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“…This textbook offers an invitation to modern algebra through number systems of increasing complexity, beginning with the natural numbers and culminating with Hamilton's quaternions. …”
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“…However, much less attention was devoted to the topological features of congruence relations among natural numbers. Here, we explore the congruence relations in the setting of a multiplex network and unveil some unique and outstanding properties of the multiplex congruence network. …”
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“…Investigation of divisibility properties of natural numbers is one of the most important themes in the theory of numbers. …”
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“…Unlike natural numbers, negative numbers do not have natural physical referents. …”
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“…In this article, we find some properties of certain types of entropies of a natural number. We are studying a way of measuring the “disorder” of the divisors of a natural number. …”
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“…Nevertheless, recent research suggested that decimal fractions may be represented differently than natural numbers because two number processing effects (i.e., semantic interference and compatibility effects) differed in their size between decimal fractions and natural numbers. …”
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“…INTRODUCTION: People often use heuristics derived from natural number tasks to solve fraction comparison tasks. …”
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“…A function f with domain and range are respectively the edge set of graph G and natural number up to [Formula: see text] , and a function f with domain and range are respectively the vertex set of graph G and the even natural number up to [Formula: see text] are called a total k-labeling where [Formula: see text]. …”
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“…This book discusses the conjecture of Goldbach; hypothesis of Gilbreath; decomposition of a natural number into prime factors; simple theorem of Fermat; and Lagrange's theorem. …”
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“…The theory primarily involves the investigation of the F-congruences (F is the the free semimodule of the rank n, where n is a given natural number). As applications, several important special cases are given. …”
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“…Our main result shows that although [Formula: see text] is computably embeddable in [Formula: see text], the class [Formula: see text] is not computably embeddable in [Formula: see text] for any natural number [Formula: see text].…”
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“…Irregular labelling on graph is a function from component of graph to non-negative natural number such that the weight of all vertices, or edges are distinct. …”
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“…An analysis of absolute transparency existence for the potential which has the inverse power dependence on space coordinate (and here tunneling is possible), i.e. which has the form $V(x) = \pm \alpha / |x-x_{0}|^{n}$ (where $\alpha$ and $x_{0}$ are constants, $n$ is natural number), is fulfilled. It is shown that such a potential can be reflectionless at n = 2 only. …”
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“…Natural number arithmetic is a simple, powerful and important symbolic system. …”
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“…In text encoding standards such as Unicode, text strings are sequences of code points, each of which can be represented as a natural number. We present a decision procedure for a concatenation-free theory of strings that includes length and a conversion function from strings to integer code points. …”
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“…The algorithm adopts the natural number coding method, and the particle corresponds to the confrontation strategy. …”
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