Every sufficiently large even number is the sum of two primes

The binary Goldbach conjecture asserts that every even integer greater than $4$ is the sum of two primes. In this paper, we prove that there exists an integer $K_\alpha$ such that every even integer $x > p_k^2$ can be expressed as the sum of two primes, where $p_k$ is the $k$th prime number and $k > K_\alpha$. To prove this statement, we begin by introducing a type of double sieve of Eratosthenes as follows. Given a positive even integer $x > 4$, we sift from $[1, x]$ all those elements that are congruents to $0$ modulo $p$ or congruents to $x$ modulo $p$, where $p$ is a prime less than $\sqrt{x}$. Therefore, any integer in the interval $[\sqrt{x}, x]$ that remains unsifted is a prime $q$ for which either $x-q = 1$ or $x-q$ is also a prime. Then, we introduce a new way of formulating a sieve, which we call the sequence of $k$-tuples of remainders. By means of this tool, we prove that there exists an integer $K_\alpha > 5$ such that $p_k / 2$ is a lower bound for the sifting function of this sieve, for every even number $x$ that satisfies $p_k^2 < x < p_{k+1}^2$, where $k > K_\alpha$, which implies that $x > p_k^2 \; (k > K_\alpha)$ can be expressed as the sum of two primes.Comment: 32 pages. The manuscript was edited for proper English language by one editor at American Journal Experts (Certificate Verification Key: C0C3-5251-4504-E14D-BE84). However, afterwards some changes have been made in sections 1, 6, 7 and

An Agenda for a Reformed Cohesion Policy A place-based approach to meeting European Union challenges and expectations

EU regional policy is an investment policy. It supports job creation, competitiveness, economic growth, improved quality of life and sustainable development. These investments support the delivery of the Europe 2020 strategy. The present paper analysis two strategically different options of EU regional policy: place-neutral versus place-based policies for economic development. Our results suggest that in many EU regions the place-neutral policies may no be the best policy response to facing new challenges posed by deeper economic integration and globalisation.Place-based; development; policy; institutions; globalisation; economic geography.

Dimuon results in PbPb and pp collisions in CMS

The LHC offers unique opportunities for studying the properties of hot QCD matter created in Pb+Pb collisions at extreme temperatures and very low parton momentum fractions. With its high precision, large acceptance for tracking and calorimetry, and a trigger scheme that allows analysis of each minimum bias Pb+Pb event, CMS is fully equipped to measure dimuons in the high multiplicity environment of Pb+Pb collisions. Such probes are especially relevant since they are produced at early times and propagate through the medium, mapping its evolution. The capabilities of the CMS experiment to study dimuon production in pp and Pb+Pb collisions based on the 2010 LHC runs will be reviewed. CMS is able to measure primary and secondary J/psi, as well as the three Upsilon states. Quarkonia results at sqrt(s)=2.76 TeV in pp and Pb+Pb will be presented, including a tantalizing observation of suppression of the Upsilon excited states. The Z0 boson inclusive and differential measurement as a probe of the initial state will be described.Comment: 3 pages, 4 figures. To appear in the proceedings of PANIC 201

The particularity of emotional words. A grounded approach

This work focuses on emotional concepts. We define concepts as patterns of neural activation that re-enact a given external or internal experience, for example the interoceptive experience related to fear. Concepts are mediated and expressed through words. In the following, we will use “words” to refer to word meanings, assuming that words mediate underlying concepts. Since emotional concepts and the words that mediate them are less related to the physical environment than concrete ones, at first sight they might be depicted as abstract concepts. Evidence coming from several studies shows, instead, that the issue is more complex. In this work, we will briefly outline the debate and illustrate results from recent studies on comprehension of concrete, emotional and abstract words in children and adults. We will argue that emotional words can be accounted for from a grounded perspective and will contend that emotional words represent a particular set of words that differs from both the concrete and purely abstract ones

Pacifier overuse and conceptual relations of abstract and emotional concepts

This study explores the impact of the extensive use of an oral device since infancy (pacifier) on the acquisition of concrete, abstract, and emotional concepts. While recent evidence showed a negative relation between pacifier use and children’s emotional competence (Niedenthal et al., 2012), the possible interaction between use of pacifier and processing of emotional and abstract language has not been investigated. According to recent theories, while all concepts are grounded in sensorimotor experience, abstract concepts activate linguistic and social information more than concrete ones. Specifically, the Words As Social Tools (WAT) proposal predicts that the simulation of their meaning leads to an activation of the mouth (Borghi and Binkofski, 2014; Borghi and Zarcone, 2016). Since the pacifier affects facial mimicry forcing mouth muscles into a static position, we hypothesize its possible interference on acquisition/consolidation of abstract emotional and abstract not-emotional concepts, which aremainly conveyed during social and linguistic interactions, than of concrete concepts. Fifty-nine first grade children, with a history of different frequency of pacifier use, provided oral definitions of the meaning of abstract not-emotional, abstract emotional, and concrete words. Main effect of concept type emerged, with higher accuracy in defining concrete and abstract emotional concepts with respect to abstract not-emotional concepts, independently from pacifier use. Accuracy in definitions was not influenced by the use of pacifier, butcorrespondence and hierarchical clustering analyses suggest that the use of pacifier differently modulates the conceptual relations elicited by abstract emotional and abstract not-emotional. While the majority of the children produced a similar pattern of conceptual relations, analyses on the few (6) children who overused the pacifier (for more than 3 years) showed that they tend to distinguish less clearly between concrete and abstract emotional concepts and between concrete and abstract not-emotional concepts than children who did not use it (5) or used it for short (17). As to the conceptual relations they produced, children who overused the pacifier tended to refer less to their experience and to social and emotional situations, usemore exemplifications and functional relations, and less free associations

Negatively Charged Hadron Spectra in Au+Au Collisions at sqrt(s_NN) = 130 GeV

Negatively charged hadron (h-) production in Au+Au collisions at BNL-RHIC is studied with the STAR experiment. Results are presented on h- multiplicity, pseudorapidity and transverse momentum distributions at sqrt(s_NN) = 130 GeV.Comment: 4 pages, 4 figures. Presented at Quark Matter 200

Abstract concepts, language and sociality. From acquisition to inner speech

The problem of representation of abstract concepts, such as “freedom” and “justice”, has become particularly crucial in recent years, due to the increased success of embodied and grounded views of cognition. We will present a novel view on abstract concepts and abstract words. Since abstract concepts do not have single objects as referents, children and adults might rely more on input from others in learning them; we therefore suggest that linguistic and social experience play an important role for abstract concepts. We will discuss evidence obtained in our and other labs showing that processing of abstract concepts evokes linguistic interaction and social experiences, leading to the activation of the mouth motor system. We will discuss the possible mechanisms that underlie this activation. Mouth activation can be due to re-enactment of the experience of conceptual acquisition, which occurred through the mediation of language. Alternatively, it could be due to the re-explanation of the word meaning, possibly through inner speech. Finally, it can be due to a metacognitive process revealing low confidence on the meaning of our concepts. This process induces in us the need to rely on others to ask/negotiate conceptual meaning. We conclude that with abstract concepts words work as social tools: they extend our thinking abilities and push us to rely on others to integrate our knowledge