Table of Contents Details
...of New Planetoids in the Solar System and Quantization of Celestial System, by V. Christianto, F. Smarandache..................28 3. Open and Solved Elementary Questions in Astronomy, by Florentin Smarandache.. 36 BIOLOGY......................................40 4. Statistical Modeling of Primary Ewing Tumors of the Bone, by Sreepurna Malakar, Florentin Smarandache, Suka...

Table of Contents Details
...of New Planetoids in the Solar System and Quantization of Celestial System, by V. Christianto, F. Smarandache..................28 3. Open and Solved Elementary Questions in Astronomy, by Florentin Smarandache.. 36 BIOLOGY......................................40 4. Statistical Modeling of Primary Ewing Tumors of the Bone, by Sreepurna Malakar, Florentin Smarandache, Suka...

Description Details
...n, let (n) be the Euler function, and am(n) denotes the Smarandache m-th power residues function of n. The main purpose of this paper is using the elementary method to study the number of the solutions of the equation (n) = am(n), and give all solutions for this equation....

Full Text Search Details
...a m (n) both are multiplicative functions. In this paper, we shall use the elementary method to study the solutions of the equation involving these tw... ...aanxi,P.R.China yuanyi@mail.xjtu.edu.cn Abstract In this paper, we use the elementary methods to study the number of the solu tionsofanequationinvolv... ...gersn satisfying the equation φ 2 (n) = nJ(n). In this paper, we using the elementary methods to study the convergent properties of a new Dirichlet’s ... ...China zfxu@nwu.edu.cn Abstract The main purpose of this paper is using the elementary method to study the divisibilityofδ k (n)byϕ(n),andfindallthensuc... ...’an,Shaanxi,P.R.China Abstract The main purpose of this paper is using the elementary and analytic methods to study the mean value properties of the a... ...ar number, because there are close relations between these numbers and the geometry. Now for any positive integern, we definearithmeticalfunctionc(n)as...

Full Text Search Details
... 4. Lifetime Paradox: Long-lived matter particles are formed of short-lived elementary particles. 5. FTL Hypothesis: Quantum behavior implies instan... ...ure 1b.] S’ S a 1 θ r a 2 v Figure 1. GDT Projective and Elliptic Geometry Theorems a.) Right conic projection in G determining S’ ellipse... ... ,b 2 } are the corresponding minor axial radii as determined from elliptic geometry. We only require reference to one of the ellipse's two focal po... ... be heterogeneous with electron well loci determined by intranuclear proton geometry. It is obvious that proton charge repulsion, interior to a spher... ... (cubic) surface. Coupled with proton repulsion, the logical result of this geometry is eight proton potential wells, (octet sites) with lowest pot... ...applies to ϒ in regard to spatial curvature and spatial surface tension. At elementary particle/quanta levels, and given proper conditions, this pri... ...ter, which is under the 'determinist principle', is formed by a totality of elementary particles, which are under Heisenberg's 'indeterminacy princip... ...tivity, a fundamental assumption in the scientific method. Indeterminacy in elementary particles refers to our limits of resolution, in regards to m... ...eory. 5.3 Unstable Paradox (SQP-3): Stable matter is formed of unstable elementary particles (elementary particles decay when free). The parad...

Full Text Search Details
...ctiveness. Concerning all acts of initiative (and creation), there is one elementary truth the ignorance of which kills countless ideas and splendid... ...d Game, the Dymaxion Airocean World Map, his develop, ment of Synergetic Geometry and his most famous invention, the Geodesic Dome. I was stationed...

Description Details
...nd theories, especially if they run counter to the classical ones.” In a manner consistent with his unique point of view, he defined several types of geometry that are purposefully not Euclidean and that focus on structures that the rest of us can use to enhance our understanding of geometry in general....

