise. The solution based on the Gibbs principle of the maximum entropy of probability could potentially be implemented in various branches of engineering. The search for the extreme of the Gibbs entropy functional is formulated as a constrained optimization problem. The secondary constraints follow from the Fokker–Planck equation (FPE) for the system considered or from the system of ordinary differential equations for the stochastic moments of the response derived from the relevant FPE. In terms of the application type, this strategy is most suitable for SDOF/MDOF systems containing polynomial type nonlinearities. Thus, the solution links up with the customary formulation of the finite elements discretization for strongly nonlinear continuous systems.

Variation across two dimensions: testing the Complexity Principle and the Uniform Information Density Principle on adjectival data

This study tests the applicability of the Complexity Principle (Rohdenburg 1996) and the Uniform Information Density Principle (Jaeger 2010) on adjectival data as regards the variation between retaining and omitting the complementizer that in English adjectival complementation constructions. More specifically, the study tests the effect of different factors of potential importance on this variation across extraposed (e.g. It was inevitable (that) he should be nicknamed ‘the Ferret’) and post-predicate clauses (e.g. I'm happy (that) we are married). While both the factors concerned with the Complexity Principle and the Uniform Information Density Principle are found to have an effect on post-predicate clauses, less clear effects are found concerning extraposed clauses. I attribute these findings to the difference between the two constructions in terms of their frequency of co-occurrence with different matrix subject types and with different adjectives.

Generalized Solutions of Functional Differential Inclusions

We consider the initial value problem for a functional differential inclusion with a Volterra multivalued mapping that is not necessarily decomposable inL1n[a,b]. The concept of the decomposable hull of a set is introduced. Using this concept, we define a generalized solution of such a problem and study its properties. We have proven that standard results on local existence and continuation of a generalized solution remain true. The question on the estimation of a generalized solution with respect to a given absolutely continuous function is studied. The density principle is proven for the generalized solutions. Asymptotic properties of the set of generalized approximate solutions are studied.

On the Theory of Functional-Differential Inclusion of Neutral Type

A Cauchy problem for a functional-differential inclusion of neutral type with a nonconvex right-hand side is investigated. Questions of the solvability of such a problem are considered, estimates analogous to the Filippov's estimates are obtained and the density principle is proved.

Application of the sparse density principle: a statistical evaluation of the phase ambiguity in the single-wavelength anomalous scattering method (SAS)

The method of single-wavelength anomalous scattering (SAS) allows the determination of structure-factor phases apart from a two-fold phase ambiguity. A statistical procedure is described, based on the joint probability distribution of three structure-factors, in which