[85] **viXra:1404.0419 [pdf]**
*submitted on 2014-04-18 05:23:18*

**Authors:** Florentin Smarandache

**Comments:** 23 Pages.

This chapter further extends the results obtained in chapters 4 and 5 (from linear equation to linear systems). Each algorithm is thoroughly proved and then an example is given.
Five integer number algorithms to solve linear systems are further given.

**Category:** General Mathematics

[84] **viXra:1404.0418 [pdf]**
*submitted on 2014-04-18 05:24:21*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

This autumn will be a few years since the school journal “Gamma” was founded at Lyceum “Steagul Roşu” in Braşov, Romania, under the guidance of the good hearted professor MIHAIL BENCZE, who has not spared any effort for it.

**Category:** General Mathematics

[83] **viXra:1404.0417 [pdf]**
*submitted on 2014-04-18 05:25:56*

**Authors:** Florentin Smarandache

**Comments:** 1 Page.

Due to professor Gane Policarp’s kindness, I have several issues of “Caietul de informare matematică” (“The notebook of mathematical information”), which has been put together with attention to detail and skill, and which attracted and persuaded me, from the very beginning, to collaborate with small materials.

**Category:** General Mathematics

[82] **viXra:1404.0416 [pdf]**
*submitted on 2014-04-18 05:27:56*

**Authors:** S. Bhattacharya, F. Smarandache, M. Khoshnevisan

**Comments:** 11 Pages.

In this paper we have proposed a semi-heuristic optimization algorithm for designing optimal plant layouts in process-focused manufacturing/service facilities. Our proposed algorithm marries the well-known CRAFT (Computerized Relative Allocation of Facilities Technique) with the Hungarian assignment algorithm. Being a semi-heuristic search, MASS
can be potentially more efficient in terms of CPU engagement time as it can converge on the global optimum faster than the traditional CRAFT,
which is a pure heuristic. We also present a numerical illustration of our proposed algorithm.

**Category:** General Mathematics

[81] **viXra:1404.0414 [pdf]**
*submitted on 2014-04-18 05:36:56*

**Authors:** Florentin Smarandache

**Comments:** 6 Pages.

Here, we show that: if the equation has an integer solution and a b is not a perfect square, then (1) has an infinitude of integer solutions; in this case we find a closed expression for (xn, yn ) , the
general positive integer solution, by an original method. More, we generalize it for any
Diophantine equation of second degree and with two unknowns.

**Category:** General Mathematics

[80] **viXra:1404.0413 [pdf]**
*submitted on 2014-04-18 05:38:21*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

Letter series problems occur in many American tests for measuring quantitative ability of supervisory personnel.They are more difficult than number-series used for measuring mathematical
ability because are unusual and complex.
According to the English alphabetic order:

**Category:** General Mathematics

[79] **viXra:1404.0411 [pdf]**
*submitted on 2014-04-18 05:45:57*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

In this note, the author answers this question using as reference F. Lazebnik & Y. Pilipenko’s E 3036 problem from A. M. M., Vol. 91, No. 2/1984, p. 140.An interesting property of functions admitting fixed points is obtained.

**Category:** General Mathematics

[78] **viXra:1404.0402 [pdf]**
*submitted on 2014-04-17 00:53:24*

**Authors:** V. Christianto, F. Smarandache

**Comments:** 3 Pages.

Fermat's "Last Theorem" asserts that if n > 2, the equation x^n + y^n = z^n cannot be solved in integers x, y, z, with xyz <> 0:

**Category:** General Mathematics

[77] **viXra:1404.0400 [pdf]**
*submitted on 2014-04-17 00:57:19*

**Authors:** Vic Christianto, Diego L. Rapoport, Florentin Smarandache

**Comments:** 5 Pages.

In recent years, there are attempts to describe quantization of planetary distance based on time-independent gravitational Schr¨odinger equation, including Rubcic & Rubcic’s method and also Nottale’s Scale Relativity method. Nonetheless, there is no solution yet for time-dependent gravitational Schr ¨odinger equation (TDGSE). In the present paper, a numerical solution of time-dependent gravitational Schrodinger equation is presented, apparently for the first time. This numerical solution leads to gravitational Bohr-radius, as expected. In the subsequent section, we also discuss plausible extension of this gravitational Schr¨odinger equation to include the effect
of phion condensate via Gross-Pitaevskii equation, as described recently by Moffat.
Alternatively one can consider this condensate from the viewpoint of Bogoliubov de Gennes
theory, which can be approximated with coupled time-independent gravitational Schr¨odinger equation. Further observation is of course recommended in order to refute or verify this proposition.

