7,311 research outputs found
State space formulas for stable rational matrix solutions of a Leech problem
Given stable rational matrix functions and , a procedure is presented
to compute a stable rational matrix solution to the Leech problem
associated with and , that is, and . The solution is given in the form of a state space
realization, where the matrices involved in this realization are computed from
state space realizations of the data functions and .Comment: 25 page
All solutions to the relaxed commutant lifting problem
A new description is given of all solutions to the relaxed commutant lifting
problem. The method of proof is also different from earlier ones, and uses only
an operator-valued version of a classical lemma on harmonic majorants.Comment: 15 page
State space formulas for a suboptimal rational Leech problem I: Maximum entropy solution
For the strictly positive case (the suboptimal case) the maximum entropy
solution to the Leech problem and
, with and stable rational
matrix functions, is proved to be a stable rational matrix function. An
explicit state space realization for is given, and turns out
to be strictly less than one. The matrices involved in this realization are
computed from the matrices appearing in a state space realization of the data
functions and . A formula for the entropy of is also given.Comment: 19 page
State space formulas for a suboptimal rational Leech problem II: Parametrization of all solutions
For the strictly positive case (the suboptimal case), given stable rational
matrix functions and , the set of all solutions to the
Leech problem associated with and , that is, and
, is presented as the range of a linear
fractional representation of which the coefficients are presented in state
space form. The matrices involved in the realizations are computed from state
space realizations of the data functions and . On the one hand the
results are based on the commutant lifting theorem and on the other hand on
stabilizing solutions of algebraic Riccati equations related to spectral
factorizations.Comment: 28 page
Exploring the temporally resolved electron density evolution in EUV induced plasmas
We measured for the first time the electron density in an Extreme
Ultra-Violet induced plasma. This is achieved in a low-pressure argon plasma by
using a method called microwave cavity resonance spectroscopy. The measured
electron density just after the EUV pulse is m. This
is in good agreement with a theoretical prediction from photo ionization, which
yields a density of m. After the EUV pulse the density
slightly increase due to electron impact ionization. The plasma (i.e. electron
density) decays in tens of microseconds.Comment: 3 pages, 4 figure
Why do little kids ask to hear the same story over and over?
One way people learn new words is through reading books and stories. Little kids love hearing their favorite stories over and over and are also very good at learning new words. We wondered if reading the same stories could be helping preschool kids learn new words. Our research tested if it was better to read the same stories over and over or to read a few different stories. Here we tell you about three studies that show preschool kids learn more words from the same stories over and over. Our research suggests that it’s easier to learn new words from stories when you have heard the story before and know what is going to happen
New economic geography, empirics, and regional policy
There are doubts about the effectiveness of regional policy. Well known are the fruitless attempts of Italy to bridge the gap between the Mezzogiorno and the North, of Germany to bridge the gap between the Neue Länder and the West, and of the European Commission to reduce regional disparities in general. We validate one explanation: agglomeration advantages lock business activity in relatively prosperous core regions, even though wages – and thus production costs – tend to be higher there. We set off from the ‘New Economic Geography’, a set of general equilibrium models that focus on location choice. Theory, descriptive statistics, and econometric analysis support the conclusion that the European economic geography is characterized by a network of local and stable core periphery systems. This implies that disparities between core regions and their peripheries at a (sub) provincial level of regional aggregation are with us to stay, as regional policy targeted on peripheries tends to be insufficient to counter centripetal market forces. Moreover, even if such policy has an impact, it may be adverse, as core regions may benefit disproportionately in the long run. A focus of regional policy on local agglomerations, which have a realistic chance to hold on to economic activity, is therefore desirable.
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