Showing papers in "viXra in 2006"
Posted Content•
TL;DR: This work presents two new promising combina- tion rules for the fusion of uncertain and potentially highl y conflicting sources of evidences in the theory of belief: the class of Adaptive Combination Rules (ACR) and a new effi- cient Proportional Conflict Redistribution (PCR) rule.
Abstract: This paper presents two new promising combina- tion rules for the fusion of uncertain and potentially highl y conflicting sources of evidences in the theory of belief func - tions established first in Dempster-Shafer Theory (DST) and then recently extended in Dezert-Smarandache Theory (DSmT). Our work is to provide here new issues to palliate the well-known limitations of Dempster's rule and to work beyond its limits of applicability. Since the famous Zadeh' s criticism of Dempster's rule in 1979, many researchers have proposed new interesting alternative rules of combination to palliate the weakness of Dempster's rule in order to provide acceptable results specially in highly conflicting situati ons. In this work, we present two new combination rules: the class of Adaptive Combination Rules (ACR) and a new effi- cient Proportional Conflict Redistribution (PCR) rule. Bot h rules allow to deal with highly conflicting sources for stati c and dynamic fusion applications. We present some inter- esting properties for ACR and PCR rules and discuss some simulation results obtained with both rules for Zadeh's pro b- lem and for a target identification problem.
30 citations
TL;DR: In this paper, the authors discussed the solutions of the following equation involving the Smarandache function: S(m1)+S(m2)+¢¢¢+S(mk) = S (m1 +m2 +¢¢−¢+mk).
Abstract: Let n be any positive integer, the Smarandache function S(n) is deflned as S(n) = minfm : njm!g: In this paper, we discussed the solutions of the following equation involving the Smarandache function: S(m1)+S(m2)+¢¢¢+S(mk) = S(m1 +m2 +¢¢¢+mk); and proved that the equation has inflnity positive integer solutions.
18 citations
Posted Content•
TL;DR: In this article, it is shown that it is possible to derive a new wave equation as alternative to Barut-Dirac's equation from the known exact correspondence (isomorphism) between Dirac equation and Maxwell electromagnetic equations via biquaternionic representation.
Abstract: It is known that Barut's equation could predict lepton and hadron mass with remarkable precision. Recently some authors have extended this equation, resulting in Barut-Dirac equation. In the present article we argue that it is possible to derive a new wave equation as alternative to Barut-Dirac's equation from the known exact correspondence (isomorphism) between Dirac equation and Maxwell electromagnetic equations via biquaternionic representation. Furthermore, in the present note we submit the viewpoint that it would be more conceivable if we interpret the vierbein of this equation in terms of
superfluid velocity, which in turn brings us to the notion of topological electronic liquid. Some implications of this proposition include quantization of celestial systems. We also argue that it is possible to find some signatures of Bose-Einstein cosmology, which thus far is not explored
sufficiently in the literature. Further experimental observation to verify or refute this proposition
is recommended.
17 citations
TL;DR: In this paper, a generalized real Fourier transform on Clifford multivector-valued functions (f : ℝn → Cl n,0, n = 3 (mod 4)).
Abstract: First, the basic concepts of the multivector functions, vector differential and vector derivative in geometric algebra are introduced. Second, we define a generalized real Fourier transform on Clifford multivector-valued functions (f : ℝn → Cl n,0, n = 3 (mod 4)). Third, we introduce a set of important properties of the Clifford Fourier transform on Cl n,0, n = 3 (mod 4) such as differentiation properties, and the Plancherel theorem. Finally, we apply the Clifford Fourier transform properties for proving a directional uncertainty principle for Cl n,0 n = 3 (mod 4) multivector functions.
16 citations
10 citations
TL;DR: In this paper, a general way for con-structing dimensional n pseudo-manifolds is presented for any integer n ≥ 2, where connection and principal fiber bundles are also defined on these manifolds.