**Category:** General Mathematics

[76] **viXra:1404.0391 [pdf]**
*submitted on 2014-04-17 01:06:44*

**Authors:** Florentin Smarandache

**Comments:** 4 Pages.

Let's consider a tunnel getting from a side to the other side of the Earth, and passing through the
center of the Earth.

**Category:** General Mathematics

[75] **viXra:1404.0385 [pdf]**
*submitted on 2014-04-17 01:13:49*

**Authors:** Ion Patrascu, Florentin Smarandache

**Comments:** 4 Pages.

În cele ce urmează stabilim o legătură între noţiunea de simediană a unui triunghi şi noţiunea
de polară a unui punct în raport cu un cerc.

**Category:** General Mathematics

[74] **viXra:1404.0382 [pdf]**
*submitted on 2014-04-17 01:17:19*

**Authors:** Vic Christianto, Florentin Smarandache

**Comments:** 5 Pages.

Despite growing popularity for the use of biofuel and other similar methods to generate renewable energy sources from natural plantation in recent years, there is also growing concern over its disadvantage, i.e. that the energy use of edible plants may cause unwanted effects, because the
plantation price tends to increase following the oil price. Therefore an alternative solution to this problem is to find ‘natural plantation’ which have no direct link to ‘food chain’ (for basic foods, such as palm oil etc).

**Category:** General Mathematics

[73] **viXra:1404.0380 [pdf]**
*submitted on 2014-04-17 01:19:01*

**Authors:** Ion Patrascu, Florentin Smarandache

**Comments:** 5 Pages.

In this article we’ll present a new proof of Dergiades’ Theorem, and we’ll use this theorem
to prove that the orthological triangles with the same orthological center are homological triangles.

**Category:** General Mathematics

[72] **viXra:1404.0378 [pdf]**
*submitted on 2014-04-17 01:20:25*

**Authors:** Ion Patrascu, Florentin Smarandache

**Comments:** 5 Pages.

In this article we’ll present the properties of the radicale axes and the adjoin circles of a
triangle.

**Category:** General Mathematics

[71] **viXra:1404.0376 [pdf]**
*submitted on 2014-04-17 01:22:10*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

This article generalizes certain results on the nedianes (see [1], pp. 97-99). One calls nedianes the segments of a line that passes through a vertex of a triangle and partitions the opposite side in n equal parts.

**Category:** General Mathematics

[70] **viXra:1404.0374 [pdf]**
*submitted on 2014-04-17 01:23:55*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

There are many papers on this subject, but the author cites the papers which have influenced him, especially Klee’s papers. Let n be a counterexample to Carmichaël’s conjecture.

**Category:** General Mathematics

[69] **viXra:1404.0373 [pdf]**
*submitted on 2014-04-17 01:24:51*

**Authors:** Ion Patrascu, Florentin Smarandache

**Comments:** 4 Pages.

Proprietăţile prezentate în acest articol se referă la axele radicale şi la centrele radicale ale
cercurilor adjuncte unui triunghi.

**Category:** General Mathematics

[68] **viXra:1404.0356 [pdf]**
*submitted on 2014-04-17 01:44:45*

**Authors:** Vic Christianto, Florentin Smarandache

**Comments:** 4 Pages.

Asymmetrical information is referring to the case when one side of the market (seller or buyer) has information about the product that other side doesn’t. This information can be used by the knowledgeable side in its advantage.

**Category:** General Mathematics

[67] **viXra:1404.0355 [pdf]**
*submitted on 2014-04-17 01:45:43*

**Authors:** Florentin Smarandache, Vic Christianto

**Comments:** 5 Pages.

In the present article, we argue that it is possible to generalize Schr ¨odinger equation
to describe quantization of celestial systems. While this hypothesis has been described
by some authors, including Nottale, here we argue that such a macroquantization was formed by topological superfluid vortice. We also provide derivation of Schr¨odinger equation from Gross-Pitaevskii-Ginzburg equation, which supports this superfluid dynamics interpretation.

