5,135 research outputs found
Tensor Products, Positive Linear Operators, and Delay-Differential Equations
We develop the theory of compound functional differential equations, which
are tensor and exterior products of linear functional differential equations.
Of particular interest is the equation with a single delay, where the delay
coefficient is of one sign, say with .
Positivity properties are studied, with the result that if then
the -fold exterior product of the above system generates a linear process
which is positive with respect to a certain cone in the phase space.
Additionally, if the coefficients and are periodic of
the same period, and satisfies a uniform sign condition, then there
is an infinite set of Floquet multipliers which are complete with respect to an
associated lap number. Finally, the concept of -positivity of the exterior
product is investigated when satisfies a uniform sign condition.Comment: 84 page
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Taricha torosa
Number of Pages: 4Integrative BiologyGeological Science
The horofunction boundary of the Hilbert geometry
We investigate the horofunction boundary of the Hilbert geometry defined on
an arbitrary finite-dimensional bounded convex domain D. We determine its set
of Busemann points, which are those points that are the limits of
`almost-geodesics'. In addition, we show that any sequence of points converging
to a point in the horofunction boundary also converges in the usual sense to a
point in the Euclidean boundary of D. We prove that all horofunctions are
Busemann points if and only if the set of extreme sets of the polar of D is
closed in the Painleve-Kuratowski topology.Comment: 24 pages, 2 figures; minor changes, examples adde
Existence of positive solutions of a superlinear boundary value problem with indefinite weight
We deal with the existence of positive solutions for a two-point boundary
value problem associated with the nonlinear second order equation
. The weight is allowed to change its sign. We assume
that the function is
continuous, and satisfies suitable growth conditions, so as the case
, with , is covered. In particular we suppose that is
large near infinity, but we do not require that is non-negative in a
neighborhood of zero. Using a topological approach based on the Leray-Schauder
degree we obtain a result of existence of at least a positive solution that
improves previous existence theorems.Comment: 12 pages, 4 PNG figure
A Metric Inequality for the Thompson and Hilbert Geometries
There are two natural metrics defined on an arbitrary convex cone: Thompson's
part metric and Hilbert's projective metric. For both, we establish an
inequality giving information about how far the metric is from being
non-positively curved.Comment: 15 pages, 0 figures. To appear in J. Inequalities Pure Appl. Mat
The Shortcomings of New York\u27s Long-Arm Statute: Defamation in the Age of Technology
(Excerpt)
This Note suggests that the New York legislature amend New York\u27s long-arm statute so that it no longer excludes the tort of defamation as a basis for long-arm jurisdiction. Part I provides a brief background and history of jurisdiction and longarm statutes in general. It also focuses on New York\u27s statute more specifically. Part II focuses on the arguments for excluding acts of defamation from long-arm jurisdiction and compares New York\u27s statute to those of other states. Finally, Part III examines the different policy reasons for changing the statute and argues that such a change will not offend Due Process or First Amendment protections of free speech
Ten myths about character, virtue and virtue education – plus three well-founded misgivings
Initiatives to cultivate character and virtue in moral education at school continue to provoke sceptical responses. Most of those echo familiar misgivings about the notions of character, virtue and education in virtue – as unclear, redundant, old-fashioned, religious, paternalistic, anti-democratic, conservative, individualistic, relative and situation dependent. I expose those misgivings as ‘myths’, while at the same time acknowledging three better-founded historical, methodological and practical concerns about the notions in question
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