Aggregation equations with fractional diffusion : preventing concentration by mixing

We investigate a class of aggregation-diffusion equations with strongly singular kernels and weak (fractional) dissipation in the presence of an incompressible flow. Without the flow the equations are supercritical in the sense that the tendency to concentrate dominates the strength of diffusion and solutions emanating from sufficiently localised initial data may explode in finite time. The main purpose of this paper is to show that under suitable spectral conditions on the flow, which guarantee good mixing properties, for any regular initial datum the solution to the corresponding advection-aggregation-diffusion equation is global if the prescribed flow is sufficiently fast. This paper can be seen as a partial extension of [Kiselev & Xu, Arch. Rat. Mech. Anal., 222(2):1077-1112, 2016], and our arguments show in particular that the suppression mechanism for the classical 2D parabolic-elliptic Keller–Segel model devised by Kiselev and Xu also applies to the fractional Keller–Segel model (where Δ is replaced by −(−Δ)γ2) requiring only that γ>1. In addition, we remove the restriction to dimension d<4. As a by-product, a characterisation of the class of relaxation enhancing flows on the d-torus is extended to the case of fractional dissipation

Local existence of analytic sharp fronts for singular SQG

In this paper, we prove local existence and uniqueness of analytic sharp-front solutions to a generalised SQG equation by the use of an abstract Cauchy–Kovalevskaya theorem. Here, the velocity is determined by $u=|nabla|^{-2beta} nabla^{perp} \theta$ which (for $1<beta \leq 2$ ) is more singular than in SQG. This is achieved despite the appearance of pseudodifferential operators of order higher than one in our equation, by recasting our equation in a suitable integral form. We also provide a full proof of the abstract version of the Cauchy–Kovalevskaya theorem we use

Asymptotics for vortex filaments using a modified Biot-Savart kernel

We consider a family of approximations to the Euler equations obtained by adding to the non-locality in the Biot-Savart kernel together with a mollification (with parameter ε). We consider the evolution of a thin vortex tube. We show that the velocity on the filament (core of the tube) in the limit as is given where κ and B are the curvature and binormal of the curve, and C, are uniformly bounded

On the singularity formation and relaxation to equilibrium in 1D Fokker-Planck model with superlinear drift

We consider a class of Fokker--Planck equations with linear diffusion and superlinear drift enjoying a formal Wasserstein-like gradient flow structure with convex mobility function. In the drift-dominant regime, the equations have a finite critical mass above which the measure minimising the associated entropy functional displays a singular component. Our approach, which addresses the one-dimensional case, is based on a reformulation of the problem in terms of the pseudo-inverse distribution function. Motivated by the structure of the equation in the new variables, we establish a general framework for global-in-time existence, uniqueness and regularity of monotonic viscosity solutions to a class of nonlinear degenerate (resp. singular) parabolic equations, using as a key tool comparison principles and maximum arguments. We then focus on a specific equation and study in more detail the regularity and dynamics of solutions. In particular, blow-up behaviour, formation of condensates (i.e. Dirac measures at zero) and long-time asymptotics are investigated. As a consequence, in the mass-supercritical case, solutions will blow up in L∞ in finite time and---understood in a generalised, measure sense---they will eventually have condensate. We further show that the singular part of the measure solution does in general interact with the density and that condensates can be transient. The equations considered are motivated by a model for bosons introduced by Kaniadakis and Quarati (1994), which has a similar entropy structure and a critical mass if d≥3

Las razones de por qué Chile debe detener la importación del abejorro comercial Bombus terrestris (Linnaeus) y comenzar a controlarlo

The global pollination crisis is not only produced by loss of pollinators but also by their homogenization, both processes caused by humans. This crisis impacts the persistence of many native plants species worldwide. In this document we analyze the ecological impacts that warrant the prohibition of new income of commercial bumblebee, Bombus terrestris to Chile. This species is highly invasive, it has been banned in other countries, but in Chile its entry is allowed since 1997. Thousands of colonies and fertilized queens entered the country every year and expand throughout the rest of South America. We give eleven reasons to stop B. terrestris entry to Chile and start controlling it. We justify these reasons based on work done both in the country and outside of it. At the same time, through the conclusions, we mentioned what should be the steps to followed regarding the prohibition B. terrestris entry to Chile.La crisis mundial de polinización no solo es producida por la pérdida de polinizadores, sino también por su homogeneización, ambos procesos causados por el ser humano. En este documento analizamos los impactos ecológicos que justifi can la prohibición de nuevos ingresos del abejorro comercial Bombus terrestris a Chile. Esta especie es altamente invasiva y ha sido prohibida en otros países, pero en Chile se permite su ingreso desde 1997. Miles de colonias y reinas fertilizadas ingresan al país cada año y se expanden por el resto de Sudamérica. En este artículo entregamos once razones para detener los ingresos de B. terrestris a Chile y comenzar a controlarlo. Justifi camos estas razones en base al trabajo realizado tanto en el país como fuera de él. Al mismo tiempo, a través de las conclusiones, mencionamos cuáles deberían ser los pasos a seguir respecto a la prohibición de ingreso de B. terrestris a Chile