**Category:** General Mathematics

[66] **viXra:1404.0354 [pdf]**
*submitted on 2014-04-17 01:46:57*

**Authors:** Vic Christianto, Florentin Smarandache

**Comments:** 2 Pages.

In this article, we find out some analytical and numerical solutions to the problem of barrier tunneling for cluster deuterium, in particular using Langevin method to solve the time-independent Schr¨odinger equation.

**Category:** General Mathematics

[65] **viXra:1404.0342 [pdf]**
*submitted on 2014-04-17 02:08:42*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

In this short note we study the existence and number of solutions in the set of integers (Z) and in the set of natural numbers (N) of Diophantine equations.

**Category:** General Mathematics

[64] **viXra:1404.0340 [pdf]**
*submitted on 2014-04-17 02:10:52*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

In the High School Algebra manual for grade IX (1981), pp. 103-104, is presented a method for solving systems of two homogenous equations of second degree, with two unknowns. In this article we’ll present another method of solving them.

**Category:** General Mathematics

[63] **viXra:1404.0334 [pdf]**
*submitted on 2014-04-17 02:18:39*

**Authors:** Florentin Smarandache

**Comments:** 6 Pages.

The paper presents an initial explorations on T, I, F operations based on genetic concept
hierarchy and genetic referential hierarchy, as a novel proposal to the indeterminacy issue in
neutrosophic logic, in contrast to the T, I, F values inherited from conventional logics in which
those values would fail to demonstrate the genetic aspect of a concept and accordingly loose the
connection between generality and practicality.

**Category:** General Mathematics

[62] **viXra:1404.0327 [pdf]**
*submitted on 2014-04-17 02:27:11*

**Authors:** Florentin Smarandache

**Comments:** 5 Pages.

Did you ever question yourself what happens if the module m is not anymore prime?

**Category:** General Mathematics

[61] **viXra:1404.0320 [pdf]**
*submitted on 2014-04-17 02:35:04*

**Authors:** Florentin Smarandache

**Comments:** 3 Pages.

This short note presents some remarks and conjectures on two open problems proposed
by P. Erdös.

**Category:** General Mathematics

[60] **viXra:1404.0318 [pdf]**
*submitted on 2014-04-17 02:38:11*

**Authors:** Florentin Smarandache

**Comments:** 1 Page.

Ming Zhang, Ling Zhang, H. D. Cheng use a novel approach, i.e. neutrosophic logic which is a
generalization of fuzzy logic and especially of intuitionistic fuzzy logic, to image segmentation -
following one of the authors (H. D. Cheng) together with his co-author Y. Guo previous published paper on neutrosophic approach to image thresholding

**Category:** General Mathematics

[59] **viXra:1404.0317 [pdf]**
*submitted on 2014-04-17 02:39:14*

**Authors:** Florentin Smarandache

**Comments:** 1 Page.

In this short note we give a formula for the unification of a class of fusion rules
based on the conjunctive and/or disjunctive rule at the first step, and afterwards the
redistribution of the conflicting and/or non-conflicting mass to the non-empty sets at the
second step.

**Category:** General Mathematics

[58] **viXra:1404.0314 [pdf]**
*submitted on 2014-04-17 02:43:42*

**Authors:** Florentin Smarandache, Vic Christianto

**Comments:** 4 Pages.

Recently we’ve read that there is an excellent Cold Fusion experiment performed by Prof. Arata, showing that the promise of CF/LENR (Low Energy Nuclear Reaction) is rekindled.

**Category:** General Mathematics

[57] **viXra:1404.0300 [pdf]**
*submitted on 2014-04-16 06:52:17*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

НЕЙТРОСОФИЯ (neutrosophy, от фр. и латин. neuter, что значит «нейтральное» и греч. sophia, что значит «мудрость», «учение») – знание о нейтральный объектах. Н. является теорией, созданной как обобщение диалектики.

**Category:** General Mathematics

[56] **viXra:1404.0298 [pdf]**
*submitted on 2014-04-16 06:54:56*

**Authors:** Florentin Smarandache

**Comments:** 3 Pages.

Neutrosophic Transdisciplinarity means to find common features to uncommon entities, i.e., for
vague, imprecise, not-clear-boundary entity one has:

**Category:** General Mathematics

[55] **viXra:1404.0296 [pdf]**
*submitted on 2014-04-16 06:59:12*

**Authors:** V. Christianto, F. smarandache

**Comments:** 3 Pages.

In the preceding article we argue that biquaternionic extension of Klein-Gordon equation
has solution containing imaginary part, which diers appreciably from known solution of KGE. In the present article we discuss some possible interpretation of this imaginary part of the solution of biquaternionic KGE (BQKGE); thereafter we oer a new derivation of biquaternion Schrodinger equation using this method. Further observation is of course recommended in order to refute or verify this proposition.

