Some remarks on nonlinear consolidation models

This paper deals with the modelling of nonlinear consolidation phenomena in a homogenous clay changing from an over to a normal consolidation regime. Specifically this paper develops a technical analysis of the model under the assumption of small deformations to derive a new class of models and to show how classical models known in the literature can be regarded as a particular case of the one dealt with in this paper.     

Some remarks on spectral representation for symmetric stable processes

For the symmetric α-stable stochastic process X={X_t∶t∈T} with reproducing kernel space H(X) ? L_α constructed in § 1 we define the following parameters: $\alpha _0 = \sup {\mathbf{ }}\{ \beta \in (0.2]:{\mathbf{ }}\mathcal{H}\mathcal{X}$ embeds isometrically into some L^β}, containsl _β ⁿ 's uniformly}. In §2 we show that for α₀ > α the stochastic process X admits the representation $$X_t = \smallint Y_t (w){\mathbf{ }}Z_\alpha (dw),{\mathbf{ }}t \in T,$$ where {Y_t∶t∈T} itself is a symmetric stable process and Z_α is a symmetric α-stable independently scattered random measure. We show also how some properties of the stochastic process {X_t∶t∈T} depend on the corresponding properties of the process {Y_t∶t∈T}.     

Some remarks on Bayesian inference for one-way ANOVA models

We consider the standard one-way ANOVA model; it is well-known that classical statistical procedures are based on a scalar non-centrality parameter. In this paper we explore both marginal likelihood and integrated likelihood functions for this parameter and we show that they exactly lead to the same answer. On the other hand, we prove that a fully Bayesian testing procedure may provide different conclusions, depending on what is considered to be the real quantity of interest in the model or, said differently, which are the competing hypotheses. We illustrate these issues via a real data example.     

Some remarks on filtering and prediction of stationary processes

This note contains a some remarks concerning filtering and prediction theory. One of them is a solution to an old question of H. Furstenberg which indicates an unexpected phenomenon arising from the lack of integrability. Another gives some general results on the possibility of constructing two valued universal guessing schemes for distinguishing between classes of stochastic processes.     

Some remarks on spreading models and mixed Tsirelson spaces

We prove that if a Banach space with a bimonotone shrinking basis does not contain spreading models but every block sequence of the basis contains a further block sequence which is a spreading model for every , then every subspace has a further subspace which is arbitrarily distortable. We also prove that a mixed Tsirelson space , such that , does not contain spreading models.

     

Some remarks on time-dependent variational problems and their asymptotic behaviour

The subject matter of this paper is the asymptotic behaviour of quasi-static variational inequalities, as regards physical parameters like the friction coefficient, compliance coefficient, etc. By convex duality, the quasi-static problems can be recast into the forms of standard evolution problems, whose study relies on well-known methods. In this framework the stability with respect to small friction coefficients reduces to long time behaviour for evolution problems.     

Some remarks on stable stochastic processes andα-superharmonic functions

An integral representation is established for a stable multidimensional probability density. It is used for a new and direct proof of the fact that an-superharmonic function considered on the trajectories of a stable symmetric stochastic process with parameter a is a super-martingale. It is moreover established that the stable density belongs to the convex cone generated by the functions _f ^(r) (x) of M. Riesz.Translated from Matematicheskie Zametki, Vol. 14, No. 6, pp. 901–912, December, 1973.The author wishes to thank V. S. Ignachkov who at the author's request carried out a number of the computations used in the proof of Lemma 3.     

Some remarks on the numerical solution of bang-bang type optimal control problems

This paper is concerned with the numerical solution of optimal control problems for which each optimal control is bang-bang. Especially, the results apply to parabolic boundary control Problems. Starting from a sequence of feasible solutions converging to an optimal control u, a sequence of bang-bang controls converging to u is constructed. Bang-bang approximations of u are desirable for certain numerical reasons. Sequences of arbitrary feasible controls converging to u may be obtained by discretization or by a descent method. Numerical examples are also given.     

Some remarks on comparison of predictors in seemingly unrelated linear mixed models

Applications of Mathematics - In this paper, we consider a comparison problem of predictors in the context of linear mixed models. In particular, we assume a set of m different seemingly unrelated...     

Some remarks on the asymptotic behaviour of the solutions of a class of parabolic problems

This paper deals with a class of semilinear parabolic problems. We establish sufficient conditions on the data forcing the solution to blow up at finite time τ and derive an upper bound for τ. Moreover, we show that if the problem is modified in some way, the solution decays exponentially in time and depends continuously on the data. Copyright © 2005 John Wiley & Sons, Ltd.     

Some remarks on the ring

Some properties like factoriality, seminormality and being a Krull domain, … are studied on power series rings , and over a commutative ring A. If \(\mathbb{X}\) is an uncountable set, there is an other sub-ring of that stands strictly between and , we denote it by . In this paper, we study properties mentioned before on the ring .     

Some remarks on the Clebsch's system

The almost Hamilton-Poisson realization, the stability problem, the existence of periodic solutions and the numerical integration via the Lie-Trotter integrator for the Clebsch system are discussed and some of their properties are pointed out.     

Some comments on preference order dynamic programming models

A simple deterministic dynamic programming model is used as a general framework for the analysis of stochastic versions of three classical optimization problems: knapsack, traveling salesperson, and assembly line balancing problems. It is shown that this model can provide an alternative to the preference order models proposed for these problems. Counterexample to the optimality of the preference order models are presented.