5,598 research outputs found
Finite difference approximations for a size-structured population model with distributed states in the recruitment
In this paper we consider a size-structured population model where
individuals may be recruited into the population at different sizes. First and
second order finite difference schemes are developed to approximate the
solution of the mathematical model. The convergence of the approximations to a
unique weak solution with bounded total variation is proved. We then show that
as the distribution of the new recruits become concentrated at the smallest
size, the weak solution of the distributed states-at-birth model converges to
the weak solution of the classical Gurtin-McCamy-type size-structured model in
the weak topology. Numerical simulations are provided to demonstrate the
achievement of the desired accuracy of the two methods for smooth solutions as
well as the superior performance of the second-order method in resolving
solution-discontinuities. Finally we provide an example where supercritical
Hopf-bifurcation occurs in the limiting single state-at-birth model and we
apply the second-order numerical scheme to show that such bifurcation occurs in
the distributed model as well
Syzygies of torsion bundles and the geometry of the level l modular variety over M_g
We formulate, and in some cases prove, three statements concerning the purity
or, more generally the naturality of the resolution of various rings one can
attach to a generic curve of genus g and a torsion point of order l in its
Jacobian. These statements can be viewed an analogues of Green's Conjecture and
we verify them computationally for bounded genus. We then compute the
cohomology class of the corresponding non-vanishing locus in the moduli space
R_{g,l} of twisted level l curves of genus g and use this to derive results
about the birational geometry of R_{g, l}. For instance, we prove that R_{g,3}
is a variety of general type when g>11 and the Kodaira dimension of R_{11,3} is
greater than or equal to 19. In the last section we explain probabilistically
the unexpected failure of the Prym-Green conjecture in genus 8 and level 2.Comment: 35 pages, appeared in Invent Math. We correct an inaccuracy in the
statement of Prop 2.
Production Technology and Competitiveness In the Hungarian Manufacturing Industry
Following the big transformations of the 1990s, enterprise structure and technological level seem to
have become stabilised in Hungary. Under these circumstances it is especially interesting to identify
the elements responsible for competitiveness in general, and the role technology plays in development
in particular, according to managers experienced in production and marketing. This empirical
study – based on in-depth interviews and field research – summarises characteristics of the technological
level in the sectors examined, role of technology and labour in production, effects of foreign
direct investment, relations between competition and firm-level factors determining competitiveness,
and concludes by summing up those most frequently mentioned proposals that should be incorporated
into economic policy according to managers. Main findings indicate that more qualified,
more intensive and cheaper labour can be substituted for high technology. The competitiveness of an
enterprise is not determined by technology alone, but rather by a combination of technology, the parameters
of available labour and the costs of investment increasing productivity. The insufficiency
of inter-company relations, together with a shortage of available assets necessary for investment
constitute the major threat undermining the competitiveness of enterprises in present-day Hungary
Incorporating model uncertainty into optimal insurance contract design
In stochastic optimization models, the optimal solution heavily depends on the selected probability model for the scenarios. However, the scenario models are typically chosen on the basis of statistical estimates and are therefore subject to model error. We demonstrate here how the model uncertainty can be incorporated into the decision making process. We use a nonparametric approach for quantifying the model uncertainty and a minimax setup to find model-robust solutions. The method is illustrated by a risk management problem involving the optimal design of an insurance contract
An extremal effective survey about extremal effective cycles in moduli spaces of curves
We survey recent developments and open problems about extremal effective
divisors and higher codimension cycles in moduli spaces of curves.Comment: Submitted to the Proceedings of the Abel Symposium 2017. Comments are
welcom
Vortices on Hyperbolic Surfaces
It is shown that abelian Higgs vortices on a hyperbolic surface can be
constructed geometrically from holomorphic maps , where is also
a hyperbolic surface. The fields depend on and on the metrics of and
. The vortex centres are the ramification points, where the derivative of
vanishes. The magnitude of the Higgs field measures the extent to which
is locally an isometry.
Witten's construction of vortices on the hyperbolic plane is rederived, and
new examples of vortices on compact surfaces and on hyperbolic surfaces of
revolution are obtained. The interpretation of these solutions as
SO(3)-invariant, self-dual SU(2) Yang--Mills fields on is also given.Comment: Revised version: new section on four-dimensional interpretation of
hyperbolic vortices added
A Change of Variables to the Dual and Factorization of Composite Anomalous Jacobians
Changes of variables giving the dual model are constructed explicitly for
sigma-models without isotropy. In particular, the jacobian is calculated to
give the known results. The global aspects of the abelian case as well as some
of those of the cases where the isometry group is simply connected are
considered.
Considering the anomalous case, we infer by a consistency argument that the
`multiplicative anomaly' should be replaceable by adequate rules for
factorization of composite jacobians. These rules are then generalized in a
simple way for composite jacobians defined in spaces of different types.
Implimentation of these rules then gives specific formulas for the anomally for
semisimple algebras and also for solvable ones.Comment: 15 pages, no figures, Latex file, A treatment of the global aspects
of the abelian and of semisimple duality groups are added. General formulas
for the mixed anomaly are derive
On quasi-local charges and Newman--Penrose type quantities in Yang--Mills theories
We generalize the notion of quasi-local charges, introduced by P. Tod for
Yang--Mills fields with unitary groups, to non-Abelian gauge theories with
arbitrary gauge group, and calculate its small sphere and large sphere limits
both at spatial and null infinity. We show that for semisimple gauge groups no
reasonable definition yield conserved total charges and Newman--Penrose (NP)
type quantities at null infinity in generic, radiative configurations. The
conditions of their conservation, both in terms of the field configurations and
the structure of the gauge group, are clarified. We also calculate the NP
quantities for stationary, asymptotic solutions of the field equations with
vanishing magnetic charges, and illustrate these by explicit solutions with
various gauge groups.Comment: 22 pages, typos corrected, appearing in Classical and Quantum Gravit
Steady states in a structured epidemic model with Wentzell boundary condition
We introduce a nonlinear structured population model with diffusion in the
state space. Individuals are structured with respect to a continuous variable
which represents a pathogen load. The class of uninfected individuals
constitutes a special compartment that carries mass, hence the model is
equipped with generalized Wentzell (or dynamic) boundary conditions. Our model
is intended to describe the spread of infection of a vertically transmitted
disease, for example Wolbachia in a mosquito population. Therefore the
(infinite dimensional) nonlinearity arises in the recruitment term. First we
establish global existence of solutions and the Principle of Linearised
Stability for our model. Then, in our main result, we formulate simple
conditions, which guarantee the existence of non-trivial steady states of the
model. Our method utilizes an operator theoretic framework combined with a
fixed point approach. Finally, in the last section we establish a sufficient
condition for the local asymptotic stability of the positive steady state
Simulation of Plasticity in Nanocrystalline Silicon
Molecular dynamics investigation of plasticity in a model nanocrystalline silicon system demonstrates that inelastic deformation localizes in intergranular regions. The carriers of plasticity in these regions are atomic environments that can be described as high-density liquid-like amorphous silicon. During fully developed flow, plasticity is confined to system-spanning intergranular zones of easy flow. As an active flow zone rotates out of the plane of maximum resolved shear stress during deformation to large strain, new zones of easy flow are formed. Compatibility of the microstructure is accommodated by processes such as grain rotation and formation of new grains. Nano-scale voids or cracks may form if there emerge stress concentrations that cannot be relaxed by a mechanism that simultaneously preserves microstructural compatibility
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