**Category:** General Mathematics

[54] **viXra:1404.0295 [pdf]**
*submitted on 2014-04-16 07:01:06*

**Authors:** Florentin Smarandache

**Comments:** 3 Pages.

This article is an improved version of an old manuscript. This is a theoretical assumption about the possible existence of a new form of matter. Up to day the unmatter was not checked in the lab.

**Category:** General Mathematics

[53] **viXra:1404.0294 [pdf]**
*submitted on 2014-04-16 07:03:03*

**Authors:** Said Broumi, Pinaki Majumdar, Florentin Smarandache

**Comments:** 7 Pages.

In this paper, three new operations have been introduced on intuitionistic fuzzy soft sets. They are based on Second Zadeh‟s implication, conjunction and disjunction operations on intuitionistic fuzzy sets. Some examples of these operations were given and a few important properties were also studied.

**Category:** General Mathematics

[52] **viXra:1404.0292 [pdf]**
*submitted on 2014-04-16 07:06:51*

**Authors:** Said Broumi, Florentin Smarandache

**Comments:** 10 Pages.

Hesitancy is the most common problem in decision making, for which hesitant fuzzy set can be considered as a useful tool allowing several possible degrees of membership of an element to a set. Recently, another suitable means were defined by Zhiming Zhang [1], called interval valued intuitionistic hesitant fuzzy sets, dealing with uncertainty and vagueness, and which is more powerful than the hesitant fuzzy sets. In this paper, four new operations are introduced on interval-valued intuitionistic hesitant fuzzy sets and several important properties are also studied.

**Category:** General Mathematics

[51] **viXra:1404.0289 [pdf]**
*submitted on 2014-04-16 07:10:21*

**Authors:** Said Broumi, Florentin Smarandache, Mamoni Dhar, Pinaki Majumdar

**Comments:** 6 Pages.

In this paper, three new operations are introduced on intuitionistic fuzzy soft sets .They are based on concentration, dilatation and normalization of intuitionistic fuzzy sets. Some examples of these operations were given and a few important properties were also studied.

**Category:** General Mathematics

[50] **viXra:1404.0287 [pdf]**
*submitted on 2014-04-16 07:12:40*

**Authors:** Florentin Smarandache

**Comments:** 12 Pages.

In this paper we review nine previous proposed and solved problems of elementary 2D geometry [4] and [6], and we extend them either from triangles to polygons or polyhedrons, or from circles to spheres (from 2D-space to 3D-space), and make some comments, conjectures and open questions about them.

**Category:** General Mathematics

[49] **viXra:1404.0274 [pdf]**
*submitted on 2014-04-16 04:04:36*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

Theorem of Carnot: Let M be a point on the diagonal AC of an arbitrary quadrilateral ABCD.

**Category:** General Mathematics

[48] **viXra:1404.0272 [pdf]**
*submitted on 2014-04-16 04:10:11*

**Authors:** Florentin Smarandache

**Comments:** 4 Pages.

In these paragraphs one presents three generalizations of the famous theorem of Ceva, which states:

**Category:** General Mathematics

[47] **viXra:1404.0270 [pdf]**
*submitted on 2014-04-16 04:13:28*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

Er’s matrix method for computing Fibonacci numbers and their sums can be extended to the s-additive sequence:

**Category:** General Mathematics

[46] **viXra:1404.0267 [pdf]**
*submitted on 2014-04-16 04:16:06*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

After a passionate lecture of this book [1] (Mathematics plus literature!) I stopped
at one of the problems explained here:

**Category:** General Mathematics

[45] **viXra:1404.0266 [pdf]**
*submitted on 2014-04-16 04:17:24*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

One generalizes the inequality of Hödler thanks to a reasoning by recurrence. As particular cases, one obtains a generalization of the inequality of Cauchy-Buniakovski-Scwartz, and some interesting applications.

**Category:** General Mathematics

[44] **viXra:1404.0259 [pdf]**
*submitted on 2014-04-16 04:24:27*

**Authors:** Claudiu Coandă, C. Florentin Smarandache, Ion Pătrașcu

**Comments:** 5 Pages.

In this article we prove a theorem that will generalize the concurrence theorems that are
leading to the Franke’s point, Kariya’s point, and to other remarkable points from the triangle
geometry.

