71 research outputs found
Financial performance of groups of companies in Poland against the background of historical determinants and knowledge management procedures applied
Polish businesses are passing the fifteen year mark of the free market experience. The important processes that could be observed during that time include the formation of groups of companies. What were the establishment paths of these multiple organisations and what was the impact of historical determinants on their operation and financial performance? What is the extent of contribution of subsidiaries to the financial performance of the groups? And finally what are the main drivers of their effectiveness in the context of group management system applied and knowledge management procedures?
This paper attempts to provide answers to these questions. It presents insights, observations and selected findings of research conducted over the period of the last five years. It is shown that the operation of these organisations is on the one hand strongly determined by historical factors, and on the other the strength of this impact diminishes with time. Groups of companies see positive operational changes, reflected mainly in improved financial performance, growing significance of subsidiaries and the enhanced effectiveness of the management systems applied which are broadly based on knowledge management procedures
On Blowup for time-dependent generalized Hartree-Fock equations
We prove finite-time blowup for spherically symmetric and negative energy
solutions of Hartree-Fock and Hartree-Fock-Bogoliubov type equations, which
describe the evolution of attractive fermionic systems (e. g. white dwarfs).
Our main results are twofold: First, we extend the recent blowup result of
[Hainzl and Schlein, Comm. Math. Phys. \textbf{287} (2009), 705--714] to
Hartree-Fock equations with infinite rank solutions and a general class of
Newtonian type interactions. Second, we show the existence of finite-time
blowup for spherically symmetric solutions of a Hartree-Fock-Bogoliubov model,
where an angular momentum cutoff is introduced. We also explain the key
difficulties encountered in the full Hartree-Fock-Bogoliubov theory.Comment: 24 page
Instabilities in the dissolution of a porous matrix
A reactive fluid dissolving the surrounding rock matrix can trigger an
instability in the dissolution front, leading to spontaneous formation of
pronounced channels or wormholes. Theoretical investigations of this
instability have typically focused on a steadily propagating dissolution front
that separates regions of high and low porosity. In this paper we show that
this is not the only possible dissolutional instability in porous rocks; there
is another instability that operates instantaneously on any initial porosity
field, including an entirely uniform one. The relative importance of the two
mechanisms depends on the ratio of the porosity increase to the initial
porosity. We show that the "inlet" instability is likely to be important in
limestone formations where the initial porosity is small and there is the
possibility of a large increase in permeability. In quartz-rich sandstones,
where the proportion of easily soluble material (e.g. carbonate cements) is
small, the instability in the steady-state equations is dominant.Comment: to be published in Geophysical Research Letter
On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction
In the mean-field limit the dynamics of a quantum Bose gas is described by a
Hartree equation. We present a simple method for proving the convergence of the
microscopic quantum dynamics to the Hartree dynamics when the number of
particles becomes large and the strength of the two-body potential tends to 0
like the inverse of the particle number. Our method is applicable for a class
of singular interaction potentials including the Coulomb potential. We prove
and state our main result for the Heisenberg-picture dynamics of "observables",
thus avoiding the use of coherent states. Our formulation shows that the
mean-field limit is a "semi-classical" limit.Comment: Corrected typos and included an elementary proof of the Kato
smoothing estimate (Lemma 6.1
Magnetic Monopoles, Electric Neutrality and the Static Maxwell-Dirac Equations
We study the full Maxwell-Dirac equations: Dirac field with minimally coupled
electromagnetic field and Maxwell field with Dirac current as source. Our
particular interest is the static case in which the Dirac current is purely
time-like -- the "electron" is at rest in some Lorentz frame. In this case we
prove two theorems under rather general assumptions. Firstly, that if the
system is also stationary (time independent in some gauge) then the system as a
whole must have vanishing total charge, i.e. it must be electrically neutral.
In fact, the theorem only requires that the system be {\em asymptotically}
stationary and static. Secondly, we show, in the axially symmetric case, that
if there are external Coulomb fields then these must necessarily be
magnetically charged -- all Coulomb external sources are electrically charged
magnetic monopoles
Existence of global-in-time solutions to a generalized Dirac-Fock type evolution equation
We consider a generalized Dirac-Fock type evolution equation deduced from
no-photon Quantum Electrodynamics, which describes the self-consistent
time-evolution of relativistic electrons, the observable ones as well as those
filling up the Dirac sea. This equation has been originally introduced by Dirac
in 1934 in a simplified form. Since we work in a Hartree-Fock type
approximation, the elements describing the physical state of the electrons are
infinite rank projectors. Using the Bogoliubov-Dirac-Fock formalism, introduced
by Chaix-Iracane ({\it J. Phys. B.}, 22, 3791--3814, 1989), and recently
established by Hainzl-Lewin-Sere, we prove the existence of global-in-time
solutions of the considered evolution equation.Comment: 12 pages; more explanations added, some final (minor) corrections
include
Setting and analysis of the multi-configuration time-dependent Hartree-Fock equations
In this paper we motivate, formulate and analyze the Multi-Configuration
Time-Dependent Hartree-Fock (MCTDHF) equations for molecular systems under
Coulomb interaction. They consist in approximating the N-particle Schrodinger
wavefunction by a (time-dependent) linear combination of (time-dependent)
Slater determinants. The equations of motion express as a system of ordinary
differential equations for the expansion coefficients coupled to nonlinear
Schrodinger-type equations for mono-electronic wavefunctions. The invertibility
of the one-body density matrix (full-rank hypothesis) plays a crucial role in
the analysis. Under the full-rank assumption a fiber bundle structure shows up
and produces unitary equivalence between convenient representations of the
equations. We discuss and establish existence and uniqueness of maximal
solutions to the Cauchy problem in the energy space as long as the density
matrix is not singular. A sufficient condition in terms of the energy of the
initial data ensuring the global-in-time invertibility is provided (first
result in this direction). Regularizing the density matrix breaks down energy
conservation, however a global well-posedness for this system in L^2 is
obtained with Strichartz estimates. Eventually solutions to this regularized
system are shown to converge to the original one on the time interval when the
density matrix is invertible.Comment: 48 pages, 1 figur
Wormhole formation in dissolving fractures
We investigate the dissolution of artificial fractures with
three-dimensional, pore-scale numerical simulations. The fluid velocity in the
fracture space was determined from a lattice-Boltzmann method, and a stochastic
solver was used for the transport of dissolved species. Numerical simulations
were used to study conditions under which long conduits (wormholes) form in an
initially rough but spatially homogeneous fracture. The effects of flow rate,
mineral dissolution rate and geometrical properties of the fracture were
investigated, and the optimal conditions for wormhole formation determined.Comment: to be published in J. Geophys Re
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