Scientia Magna back issues from December 2008:
An equation involving the Smarandache function and its positive integer solutions.(Report)
Dec 01, 2008; ... [section] 1. Introduction For any positive integer n, the famous Smarandache function S(n) is defined as the smallest positive integer m such that n | m!. That is, S(n) = min{m : n | m!, m [member of] N}. From the definition of S(n) one can easily deduce that if [MATHEMATICAL ...
On the Smarandache kn-digital subsequence.(Report)
Dec 01, 2008; ... [section] 1. Introduction For any positive integer n and any fixed positive integer k [greater than or equal to] 2, the Smarandache kn-digital subsequence {[S.sub.k](n)} is defined as the numbers [S.sub.k](n), which can be partitioned into two groups such that the second is k ...
On the Pseudo-Smarandache-Squarefree function and Smarandache function.(Report)
Dec 01, 2008; ... [section] 1. Introduction and result For any positive integer n, the famous Smarandache function S(n) is defined as S(n) = Min{m : n|m!, m [member of] N}, Pseudo-Smarandache-Squarefree function [Z.sub.w](n) is defined as the smallest positive integer m such that n | [m.sup.n] ....
On the Smarandache prime-digital subsequence sequences.(Report)
Dec 01, 2008; ... [section] 1. Introduction and results For any positive integer n, the Smarandache Prime-Digital Subsequence (SPDS) is defined as follows: A positive integer n is an element of SPDS, if it satisfies the following properties: a) m is a prime. b) ...
On the mean value of [a.sup.2](n).(Report)
Dec 01, 2008; ... [section] 1. Introduction and main results Let a(n) denote the number of nonisomorphic Abelian groups with n elements. The mean value of a(n) was first studied by P. Erdos and G. Szekeres [1], who proved that [summation over (n [less than or equal to] x] a(n) = ...
Monotonicity properties for the gamma and psi functions.(Report)
Dec 01, 2008; ... [section] 1. Introduction and result The classical gamma function is usually defined for x > 0 by [GAMMA](x) = [integral].sup.[infinity].sub.0] [t.sup.x-1] [e.sup.-t] dt, (1) which is one of the most important special functions and has much extensive ...
Resolvent dynamical systems for set-valued quasi variational inclusions in Banach spaces.(Report)
Dec 01, 2008; ... [section] 1. Introductions In recent years, variational inequalities have been extended and generalized in different directions by using novel and innovative techniques and ideas both for their own sake and for their applications. An important and useful generalization is called ...
A note on a theorem of Calderon.(Report)
Dec 01, 2008; ... [section] 1. Introduction Let a(n) denote the number of non-isomorphic finite abelian groups with n elements. This is a well-known multiplicative function, such that a([p.sup.[alpha]]) = P([alpha]), where P([alpha]) is the unrestricted partition function. Define [omega](n) = (a ...
On the Smarandache sequences.(Florentin Smarandache)(Report)
Dec 01, 2008; ... [section] 1. Introduction and results For any positive integer n, the Smarandache alternate consecutive and reverse Fibonacci sequence a(n) is defined as follows: a(1) = 1, a(2) = 11, a(3) = 112, a(4) = 3211, a(5) = 11235, a(6) = 853211, a(7) = 11235813, a(8) = 2113853211, a(9) ...
The study of [sigma]--index on [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] graphs.(Report)
Dec 01, 2008; ... [section] 1. Introduction Let G = (V, E) be a simple connected graph with the vertex set V(G) and the edge set E(G). For any [upsilon] [member of] V, [N.sub.G]([upsilon]) = {u | u[upsilon] [member of] E(G)} denotes the neighbors of [upsilon], and [d.sub.G]([upsilon]) =| ...
The natural partial order on Semiabundant semigroups.(Report)
Dec 01, 2008; ... [section] 1. Introduction As we know, constructions and many properties on regular and abundant semigroups have been described in terms of their natural partial orders (see [1]-[3]). The natural partial orders on these two classes of semigroups were firstly investigated by ...
On the Smarandache ceil function and the Dirichlet divisor function.(Florentin Smarandache)(Report)
Dec 01, 2008; ... [section] 1. Introduction For a fixed positive integer k and any positive integer n, the Smarandache ceil function [S.sub.k] (n) is defined as {[S.sub.k](n) = min m [member of] N : n|[m.sup.k]}. This function was introduced by Professor Smarandache. About ...
On fuzzy number valued Choquet integral.(Report)
Dec 01, 2008; ... [section] 1. Introduction After the formulation of fuzzy integral by Sugeno, various generalizations of fuzzy integral were introduced and investigated. Fuzzy number fuzzy integral (FNFI) were defined by various authors in [3], [5] and [6]. Zhang Guang-Quan [5] used ...
The Smarandache bisymmetric arithmetic determinant sequence.(Florentin Smarandache)(Report)
Dec 01, 2008; ... [section] 1. Introduction and results The Smarandache bisymmetric arithmetic determinant sequence (SBADS), introduced by Murthy [1], is defined as follows. Definition 1. The Smarandache bisymmetric arithmetic determinant sequence, {SBADS(n)}, is ...
On the divisor function and the number of finite abelian groups.(Report)
Dec 01, 2008; ... [section] 1. Introduction Let a(n) denote the number of non-isomorphic abelian groups with n elements. This is a well-known multiplicative function such that for any prime p we have a([p.sup.[alpha]]) = P([alpha]), where P([alpha]) is the unrestricted partition function. Let l ...
The quintic supported spline wavelets with numerical integration.(Report)
Dec 01, 2008; ... [section] 1. Introduction of the quintic supported spline wavelets In 1992, C. K. Chui and J. Z. Wang have constructed the supported spline wavelets with B-spline as scaling function, and this kind of wavelets can be used in many areas(the reference[1]). Because of the spline ...
Approximation in Hilbert algebras.(Report)
Dec 01, 2008; ... [section] 1. Introduction The notion of a Hilbert algebra was introduced in early 50-ties by L. Henkin and T. Skolem for some investigations of implicative in intuitionistic and other non-classical logics. In 60-ties, these algebras were studied especially by A. Horn and A ....
On v--[T.sub.i]--, v--[R.sub.i]--and v--[C.sub.i]--axioms.(semi-open and closed sets)(Report)
Dec 01, 2008; ... [section] 1. Introduction Norman Levine [6] introduced the concept of semi open sets in topological spaces. After the introduction of semi open sets by Norman Levine [6] various authors have turned their attentions to this concept and it becomes the primary aim of many ...
A note on the near pseudo Smarandache function.(Report)
Dec 01, 2008; ... [section] 1. Introduction Vyawahare and Purohit [1] introduced a new function, called the near pseudo Smarandache function, and denoted by K(n), is defined as follows. Definition 1.1. The near pseudo Smarandache function, K : N [right arrow] N, is K(n) = ...
Research on the scheduling decision in fuzzy multi-resource emergency systems.(Report)
Dec 01, 2008; ... [section] 1. Introduction The scheduling problem of resources in emergency systems has become a hot topic. For the emergency-time is a certain number or interval number and the different type of the resource consumption are discussed [4-5]. The fewest of retrieval depots as the ...
On the Smarandache 3n-digital sequence and the Zhang Wenpeng's conjecture.(Florentin Smarandache)(Report)
Dec 01, 2008; ... [section] 1. Introduction and results For any positive integer n, the famous Smarandache 3n-digital sequence is defined as {[a.sub.n]} = {13, 26, 39, 412, 515, 618, 721, 824, ...,}. That is, the numbers that can be partitioned into two groups such that the second is three times ...