**Category:** General Mathematics

[43] **viXra:1404.0256 [pdf]**
*submitted on 2014-04-16 04:28:20*

**Authors:** Florentin Smarandache

**Comments:** 8 Pages.

Extension Theory (or Extenics) was developed by Professor Cai Wen in 1983 by publishing a paper called Extension Set and Non-Compatible Problems. Its goal is to solve contradictory problems and also nonconventional, nontraditional ideas
in many fields.

**Category:** General Mathematics

[42] **viXra:1404.0252 [pdf]**
*submitted on 2014-04-16 04:34:10*

**Authors:** V. Christianto, F. smarandache

**Comments:** 11 Pages.

Despite incomparable achievement of Quantum
Electrodynamics and its subsequent theories, there are some known limitations and unsolved theoretical problems until this time, including 'renormalization’ condition [1][2] and its
generalization to larger systems.

**Category:** General Mathematics

[41] **viXra:1404.0244 [pdf]**
*submitted on 2014-04-16 04:51:11*

**Authors:** Florentin Smarandache, Catalin Barbu

**Comments:** 6 Pages.

In this note, we present the hyperbolic Menelaus theorem in the Poincare disc of hyperbolic geometry.

**Category:** General Mathematics

[40] **viXra:1404.0242 [pdf]**
*submitted on 2014-04-16 04:53:05*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

The problems of cross words are composed, as we know, of grids and definitions. In the Romanian language one imposes the condition that the percentage of black boxes compared to the total number of boxes of the grid not to go over 15%.

**Category:** General Mathematics

[39] **viXra:1404.0234 [pdf]**
*submitted on 2014-04-16 05:07:47*

**Authors:** Florentin Smarandache

**Comments:** 8 Pages.

In this paper at the beginning, we make a short history of the logics, from the classical
Boolean logic to the most general logic of today neutrosophic logic. We define the general logic
space and give the definition of the neutrosophic logic. Then we introduce the indeterminate
models in information fusion, which are due either to the existence of some indeterminate
elements in the fusion space or to some indeterminate masses. The best approach for dealing with such models is the neutrosophic logic, which is part of neutrosophy. Neutrosophic logic is connected with neutrosophic set and neutrosophic probability and statistics.

**Category:** General Mathematics

[38] **viXra:1404.0233 [pdf]**
*submitted on 2014-04-16 05:09:11*

**Authors:** Florentin Smarandache

**Comments:** 4 Pages.

In this article we will prove some inequalities for the integer part function, and we’ll give some applications in the number theory.

**Category:** General Mathematics

[37] **viXra:1404.0231 [pdf]**
*submitted on 2014-04-16 05:12:21*

**Authors:** Florentin Smarandache

**Comments:** 12 Pages.

Definitions and Properties of the Integer Solution of a Linear System.

**Category:** General Mathematics

[36] **viXra:1404.0228 [pdf]**
*submitted on 2014-04-16 05:27:38*

**Authors:** V. Christianto, F. smarandache

**Comments:** 8 Pages.

It is known that quaternion number has wide application in theoretical physics and engineering fields alike, in particular to describe Maxwell electrodynamics. In the meantime, recently this quaternion number has
also been used to draw fractal graph. The present note is intended as an introduction to this very interesting study, i.e. to find linkage between quaternion/biquaternion number, quantum mechanical equation (Schrödinger equation) and fractal graph. Hopefully this note will be found useful for subsequent study.

**Category:** General Mathematics

[35] **viXra:1404.0221 [pdf]**
*submitted on 2014-04-16 05:40:02*

**Authors:** F. Smarandache, V. Christianto

**Comments:** 7 Pages.

It was known for quite long time that a quaternion space can be generalized to a Cliord space, and vice versa; but how to find its neat link with more convenient metric form in the General Relativity theory, has not been explored extensively.

**Category:** General Mathematics

[34] **viXra:1404.0220 [pdf]**
*submitted on 2014-04-16 05:41:14*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

A sequence of rational integers g is called a divisibility sequence if and only if...

**Category:** General Mathematics

[33] **viXra:1404.0217 [pdf]**
*submitted on 2014-04-16 05:44:43*

**Authors:** Florentin Smarandache

**Comments:** 6 Pages.

“The rebus’ language” is somewhere at the border of the scientific language and, that, perhaps, having many common things with usual language too, and even with the musical one (the puzzles, because they have a certain acoustic resonance).

