Global attractivity of the equilibrium of a nonlinear difference equation

summary:The authors consider the nonlinear difference equation $$x_{n+1}=\alpha x_n + x_{n-k}f(x_{n-k}), \quad n=0, 1,\dots .1 \text{where} \alpha \in (0, 1),\hspace{5.0pt}k \in \lbrace 0, 1, \dots \rbrace \hspace{5.0pt}\text{and}\hspace{5.0pt}f\in C^1[[0, \infty ),[0, \infty )] \qquad \mathrm{(0)}$$ with $f^{\prime }(x)<0$. They give sufficient conditions for the unique positive equilibrium of (0.1) to be a global attractor of all positive solutions. The results here are somewhat easier to apply than those of other authors. An application to a model of blood cell production is given

Statebuilding and narrative

In recent years, narrative approaches have become increasingly popular in the study of peaceand statebuilding. Yet, the conceptual and empirical idiosyncrasies of stories and storytelling are rarely acknowledged. This chapter provides an overview of the uses of narrative in the field to date. It highlights its value for understanding power imbalances, the complexity of human experiences and knowledge creation, and ethical challenges connected to fieldwork. Engaging in greater depth with conceptual and analytical perspectives on narrative, not least by drawing on insights from related social science disciplines, will help to uncover the unique contribution these perspectives can make to researching and practicing peace- and statebuilding.info:eu-repo/semantics/submittedVersio

Magnetic transitions and magnetodielectric effect in the antiferromagnet SrNdFeO4_4

We investigated the magnetic phase diagram of single crystals of SrNdFeO$_{4}$ by measuring the magnetic properties, the specific heat and the dielectric permittivity. The system has two magnetically active ions, Fe$^{3+}$ and Nd$^{3+}$. The Fe$^{3+}$ spins are antiferromagnetically ordered below 360 K with the moments lying in the ab-plane, and undergo a reorientation transition at about 35-37 K to an antiferromagnetic order with the moments along the c-axis. A short-range, antiferromagnetic ordering of Nd$^{3+}$ along the c-axis was attributed to the reorientation of Fe$^{3+}$ followed by a long-range ordering at lower temperature [S. Oyama {\it et al.} J. Phys.: Condens. Matter. {\bf 16}, 1823 (2004)]. At low temperatures and magnetic fields above 8 T, the Nd$^{3+}$ moments are completely spin-polarized. The dielectric permittivity also shows anomalies associated with spin configuration changes, indicating that this compound has considerable coupling between spin and lattice. A possible magnetic structure is proposed to explain the results.Comment: 8 pages, 10 figures, submitted to PR

ON HIGHER ORDER NONLINEAR IMPULSIVE BOUNDARY VALUE PROBLEMS

This work studies some two point impulsive boundary value problems composed by a fully differential equation, which higher order contains an increasing homeomorphism, by two point boundary conditions and impulsive e ects. We point out that the impulsive conditions are given via multivariate generalized functions, including impulses on the referred homeomorphism. The method used apply lower and upper solutions technique together with xed point theory. Therefore we have not only the existence of solutions but also the localization and qualitative data on their behavior. Moreover a Nagumo condition will play a key role in the arguments

Existence Results for Periodic Boundary Value Problems with a Convenction Term

By using an abstract coincidence point theorem for sequentially weakly continuous maps the existence of at least one positive solution is obtained for a periodic second order boundary value problem with a reaction term involving the derivative of the solution u: the so called convention term. As a consequence of the main result also the existence of at least one positive solution is obtained for a parameter-depending problem

Social media for research discourse, dissemination, and collaboration in rheumatology

Social media has become an important venue for rheumatologists, patients, organizations, and other stakeholders to discuss recent research advances in diagnosis and management of rheumatic disorders. In this article, we describe the current state of how social media may enhance dissemination, discourse, and collaboration in rheumatology research. Social media may refer to social platforms like Twitter and Instagram or digital media like podcasts and other websites that are operated for providing as free, open-access medical education (FOAM). Twitter has been one of the most active social media venues and continues to host a vibrant rheumatology community. Examples of research discussions on Twitter include organic user tweets, educational threads ( tweetorials ), live-tweeting academic conferences, and journals posting recently-accepted articles. Some research collaborations have been initiated through social media interactions. Social media may also directly contribute to research by facilitating the recruitment of study participants and the collection of survey-based data. Thus, social media is an evolving and important tool to enhance research discourse, dissemination, and collaboration in rheumatology

