Let
L
be a linear differential operator with constant coefficients of order
n
and complex eigenvalues
λ
0
,...,λ
n
. Assume that the set
U
n
of all solutions of the
equation
Lf
= 0 is closed under complex ...
Background: Obesity and its measure of body mass index are strongly determined by parental body size. Debate continues as to whether both parents contribute equally to offspring body mass which is key to understanding the ...
It is known that, for any simply connected proper subdomain Ω of the complex plane and any point ζ in Ω, there are holomorphic functions on Ω that possess ‘universal’ Taylor series expansions about ζ; that is, partial sums ...
A power series that converges on the unit disc D is called universal if its partial sums approx-
imate arbitrary polynomials on arbitrary compacta in CnD that have connected complement.
This paper shows that such series ...
Certain families of quaternion and octonion algebras are conjectured to be of level and sublevel n. A proof of this conjecture is offered in the case where n is a power of two. Hoffmann's proof of the existence of infinitely ...
n this paper we survey recent results about Fischer decomposi-
tions of polynomials or entire functions and their applications to holomorphic
partial di erential equations. We discuss Cauchy and Goursat problems for ...
This paper proposes a new probabilistic classification algorithm using a Markov random field approach. The joint distribution of class labels is explicitly modelled using the distances between feature vectors. Intuitively, ...
Item response modelling is a well established method for analysing ordinal response data. Ordinal data are typically collected as responses to a number
of questions or items. The observed data can be viewed as discrete ...
Ranked preference data arise when a set of judges rank, in order of their preference, a set of objects. Such data arise in preferential voting systems and market
research surveys. Covariate data associated with the judges ...
Let
p,n
∈
N
with 2
p
≥
n
+ 2
,
and let
I
a
be a polyharmonic spline of
order
p
on the grid
Z
×
a
Z
n
which satisfies the interpolating conditions
I
a
(
j,am
) =
d
j
(
am
) for
j
∈
Z
,m ...
In this paper we discuss convergence properties and error estimates of rational
Bernstein operators introduced by P. Pit¸ul and P. Sablonni`ere. It is shown that the
rational Bernstein operators converge to the identity ...
The known proofs for universal Taylor series do not determine a specific universal
Taylor series. In the present paper, we isolate a specific universal Taylor series by
modifying the proof in [30]. Thus we determine all ...
The p* model is widely used in social network analysis. The likelihood of a network under this model is impossible to calculate for all but trivially small networks. Various approximation have been presented in the literature, ...
Mycobacterium bovis infects the wildlife species badgers Meles meles who are linked with the spread of the associated disease tuberculosis (TB) in cattle. Control of livestock infections depends in part on the spatial and ...
It is known that, for any simply connected proper subdomain Ω of the complex plane and any point ζ in Ω, there are holomorphic functions on Ω that possess “universal” Taylor series expansions about ζ; that is, partial sums ...
The development of computer models for numerical simulation of the atmosphere
and oceans is one of the great scientific triumphs of the past fifty years. These
models have added enormously to our understanding of the ...
Let Ω be a simply connected proper subdomain of the complex plane and z0 be a point in Ω. It is known that there are holomorphic functions f on Ω for which the partial sums (Sn(f,z0)) of the Taylor series about z0 have ...
We consider the Goursat problem in the plane for partial differential operators whose principal part is the pth power of the standard Laplace operator. The data is posed on a union of 2p distinct lines through the origin. ...
Let
Pn
(α,β
)
(
x
)
be the Jacobi polynomial of degree
n
with parameters
αβ
The main result of the paper states the following: If
b≠
1
;
3
and
c
are non-zero rel-
atively prime natural numbers ...
The spectrum of atmospheric motions is vast, encompassing phenomena having periods ranging
from seconds to millennia. The motions of interest to the forecaster typically have time-scales of a day or longer, but the ...