65 research outputs found
Tame Functions with strongly isolated singularities at infinity: a tame version of a Parusinski's Theorem
Let f be a definable function, enough differentiable. Under the condition of
having strongly isolated singularities at infinity at a regular value c we give
a sufficient condition expressed in terms of the total absolute curvature
function to ensure the local triviality of the function f over a neighbourhood
of c and doing so providing the tame version of Parusinski's Theorem on complex
polynomials with isolated singularities at infinity.Comment: 20 page
REFLEXIONES ACERCA DEL PROBLEMA TEOLĂGICO-JURĂDICO SOBRE EL ORIGEN DEL PODER POLĂTICO EN DANTE ALIGHIERI Y MARSILIO DE PADUA
Dante Alighieri y Marsilio de Padua fueron dos pensadores involucrados en los conflictos polĂticos de las primeras dĂ©cadas del siglo XIV entre el Papado y el Imperio. Ambos autores propusieron modelos de organizaciĂłn en los que buscaron asignar las atribuciones y jurisdicciones de cada investidura para poner fin a los litigios que aquejaban a las ciudades-Estado del norte de la penĂnsula itĂĄlica, al reino de Francia y al Sacro Imperio Romano GermĂĄnico. Sin embargo, si bien comparten algunos aspectos de sus postulados sobre el poder polĂtico y el espiritual, Dante se inclina por el equilibrio de las investiduras donde el Dios y el derecho es fundamento del Imperio, mientras que el paduano aboga a fondo por la superioridad del Emperador sobre el PontĂfice fundamentado en la comunidad como origen de la ley.Â
Microbial colonization of anaerobic biofilms: a mathematical model
A 1-D mathematical model for analysis and prediction of microbial colonization of anaerobic multispecies biofilms for methane production is presented. The model combines the related processes of hydrolysis,
acidogenesis, acetogenesis, methanogenesis and takes into account phenomena of substrate reaction and diffusion, biomass growth, detachment and, in particular, the colonization of new species from bulk liquid
to biofilm. The colonization phenomenon is initiated by planktonic cells, present in the bulk liquid but not initially in the biofilm, which thanks to the characteristic porous structure of biofilm matrix, may enter the channels and establish where they find favorable growth conditions. The model consists of a free boundary value problem where the biofilm growth process is governed by nonlinear hyperbolic PDEs and substrate dynamics are dominated by semilinear parabolic PDEs. The transport of colonizing bacteria from the bulk liquid to the biofilm is modelled by using a diffusionreaction equation, where the reaction term represents the loss of planktonic bacteria due to their establishment within the biofilm. The method of characteristics is used for numerical purposes. The model is based on the biological framework of ADM1 and has been applied to simulate microbial competition and evaluate the influence of substrate diffusion on microbial stratification. Specific scenarios have been simulated describing the effect of colonization of motile bacteria into an established anaerobic biofilm
The Effect of Cell Death on the Stability of a Growing Biofilm
In this paper, we investigate the role of cell death in promoting pattern formation within bacterial biofilms. To do this we utilise an extension of the model proposed by Dockery and Klapper [13], and consider the effects of two distinct death rates. Equations describing the evolution of a moving biofilm interface are derived, and properties of steady state solutions are examined. In particular, a comparison of the planar behaviour of the biofilm interface in the different cases of cell death is investigated. Linear stability analysis is carried out at steady state solutions of the interface, and it is shown that, under certain conditions, instabilities may arise. Analysis determines that, while the emergence of patterns is a possibility in `deepâ biofilms, it is unlikely that pattern formation will arise in `shallowâ biofilms
Is the astronomical forcing a reliable and unique pacemaker for climate? A conceptual model study
There is evidence that ice age cycles are paced by astronomical forcing,
suggesting some kind of synchronisation phenomenon. Here, we identify the type
of such synchronisation and explore systematically its uniqueness and
robustness using a simple paleoclimate model akin to the van der Pol relaxation
oscillator and dynamical system theory. As the insolation is quite a complex
quasiperiodic signal involving different frequencies, the traditional concepts
used to define synchronisation to periodic forcing are no longer applicable.
