For any positive integer n, the F.Smarandache LCM function SL(n) is defined as the smallest positive integer k such that n | [1, 2, · · · , k], where [1, 2, · · · , k] denotes the least common multiple of 1, 2, · · · , k. The main purpose of this paper is using the elementary methods to study the mean value properties of P (n)SL(n) and p(n)SL(n), and give two sharper asymptotic formulas for them.

This paper presents a model that enables the optimal interpretation of Prognostics and Health Management (PHM) results for electronic systems. In this context, optimal interpretation of PHM results means translating PHM information into maintenance policies and decisions that minimize life cycle costs, or maximize availability or some other utility function. The electronics PHM problem is chara...

This paper proves that if a Carmichael number is composed of primes pi, then the LCM of the pi − 1’s can never be of the form 2 and can be of the form 2 ∗P for only four prime values of P ≤ 127. Moreover, if the LCM of a Carmichael number is 2 ∗ P and a Carmichael number m has all of its Fermat prime factors among the five known Fermat primes, then P must be one of the four possibilities mentio...

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This study presents a general framework for single-administration reliability methods, such as Cronbach’s alpha, Guttman’s lambda-2, and method MS. This general framework was used to derive a new approach to estimating test-score reliability by means of the unrestricted latent class model. This new approach is the latent class reliability coefficient (LCRC). Unlike other single-administration r...

In the [20], it had been proven that the Integers modulo p, in this article we shall refer as Z/pZ, constitutes a field if and only if p is a prime. Then the prime modulo Z/pZ is an additive cyclic group and Z/pZ∗ = Z/pZ\{0} is a multiplicative cyclic group, too. The former has been proven in the [23]. However, the latter had not been proven yet. In this article, first, we prove a theorem conce...

Soil application of liquid cattle manure (LCM) (excrements plus urine, occasionally containing bedding material) can enhance plant growth and increase crop yield (Beauchamp, 1986; Culley et al., 1981; Evans et al., 1977; Kaffka & Kanneganti, 1996; Lithourgidis et al., 2007; Matsi et al., 2003; Motavalli et al., 1989; Sutton et al., 1986; Zhang et al., 2006; Zebarth et al., 1996). In most of the...

This paper makes estimates of the level of underreporting of consumer expenditures. The paper examines reporting in particular commodity categories and attempts only to make estimates of underreporting among those that report at least one expenditure in the category. The measure of the level of underreporting in a category by a particular responding unit is based on latent class analysis using ...

Increased awareness among professionals and the lay public about potential shortand long-term consequences associated with mild brain injuries (BIs) has prompted considerable interest in the topic of identification and recovery patterns. One issue that arises repeatedly relates to distinguishing injuries resulting in chronic symptoms from those to which people appear to have relatively rapid an...

Abstract For any positive integer n, the famous Smarandache function S(n) defined as the smallest positive integer m such that n | m!. That is, S(n) = min{m : n | m!, n ∈ N}. The Smarandache LCM function SL(n) the smallest positive integer k such that n | [1, 2, · · · , k], where [1, 2, · · · , k] denotes the least common multiple of 1, 2, · · · , k. The main purpose of this paper is using the ...