**Category:** General Mathematics

[32] **viXra:1404.0215 [pdf]**
*submitted on 2014-04-16 06:04:24*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

Analyzing the deterioration’s degree of the keys of a typing machine which functioned for more than 40 years at the clerk's office of a court of a Rumanian district (Vâlcea), one partitions them in the following groups:

**Category:** General Mathematics

[31] **viXra:1404.0213 [pdf]**
*submitted on 2014-04-16 06:07:14*

**Authors:** Florentin Smarandache

**Comments:** 8 Pages.

“Mathematics is logical enough to be able to detect the internal logics of poetry and crazy enough not to lag behind the poetic ineffable” (Solomon Marcus).

**Category:** General Mathematics

[30] **viXra:1404.0211 [pdf]**
*submitted on 2014-04-16 06:09:51*

**Authors:** Florentin Smarandache

**Comments:** 16 Pages.

Archimedes’ “fixed point theorem”: Give me a fixed point in space, and I shall upset the Earth”.

**Category:** General Mathematics

[29] **viXra:1404.0210 [pdf]**
*submitted on 2014-04-16 06:13:10*

**Authors:** Florentin Smarandache

**Comments:** 10 Pages.

The aim of this paper is the investigation of some combinatorial aspects of written language, within the framework determined by the well-known game of crossword puzzles. Various types of probabilistic regularities appearing in such puzzles reveal some
hidden, not well-known restrictions operating in the field of natural languages. Most of
the restrictions of this type are similar in each natural language. Our direct concern will
be the Romanian language.

**Category:** General Mathematics

[28] **viXra:1404.0208 [pdf]**
*submitted on 2014-04-16 06:16:19*

**Authors:** Florentin Smarandache

**Comments:** 1 Page.

A great number of articles widen known results, and this is due to a simple procedure, of which it is good to say a few words.

**Category:** General Mathematics

[27] **viXra:1404.0207 [pdf]**
*submitted on 2014-04-16 06:17:42*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

Let’s consider a polynomial with integer coefficients, of degree m.

**Category:** General Mathematics

[26] **viXra:1404.0206 [pdf]**
*submitted on 2014-04-16 06:19:19*

**Authors:** Ion Patrascu, Florentin Smarandache

**Comments:** 4 Pages.

We suppose known the definitions of the isogonal cevian and isometric cevian; we remind that the anti-bisector, the anti-symmedian, and the anti-height are the isometrics of the
bisector, of the symmedian and of the height in a triangle.

**Category:** General Mathematics

[25] **viXra:1404.0201 [pdf]**
*submitted on 2014-04-16 06:27:10*

**Authors:** Victor Vladareanu, Gabriela Tont, Luige Vladareanu, Florentin Smarandache

**Comments:** 11 Pages.

The paper presents the navigation of mobile walking robot systems for movement in
non-stationary and non-structured environments. In the first approach are presented main
elements for the successful completion of intelligent navigation. The wireless sensor networks (WSN), dynamical stability control, strategies for dynamical control and a Bayesian approach of simultaneous localisation and mapping (SLAM) for avoiding obstacles and dynamical stability control for motion on rough terrain are studied.

**Category:** General Mathematics

[24] **viXra:1404.0199 [pdf]**
*submitted on 2014-04-16 06:31:32*

**Authors:** Florentin Smarandache

**Comments:** 4 Pages.

În aceasta lucrare este prezentata o noua
ramura a filosofiei, numita neutrosofie, care
studiaza originea, natura si scopul neutralita-
tilor, precum si interactiunile lor cu diferite
spectre de ideatic.

**Category:** General Mathematics

[23] **viXra:1404.0194 [pdf]**
*submitted on 2014-04-16 00:33:50*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

In this article one builds sets which have the following property: for any division in two subsets, at least one of these subsets contains at least three elements in arithmetic (or geometrical) progression.

**Category:** General Mathematics

[22] **viXra:1404.0192 [pdf]**
*submitted on 2014-04-16 00:38:11*

**Authors:** Florentin Smarandache

**Comments:** 3 Pages.

It is easy to deal with a Venn Diagram for 1 ≤ n ≤ 3 sets. When n gets larger, the picture becomes more complicated, that's why we thought at the following codification. That’s why we propose an easy and systematic algebraic way of dealing with the representation of intersections and unions of many sets.