Abstract: A Smarandache geometry is a geometry which has at least one Smarandachely denied axiom(1969), i.e., an axiom behaves in at least two different ways within the same space, i.e., validated and invalided, or only invalided but in multiple distinct ways and a Smarandache n-manifold is a n-manifold that support a Smarandache geometry. Iseri pro- vided a construction for Smarandache 2-manifolds by equilateral triangular disks on a plane and a more general way for Smarandache 2-manifolds on surfaces, called map geometries was presented by the author in (9) − (10) and (12). However, few observations for cases of n ≥ 3 are found on the journals. As a kind of Smarandache geometries, a general way for con- structing dimensional n pseudo-manifolds are presented for any integer n ≥ 2 in this paper. Connection and principal fiber bundles are also defined on these manifolds. Following these constructions, nearly all existent geometries, such as those of Euclid geometry, Lobachevshy- Bolyai geometry, Riemann geometry, Weyl geometry, Kahler geometry and Finsler geometry,
8 citations
Posted Content•
TL;DR: In this paper, the authors give some results and observations related to the Pseudo-Smarandache function Z(n) for some particular cases of n and give explicit expressions for some specific classes of n.
Abstract: This paper gives some results and observations related to the Pseudo-Smarandache function Z(n). Some explicit expressions of Z(n) for some particular cases of n are also given.
5 citations
TL;DR: In this article, the author used the analytic method to consider the special case: p1 and p2 are two fixed distinct primes, where p1 is a fixed distinct prime.
Abstract: The author had used the analytic method to consider the special case: p1 and p2 are two fixed distinct primes.
5 citations
TL;DR: The main purpose of as discussed by the authors is to study the arithmetical properties of the primitive numbers of power p by using the elementary method, and give some interesting identities and asymptotic formulae.
Abstract: The main purpose of this paper is to study the arithmetical properties of the primitive numbers of power p by using the elementary method, and give some interesting identities and asymptotic formulae.
5 citations
TL;DR: In this paper, a reduction formula for Smarandache LCM ratio sequences SLR(6) and SLR (7) is given, and a reduction algorithm for SLR-LCM pairs is presented.
Abstract: In this paper, a reduction formula for Smarandache LCM ratio sequences SLR(6)and SLR(7) are given.
5 citations
Posted Content•
TL;DR: Five kinds of expanded space-time for General Relativity are obtained, including regions where the metric fully degenerates: there may be non-quantum teleportation, and a home for virtual photons.
Abstract: We apply the S-denying procedure to signature conditions in a four-dimensional pseudo-Riemannian space - i. e. we change one (or even all) of the conditions to be partially true and partially false. We obtain five kinds of expanded space-time for General Relativity. Kind I permits the space-time to be in collapse. Kind II permits the space-time to change its own signature. Kind III has peculiarities, linked to the third signature condition. Kind IV permits regions where the metric fully degenerates: there may be non-quantum teleportation, and a home for virtual photons. Kind V is common for kinds I, II, III, and IV.
TL;DR: For any fixed prime p and any positive integer n, Zhang and Liu as discussed by the authors obtained an interesting asymptotic formula for the problem, where p is a fixed prime and n a positive integer.
Abstract: About this problem, Professor Zhang and Liu in [2] have studied it and obtained an interesting asymptotic formula. That is, for any fixed prime p and any positive integer n...
TL;DR: In this paper, the authors studied the mean value properties of f(n) and gave an interesting mean value formula for it, which they used in their paper "The Mean Value of F(n).
Abstract: In this paper, we study the mean value properties of f(n), and give an interesting mean value formula for it.
TL;DR: For any fixed positive integer n, the Smarandache ceil function of order k is denoted by (1) as discussed by the authors, where k is the number of vertices in order k.
Abstract: For any ¯fixed positive integer n, the Smarandache ceil function of order k is denoted by...
TL;DR: In this article, the mean value properties of Smarandache-type multiplicative functions Km(n) were studied and the convolution method was used to improve the error term.
Abstract: In this paper, we use analytic method to study the mean value properties of Smarandache-Type Multiplicative Functions Km(n), and give its asymptotic formula . Finally, the convolution method is used to improve the error term.
