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Scientia Magna : An International Journal : Volume 2, No. 2, 2006

By Xi'an, Shaanxi

Book Id:WPLBN0002828566 Format Type:PDF (eBook) File Size:3.69 mb Reproduction Date:8/7/2013

Xi'anitor, S. (Ed.). (2013). Scientia Magna : An International Journal : Volume 2, No. 2, 2006. Retrieved from http://www.gutenberg.cc/

Description
In the volume we assemble not only those papers which were presented at the conference but also those papers which were submitted later and are concerned with the Smarandache type problems. There are a few papers which are not directly related to but should fall within the scope of Smarandache type problems. They are 1. L. Liu and W. Zhou, On conjectures about the class number of binary quadratic forms; 2. W. Liang, An identity for Stirling numbers of the second kind; 3. Y. Wang and Z. Sheng, Two formulas for x^n in terms of Chebyshev polynomials. Other papers are concerned with the number-theoretic Smarandache problems and will enrich the already rich stock of results on them. Readers can learn various techniques used in number theory and will get familiar with the beautiful identities and sharp asymptotic formulas obtained in the volume.

Summary
Scientia Magna is published annually in 400-500 pages per volume and 1,000 copies on topics such as mathematics, physics, philosophy, psychology, sociology, and linguistics.

Excerpt
On Algebraic Multi-Vector Spaces
Abstract A Smarandache multi-space is a union of n spaces A1;A2;An with some additional conditions hold. Combining these Smarandache multi-spaces with linear vector spaces in classical linear algebra, the conception of multi-vector spaces is introduced. Some characteristics of multi-vector spaces are obtained in this paper.
Keywords Vector, multi-space, multi-vector space, dimension of a space.
x1. Introduction
These multi-spaces was introduced by Smarandache in under his idea of hybrid mathematics: combining different fields into a unifying field, which can be formally defined with mathematical words by the next definition.

Table of Contents
L. Mao : On Algebraic Multi-Vector Spaces 1
L. Liu and W. Zhou : On conjectures concerning class number of binary
quadratic forms 7
W. Zhai and H. Liu : On square-free primitive roots mod p 15
X. Pan : A new limit theorem involving the Smarandache LCM sequence 20
M. Le : The Smarandache Perfect Numbers 24
N. Yuan : On the solutions of an equation involving the Smarandache
dual function 27
J. Wang : Mean value of a Smarandache-Type Function 31
H. Yang and R. Fu : On the mean value of the Near Pseudo
Smarandache Function 35
W. Liang : An Identity of Stirling Numbers of the Second Kind 40
R. Ma : On the F.Smarandache LCM Ratio Sequence 44
L. Mao : On Algebraic Multi-Ring Spaces 48
Y. Han : On the Product of the Square-free Divisor of a Natural Number 55
P. Zhang : Some identities on k-power complement 60
Y. Wang and Z. Sheng : Two Formulas for xn being Represented by
Chebyshev Polynomials 64
X. Chen : Two Problems About 2-Power Free Numbers 70
X. Ma : The Asymptotic Formula of
P
n·x
log Pad(n) 72
Q. Tian : On the K-power free number sequence 77
C. Lv : On a generalized equation of Smarandache and its integer solutions 82
X. Du : On the mean value of the Smarandache LCM function SL(n) 85
Q. Yang : On the generalized constructive set 91
G. Chen : Some exact calculating formulas for the Smarandache function 95
H. Liu : On the F.Smarandache simple function 98
Y. Liu and J. Ma : Some identities involving the k-th power complements 101
Y. Zhao : An equation involving the function Sp(n) 105