**Category:** General Mathematics

[21] **viXra:1404.0191 [pdf]**
*submitted on 2014-04-16 00:39:22*

**Authors:** Florentin Smarandache

**Comments:** 9 Pages.

In this paper one proposes a simple algorithm of combining the fusion rules, those rules which first use the conjunctive rule and then the transfer of conflicting mass to the non-empty sets, in such a way that they gain the property of associativity and fulfill the Markovian requirement for dynamic fusion.

**Category:** General Mathematics

[20] **viXra:1404.0189 [pdf]**
*submitted on 2014-04-16 00:45:22*

**Authors:** Florentin Smarandache

**Comments:** 14 Pages.

Since no fusion theory neither rule fully satisfy all needed applications, the author proposes an algorithm for the Unification of Fusion Theories and a combination of fusion rules in solving problems/applications. For each particular application, one selects the most appropriate model, rule(s), and algorithm of implementation.
We are working in the unification of the fusion theories and rules, which looks like a cooking recipe, better we'd say like a logical chart for a computer programmer, but we don't see another method to comprise/unify all things.
The unification scenario presented herein, which is now in an incipient form, should periodically be updated incorporating new discoveries from the fusion and engineering research.

**Category:** General Mathematics

[19] **viXra:1404.0187 [pdf]**
*submitted on 2014-04-16 00:48:41*

**Authors:** Florentin Smarandache

**Comments:** 27 Pages.

In this paper we introduce a new procedure called α -Discounting Method for Multi-Criteria Decision Making (α-D MCDM), which is as an alternative and extension of Saaty’s Analytical Hierarchy Process (AHP). It works for any number of preferences that
can be transformed into a system of homogeneous linear equations. A degree of consistency (and implicitly a degree of inconsistency) of a decision-making problem are defined. α-D MCDM is generalized to a set of preferences that can be transformed into a system of linear and/or non-linear homogeneous and/or non-homogeneous equations and/or inequalities.
Many consistent, weak inconsistent, and strong inconsistent examples are given.

**Category:** General Mathematics

[18] **viXra:1404.0185 [pdf]**
*submitted on 2014-04-16 00:51:28*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

Paul Erdös has proposed the following problem:

**Category:** General Mathematics

[17] **viXra:1404.0184 [pdf]**
*submitted on 2014-04-16 00:52:38*

**Authors:** Florentin Smarandache

**Comments:** 7 Pages.

In this section is presented a new integer number algorithm for linear equation. This algorithm is more “rapid” than W. Sierpinski’s presented in [1] in the sense that it reaches the general solution after a smaller number of iterations. Its correctness will be thoroughly demonstrated.

**Category:** General Mathematics

[16] **viXra:1404.0182 [pdf]**
*submitted on 2014-04-16 00:55:03*

**Authors:** Florentin Smarandache

**Comments:** 3 Pages.

Let us consider a polygon A1,A2 ...An inserted in a circle.

**Category:** General Mathematics

[15] **viXra:1404.0172 [pdf]**
*submitted on 2014-04-16 01:23:42*

**Authors:** Florentin Smarandache

**Comments:** 3 Pages.

Carmichaël’s conjecture is the following: “the equation ϕ (x) = n cannot have a unique solution.

**Category:** General Mathematics

[14] **viXra:1404.0164 [pdf]**
*submitted on 2014-04-16 01:52:47*

**Authors:** Florentin Smarandache

**Comments:** 1 Page.

Let’s consider a, b integers ≥ 2 and k an integer such that a, c=1.

**Category:** General Mathematics

[13] **viXra:1404.0159 [pdf]**
*submitted on 2014-04-16 02:03:07*

**Authors:** Florentin Smarandache

**Comments:** 1 Page.

Inceputul secolului al 21-lea reflecta mai mult decat oricand ın istoria omenirii, rolul adanc,si significant al stiintei ¸si tehnologiei ın activitatile umane.

**Category:** General Mathematics

[12] **viXra:1404.0158 [pdf]**
*submitted on 2014-04-16 02:05:22*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

Le debut du 21eme siecle reflete, plus qu’aucun autre temps de l’histoire, la profondeur et l’importance de la science et la technologie dans les affaires humaines.

