Background: Determining sample sizes for metabolomic experiments is important but due to the complexity of these experiments, there are currently no standard methods for sample size estimation in metabolomics. Since pilot ...
A new family of mixture models for the model-based clustering of longitudinal data is introduced.
The covariance structures of eight members of this new family of models are given and the associated maximum likelihood ...
In recent years, work has been carried out on clustering gene expression microarray data. Some approaches are developed from an algorithmic viewpoint whereas others are developed via the application of mixture models. In ...
Monte Carlo algorithms often aim to draw from a distribution π by simulating a Markov chain with transition kernel P such that π is invariant under P. However, there are many situations for which it is impractical or ...
Let D be a masa in B(H) where H is a separable Hilbert space. We find real numbers η0 < η1 < η2 < · · · < η6 so that for every bounded, normal D-bimodule map Φ on B(H), either kΦk > η6 or kΦk = ηk for some k ∈ {0, 1, 2, ...
We give a simple presentation of the additive Milnor-Witt K-theory groups KMWn(F) of the field F, for n≥2, in terms of the natural small set of generators. When n = 2, this specialises to a theorem of Suslin which essentially ...
Let LN+1 be a linear differential operator of order N + 1 with constant coefficients
and real eigenvalues λ 1, ..., λ N+1, let E( N+1) be the space of all C∞-solutions of
LN+1 on the real line.We show that for N 2 and ...
The dynamics of non-divergent flow on a rotating sphere are described by the conservation of absolute vorticity. The
analytical study of the non-linear barotropic vorticity equation is greatly facilitated by the expansion ...
We prove analogues of the fundamental theorem of K -theory for the second and the third homology of SL2 over an infinite field. The statements of the theorems involve Milnor–Witt K -theory and refined scissors congruence ...
We consider a problem of mixed Cauchy type for certain holomorphic partial differential
operators with the principal part Q2p(D) essentially being the (complex) Laplace operator to
a power, Δp. We provide inital data on ...
A bounded linear operator T on a Banach space X is called an (m, p)-isometry if it satisfies the equation TeX , for all TeX . In this paper we study the structure which underlies the second parameter of (m, p)-isometric ...
Ostrowski showed that there are intimate connections between the gap structure of a Taylor series and the behaviour of its partial sums outside the disk of convergence. This paper investigates the corresponding problem for ...
Methods of Padè approximation are used to analyse a multivariate
Markov transform which has been recently introduced by the authors.
The first main result is a characterization of the rationality of the
Markov transform ...
Polyharmonic functions f of in nite order and type on annular regions are
systematically studied. The rst main result states that the Fourier-Laplace coefficients
fk;l (r) of a polyharmonic function f of in nite order ...
The present paper has a twofold contribution: first, we intro-
duce a new concept of Hardy spaces on a multidimensional complexified
annular domain which is closely related to the annulus of the Klein-Di
rac
quadric ...
Our main result states that two signed measures μ and ν with bounded
support contained in the zero set of a polynomial P(χ) are equal if they coincide on the
subspace of all polynomials of polyharmonic degree NP where ...
The positivity preserving property for the biharmonic operator with Dirichlet boundary condition is investigated. We discuss here the case where the domain is an ellipse (that may degenerate to a strip) and the data is ...
We study the dynamics of a spherical rigid body that rocks and rolls on a plane
under the effect of gravity. The distribution of mass is non-uniform and the
centre of mass does not coincide with the geometric centre. The ...