5,877 research outputs found
Size-structured populations: immigration, (bi)stability and the net growth rate
We consider a class of physiologically structured population models, a first
order nonlinear partial differential equation equipped with a nonlocal boundary
condition, with a constant external inflow of individuals. We prove that the
linearised system is governed by a quasicontraction semigroup. We also
establish that linear stability of equilibrium solutions is governed by a
generalized net reproduction function. In a special case of the model
ingredients we discuss the nonlinear dynamics of the system when the spectral
bound of the linearised operator equals zero, i.e. when linearisation does not
decide stability. This allows us to demonstrate, through a concrete example,
how immigration might be beneficial to the population. In particular, we show
that from a nonlinearly unstable positive equilibrium a linearly stable and
unstable pair of equilibria bifurcates. In fact, the linearised system exhibits
bistability, for a certain range of values of the external inflow, induced
potentially by All\'{e}e-effect.Comment: to appear in Journal of Applied Mathematics and Computin
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.
Using Personal Photos in the ESL Classroom
The purpose of this project is to demonstrate how relatively common- place materials such as personal photos can be meaningfully utilized in the ESL classroom. The project contains a collection of simulated personal photographs which are divided into four topic areas. One authentic photo has been selected to represent each topic area. Immediately following the photographs in each topic area is a summary of lexical, structural and cross-cultural items which can be determined from the photos. The main body of each topic area is made up of teaching activities divided into two categories: focused activities and discussion/ cross-cultural activities
Gravity from the extension of spatial diffeomorphisms
The possibility of the extension of spatial diffeomorphisms to a larger
family of symmetries in a class of classical field theories is studied. The
generator of the additional local symmetry contains a quadratic kinetic term
and a potential term which can be a general (not necessarily local) functional
of the metric. From the perspective of the foundation of Einstein's gravity our
results are positive: The extended constraint algebra is either that of
Einstein's gravity, or ultralocal gravity. If our goal is a simple modification
of Einstein's gravity that for example makes it perturbatively renormalizable,
as has recently been suggested, then our results show that there is no such
theory within this class.Comment: 34 page
Trends and tendencies in management consulting in light of local and international development
The field of management consulting is now over 100 years old, but there are definite gaps in information about the size and nature of this field at the national, regional, and global levels. The aim of our contribution is to analyze the major trends in management consulting in Hungary and contrast the findings with those reported by FEACO, the European Federation of Management Consulting. The authors were and are actively involved in assmebling data for Hungary, for the EU, and at the global level. We include a brief bird's eye-view on the evolution of this important professional sector.
Unanticipated differences between α- and γ-diaminobutyric acid-linked hairpin polyamide-alkylator conjugates
Hairpin polyamide–chlorambucil conjugates containing an {alpha}-diaminobutyric acid ({alpha}-DABA) turn moiety are compared to their constitutional isomers containing the well-characterized {gamma}-DABA turn. Although the DNA-binding properties of unconjugated polyamides are similar, the {alpha}-DABA conjugates display increased alkylation specificity and decreased rate of reaction. Treatment of a human colon carcinoma cell line with {alpha}-DABA versus {gamma}-DABA hairpin conjugates shows only slight differences in toxicities while producing similar effects on cell morphology and G2/M stage cell cycle arrest. However, striking differences in animal toxicity between the two classes are observed. Although mice treated with an {alpha}-DABA hairpin polyamide do not differ significantly from control mice, the analogous {gamma}-DABA hairpin is lethal. This dramatic difference from a subtle structural change would not have been predicted
Heat storage in alloy transformations
The feasibility of using metal alloys as thermal energy storage media was determined. The following major elements were studied: (1) identification of congruently transforming alloys and thermochemical property measurements; (2) development of a precise and convenient method for measuring volume change during phase transformation and thermal expansion coefficients; (3) development of a numerical modeling routine for calculating heat flow in cylindrical heat exchangers containing phase change materials; and (4) identification of materials that could be used to contain the metal alloys. Several eutectic alloys and ternary intermetallic phases were determined. A method employing X-ray absorption techniques was developed to determine the coefficients of thermal expansion of both the solid and liquid phases and the volume change during phase transformation from data obtained during one continuous experimental test. The method and apparatus are discussed and the experimental results are presented. The development of the numerical modeling method is presented and results are discussed for both salt and metal alloy phase change media
Asymptotic analysis of a size-structured cannibalism model with infinite dimensional environmental feedback
In this work we consider a size-structured cannibalism model with the model
ingredients (fertility, growth, and mortality rate) depending on size (ranging
over an infinite domain) and on a general function of the standing population
(environmental feedback). Our focus is on the asymptotic behavior of the
system, in particular on the effect of cannibalism on the long-term dynamics.
To this end, we formally linearize the system about steady state and establish
conditions in terms of the model ingredients which yield uniform exponential
stability of the governing linear semigroup. We also show how the point
spectrum of the linearized semigroup generator can be characterized in the
special case of a separable attack rate and establish a general instability
result. Further spectral analysis allows us to give conditions for asynchronous
exponential growth of the linear semigroup
The Vacuum Structure and Spectrum of N=2 Supersymmetric SU(N) Gauge Theory
We present an exact description of the metric on the moduli space of vacua
and the spectrum of massive states for four dimensional N=2 supersymmetric
SU(n) gauge theories. The moduli space of quantum vacua is identified with the
moduli space of a special set of genus n-1 hyperelliptic Riemann surfaces.Comment: 11 pages, Revtex, 2 figures. Reference adde
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