**Category:** General Mathematics

[11] **viXra:1404.0154 [pdf]**
*submitted on 2014-04-16 02:18:31*

**Authors:** C.Castro, F. Smarandache, V. Christianto

**Comments:** 8 Pages.

This proposal is intended to develop a free digital preprint service for physical sciences to enable scientists/physicists publishing their preprint articles prior to submitting for formal
publication in scientific journals, or perhaps they only want to see if their idea(s) received
proper response prior to submitting it to journal editors.

**Category:** General Mathematics

[10] **viXra:1404.0146 [pdf]**
*submitted on 2014-04-16 02:59:00*

**Authors:** Sukanto Bhattacharya, Florentin Smarandache

**Comments:** 10 Pages.

In this short, technical paper we have saught to derive under a posited formal model of political equilibrium.

**Category:** General Mathematics

[9] **viXra:1404.0145 [pdf]**
*submitted on 2014-04-16 02:59:51*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

Coming from Eastern Europe where, even under communism, the Dean and President were elected for a temporary period, I was surprised to see that in USA they are elected or appointed for permanent positions.

**Category:** General Mathematics

[8] **viXra:1404.0142 [pdf]**
*submitted on 2014-04-16 03:03:56*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

In one of his books (“Analysis…”) Mr. Paul Erdös proposed the following problem:

**Category:** General Mathematics

[7] **viXra:1404.0140 [pdf]**
*submitted on 2014-04-16 03:06:23*

**Authors:** Vic Christianto, Florentin Smarandache

**Comments:** 2 Pages.

In the present article we argue that it is possible to write down Schr¨odinger representation
of Navier-Stokes equation via Riccati equation. The proposed approach, while diers appreciably from other method such as what is proposed by R. M. Kiehn, has an advantage, i.e. it enables us extend further to quaternionic and biquaternionic version of Navier-Stokes equation, for instance via Kravchenko’s and Gibbon’s route. Further
observation is of course recommended in order to refute or verify this proposition

**Category:** General Mathematics

[6] **viXra:1404.0139 [pdf]**
*submitted on 2014-04-16 03:09:15*

**Authors:** Florentin Smarandache, Jean Dezert, Valeri Kroumov

**Comments:** 3 Pages.

In this paper we present several counter-examples
to the Conjunctive rule and to Dempster rule of combinations in information fusion.

**Category:** General Mathematics

[5] **viXra:1404.0137 [pdf]**
*submitted on 2014-04-16 03:13:23*

**Authors:** Victor VLADAREANU, Florentin SMARANDACHE, Luige VLADAREANU

**Comments:** 10 Pages.

The paper presents an advanced method for solving contradictory problems of hybrid position-force control of the movement of walking robots by applying a 2D Extension Set.

**Category:** General Mathematics

[4] **viXra:1404.0136 [pdf]**
*submitted on 2014-04-16 03:21:47*

**Authors:** Florentin SMARANDACHE

**Comments:** 7 Pages.

In this paper we extend Inagaki Weighted Operators Fusion Rule in information fusion by doing redistribution of not only the conflicting mass.

**Category:** General Mathematics

[3] **viXra:1404.0133 [pdf]**
*submitted on 2014-04-16 03:25:38*

**Authors:** V. Christianto, F. smarandache

**Comments:** 12 Pages.

We interpret ‘Sustainable construction’ theme in its widest possible meaning, i.e. the preservation
of sustainability of environment to support mankind. In this regard, it is realized that this Earth is likely to continue to deteriorate and therefore its capability to sustain mankind is diminishing.

**Category:** General Mathematics

[2] **viXra:1404.0129 [pdf]**
*submitted on 2014-04-16 03:51:02*

**Authors:** Florentin Smarandache

**Comments:** 1 Page.

Traveling to the past
Joe40, who is 40 years old, travels 10 years back to the past when he was 30 years old. He meets himself when he was 30 years old, let’s call this Joe30.
Joe40 kills Joe30.
If so, we mean if Joe died at age 30 (because Joe30 was killed), how could he live up to age 40?

**Category:** General Mathematics

[1] **viXra:1404.0128 [pdf]**
*submitted on 2014-04-16 03:52:30*

**Authors:** Ion Patrascu, Florentin Smarandache

**Comments:** 4 Pages.

In this article we’ll prove the Newton’s theorem relative to the circumscribed quadrilateral, we’ll transform it through duality, and we obtain another theorem which is true for an inscribable quadrilateral, which transformed through duality, we’ll obtain a theorem which is true for a circumscribable octagon.

**Category:** General Mathematics