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...erican Research Press Rehoboth 2002 József Sándor DEPARTMENT OF MATHEMATICS BABE Ş-BOLYAI UNIVERSITY 3400 CLUJ-NAPOCA, ROMANIA Geome... ...n its inexhaustible wealth, wherein it so greatly surpasses other parts of mathematics..." (K.F. Gauss, Disquisitiones arithmeticae, G ottingen, 1801... ...uable advice or support in the preparation of this material. These are the Mathematics Department of the Babe s-Bolyai University, the Domus Hun- gar... ...ntimate correlation between the Theory of numbers and other departments of Mathematics, not excluding geometry..." (Felix Klein, Evanston Colloquium L... ...sidered (see [1]) certain inequalities for such triangles. A basic result, applied by them is the following inequality of Emmerich (see [2]) R r p 2... ... 2 2(PA 2 1 +AA 2 1 ) =PB 2 +PC 2 2 a 2 4 AA 2 1 ; where we have applied the known formula for the median PA 1 . It is well known that: for ... ...bed circle of triangle A 1 B 1 C 1 , and the above proved relations may be applied. In fact, one can consider any circle which is concentrical with th... ...visible by (x + 1) 2 . In other words, the implication bja 2 ) b 2 ja 2 is applied. This implication is clearly false (e.g. 4j6 2 but 4 2 = 16- 6 2 , ... ...x 2 ( 0 (x)= ( x) x 1 ln ( x) 1) 2 0: 106 This method cannot be applied for the function f(x), because of 0 (x + 1)= ( x + 1) < 1=x (see ...

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... Ritter Smarandache Smith Welsh / / / / / / / / / / / / / Mathematics Mathematics Mathematics Astronomy Mathematics Mathemati... ...Mathematics Mathematics Mathematics Astronomy Mathematics Mathematics Mathematics Computer Science President Mathematics Mathematics Mathe... ...matics Computer Science President Mathematics Mathematics Mathematics Mathematics / / / / / / / / / / / / / Pima Community Colleg... ... perhaps it is only a contemporary myth. Such action is not built into the mathematics. 13 We strive here and now for understanding. We mus... ... 17 Why You Can't Exceed the Speed of Light Jim Malmberg Dept. of Mathematics and Engineering Pima Community College, East Campus 8181 E.... ...ent with equation (5) which gives 0.569 (The disagreement comes because we applied equation (5) to the 0.1c increment as one increment rather than ... ...author): “It appears that the only things the Smarandache hypothesis can be applied to are entities that do not have real mass or energy or informat... ...orentin, "There Is No Speed Barrier In The Universe", <Bulletin of Pure and Applied Sciences>, Delhi, India, Vol. 17D (Physics), No. 1, p. 61, 1998;... ...Wright, Jason, “Superluminals and the Speed of Light”, Bulletin of Pure and Applied Sciences, Delhi, India, Vol. 20, Series D (Physics), No. 2, 107-...

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...A combinatorial map is a connected topological graph cellularly embedded in a surface. As a linking of combinatorial configuration with the classical mathematics, it fascinates more and more mathematician’s interesting. Its function and role in mathematics are widely accepted by mathematicians today. On the last century, many works are concentrated on the combinatorial pro...

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...ress Rehoboth, NM 2005 Linfan MAO Institute of Systems Science Academy of Mathematics and Systems Chinese Academy of Sciences Beijing 100080, P.R.Chi... ...lib.umi.com/bod/search/basic Peer Reviewers: F.Tian and X.D.Hu, Academy of Mathematics and Systems, Chinese Academy of Sciences, Beijing 100080, P.R.C... ...of Sciences, Beijing 100080, P.R.China. Y.P.Liu and R.X.Hao, Department of Applied Mathematics, Beijing Jiaotong Uni- versity, Beijing 100044, P.R.Chi... ...ces, Beijing 100080, P.R.China. Y.P.Liu and R.X.Hao, Department of Applied Mathematics, Beijing Jiaotong Uni- versity, Beijing 100044, P.R.China. S.Bh... ... S.Bhattacharya, Alaska Pacific University, AK, USA. H.Iseri, Department of Mathematics and Computer Information Science, Mansfield University, Mansfield... ...S.ChimientiandM.Bencze, Smarandacheparadoxistgeometry,Bulletin of Pure and Applied Sciences, Delhi, India, Vol.17E, No.1(1998), 123-1124. [17] J.Edmon... ...ao and Y.P.Liu, Group action approach for enumerating maps on sur- faces,J.Applied Math. & Computing, vol.13, No.1-2,201-215. [47] L.F.Mao and Y.P.Liu... ...rationresearchinjournals. He was born in December 31,1962and got his BA in applied mathematics in Peking University in 1995 learnt by himself. In 2002... ...he automorphism groups of a Klein surface and a Smarandache manifold, also applied to the enumeration of unrooted mapsonorientableandnon-orientablesur...

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...ical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitational fields; Mathematical theory on parallel universes; Other applications of Smarandache multi-space and combinatorics....

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... on nature, which is also included in an ancient book of China, TAO TEH KING written by Lao Zi, an ancient philosopher of China. Then how it works to mathematics, not suspended in thought? This paper explains this action by mathematical logic on mathematical systems generalized to Smarandache systems, or such systems with combinatorial structures, i.e., combinatorial syste...

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...re acute logician than Mr. Locke, and yet he was not deeply skilled in the mathematics. This great man could never subject himself to the tedious fati... ...of Sir Isaac, because to do this the student must be deeply skilled in the mathematics, otherwise those works will be unintelligible to him. But notwi... ... in Holland, and Format in France, were the only men who understood it. He applied this geometrical and inventive genius to diop- trics, which, when t... ...deed small expense. Any man in England who declares himself a lover of the mathematics and natural philosophy, and expresses an inclination to be a me... ...lly found in those who devote themselves to that perti- nacious study, the mathematics. The Academy of Sciences is prudently confined to the study of ...

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...S....................................53 5. A Triple Inequality with Series and Improper Integrals, by Florentin Smarandache, in Bulletin of Pure and Applied Sciences, Vol. 25E, No. 1, 215-217, 2006.........54 6. Immediate Calculation of Some Poisson Type Integrals Using SuperMathematics Circular Ex-Centric Functions, by Florentin Smarandache & Mircea Eugen..................

Table of Contents Details
...S....................................53 5. A Triple Inequality with Series and Improper Integrals, by Florentin Smarandache, in Bulletin of Pure and Applied Sciences, Vol. 25E, No. 1, 215-217, 2006.........54 6. Immediate Calculation of Some Poisson Type Integrals Using SuperMathematics Circular Ex-Centric Functions, by Florentin Smarandache & Mircea Eugen..................