10,342 research outputs found
The sources of Mill's views of ratiocination and induction
Steffen Ducheyne and John P. McCaskey (2014). “The Sources of Mill’s Views of Ratiocination and Induction,” in: Antis Loizides (ed.), John Stuart Mill’s ‘A System of Logic’: A Critical Guide (London, Routledge), pp. 63-8
Geometry of canonical self-similar tilings
We give several different geometric characterizations of the situation in
which the parallel set of a self-similar set can be described
by the inner -parallel set of the associated
canonical tiling , in the sense of \cite{SST}. For example,
if and only if the boundary of the
convex hull of is a subset of , or if the boundary of , the
unbounded portion of the complement of , is the boundary of a convex set. In
the characterized situation, the tiling allows one to obtain a tube formula for
, i.e., an expression for the volume of as a function of
. On the way, we clarify some geometric properties of canonical
tilings.
Motivated by the search for tube formulas, we give a generalization of the
tiling construction which applies to all self-affine sets having empty
interior and satisfying the open set condition. We also characterize the
relation between the parallel sets of and these tilings.Comment: 20 pages, 6 figure
Aggregation of Red Blood Cells: From Rouleaux to Clot Formation
Red blood cells are known to form aggregates in the form of rouleaux. This
aggregation process is believed to be reversible, but there is still no full
understanding on the binding mechanism. There are at least two competing
models, based either on bridging or on depletion. We review recent experimental
results on the single cell level and theoretical analyses of the depletion
model and of the influence of the cell shape on the binding strength. Another
important aggregation mechanism is caused by activation of platelets. This
leads to clot formation which is life saving in the case of wound healing but
also a major cause of death in the case of a thrombus induced stroke. We review
historical and recent results on the participation of red blood cells in clot
formation
Inflation convergence after the introduction of the Euro
Using the Johansen test for cointegration, we examine to which extent inflation rates in the Euro area have converged after the introduction of a single currency. Since the assumption of non-stationary variables represents the pivotal point in cointegration analyses we pay special attention to the appropriate identification of non-stationary inflation rates by the application of six different unit root tests. We compare two periods, the first ranging from 1993 to 1998 and the second from 1993 to 2002 with monthly observations. The Johansen test only finds partial convergence for the former period and no convergence for the latter.Unit root, Cointegration, Inflation convergence
Inflation Risk Analysis of European Real Estate Securities
The focus of this paper is the analysis of the inflation risk of European real estate securities. Following both a causal and a final understanding of risk, the analysis is twofold: First, to examine the causal influence of inflation on short- and long-term asset returns, we employ different regression approaches based on the methodology of Fama/Schwert 1977. Hedging capacities against expected inflation are found only for German open-end funds. Furthermore, different shortfall risk measures are used to study whether an investment in European real estate securities protects against a negative real return at the end of a given investment period.
Hedonic Price Indices for the Paris Housing Market
In this paper, we calculate a transaction-based price index for apartments in Paris (France). The heterogeneous character of real estate is taken into account using an hedonic model. The functional form is specified using a general Box-Cox function. The data basis covers 84 686 transactions of the housing market in 1990:01-1999:12, which is one of the largest samples ever used in comparable studies. Low correlations of the price index with stock and bond indices (first differences) indicate diversification benefits from the inclusion of real estate in a mixed asset portfolio
Kinetic induced phase transition
An Ising model with local Glauber dynamics is studied under the influence of
additional kinetic restrictions for the spin-flip rates depending on the
orientation of neighboring spins. Even when the static interaction between the
spins is completely eliminated and only an external field is taken into account
the system offers a phase transition at a finite value of the applied field.
The transition is realized due to a competition between the activation
processes driven by the field and the dynamical rules for the spin-flips. The
result is based on a master equation approach in a quantum formulation.Comment: 13 page
Lattice-type self-similar sets with pluriphase generators fail to be Minkowski measurable
A long-standing conjecture of Lapidus claims that under certain conditions,
self-similar fractal sets fail to be Minkowski measurable if and only if they
are of lattice type. The theorem was established for fractal subsets of
by Falconer, Lapidus and v.~Frankenhuijsen, and the forward
direction was shown for fractal subsets of , , by
Gatzouras. Since then, much effort has been made to prove the converse. In this
paper, we prove a partial converse by means of renewal theory. Our proof allows
us to recover several previous results in this regard, but is much shorter and
extends to a more general setting; several technical conditions appearing in
previous versions of this result have now been removed.Comment: 20 pages, 6 figure
Pointwise tube formulas for fractal sprays and self-similar tilings with arbitrary generators
In a previous paper by the first two authors, a tube formula for fractal
sprays was obtained which also applies to a certain class of self-similar
fractals. The proof of this formula uses distributional techniques and requires
fairly strong conditions on the geometry of the tiling (specifically, the inner
tube formula for each generator of the fractal spray is required to be
polynomial). Now we extend and strengthen the tube formula by removing the
conditions on the geometry of the generators, and also by giving a proof which
holds pointwise, rather than distributionally.
Hence, our results for fractal sprays extend to higher dimensions the
pointwise tube formula for (1-dimensional) fractal strings obtained earlier by
Lapidus and van Frankenhuijsen.
Our pointwise tube formulas are expressed as a sum of the residues of the
"tubular zeta function" of the fractal spray in . This sum ranges
over the complex dimensions of the spray, that is, over the poles of the
geometric zeta function of the underlying fractal string and the integers
. The resulting "fractal tube formulas" are applied to the important
special case of self-similar tilings, but are also illustrated in other
geometrically natural situations. Our tube formulas may also be seen as fractal
analogues of the classical Steiner formula.Comment: 43 pages, 13 figures. To appear: Advances in Mathematic
Minkowski measurability results for self-similar tilings and fractals with monophase generators
In a previous paper [arXiv:1006.3807], the authors obtained tube formulas for
certain fractals under rather general conditions. Based on these formulas, we
give here a characterization of Minkowski measurability of a certain class of
self-similar tilings and self-similar sets. Under appropriate hypotheses,
self-similar tilings with simple generators (more precisely, monophase
generators) are shown to be Minkowski measurable if and only if the associated
scaling zeta function is of nonlattice type. Under a natural geometric
condition on the tiling, the result is transferred to the associated
self-similar set (i.e., the fractal itself). Also, the latter is shown to be
Minkowski measurable if and only if the associated scaling zeta function is of
nonlattice type.Comment: 18 pages, 1 figur
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