Positive solutions of nonlinear fourth-order boundary-value problems with local and non-local boundary conditions

We establish new existence results for multiple positive solutions of fourth-order nonlinear equations which model deflections of an elastic beam. We consider the widely studied boundary conditions corresponding to clamped and hinged ends and many non-local boundary conditions, with a unified approach. Our method is to show that each boundary-value problem can be written as the same type of perturbed integral equation, in the space $C[0,1]$, involving a linear functional $\alpha[u]$ but, although we seek positive solutions, the functional is not assumed to be positive for all positive $u$. The results are new even for the classic boundary conditions of clamped or hinged ends when $\alpha[u]=0$, because we obtain sharp results for the existence of one positive solution; for multiple solutions we seek optimal values of some of the constants that occur in the theory, which allows us to impose weaker assumptions on the nonlinear term than in previous works. Our non-local boundary conditions contain multi-point problems as special cases and, for the first time in fourth-order problems, we allow coefficients of both signs

The truth about freedom of choi

El presente es un análisis de los principales rasgos y tendencias que caracterizan hoy a la triada Sociedad-Estado-Mercado. Hace énfasis en la hegemonía del mercado y ofrece un recuento analítico de los hechos que la acompañan como son: la transnacionalización de la cadena de valor, el ascenso de la sociedad del conocimiento, el protagonismo oligopólico de la empresa transnacional, la nueva división social transnacional del trabajo, el proceso de reconfiguración cultural, la exclusión social y la subordinación del Estado, entre otros. El planteamiento que subyace a estas consideraciones es lo que acá se denomina “la verdad sobre la libertad de elegir”, con lo cual se quiere hacer referencia al hecho de que las relaciones Sociedad-Estado se encuentran hoy mediatizadas por el mercado, arrojando, como consecuencia, una involución heterónoma de la Sociedad y del mismo Estado liberal.The actual is an academic analysis of the main features on the day has the triad Society, State and Market. It emphasizes the market hegemony and offers an analytical recount of the facts that go with, as the value chain internationalization, the knowledge society rise, the translational enterprise powerful mark up, the new international social labour division, the cultural reshape process, the social exclusion, the State subordination, among others. The underlying outlining these issues is what the author calls “The truth under the free to choose”, as a reference to the fact that the relationships between the Society and the State are hindered by the Market with a heteronomous society involution as consequence

The role of authorial context in mathematicians’ evaluations of proof

We report on a series of task-based interviews in which nine mathematicians were asked to evaluate a series of six mathematical arguments, purportedly produced either by fellow mathematicians or undergraduate students. In this paper, we attend to the role of context in mathematicians’ responses, leading to four themes in expectations when evaluating the proofs that they read. First, mathematicians’ evaluations of identical arguments were sensitive to researchers’ manipulation of authorship, with most accepting arguments purportedly produced by a colleague while taking a more critical view of that same argument if produced by an undergraduate student. Our thematic analysis of interview responses led to three context-based factors influencing mathematicians’ responses when evaluating student-produced texts: course goals, instructors’ expectations, and assessment type. In the final section, we consider implications for researchers focused on understanding common practice amongst mathematicians as well as the pedagogic consequences of our findings for practice in the classroom

Balances de elementos en un agroecosistema de caña de azúcar: I. Balance de nitrógeno

In a tropical mollisol cropped with sugar cane the annual nitrogen balance was quantified taken into account the main i) inputs, ii) outputs and iii) transference of the element (N-NO3 + N-NH4) in the plant and soil subsystems. Precipitation input corresponded to 26.3 kg N.h–1.yr-1 mainly as N-NH4. After the rain water passes the sugar cane canopy there was a retention of N in the N-NH4 form, whereas N-NO3 was leached from the canopy. Outputs through leaching reached 5.3 kg N. ha-1.yr–1 mainly as N-NO3. An important part of total soil N is fixed to the 2:1 type clay particles (montmorillonitic), abundant in the studied mollisol. It is hypothesised that this fixed N could act as a soil N reserve. Net mineralization of the organic-N reached a high value (343 kg N.ha-1.yr–1) in accordance with the intense nitrification process occurring in the soil as a consequence of the convenient C/N ratio and urea fertilisation. Major N losses in the agrosystem correspond to cropping export and removal of ashes after fire. Yearly 98% of N accumulated in the aerial biomass is lost through those ways. In general the annual nitrogen budget is driven off through input by fertilisation and output through stem cropping and N volatilisation by fire

Preference purification and the inner rational agent:A critique of the conventional wisdom of behavioural welfare economics

Neoclassical economics assumes that individuals have stable and context-independent preferences, and uses preference-satisfaction as a normative criterion. By calling this assumption into question, behavioural findings cause fundamental problems for normative economics. A common response to these problems is to treat deviations from conventional rational-choice theory as mistakes, and to try to reconstruct the preferences that individuals would have acted on, had they reasoned correctly. We argue that this preference purification approach implicitly uses a dualistic model of the human being, in which an inner rational agent is trapped in an outer psychological shell. This model is psychologically and philosophically problematic

An Appraisal of the Oleocanthal-Rich Extra Virgin Olive Oil (EVOO) and Its Potential Anticancer and Neuroprotective Properties

dietary consumption of olive oil represents a key pillar of the mediterranean diet, which has been shown to exert beneficial effects on human health, such as the prevention of chronic non-communicable diseases like cancers and neurodegenerative diseases, among others. these health benefits are partly mediated by the high-quality extra virgin olive oil (EVOO), which is produced mostly in mediterranean countries and is directly made from olives, the fruit of the olive tree (Olea europaea L.). preclinical evidence supports the existence of antioxidant and anti-inflammatory properties exerted by the polyphenol oleocanthal, which belongs to the EVOO minor polar compound subclass of secoiridoids (like oleuropein). this narrative review aims to describe the antioxidant and anti-inflammatory properties of oleocanthal, as well as the potential anticancer and neuroprotective actions of this polyphenol. based on recent evidence, we also discuss the reasons underlying the need to include the concentrations of oleocanthal and other polyphenols in the EVOO's nutrition facts label. finally, we report our personal experience in the production of a certified organic EVOO with a "protected designation of origin" (PDO), which was obtained from olives of three different cultivars (rotondella, frantoio, and Leccino) harvested in geographical areas located a short distance from one another (villages' names: gorga and camella) within the southern italy "cilento, vallo di diano and alburni national park" of the campania region (province of salerno, Italy)