3,680 research outputs found
Paley-Littlewood decomposition for sectorial operators and interpolation spaces
We prove Paley-Littlewood decompositions for the scales of fractional powers
of -sectorial operators on a Banach space which correspond to
Triebel-Lizorkin spaces and the scale of Besov spaces if is the classical
Laplace operator on We use the -calculus,
spectral multiplier theorems and generalized square functions on Banach spaces
and apply our results to Laplace-type operators on manifolds and graphs,
Schr\"odinger operators and Hermite expansion.We also give variants of these
results for bisectorial operators and for generators of groups with a bounded
-calculus on strips.Comment: 2nd version to appear in Mathematische Nachrichten, Mathematical News
/ Mathematische Nachrichten, Wiley-VCH Verlag, 201
Confidence intervals for average success probabilities
We provide Buehler-optimal one-sided and some valid two-sided confidence
intervals for the average success probability of a possibly inhomogeneous fixed
length Bernoulli chain, based on the number of observed successes. Contrary to
some claims in the literature, the one-sided Clopper-Pearson intervals for the
homogeneous case are not completely robust here, not even if applied to
hypergeometric estimation problems.Comment: Revised version for: Probability and Mathematical Statistics. Two
remarks adde
Explicit bounds for the approximation error in Benford's law
Benford's law states that for many random variables X > 0 its leading digit D
= D(X) satisfies approximately the equation P(D = d) = log_{10}(1 + 1/d) for d
= 1,2,...,9. This phenomenon follows from another, maybe more intuitive fact,
applied to Y := log_{10}(X): For many real random variables Y, the remainder U
:= Y - floor(Y) is approximately uniformly distributed on [0,1). The present
paper provides new explicit bounds for the latter approximation in terms of the
total variation of the density of Y or some derivative of it. These bounds are
an interesting alternative to traditional Fourier methods which yield mostly
qualitative results. As a by-product we obtain explicit bounds for the
approximation error in Benford's law.Comment: 16 pages, one figur
Spectral multiplier theorems and averaged R-boundedness
Let be a -sectorial operator with a bounded
-calculus for some e.g. a
Laplace type operator on where is a
manifold or a graph. We show that has a H{\"o}rmander functional calculus
if and only if certain operator families derived from the resolvent the semigroup the wave operators or the
imaginary powers of are -bounded in an -averaged sense. If
is an space with -boundedness reduces
to well-known estimates of square sums.Comment: Error in the title correcte
Coding Strategies for Noise-Free Relay Cascades with Half-Duplex Constraint
Two types of noise-free relay cascades are investigated. Networks where a
source communicates with a distant receiver via a cascade of half-duplex
constrained relays, and networks where not only the source but also a single
relay node intends to transmit information to the same destination. We
introduce two relay channel models, capturing the half-duplex constraint, and
within the framework of these models capacity is determined for the first
network type. It turns out that capacity is significantly higher than the rates
which are achievable with a straightforward time-sharing approach. A capacity
achieving coding strategy is presented based on allocating the transmit and
receive time slots of a node in dependence of the node's previously received
data. For the networks of the second type, an upper bound to the rate region is
derived from the cut-set bound. Further, achievability of the cut-set bound in
the single relay case is shown given that the source rate exceeds a certain
minimum value.Comment: Proceedings of the 2008 IEEE International Symposium on Information
Theory, Toronto, ON, Canada, July 6 - 11, 200
Capacity for Half-Duplex Line Networks with Two Sources
The focus is on noise-free half-duplex line networks with two sources where
the first node and either the second node or the second-last node in the
cascade act as sources. In both cases, we establish the capacity region of
rates at which both sources can transmit independent information to a common
sink. The achievability scheme presented for the first case is constructive
while the achievability scheme for the second case is based on a random coding
argument.Comment: Proceedings of the IEEE International Symposium on Information
Theory, Austin, TX, USA, June 12 - 18, 201
Unguarded Recursion on Coinductive Resumptions
We study a model of side-effecting processes obtained by starting from a
monad modelling base effects and adjoining free operations using a cofree
coalgebra construction; one thus arrives at what one may think of as types of
non-wellfounded side-effecting trees, generalizing the infinite resumption
monad. Correspondingly, the arising monad transformer has been termed the
coinductive generalized resumption transformer. Monads of this kind have
received some attention in the recent literature; in particular, it has been
shown that they admit guarded iteration. Here, we show that they also admit
unguarded iteration, i.e. form complete Elgot monads, provided that the
underlying base effect supports unguarded iteration. Moreover, we provide a
universal characterization of the coinductive resumption monad transformer in
terms of coproducts of complete Elgot monads.Comment: 47 pages, extended version of
http://www.sciencedirect.com/science/article/pii/S157106611500079
Ethics and the credit insurance industry
Student Number : 0215239Y -
MA research project -
School of Social Sciences -
Faculty of HumanitiesThe purpose of this report is to investigate whether ethics is important to the credit
insurance industry and to consider the role a code of ethics can play in helping to make
better decisions.
The conclusions that I reach are that ethics plays a vital role in building and sustaining a
healthy credit insurance business and that a well designed and managed ethics policy is
an invaluable tool in running an ethical business and in protecting the reputation and long
term viability of a credit insurer.
The report begins by providing - in part I - a brief outline of the major ethical theories
including short reviews of the two closely related subjects of corporate governance and
sustainable development. It continues by discussing the impact of ethics on business in
general. I commence the heart of the report by examining in part II ethics in the credit
insurance industry, by defining credit insurance and describing the special roles it plays
in national and international economies. I then focus on the pertinent operational aspects
of a credit insurance business, i.e. marketing and sales, underwriting, claims and reinsurance with particular reference to the role ethics can and should play in each of
them.
By drawing together the outcomes of these various deliberations the basic guidelines for
the drafting of codes of ethics in the credit insurance industry will be developed
(obviously each company has to design its own code in line with its own corporate
culture, values and circumstances). Finally I attempt to show the benefits a well drafted
and properly managed code can have for a credit insurer (part III)
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