ABSTRACT Since ancient times, numbers have played an important role in representing the customs, traditions and beliefs of peoples, some reaching the status of sacred. For different factors there are ...common sacred numbers for different peoples, such as the numbers three, five, seven, eight, nine, twelve, forty, three hundred among others. However, in Azerbaijan, special relevance has been acquired by the numbers three, seven and forty, so the objective of this research is to analyze its importance in folklore and cultural expression. For this, various popular tales are analyzed, highlighting the relevance of these numbers, their functions and possible interpretations. It was identified that the number three is associated with success, number seven with time and forty with the concept of many. The study of their possible meanings serves for a better interpretation of ancient texts because, as shown, their interpretation cannot always be literal.
The purpose of this paper is to prove some fixed point theorems in a tvs-cone metric space using 𝑐-distances. The presented theorems extend, generalize and improve the corresponding results of ...Fadail et al. 10, Dordevic et al. 8 and the results cited therein under the continuity condition for maps. In the last section we give an examples in support of our theorems.
Only humans possess the faculty of language that allows an infinite array of hierarchically structured expressions (Hauser et al., 2002; Berwick and Chomsky, 2015). Similarly, humans have a capacity ...for infinite natural numbers, while all other species seem to lack such a capacity (Gelman and Gallistel, 1978; Dehaene, 1997). Thus, the origin of this numerical capacity and its relation to language have been of much interdisciplinary interest in developmental and behavioral psychology, cognitive neuroscience, and linguistics (Dehaene, 1997; Hauser et al., 2002; Pica et al., 2004). Hauser et al. (2002) and Chomsky (2008) hypothesize that a recursive generative operation that is central to the computational system of language (called
) can give rise to the successor function in a set-theoretic fashion, from which capacities for discretely infinite natural numbers may be derived. However, a careful look at two domains in language, grammatical number and numerals, reveals no trace of the successor function. Following behavioral and neuropsychological evidence that there are two core systems of number cognition innately available, a core system of representation of large, approximate numerical magnitudes and a core system of precise representation of distinct small numbers (Feigenson et al., 2004), I argue that grammatical number reflects the core system of precise representation of distinct small numbers alone. In contrast, numeral systems arise from integrating the pre-existing two core systems of number and the human language faculty. To the extent that my arguments are correct, linguistic representations of number, grammatical number, and numerals do not incorporate anything like the successor function.
Assuming the Riemann hypothesis, we obtain an upper bound for the moments of the Riemann zeta function on the critical line. Our bound is nearly as sharp as the conjectured asymptotic formulae for ...these moments. The method extends to moments in other families of L-functions.
Epistemic consequentialists maintain that the epistemically right (e.g., the justified) is to be understood in terms of conduciveness to the epistemic good (e.g., true belief). Given the wide variety ...of epistemological approaches that assume some form of epistemic consequentialism, and the controversies surrounding consequentialism in ethics, it is surprising that epistemic consequentialism remains largely uncontested. However, in a recent paper, Selim Berker has provided arguments that allegedly lead to a 'rejection' of epistemic consequentialism. In the present paper, it is shown that reliabilism—the most prominent form of epistemic consequentialism, and one of Berker's main targets—survives Berker's arguments unscathed.
The paper studies the zeta function
of the monoid
generated by prime numbers
of the form 3
n
+ 2. The main monoid
and the main set
are defined. For the corresponding zeta functions, explicit finite ...formulas are found that give their analytic continuations to the entire complex plane, except for a countable set of poles. Inverse series for these zeta functions are found, and functional equations are derived. Three new types of monoids of natural numbers with a unique prime factorization are defined, namely, monoids of powers, Euler monoids modulo
q
, and unit monoids modulo
q
. Expressions for their zeta functions in terms of the Euler product are given. The Davenport–Heilbronn effect for zeta functions of monoids of natural numbers is discussed, which means the appearance of zeros of the zeta functions for terms obtained by decomposition into residue classes to some modulus. For monoids with an exponential sequence of primes, the barrier series hypothesis is proved and it is shown that the holomorphic domain of the zeta function of such a monoid is the complex half-plane to the right of the imaginary axis. In conclusion, topical problems with zeta functions of monoids of natural numbers that require further investigation are considered.
Une conjecture bien connue de Chowla affirme que les corrélations des translatés de la fonction λ(n) de Liouville sont asymptotiquement nulles. Dans un article récent, les auteurs ont démontré un ...résultat partiel en direction de la conjecture d’Elliott logarithmiquement pondérée concernant les corrélations des fonctions multiplicatives, qui à son tour implique tous les cas de la conjecture de Chowla avec un nombre impair de translatés. Dans cet article, nous donnons une nouvelle démonstration de ce dernier résultat sur la conjecture de Chowla. En particulier, celle-ci évite l’usage de la théorie ergodique qui joue un rôle crucial dans notre démonstration précédente.
A famous conjecture of Chowla states that the Liouville function λ(n) has negligible correlations with its shifts. Recently, the authors established a weak form of the logarithmically averaged Elliott conjecture on correlations of multiplicative functions, which in turn implied all the odd order cases of the logarithmically averaged Chowla conjecture. In this note, we give a new proof of the odd order cases of the logarithmically averaged Chowla conjecture. In particular, this proof avoids all mention of ergodic theory, which had an important role in the previous proof.
From numerical concepts to concepts of number Rips, Lance J; Bloomfield, Amber; Asmuth, Jennifer
The Behavioral and brain sciences,
12/2008, Letnik:
31, Številka:
6
Journal Article
Recenzirano
Many experiments with infants suggest that they possess quantitative abilities, and many experimentalists believe that these abilities set the stage for later mathematics: natural numbers and ...arithmetic. However, the connection between these early and later skills is far from obvious. We evaluate two possible routes to mathematics and argue that neither is sufficient: (1) We first sketch what we think is the most likely model for infant abilities in this domain, and we examine proposals for extrapolating the natural number concept from these beginnings. Proposals for arriving at natural number by (empirical) induction presuppose the mathematical concepts they seek to explain. Moreover, standard experimental tests for children's understanding of number terms do not necessarily tap these concepts. (2) True concepts of number do appear, however, when children are able to understand generalizations over all numbers; for example, the principle of additive commutativity (a+b=b+a). Theories of how children learn such principles usually rely on a process of mapping from physical object groupings. But both experimental results and theoretical considerations imply that direct mapping is insufficient for acquiring these principles. We suggest instead that children may arrive at natural numbers and arithmetic in a more top-down way, by constructing mathematical schemas.
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