New generalized fuzzy metrics and fixed point theorem in fuzzy metric space

In this paper, in fuzzy metric spaces (in the sense of Kramosil and Michalek (Kibernetika 11:336-344, 1957)) we introduce the concept of a generalized fuzzy metric which is the extension of a fuzzy metric. First, inspired by the ideas of Grabiec (Fuzzy Sets Syst. 125:385-389, 1989), we define a new G-contraction of Banach type with respect to this generalized fuzzy metric, which is a generalization of the contraction of Banach type (introduced by M Grabiec). Next, inspired by the ideas of Gregori and Sapena (Fuzzy Sets Syst. 125:245-252, 2002), we define a new GV-contraction of Banach type with respect to this generalized fuzzy metric, which is a generalization of the contraction of Banach type (introduced by V Gregori and A Sapena). Moreover, we provide the condition guaranteeing the existence of a fixed point for these single-valued contractions. Next, we show that the generalized pseudodistance J:X×X→[0,∞) (introduced by Włodarczyk and Plebaniak (Appl. Math. Lett. 24:325-328, 2011)) may generate some generalized fuzzy metric NJ on X. The paper includes also the comparison of our results with those existing in the literature

The Spin Structure of the Nucleon

We present an overview of recent experimental and theoretical advances in our understanding of the spin structure of protons and neutrons.Comment: 84 pages, 29 figure

A Melodic Contour Repeatedly Experienced by Human Near-Term Fetuses Elicits a Profound Cardiac Reaction One Month after Birth

Human hearing develops progressively during the last trimester of gestation. Near-term fetuses can discriminate acoustic features, such as frequencies and spectra, and process complex auditory streams. Fetal and neonatal studies show that they can remember frequently recurring sounds. However, existing data can only show retention intervals up to several days after birth.Here we show that auditory memories can last at least six weeks. Experimental fetuses were given precisely controlled exposure to a descending piano melody twice daily during the 35(th), 36(th), and 37(th) weeks of gestation. Six weeks later we assessed the cardiac responses of 25 exposed infants and 25 naive control infants, while in quiet sleep, to the descending melody and to an ascending control piano melody. The melodies had precisely inverse contours, but similar spectra, identical duration, tempo and rhythm, thus, almost identical amplitude envelopes. All infants displayed a significant heart rate change. In exposed infants, the descending melody evoked a cardiac deceleration that was twice larger than the decelerations elicited by the ascending melody and by both melodies in control infants.Thus, 3-weeks of prenatal exposure to a specific melodic contour affects infants 'auditory processing' or perception, i.e., impacts the autonomic nervous system at least six weeks later, when infants are 1-month old. Our results extend the retention interval over which a prenatally acquired memory of a specific sound stream can be observed from 3-4 days to six weeks. The long-term memory for the descending melody is interpreted in terms of enduring neurophysiological tuning and its significance for the developmental psychobiology of attention and perception, including early speech perception, is discussed

QCD and strongly coupled gauge theories : challenges and perspectives

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.Peer reviewe

Constructible graphs and pursuit

A (finite or infinite) graph is called constructible if it may be obtained recursively from the one-point graph by repeatedly adding dominated vertices. In the finite case, the constructible graphs are precisely the cop-win graphs, but for infinite graphs the situation is not well understood. One of our aims in this paper is to give a graph that is cop-win but not constructible. This is the first known such example. We also show that every countable ordinal arises as the rank of some constructible graph, answering a question of Evron, Solomon and Stahl. In addition, we give a finite constructible graph for which there is no construction order whose associated domination map is a homomorphism, answering a question of Chastand, Laviolette and Polat. Lehner showed that every constructible graph is a weak cop win (meaning that the cop can eventually force the robber out of any finite set). Our other main aim is to investigate how this notion relates to the notion of `locally constructible' (every finite graph is contained in a finite constructible subgraph). We show that, under mild extra conditions, every locally constructible graph is a weak cop win. But we also give an example to show that, in general, a locally constructible graph need not be a weak cop win. Surprisingly, this graph may even be chosen to be locally finite. We also give some open problems