1,145 research outputs found
The Generalized Dirichlet to Neumann map for the KdV equation on the half-line
For the two versions of the KdV equation on the positive half-line an
initial-boundary value problem is well posed if one prescribes an initial
condition plus either one boundary condition if and have the
same sign (KdVI) or two boundary conditions if and have
opposite sign (KdVII). Constructing the generalized Dirichlet to Neumann map
for the above problems means characterizing the unknown boundary values in
terms of the given initial and boundary conditions. For example, if
and are given for the KdVI
and KdVII equations, respectively, then one must construct the unknown boundary
values and , respectively. We
show that this can be achieved without solving for by analysing a
certain ``global relation'' which couples the given initial and boundary
conditions with the unknown boundary values, as well as with the function
, where satisifies the -part of the associated
Lax pair evaluated at . Indeed, by employing a Gelfand--Levitan--Marchenko
triangular representation for , the global relation can be solved
\emph{explicitly} for the unknown boundary values in terms of the given initial
and boundary conditions and the function . This yields the unknown
boundary values in terms of a nonlinear Volterra integral equation.Comment: 21 pages, 3 figure
Why the Hamilton operator alone is not enough
In the many worlds community seems to exist a belief that the physics of a
quantum theory is completely defined by it's Hamilton operator given in an
abstract Hilbert space, especially that the position basis may be derived from
it as preferred using decoherence techniques.
We show, by an explicit example of non-uniqueness, taken from the theory of
the KdV equation, that the Hamilton operator alone is not sufficient to fix the
physics. We need the canonical operators p, q as well. As a consequence, it is
not possible to derive a "preferred basis" from the Hamilton operator alone,
without postulating some additional structure like a "decomposition into
systems". We argue that this makes such a derivation useless for fundamental
physics
Multilayered feed forward Artificial Neural Network model to predict the average summer-monsoon rainfall in India
In the present research, possibility of predicting average summer-monsoon
rainfall over India has been analyzed through Artificial Neural Network models.
In formulating the Artificial Neural Network based predictive model, three
layered networks have been constructed with sigmoid non-linearity. The models
under study are different in the number of hidden neurons. After a thorough
training and test procedure, neural net with three nodes in the hidden layer is
found to be the best predictive model.Comment: 19 pages, 1 table, 3 figure
The variational Poisson cohomology
It is well known that the validity of the so called Lenard-Magri scheme of
integrability of a bi-Hamiltonian PDE can be established if one has some
precise information on the corresponding 1st variational Poisson cohomology for
one of the two Hamiltonian operators. In the first part of the paper we explain
how to introduce various cohomology complexes, including Lie superalgebra and
Poisson cohomology complexes, and basic and reduced Lie conformal algebra and
Poisson vertex algebra cohomology complexes, by making use of the corresponding
universal Lie superalebra or Lie conformal superalgebra. The most relevant are
certain subcomplexes of the basic and reduced Poisson vertex algebra cohomology
complexes, which we identify (non-canonically) with the generalized de Rham
complex and the generalized variational complex. In the second part of the
paper we compute the cohomology of the generalized de Rham complex, and, via a
detailed study of the long exact sequence, we compute the cohomology of the
generalized variational complex for any quasiconstant coefficient Hamiltonian
operator with invertible leading coefficient. For the latter we use some
differential linear algebra developed in the Appendix.Comment: 130 pages, revised version with minor changes following the referee's
suggestion
Singularly Perturbed Monotone Systems and an Application to Double Phosphorylation Cycles
The theory of monotone dynamical systems has been found very useful in the
modeling of some gene, protein, and signaling networks. In monotone systems,
every net feedback loop is positive. On the other hand, negative feedback loops
are important features of many systems, since they are required for adaptation
and precision. This paper shows that, provided that these negative loops act at
a comparatively fast time scale, the main dynamical property of (strongly)
monotone systems, convergence to steady states, is still valid. An application
is worked out to a double-phosphorylation ``futile cycle'' motif which plays a
central role in eukaryotic cell signaling.Comment: 21 pages, 3 figures, corrected typos, references remove
Quantum and Classical Integrable Systems
The key concept discussed in these lectures is the relation between the
Hamiltonians of a quantum integrable system and the Casimir elements in the
underlying hidden symmetry algebra. (In typical applications the latter is
either the universal enveloping algebra of an affine Lie algebra, or its
q-deformation.) A similar relation also holds in the classical case. We discuss
different guises of this very important relation and its implication for the
description of the spectrum and the eigenfunctions of the quantum system.
