This paper discusses the variations in the early-age pavement smoothness at different measurement times and locations in three jointed plain concrete pavements ( JPCPs) representing different ranges of construction times. Surface profile measurements were made during the early morning and late afternoon hours at different locations of the instrumented JPCPs during the first 7 d after constructi...

In this paper, X denotes an arbitrary nonempty set, a lattice of subsets of X with ∅, X∈ , A( ) is the algebra generated by and M( ) is the set of nontrivial, finite, and finitely additive measures on A( ), and MR( ) is the set of elements of M( ) which are -regular. It is well known that any μ ∈M( ) induces a finitely additive measure μ̄ on an associated Wallman space. Whenever μ ∈MR( ), μ̄ is c...

We obtain a characterization of modulus of smoothnes of fractional order in the Lebesgue spaces Lω, 1 < p <∞, with weights ω satisfying the Muckenhoupt’s Ap condition. Also, a realization result and equivalence between modulus of smoothness and the Peetre K-functional are proved in Lω for 1 < p <∞ and ω ∈ Ap.

The Cauchy problem for first order system L(t, x, ∂t, ∂x) is known to be well posed in L when a it admits a microlocal symmetrizer S(t, x, ξ) which is smooth in ξ and Lipschitz continuous in (t, x). This paper contains three main results. First we show that a Lipsshitz smoothness globally in (t, x, ξ) is sufficient. Second, we show that the existence of symmetrizers with a given smoothness is e...

In this paper we consider the properties of moduli of smoothness of fractional order. The main result of the paper describes the equivalence of the modulus of smoothness and a function from some class.

In this paper we give asymptotic expansions for the expected number of local extremes and inflection points of kernel density estimates. We argue that these numbers can be used as an indicator for the "qualitative" smoothness of the density estimate. AMS 1980 Subject Classification : 62 G05, 62 J06

In this paper, we extend Walsh’s stochastic integral with respect to a Gaussian noise, white in time and with some homogeneous spatial correlation, in order to be able to integrate some random measure-valued processes. This extension turns out to be equivalent to Dalang’s one. Then we study existence and regularity of the density of the probability law for the real-valued mild solution to a gen...

We show that rate-adaptive multivariate density estimation can be performed using Bayesian methods based on Dirichlet mixtures of normal kernels with a prior distribution on the kernel’s covariance matrix parameter. We derive sufficient conditions on the prior specification that guarantee convergence to a true density at a rate that is minimax optimal for the smoothness class to which the true ...

An example is provided to show that the natural asymptotic equivalence does not hold between any pairs of three nonparametric experiments: density problem, white noise with drift and nonparametric regression, when the smoothness index of the unknown nonparametric function class is 1/2. 1. Introduction. There have recently been several papers demonstrating the global asymptotic equivalence of ce...