TL;DR: In this article, the idea of left(right) palindromic permutations (LPPs,RPPs) and left (right) gen- eralized Smarandache permutations(LGSPPs,RGSPPs) are introduced in symmetric groups of degree n.
Abstract: The idea of left(right) palindromic permutations(LPPs,RPPs) and left(right) gen- eralized Smarandache palindromic permutations(LGSPPs,RGSPPs) are introduced in symmetric groups Sn of degree n. It is shown that in Sn, there exist a LPP and a RPP and they are unique(this fact is demonstrated using S2 and S3). The dihedral group Dn is shown to be generated by a RGSPP and a LGSPP(this is observed to be true in S3) but the geometric interpretations of a RGSPP and a LGSPP are found not to be rotation and reflection respectively. In S3, each permutation is at least a RGSPP or a LGSPP. There are 4 RGSPPs and 4 LGSPPs in S3, while 2 permutations are both RGSPPs and LGSPPs. A permutation in Sn is shown to be a LPP or RPP(LGSPP or RGSPP) if and only if its inverse is a LPP or RPP(LGSPP or RGSPP) respectively. Problems for future studies are raised.
TL;DR: The main purpose of as mentioned in this paper is using the analytic method to study the asymptotic properties of the Near Pseudo Smarandache Function (PSF) and give two interesting formulae for it.
Abstract: The main purpose of this paper is using the analytic method to study the asymptotic properties of the Near Pseudo Smarandache Function, and give two interesting asymptotic formulae for it.
TL;DR: In this paper, the notion of Smarandache fantastic ideals is introduced, examples are given, and related properties are investigated, including the extension property for Q-Smarandache great ideals.
Abstract: The notion of Smarandache fantastic ideals is introduced, examples are given, and related properties are investigated. Relations among Q-Smarandache fresh ideals, Q- Smarandache clean ideals and Q-Smarandache fantastic ideals are given. A characterization of a Q-Smarandache fantastic ideal is provided. The extension property for Q-Smarandache fantastic ideals is established.
TL;DR: In this article, the mean value properties of the additive analogue of S(n) were studied, and an interesting mean value formula for it was given, which was later extended to the case of S (n).
Abstract: In this paper, we study the mean value properties of the additive analogue of S(n), and give an interesting mean value formula for it.
TL;DR: In this paper, the properties of the sequences of {pd(n)} and {qd(n)}, and the generalized results for the sequences {pd{n, qd{n} and qd[n] are studied.
Abstract: Let n be a positive integer, pd(n) denotes the product of all positive divisors of n, qd(n) denotes the product of all proper divisors of n. In this paper, we study the properties of the sequences of {pd(n)} and {qd(n)}, and prove that the generalized results for the sequences {pd(n)} and {qd(n)}.
TL;DR: Agarwal et al. as mentioned in this paper used the Maple system to dened mirror and symmetric Smarandache sequences of triangular numbers making use of Maple system, and showed that mirror and symmetry can be obtained using the same system.
Abstract: Shyam Sunder Gupta (3) has dened Smarandache consecutive and reversed Smarandache sequences of triangular numbers. Delm F.M.Torres and Viorica Teca (1) have further investigated these sequences and dened mirror and symmetric Smarandache sequences of triangular numbers making use of Maple system. Working on the same lines we have de- ned and investigated consecutive, reversed, mirror and symmetric Smarandache sequences of pentagonal numbers of dimension 2 using the Maple system .
TL;DR: The main purpose of as mentioned in this paper is using the elementary and analytic methods to study the asymptotic properties of the k-power part of the residue and give an interesting formula for it.
Abstract: The main purpose of this paper is using the elementary and analytic methods to study the asymptotic properties of the k-power part residue, and give an interesting asymptotic formula for it.
TL;DR: Mao et al. as discussed by the authors survey these thinking and ideas for mathematics and cosmological physics, such as those of multi-spaces, map geometries and combinatorial cosmoses.