Circadian rhythm of hepatic cytosolic and nuclear estrogen receptors

The distribution of estrogen receptor between the cytosolic and nuclear compartments were evaluated in liver of male rats to determine whether a circadian rhythm exists. Cytosolic receptor reached a maximum level at 400 hours and a minimum at 2000 and 2400 hr. Nuclear receptor reached a maximum level at 800 hr and was lowest at 1600 and 2000 hr. Serum estradiol levels were also highest at 800 hr and lowest at 1600 hr. The variations in cytosolic and nuclear receptors are not reciprocal; in fact, the overall content of receptor in the liver is not constant and also displays a circadian rhythm. © 1986 Informa UK Ltd All rights reserved: reproduction in whole or part not permitted

Studying the influence of nitrogen seeding in a detached-like hydrogen plasma by means of numerical simulations

The leading candidate for impurity seeding in ITER is currently nitrogen. To date, there are only a few studies on the plasma chemistry driven by N2/H2 seeding and its effect on the molecular-activated recombination of incoming atomic hydrogen ions in a detached-like scenario. Numerical simulations are needed to provide insights into such mechanisms. The numerous amount of plasma chemical reactions that may occur in such an environment cannot be entirely included in a 2 or 3 -dimensional code such as Eirene. A complete global plasma model, implemented with more than 100 plasma chemical equations and 20 species, has been set up on the basis of Plasimo code. This study shows two main nitrogen-included recombination reaction paths resulted to be dominant, i.e. the ion conversion of NH followed by dissociative recombination and a proton transfer between H2+ and N2, producing N2H+. These two processes are referred to as N-MAR (nitrogen-molecular activated recombination) and have subsequently been implemented into Eunomia, a spatially-resolved Monte Carlo code, designed to simulate the neutrals inventory in linear plasma machines such as Pilot-PSI and Magnum-PSI. To study the effect of N2 on the overall recombination, three cases of study have been set up: from a defined puffing location with a constant total seeding rate of H2 + N2, three N2 ratios have been simulated, i.e. 0, 5 and 10%. The parameter monitored is the density of atomic hydrogen, being the final hydrogenic product of any recombination mechanism in the scenario considered. The difference in H density between the 0% case and the 10% case is about a factor 3. The importance of NH as electron donor is highlighted and N-MARs confirmed as reaction routes enhancing the conversion of ions to neutrals, making the heat loads to the divertor plate more tolerable. This work is a further step towards the full understanding of the role of N2-H2 molecules in a detached divertor plasma.</p

SOLVABILITY OF HIGHER-ORDER BVPS IN THE HALF-LINE WITH UNBOUNDED NONLINEARITIES

This work presents suficient conditions for the existence of unbounded solutions of a Sturm-Liouville type boundary value problem on the half-line. One-sided Nagumo condition plays a special role because it allows an asymmetric unbounded behavior on the nonlinearity. The arguments are based on fixed point theory and lower and upper solutions method. An example is given to show the applicability of our results

Visual saliency and semantic incongruency influence eye movements when inspecting pictures

Models of low-level saliency predict that when we first look at a photograph our first few eye movements should be made towards visually conspicuous objects. Two experiments investigated this prediction by recording eye fixations while viewers inspected pictures of room interiors that contained objects with known saliency characteristics. Highly salient objects did attract fixations earlier than less conspicuous objects, but only in a task requiring general encoding of the whole picture. When participants were required to detect the presence of a small target, then the visual saliency of nontarget objects did not influence fixations. These results support modifications of the model that take the cognitive override of saliency into account by allowing task demands to reduce the saliency weights of task-irrelevant objects. The pictures sometimes contained incongruent objects that were taken from other rooms. These objects were used to test the hypothesis that previous reports of the early fixation of congruent objects have not been consistent because the effect depends upon the visual conspicuity of the incongruent object. There was an effect of incongruency in both experiments, with earlier fixation of objects that violated the gist of the scene, but the effect was only apparent for inconspicuous objects, which argues against the hypothesis