Nonlinear elliptic-parabolic integro-differential equations with L 1-data: existence, uniqueness, asymptotic

The work is concerned with the existence and the qualitative behavior of solutions of certain nonlinear Volterra integro-differential equations. Both abstract equations with accretive operators and concrete equations of elliptic-parabolic type are considered. Equations of this type arise in the theory of heat ow in materials with memory and diffusion of uids in porous media with memory. Existence and uniqueness of entropy solutions is obtained for a concrete history dependent elliptic-parabolic initial boundary value problem for gen-eral integrable data. Regularity properties of solutions are considered. In particular, existence of strong solutions is shown if the state space is a Banach space without the Radon-Nikodym property. The asymptotic behavior of solutions is investigated. Conditions on the data are obtained such that the solution is asymptotically almost periodic or weakly almost periodic in the sense of Eberlein. Keywords and phrases: entropy solutions, renormalized solutions, m-completely accretive operators, almost periodicity. AMS Subject Classification: 35B15, 35K65, 45K05, 45M05, 45N05, 47H06

Asymptotics of the solutions of the stochastic lattice wave equation

We consider the long time limit theorems for the solutions of a discrete wave equation with a weak stochastic forcing. The multiplicative noise conserves the energy and the momentum. We obtain a time-inhomogeneous Ornstein-Uhlenbeck equation for the limit wave function that holds both for square integrable and statistically homogeneous initial data. The limit is understood in the point-wise sense in the former case, and in the weak sense in the latter. On the other hand, the weak limit for square integrable initial data is deterministic

The US President’s Malaria Initiative and under-five child mortality in Sub-Saharan Africa: A difference-in-differences analysis

Background Despite substantial financial contributions by the United States President’s Malaria Initiative (PMI) since 2006, no studies have carefully assessed how this program may have affected important population-level health outcomes. We utilized multiple publicly available data sources to evaluate the association between introduction of PMI and child mortality rates in sub-Saharan Africa (SSA). Methods and findings We used difference-in-differences analyses to compare trends in the primary outcome of under-5 mortality rates and secondary outcomes reflecting population coverage of malaria interventions in 19 PMI-recipient and 13 non-recipient countries between 1995 and 2014. The analyses controlled for presence and intensity of other large funding sources, individual and household characteristics, and country and year fixed effects. PMI program implementation was associated with a significant reduction in the annual risk of under-5 child mortality (adjusted risk ratio [RR] 0.84, 95% CI 0.74–0.96). Each dollar of per-capita PMI expenditures in a country, a measure of PMI intensity, was also associated with a reduction in child mortality (RR 0.86, 95% CI 0.78–0.93). We estimated that the under-5 mortality rate in PMI countries was reduced from 28.9 to 24.3 per 1,000 personyears. Population coverage of insecticide-treated nets increased by 8.34 percentage points (95% CI 0.86–15.83) and coverage of indoor residual spraying increased by 6.63 percentage points (95% CI 0.79–12.47) after PMI implementation. Per-capita PMI spending was also associated with a modest increase in artemisinin-based combination therapy coverage (3.56 percentage point increase, 95% CI −0.07–7.19), though this association was only marginally significant (p = 0.054). Our results were robust to several sensitivity analyses. Because our study design leaves open the possibility of unmeasured confounding, we cannot definitively interpret these results as causal. Conclusions PMI may have significantly contributed to reducing the burden of malaria in SSA and reducing the number of child deaths in the region. Introduction of PMI was associated with increased coverage of malaria prevention technologies, which are important mechanisms through which child mortality can be reduced. To our knowledge, this study is the first to assess the association between PMI and all-cause child mortality in SSA with the use of appropriate comparison groups and adjustments for regional trends in child mortality

Design definition study of a NASA/Navy lift/cruise fan technology V/STOL airplane: Risk assessment addendum to the final report

An assessment of risk, in terms of delivery delays, cost overrun, and performance achievement, associated with the V/STOL technology airplane is presented. The risk is discussed in terms of weight, structure, aerodynamics, propulsion, mechanical drive, and flight controls. The analysis ensures that risks associated with the design and development of the airplane will be eliminated in the course of the program and a useful technology airplane that meets the predicted cost, schedule, and performance can be produced

Cellular automaton supercolliders

Gliders in one-dimensional cellular automata are compact groups of non-quiescent and non-ether patterns (ether represents a periodic background) translating along automaton lattice. They are cellular-automaton analogous of localizations or quasi-local collective excitations travelling in a spatially extended non-linear medium. They can be considered as binary strings or symbols travelling along a one-dimensional ring, interacting with each other and changing their states, or symbolic values, as a result of interactions. We analyse what types of interaction occur between gliders travelling on a cellular automaton `cyclotron' and build a catalog of the most common reactions. We demonstrate that collisions between gliders emulate the basic types of interaction that occur between localizations in non-linear media: fusion, elastic collision, and soliton-like collision. Computational outcomes of a swarm of gliders circling on a one-dimensional torus are analysed via implementation of cyclic tag systems

Exact soliton solutions, shape changing collisions and partially coherent solitons in coupled nonlinear Schroedinger equations

We present the exact bright one-soliton and two-soliton solutions of the integrable three coupled nonlinear Schroedinger equations (3-CNLS) by using the Hirota method, and then obtain them for the general $N$-coupled nonlinear Schroedinger equations (N-CNLS). It is pointed out that the underlying solitons undergo inelastic (shape changing) collisions due to intensity redistribution among the modes. We also analyse the various possibilities and conditions for such collisions to occur. Further, we report the significant fact that the various partial coherent solitons (PCS) discussed in the literature are special cases of the higher order bright soliton solutions of the N-CNLS equations.Comment: 4 pages, RevTex, 1 EPS figure To appear in Physical Review Letter