18,412 research outputs found
Some New Delay Integral Inequalities in Two Independent Variables on Time Scales
Some new Gronwall-Bellman-type delay integral inequalities in two independent variables on time scales are established, which can be used as a handy tool in the research of boundedness of solutions of delay dynamic equations on time scales. Some of the established results are 2D extensions of several known results in the literature, while some results unify existing continuous and discrete analysis
Generalized retarded integral inequalities
We prove some new retarded integral inequalities. The results generalize
those in [J. Math. Anal. Appl. 301 (2005), no. 2, 265--275].Comment: Changes suggested by the referee don
Quantum astrometric observables I: time delay in classical and quantum gravity
A class of diffeomorphism invariant, physical observables, so-called
astrometric observables, is introduced. A particularly simple example, the time
delay, which expresses the difference between two initially synchronized proper
time clocks in relative inertial motion, is analyzed in detail. It is found to
satisfy some interesting inequalities related to the causal structure of
classical Lorentzian spacetimes. Thus it can serve as a probe of causal
structure and in particular of violations of causality. A quantum model of this
observable as well as the calculation of its variance due to vacuum
fluctuations in quantum linearized gravity are sketched. The question of
whether the causal inequalities are still satisfied by quantized gravity, which
is pertinent to the nature of causality in quantum gravity, is raised, but it
is shown that perturbative calculations cannot provide a definite answer. Some
potential applications of astrometric observables in quantum gravity are
discussed.Comment: revtex4-1, 21 pages, 7 figures (published version); added journal re
An Overview of Integral Quadratic Constraints for Delayed Nonlinear and Parameter-Varying Systems
A general framework is presented for analyzing the stability and performance
of nonlinear and linear parameter varying (LPV) time delayed systems. First,
the input/output behavior of the time delay operator is bounded in the
frequency domain by integral quadratic constraints (IQCs). A constant delay is
a linear, time-invariant system and this leads to a simple, intuitive
interpretation for these frequency domain constraints. This simple
interpretation is used to derive new IQCs for both constant and varying delays.
Second, the performance of nonlinear and LPV delayed systems is bounded using
dissipation inequalities that incorporate IQCs. This step makes use of recent
results that show, under mild technical conditions, that an IQC has an
equivalent representation as a finite-horizon time-domain constraint. Numerical
examples are provided to demonstrate the effectiveness of the method for both
class of systems
Local estimates for entropy densities in coupled map lattices
We present a method to derive an upper bound for the entropy density of
coupled map lattices with local interactions from local observations. To do
this, we use an embedding technique being a combination of time delay and
spatial embedding. This embedding allows us to identify the local character of
the equations of motion. Based on this method we present an approximate
estimate of the entropy density by the correlation integral.Comment: 4 pages, 5 figures include
Nonlinear diffusions: extremal properties of Barenblatt profiles, best matching and delays
In this paper, we consider functionals based on moments and non-linear
entropies which have a linear growth in time in case of source-type so-lutions
to the fast diffusion or porous medium equations, that are also known as
Barenblatt solutions. As functions of time, these functionals have convexity
properties for generic solutions, so that their asymptotic slopes are extremal
for Barenblatt profiles. The method relies on scaling properties of the
evo-lution equations and provides a simple and direct proof of sharp
Gagliardo-Nirenberg-Sobolev inequalities in scale invariant form. The method
also gives refined estimates of the growth of the second moment and, as a
consequence, establishes the monotonicity of the delay corresponding to the
best matching Barenblatt solution compared to the Barenblatt solution with same
initial sec-ond moment. Here the notion of best matching is defined in terms of
a relative entropy
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