Abstract: Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an even more important work for mathematician is to apply combinatorics to other mathematics and other sciences beside just to find combinatorial behavior for objectives. In the past few years, works of this kind frequently appeared on journals for mathematics and theoretical physics for cosmos. The main purpose of this paper is to survey these thinking and ideas for mathematics and cosmological physics, such as those of multi-spaces, map geometries and combinatorial cosmoses, also the combinatorial conjecture for mathematics proposed by myself in 2005. Some open problems are included for the advance of 21st mathematics by a combinatorial speculation. >5eF2t >Be z. S{ ^"A& | 'p1rr N FH G&4;' # hW?_'IAE BFHrS J ℄+q3Z'rS7JN FHjmrhTFHY AEhT|HDi7^o#rI! ^"A' Reported at the 2th Conference on Combinatorics and Graph Theory of China, Aug. 1619 2006, Tianjing, P.R.China e-print: arXiv: math.GM/0606702 and Sciencepaper Online:200607-128 2 Linfan Mao: Mathematics of 21st Century–A Collection of Selected Papers N ?om 2L)BFH0w7AE H'OkrSaR fz ! ℄2HBxAE [ '9ZJ' rJC`f ! FHuw 7AE HOk/'N L) 8 3 A ,j4 N w7)) )Z0S 2005 R\ FHN l) / R oN L)B 21 4;FHIAE\ '℄2 ZOkAEUt' ℄
TL;DR: In this article, the Smarandache inversion sequence is studied and a new concept, related sequences, conjectures, properties, and problems are discussed. But the complexity of the problem is not discussed.
Abstract: We study the Smarandache inversion sequence which is a new concept, related sequences, conjectures, properties, and problems.
TL;DR: In this article, a model simplu al geometriei Smarandache si invitam cititorul, ca o distractie matematica, sa compuna alte modele.
Abstract: Prezentam aici un model simplu al geometriei Smarandache si invitam cititorul, ca o distractie matematica, sa compuna alte modele.
TL;DR: In this article, the main purpose of the paper is using the elementary method to study the prop- erties of the Smarandache Prime-Digital Subsequence, and give an interesting limit Theorem.
Abstract: The main purpose of the paper is using the elementary method to study the prop- erties of the Smarandache Prime-Digital Subsequence, and give an interesting limit Theorem. This solved a problem proposed by Charles.
TL;DR: In this article, the authors defined the multiplicative persistence of a number in the following manner: any n-digits number with n x x x X N..... 3 2 1 = in base 10.
Abstract: In [1], Sloane has defined the multiplicative persistence of a number in the following manner. Let’s N be any n-digits number with n x x x x N ..... 3 2 1 = in base 10. Multiplying together the digits of that number ( n x x x ⋅ ⋅ ⋅ ...... 2 1 ), another number ' N results. If this process is iterated, eventually a single digit number will be produced. The number of steps to reach a single digit number is referred to as the persistence of the original number N. Here an example:
TL;DR: The main purpose of as discussed by the authors is using the elementary method to study the mean value properties of a new arithmetical function involving the m-power free part of an integer, and give an interesting asymptotic formula for it.
Abstract: The main purpose of this paper is using the elementary method to study the mean value properties of a new arithmetical function involving the m-power free part of an integer, and give an interesting asymptotic formula for it.
TL;DR: The main purpose of as mentioned in this paper is using the elementary methods to study the properties of the integer part of the m-th root and the largest mth power not exceeding n, and give some interesting identities involving these numbers.
Abstract: The main purpose of this paper is using the elementary methods to study the properties of the integer part of the m-th root and the largest m-th power not exceeding n,and give some interesting identities involving these numbers.
TL;DR: In this paper, the arithmetical properties of the number set Ak,l are studied and some interesting asymptotic formulae for it are given. But they do not consider the problem of finding a number set for any positive integer l ≥ 2.
Abstract: Let Fk denotes the set of k-free number. For any positive integers l ≥ 2, we define a number set Ak,l as follows Ak,l = {n : n = m + r, m ≤ n < (m + 1), r ∈ Fk, n ∈ N}. In this paper, we study the arithmetical properties of the number set Ak,l, and give some interesting asymptotic formulae for it.