6,326 research outputs found
Brunovsky Normal Form of Monod Kinetics Models and Growth Rate Control of a Fed-batch Cultivation Process
A mathematical methodology that gives assistance to design of fed-batch stabilization and control is presented. The methodology is based both on Utility theory and optimal Control theory. The Utility theory deals with the expressed subjective preferences and allows for the expert preferences to be taken in consideration in complex biotechnological systems as criteria for control and optimization. The Control theory is used for parameters stabilization of a fed-batch cultivation process. The control is written based on information of the growth rate. The simulations show good efficiency of the control laws
Multi-Lagrangians for Integrable Systems
We propose a general scheme to construct multiple Lagrangians for completely
integrable non-linear evolution equations that admit multi- Hamiltonian
structure. The recursion operator plays a fundamental role in this
construction. We use a conserved quantity higher/lower than the Hamiltonian in
the potential part of the new Lagrangian and determine the corresponding
kinetic terms by generating the appropriate momentum map. This leads to some
remarkable new developments. We show that nonlinear evolutionary systems that
admit -fold first order local Hamiltonian structure can be cast into
variational form with Lagrangians which will be local functionals of
Clebsch potentials. This number increases to when the Miura
transformation is invertible. Furthermore we construct a new Lagrangian for
polytropic gas dynamics in dimensions which is a {\it local} functional
of the physical field variables, namely density and velocity, thus dispensing
with the necessity of introducing Clebsch potentials entirely. This is a
consequence of bi-Hamiltonian structure with a compatible pair of first and
third order Hamiltonian operators derived from Sheftel's recursion operator.Comment: typos corrected and a reference adde
Non polynomial conservation law densities generated by the symmetry operators in some hydrodynamical models
New extra series of conserved densities for the polytropic gas model and
nonlinear elasticity equation are obtained without any references to the
recursion operator or to the Lax operator formalism. Our method based on the
utilization of the symmetry operators and allows us to obtain the densities of
arbitrary homogenuity dimensions. The nonpolynomial densities with logarithmics
behaviour are presented as an example. The special attention is paid for the
singular case for which we found new non homogenious solutions
expressed in terms of the elementary functions.Comment: 11 pages, 1 figur
Variability of the Vela Pulsar-wind Nebula Observed with Chandra
The observations of the pulsar-wind nebula (PWN) around the Vela pulsar with
the Advanced CCD Imaging Spectrometer aboard the Chandra X-ray Observatory,
taken on 2000 April 30 and November 30, reveal its complex morphology
reminiscent of that of the Crab PWN. Comparison of the two observations shows
changes up to 30% in the surface brightness of the PWN features. Some of the
PWN elements show appreciable shifts, up to a few arcseconds (about 10^{16}
cm), and/or spectral changes. To elucidate the nature of the observed
variations, further monitoring of the Vela PWN is needed.Comment: 7 pages (incl. 3 embedded PS figures), AASTEX, uses emulateapj5.sty.
Submitted to ApJ Lett. For a high-resolution color PS image of Figure 3 (6.3
Mby), see http://www.astro.psu.edu/users/divas/velaneb_fig3.p
Landau quantization and neutron emissions by nuclei in the crust of a magnetar
Magnetars are neutron stars endowed with surface magnetic fields of the order
of ~G, and with presumably much stronger fields in their
interior. As a result of Landau quantization of electron motion, the
neutron-drip transition in the crust of a magnetar is shifted to either higher
or lower densities depending on the magnetic field strength. The impact of
nuclear uncertainties is explored considering the recent series of
Brussels-Montreal microscopic nuclear mass models. All these models are based
on the Hartree-Fock-Bogoliubov method with generalized Skyrme functionals. They
differ in their predictions for the symmetry energy coefficient at saturation,
and for the stiffness of the neutron-matter equation of state. For comparison,
we have also considered the very accurate but more phenomenological model of
Duflo and Zuker. Although the equilibrium composition of the crust of a
magnetar and the onset of neutron emission are found to be model dependent, the
quantum oscillations of the threshold density are essentially universal.Comment: 7 pages, 2 figure
Ranking system for Ukrainian banks based on financial standing
The paper provides a new approach to determining the financial standing of Ukrainian banks
in the long and short terms. Using the European assessing indices and the national ones, a new
ranking system is created. The authors ranked 20 biggest Ukrainian banks by assets and grouped
them into corresponding financial groups
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