Transiciones, conflictos y democracia : estudios de coyuntura

México ha vivido un largo proceso de transición que ha desencadenado dinamismos económicos, culturales y políticos. En la actual coyuntura, estos dinamismos muestran toda su complejidad, su inevitable articulación y la tensión entre las fuerzas que intentan sostener un viejo modelo de gobernar y decidir el rumbo del país, y aquellas que buscan abrirse a un espectro mucho más amplio y diversificado de actores. En ellos se conjuntan las aspiraciones más legítimas de los mexicanos por avanzar en el reconocimiento y respeto de la pluralidad étnica, de género y entre generaciones, y por impulsar una dinámica en la que —en medio de los procesos de mundialización— los distintos grupos e intereses de los mexicanos puedan ser incluidos. La transición mexicana tiende a centrarse en la dimensión política. La intensidad que cobran los procesos políticos y el énfasis que importantes analistas ponen en dichos procesos, contribuyen a que esta asociación vaya cobrandoíuerza. En este sentido, es necesario advertir que en las transiciones la tendencia privatizadora, la reducción del gasto social, así como la necesidad de pactos sociales que sean respetados, la participación creciente de la sociedad civil, etc. son factores importantes que, en medio de contradicciones, van generando nuevos esquemas de relación entre gobierno y sociedad.ITESO, A.C

Optimasi Portofolio Resiko Menggunakan Model Markowitz MVO Dikaitkan dengan Keterbatasan Manusia dalam Memprediksi Masa Depan dalam Perspektif Al-Qur`an

Risk portfolio on modern finance has become increasingly technical, requiring the use of sophisticated mathematical tools in both research and practice. Since companies cannot insure themselves completely against risk, as human incompetence in predicting the future precisely that written in Al-Quran surah Luqman verse 34, they have to manage it to yield an optimal portfolio. The objective here is to minimize the variance among all portfolios, or alternatively, to maximize expected return among all portfolios that has at least a certain expected return. Furthermore, this study focuses on optimizing risk portfolio so called Markowitz MVO (Mean-Variance Optimization). Some theoretical frameworks for analysis are arithmetic mean, geometric mean, variance, covariance, linear programming, and quadratic programming. Moreover, finding a minimum variance portfolio produces a convex quadratic programming, that is minimizing the objective function ðð¥with constraintsð ð 𥠥 ðandð´ð¥ = ð. The outcome of this research is the solution of optimal risk portofolio in some investments that could be finished smoothly using MATLAB R2007b software together with its graphic analysis

Differential cross section measurements for the production of a W boson in association with jets in proton–proton collisions at √s = 7 TeV

Measurements are reported of differential cross sections for the production of a W boson, which decays into a muon and a neutrino, in association with jets, as a function of several variables, including the transverse momenta (pT) and pseudorapidities of the four leading jets, the scalar sum of jet transverse momenta (HT), and the difference in azimuthal angle between the directions of each jet and the muon. The data sample of pp collisions at a centre-of-mass energy of 7 TeV was collected with the CMS detector at the LHC and corresponds to an integrated luminosity of 5.0 fb[superscript −1]. The measured cross sections are compared to predictions from Monte Carlo generators, MadGraph + pythia and sherpa, and to next-to-leading-order calculations from BlackHat + sherpa. The differential cross sections are found to be in agreement with the predictions, apart from the pT distributions of the leading jets at high pT values, the distributions of the HT at high-HT and low jet multiplicity, and the distribution of the difference in azimuthal angle between the leading jet and the muon at low values.United States. Dept. of EnergyNational Science Foundation (U.S.)Alfred P. Sloan Foundatio

Juxtaposing BTE and ATE – on the role of the European insurance industry in funding civil litigation

One of the ways in which legal services are financed, and indeed shaped, is through private insurance arrangement. Two contrasting types of legal expenses insurance contracts (LEI) seem to dominate in Europe: before the event (BTE) and after the event (ATE) legal expenses insurance. Notwithstanding institutional differences between different legal systems, BTE and ATE insurance arrangements may be instrumental if government policy is geared towards strengthening a market-oriented system of financing access to justice for individuals and business. At the same time, emphasizing the role of a private industry as a keeper of the gates to justice raises issues of accountability and transparency, not readily reconcilable with demands of competition. Moreover, multiple actors (clients, lawyers, courts, insurers) are involved, causing behavioural dynamics which are not easily predicted or influenced. Against this background, this paper looks into BTE and ATE arrangements by analysing the particularities of BTE and ATE arrangements currently available in some European jurisdictions and by painting a picture of their respective markets and legal contexts. This allows for some reflection on the performance of BTE and ATE providers as both financiers and keepers. Two issues emerge from the analysis that are worthy of some further reflection. Firstly, there is the problematic long-term sustainability of some ATE products. Secondly, the challenges faced by policymakers that would like to nudge consumers into voluntarily taking out BTE LEI

Search for stop and higgsino production using diphoton Higgs boson decays

Results are presented of a search for a "natural" supersymmetry scenario with gauge mediated symmetry breaking. It is assumed that only the supersymmetric partners of the top-quark (stop) and the Higgs boson (higgsino) are accessible. Events are examined in which there are two photons forming a Higgs boson candidate, and at least two b-quark jets. In 19.7 inverse femtobarns of proton-proton collision data at sqrt(s) = 8 TeV, recorded in the CMS experiment, no evidence of a signal is found and lower limits at the 95% confidence level are set, excluding the stop mass below 360 to 410 GeV, depending on the higgsino mass