Instead, we explore a different concept of generalised synchronisation in terms
of (coexisting) synchronised solutions for the forced system, their basins of
attraction and instabilities. We propose a clustering technique to compute the
number of synchronised solutions, each of which corresponds to a different
paleoclimate history. In this way, we uncover multistable synchronisation
(reminiscent of phase- or frequency-locking to individual periodic components
of astronomical forcing) at low forcing strength, and monostable or unique
synchronisation at stronger forcing. In the multistable regime, different
initial conditions may lead to different paleoclimate histories. To study their
robustness, we analyse Lyapunov exponents that quantify the rate of convergence
towards each synchronised solution (local stability), and basins of attraction
that indicate critical levels of external perturbations (global stability). We
find that even though synchronised solutions are stable on a long term, there
exist short episodes of desynchronisation where nearby climate trajectories
diverge temporarily (for about 50 kyr). (...)Comment: 22 pages, 18 figure
The restorative role of annexin A1 at the bloodâbrain barrier
Annexin A1 is a potent anti-inflammatory molecule that has been extensively studied in the peripheral immune
system, but has not as yet been exploited as a therapeutic target/agent. In the last decade, we have undertaken the
study of this molecule in the central nervous system (CNS), focusing particularly on the primary interface between the
peripheral body and CNS: the bloodâbrain barrier. In this review, we provide an overview of the role of this molecule
in the brain, with a particular emphasis on its functions in the endothelium of the bloodâbrain barrier, and the protective
actions the molecule may exert in neuroinflammatory, neurovascular and metabolic disease. We focus on the
possible new therapeutic avenues opened up by an increased understanding of the role of annexin A1 in the CNS
vasculature, and its potential for repairing bloodâbrain barrier damage in disease and aging
Mathematical modeling of the competition between sulfate reducing, acetoclastic and methanogenic bacteria within multispecies biofilms
Increasing anthropogenic activity has contributed to local imbalances in the natural sulfur cycle, leading to serious environmental problems. Industrial wastewater containing sulfate has contributed to this sulfur imbalance. Biological sulfate reducing processes that involve a bacterial biomass attached to media (biofilm), represent an attractive solution to the problem. The advantage of bacteria disposing in a biofilm is very important in an environmental industrial application, as the bacteria in the biofilm, different from suspended bacteria, cannot be washed out with the water flow. This allows to retain the biomass within the reactor and therefore to operate at shorter hydraulic retention time (HRT),and higher biomass concentration . Biological sulfate reduction in anaerobic fixed growth reactors has been investigated extensively at lab-scale. Under anaerobic conditions dissimilatory sulfate reducing bacteria use sulfate as a terminal electron acceptor for the degradation of organic compounds. In this anaerobic process, sulfate is reduced to sulfide by the action of sulfate reducing bacteria (SRB), which have the ability of coupling the oxidation of organic matter (electron donor) to the reduction of sulfate (electron acceptor) and depend on hydrolytic and fermentative bacteria that degrade complex organic matter. A major problem of sulfate-reducing fixed-growth reactors is the formation of undesired bacteria species which compete for space and substrate in the biofilm with SRB. This work presents a mathematical model able to simulate the physical, chemical and biological processes prevailing in a sulfate reducing biofilm under dynamic conditions. The proposed model includes sulfate reduction by complete and incomplete SRB; COD (lactate) removal by sulfate reduction and by acetogenic bacteria; acetate consumption via methanogenesis. The method of characteristics is used for the numerical resolution of the model equations.
In particular the effect of the COD/SO42- ratio and the effect of different simulation times on the reactor performances in terms of bacterial species distribution and substrate diffusion trends in the biofilm have been assessed
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