Search results for "differential equations"
showing 10 items of 169 documents
Amplitudes from superconformal Ward identities
2018
We consider finite superamplitudes of N=1 matter, and use superconformal symmetry to derive powerful first-order differential equations for them. Due to on-shell collinear singularities, the Ward identities have an anomaly, which is obtained from lower-loop information. We show that in the five-particle case, the solution to the equations is uniquely fixed by the expected analytic behavior. We apply the method to a non-planar two-loop five-particle integral.
Yangian Symmetry for Fishnet Feynman Graphs
2017
Various classes of fishnet Feynman graphs are shown to feature a Yangian symmetry over the conformal algebra. We explicitly discuss scalar graphs in three, four and six spacetime dimensions as well as the inclusion of fermions in four dimensions. The Yangian symmetry results in novel differential equations for these families of largely unsolved Feynman integrals. Notably, the considered fishnet graphs in three and four dimensions dominate the correlation functions and scattering amplitudes in specific double scaling limits of planar, gamma-twisted N=4 super Yang-Mills or ABJM theory. Consequently, the study of fishnet graphs allows us to get deep insights into the integrability of the plana…
A new result on impulsive differential equations involving non-absolutely convergent integrals
2009
AbstractIn this paper we obtain, as an application of a Darbo-type theorem, global solutions for differential equations with impulse effects, under the assumption that the function on the right-hand side is integrable in the Henstock sense. We thus generalize several previously given results in literature, for ordinary or impulsive equations.
On Differential Equations with Delay in Banach Spaces and Attractors for Retarded Lattice Dynamical Systems
2014
In this paper we first prove a rather general theorem about existence of solutions for an abstract differential equation in a Banach space by assuming that the nonlinear term is in some sense weakly continuous. We then apply this result to a lattice dynamical system with delay, proving also the existence of a global compact attractor for such system.
Changing the General Factor of Personality and the c-fos Gene Expression with Methylphenidate and Self-Regulation Therapy
2012
[EN] A deepening in the biological nature of the general factor of personality (GFP) is suggested: the activation level of the stress system is here represented by the gene expression of c-fos. The results of a single case experimental design are reported. A model of four coupled differential equations that explains the human personality dynamics as a consequence of a single stimulant drug intake has been fitted to psychological and biological experimental data. The stimulant-drug conditioning and its adaptation to the considered mathematical model is also studied for both kinds of measures. The dynamics of the cfos expression presents a similar pattern to the dynamics of the psychological …
Spatio-temporal behaviour of five picophytoplankton populations in Tyrrhe- nian Sea: Model and data
2014
Recent works presented detailed analyses of spatio-temporal dynamics in marine ecosystems, reproducing real vertical distributions of phytoplankton biomass. These study however do not take into account the changes in environmental variables. On the contrary, seasonal variations can influence considerably the primary production, i.e. phytoplankton biomass, in marine ecosystems, determining significative consequences in the whole food chain, in particular fish species, whose growth is mainly explained by seasonal changes in the chlorophyll concentration, a marker of phytoplankton species. Here we present a one-dimensional reaction-diffusion-taxis model to describe the spatio-temporal dynamics…
Reaction-diffusion-taxis model for spatio-temporal dynamics of five picophytoplankton populations
2014
Recently new models were devised to study spatio-temporal dynamics of phytoplankton populations in view of obtaining more precise predictions of the vertical biomass distributions in marine ecosystems. These studies can be crucial from the point of view of shery. Indeed the abundance of fi sh species is strictly connected with primary production, i.e. phytoplankton biomass, responsible for chlorophyll concentration. In this work a one-dimensional deterministic reaction-di ffusion-taxis model is used to reproduce the spatio-temporal dynamics, along a water column, of five picophytoplankton populations sampled in a real ecosystem. In our analysis, to better reproduce the spatio-temporal behav…