Parallels between the classical and the quantum cases are thoroughly discussed.Comment: 59 pages, LaTeX2.09 with AMS symbols. Lectures at the CIMPA Winter
School on Nonlinear Systems, Pondicherry, January 199
A terminal assessment of stages theory : introducing a dynamic states approach to entrepreneurship
Stages of Growth models were the most frequent theoretical approach to understanding entrepreneurial business growth from 1962 to 2006; they built on the growth imperative and developmental models of that time. An analysis of the universe of such models (N=104) published in the management literature shows no consensus on basic constructs of the approach, nor is there any empirical confirmations of stages theory. However, by changing two propositions of the stages models, a new dynamic states approach is derived. The dynamic states approach has far greater explanatory power than its precursor, and is compatible with leading edge research in entrepreneurship
Dynamical stability of infinite homogeneous self-gravitating systems: application of the Nyquist method
We complete classical investigations concerning the dynamical stability of an
infinite homogeneous gaseous medium described by the Euler-Poisson system or an
infinite homogeneous stellar system described by the Vlasov-Poisson system
(Jeans problem). To determine the stability of an infinite homogeneous stellar
system with respect to a perturbation of wavenumber k, we apply the Nyquist
method. We first consider the case of single-humped distributions and show
that, for infinite homogeneous systems, the onset of instability is the same in
a stellar system and in the corresponding barotropic gas, contrary to the case
of inhomogeneous systems. We show that this result is true for any symmetric
single-humped velocity distribution, not only for the Maxwellian. If we
specialize on isothermal and polytropic distributions, analytical expressions
for the growth rate, damping rate and pulsation period of the perturbation can
be given. Then, we consider the Vlasov stability of symmetric and asymmetric
double-humped distributions (two-stream stellar systems) and determine the
stability diagrams depending on the degree of asymmetry. We compare these
results with the Euler stability of two self-gravitating gaseous streams.
Finally, we determine the corresponding stability diagrams in the case of
plasmas and compare the results with self-gravitating systems
Search for and Using Genetic Programming Event Selection
We apply a genetic programming technique to search for the double Cabibbo
suppressed decays and .
We normalize these decays to their Cabibbo favored partners and find
\Lambda_c^+ \to p K^+ \pi^-\Lambda_c^+ \to p K^-
\pi^+ and D_s^+ \to K^+ K^+
\pi^-D_s^+ \to K^+ K^- \pi^+ where
the first errors are statistical and the second are systematic. Expressed as
90% confidence levels (CL), we find and respectively.
This is the first successful use of genetic programming in a high energy
physics data analysis.Comment: 10 page
Measurement of the D+ and Ds+ decays into K+K-K+
We present the first clear observation of the doubly Cabibbo suppressed decay
D+ --> K-K+K+ and the first observation of the singly Cabibbo suppressed decay
Ds+ --> K-K+K+. These signals have been obtained by analyzing the high
statistics sample of photoproduced charm particles of the FOCUS(E831)
experiment at Fermilab. We measure the following relative branching ratios:
Gamma(D+ --> K-K+K+)/Gamma(D+ --> K-pi+pi+) = (9.49 +/- 2.17(statistical) +/-
0.22(systematic))x10^-4 and Gamma(Ds+ --> K-K+K+)/Gamma(Ds+ --> K-K+pi+) =
(8.95 +/- 2.12(statistical) +2.24(syst.) -2.31(syst.))x10^-3.Comment: 10 pages, 8 figure
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