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Scientia Magna : An International Journal : Volume 1, No. 2, 2005

By Xi'an, Shaanxi


Description
Scientia Magna is published annually in 200-300 pages per volume and 1,000 copies on topics such as mathematics, physics, philosophy, psychology, sociology, and linguistics.

Excerpt
0. In 1999, the second author of this remarks published a book over 30 of Smarandache's problems in area of elementary number theory (see [1, 2]). After this, we worked over new 20 problems that we collected in our book [28]. These books contain Smarandache's problems, described in [10, 16]. The present paper contains some of the results from [28]. In [16] Florentin Smarandache formulated 105 unsolved problems, while in [10] C.Dumitresu and V. Seleacu formulated 140 unsolved problems of his. The second book contains almost all the problems from [16], but now each problem has unique number and by this reason in [1, 28] and here the authors use the numeration of the problems from [10]. In the text below the following notations are used.

Table of Contents
V. Mladen and T. Krassimir : Remarks on some of the Smarandache's problem. Part 2 1 W. Kandasamy : Smarandache groupoids 27 L. Ding : On the primitive numbers of power P and its mean value properties 36 D. Torres and V. Teca : Consecutive, reversed, mirror, and symmetric Smarandache sequence of triangular numbers 39 D. Ren : On the square-free number sequence 46 T. Ramaraj and N. Kannappa : On ¯nite Smarandache near-rings 49 X. Kang : Some interesting properties of the Smarandache function 52 L. Mao : On Automorphism Groups of Maps, Surfaces and Smarandache Geometries 55 L. Ding : On the mean value of Smarandache ceil function 74 M. Le : An equation concerning the Smarandache function 78 M. Bayat, H. Teimoori and M. Hassani : An extension of ABC-theorem 81 J. Ma : An equation involving the Smarandache function 89 C. Chen : Inequalities for the polygamma functions with application 91 W. Vasantha and M. Chetry : On the number of Smarandache zero-divisors and Smarandache weak zero-divisors in loop rings 96 M. Le : The function equation S(n) = Z(n) 109 Z. Li : On the Smarandache Pseudo-number Sequences 111 D. Mehendale : The classical Smarandache function and a formula for twin primes 114 J. Sandor : On completely f-perfect numbers 116 L. Mao : Parallel bundles in planar map geometries 120 H. Yang and R. Fu : On the asymptotic properties of odd sieve sequence 134 A. Muktibodh : Smarandache quasigroup rings 139 H. Shen : Two asymptotic formulae on the k + 1-power free numbers 145 Y. Ji : An equation involving the Smarandache ceil function 149 J. Young : Smarandache BCC-algebras 152 M. Yang and Q. Yang : On the asymptotic property for Smarandache additive factorial complements 159 J. Sandor : The Smarandache minimum and maximum functions 162 R. Pinch : Some properties of the Pseudo-Smarandache function 167 Y. Yi : An equation involving the Euler function and Smarandache function 173 J. Earls : Recursive Palindromic Smarandache Values 176 W. Vasantha and M. Chetry Smarandache Idempotents in ¯nite ring Zn and in Group Ring ZnG 179 W. Vasantha and M. Chetry Smarandache Idempotents in Loop Rings ZtLn(m) of the Loops Ln(m) 188

 

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