“…The developers claim that the security of their proposed scheme depends on the fact that a polynomial system consisting of 2n (where n is a natural number) equations and 3n unknowns constructed by using quasigroup string transformations, has infinitely many solutions and finding exact solution is not possible. …”
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“…When looking at a sequence of numbers, one that can be defined by a polynomial function of a natural number degree, one most commonly would use a difference table to find the degree followed by a system of equations to find the equation that models the sequence. …”
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“…Our computations reveal two topologically different families of two-start 30-nm fiber conformations distinguished by the linker length L; fibers with L ≈ 10n and L ≈ 10n+5 basepairs have DNA linking numbers per nucleosome of ΔLk ≈ −1.5 and −1.0, respectively (where n is a natural number). Although fibers with ΔLk ≈ −1.5 were observed earlier, the topoisomer with ΔLk ≈ −1.0 is novel. …”
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“…A drawback of most clustering algorithms is that they cannot automatically detect the "natural" number of clusters underlying the data, and in many cases we have no enough "a priori" biological knowledge to evaluate both the number of clusters as well as their validity. …”
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“…More precisely, the signatures of the genetic data are the frequencies of k-mers occurring in them, with k being a natural number. We considered an entropy-based distance between signatures, similar to the Kullback-Leibler distance in information theory, and investigated its ability to categorize negative-sense single-stranded RNA (ssRNA) viral genetic data. …”
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“…Here we report a simple modular strategy for efficient preparation of N = 6 aGNR, the narrowest member in the N = 3p (p: natural number) aGNR family, and two unsymmetrically edge-functionalized GNRs that contain benzothiadiazole and benzotriazole moieties. …”
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“…The HCHMs formation depends on the stepwise decomposition of the two Zn(2+) complexes ([Zn(en)(m)(H(2)O)(2(3−m))](2+) and [Zn(en)(m)(NH(3))(2(3−m))](2+), natural number m < 3). As the reaction proceeds, [Zn(2+)] has been distinctly reduced due to the transformation from [Zn(en)(m)(H(2)O)(2(3−m))](2+) to [Zn(en)(m)(NH(3))(2(3−m))](2+) with a high stability constant, leading to a low crystal growth rate to obtain single crystalline nanorods. …”
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“…We show that over a several-fold range of both of these parameters, and over multiple orders-of-magnitude of memory size, capacity is maximized when dendrites contain a few hundred synapses—roughly the natural number found in memory-related areas of the brain. …”
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“…Task items were selected according to a number of mathematically and/or cognitively relevant characteristics: (a) whether the fractions to be compared shared a common component, (b) the numerical distance between fractions, and (c) the applicability of two strategies to answer successfully: a congruency strategy (a fraction is larger if it has larger natural number components than another) and gap thinking (a fraction is larger if it is missing fewer pieces than another to complete the whole). …”
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“…Second, we investigated whether children’s estimates of nonsymbolic ratios of natural numbers relied at least in part on ratios of surface areas by contrasting a condition in which the ratio of surface areas occupied by dots covaried with the ratio of natural numbers and a condition in which this ratio of surface areas was kept constant across ratios of natural numbers. …”
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“…In this volume the author develops and applies methods for proving, from large cardinals, the determinacy of definable games of countable length on natural numbers. The determinacy is ultimately derived from iteration strategies, connecting games on natural numbers with the specific iteration games that come up in the study of large cardinals. …”
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“…The original Goodstein process proceeds by writing natural numbers in nested exponential k-normal form, then successively raising the base to [Formula: see text] and subtracting one from the end result. …”
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“…The order and disorder of binary representations of the natural numbers < 2(8) is measured using the BiEntropy function. …”
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“…Using transversality and a dimension reduction argument, a result of Bezdek and Kuperberg is applied to polycylinders, showing that the optimal packing density of [Formula: see text] equals [Formula: see text] for all natural numbers n.…”
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“…We show that a variant of Angluin’s seminal [Formula: see text] algorithm works when the semiring is a principal ideal domain, but not for general semirings such as the natural numbers.…”
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“…A numerical study on the distributions of primes in short intervals of length $h$ over the natural numbers $N$ is presented. Based on Cram\'er's model in Number Theory, we obtain a heuristic expression applicable when $h \gg \log{N}$ but $h \ll N$, providing support to the Montgomery and Soundararajan conjecture on the variance of the prime distribution at this scale.…”
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“…This review describes the relationship between the properties of functionalized polyanilines depending on the nature, number and position of the substituents at the aromatic ring.…”
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“…The rickettsial organisms in common with the elementary bodies of vaccinia virus and all bacteria would appear to have a limiting membrane which surrounds a substance that seems to be protoplasmic in nature; numbers of dense granules are embedded in the inner protoplasm.…”
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“…We establish that if [Formula: see text] are positive real numbers, at least one of the ratios [Formula: see text] ([Formula: see text] ) is irrational, then the integer parts of [Formula: see text] are prime infinitely often for [Formula: see text] , where [Formula: see text] are natural numbers.…”
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