Full Text Search Details
... a manner consistent with his unique point of view, he defined several types of geometry that are purposefully not Euclidean and that focus on struc... ... focus on structures that the rest of us can use to enhance our understanding of geometry in general. To most of us, Euclidean geometry seems self... ... and continued with Riemann, when they found counterexamples to the notion that geometry is precisely Euclidean geometry. This opened a whole univer... ...sely Euclidean geometry. This opened a whole universe of possibilities for what geometry could be, and many years later, Smarandache’s imagination h... ...rs later, Smarandache’s imagination has wandered off into this universe. The geometry associated with Gauss, Bolyai, and Lobachevski is now genera... ... New York: Dover Publications, Inc. 5. Boyce, W.E. and DiPrima, R.C. (1992). Elementary Differential Equations and Boundary Value Problems (5 th ...

Description Details
...This book contains short notes or articles, as well as studies on several topics of Geometry and Number theory. The material is divided into ve chapters: Geometric theorems; Diophantine equations; Arithmetic functions; Divisibility properties of numbers and functions; and Some irrationality results. Chapter ...

Full Text Search Details
... contains short notes or articles, as well as studies on several topics of Geometry and Number theory. The material is divided into ve chapters: Geom... ...mes have an arithmetic character (as 9-12) on number theoretic problems in Geometry. Chapter 2 includes various diophantine equations, some of which a... ...r 2 includes various diophantine equations, some of which are treatable by elementary meth- ods; others are partial solutions of certain unsolved prob... .... . . . . . . . . . . . . . . . . . . . . 27 9 On certain constants in the geometry of equilateral triangle . . . . . . . . . 35 10 The area of a Pyth... .... . . . . . . . . . . . . . . . . . . . . . 42 12 An arithmetic problem in geometry . . . . . . . . . . . . . . . . . . . . . . 53 Chapter 2. Diophant... ...For questions of priority (which is very di cult to decide in this eld of Elementary Geometry - Algebra - Analysis) we note that (1) appears in [R. S... ... this is impossible, by assumption. Certain direct results follow from the elementary connections existing between the elements of a triangle. For exa... ...K. H artig, J. Sur anyi, Combinatorial and geometrical investigations in elementary number theory, Periodica Mat. Hunarica 6(3)(1975), 235-240. 3. J... ...a = m, b = n, c =m +p, d =n +q). For other connections of this equation to Elementary Number Theory, see [3]. Bibliography 1. G.H. Hardy and E.M. Wrig...

Excerpt Details
...In a lecture that Einstein gave to the Prussian Academy of Sciences in 1921, he said the following: "Geometry predicates nothing about relations of real things, but only geometry together with the purport of physical laws can do so... The idea of the measuring rod and the idea of the clock contained with it in the theory of ...

Full Text Search Details
...n gave to the Prussian Academy of Sciences in 1921, he said the following: "Geometry predicates nothing about relations of real things, but only ge... ...ther, is not invariant ∗ Any space of Riemannian geometry has the strictly non-degenerated metric by definition of such me... ... 2 ≠ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = = c c U U g U U k i ik k i so that looking Riemannian geometry for a regular observer, the real geometry of zero-space within ... ...nsolved Problems, Conjectures, and Theorems in Number Theory and 41 Geometry", edited by M. L. Perez, 86 p., Xiquan Publishing House, Phoeni... ...g simply use logically inconsistent language. Namely, one cannot introduce geometry into a probability theory, because a probability theory has the ... ...ies. 10. Dark material of galaxies and other systems. This list contains elementary, fundamental physical systems that go without adequate descri... ...ometric shapes. These new ideas can account for many properties of what are elementary physical systems which the currently accepted paradigm cannot... ... series RLC circuit (resistance, R, inductance, L, and capacitance, C) (see elementary physics text). The energy generating oscillating space-for... ...nce, R, inductance, L, and capacitance, C) circuit's natural frequency (see elementary physics text). This could be accommodated by a choice of circ...

Description Details
..., Mohar and Thomassen [53] and White [70], especially the [53] for detail. The construction of regular maps on surfaces, related maps with groups and geometry is a glimmer of the map theory with other mathematics....

Full Text Search Details
...The construction of regular maps on surfaces, related maps with groups and geometry is a glimmer of the map theory with other mathematics. In fact, ma... ...zation or making combinatorial refinement for the Riemann surfaces, Riemann geometry and finally, the Smarandache geometries by maps is a very interesti... ...aces and s-manifolds in this book. Although the results obtained are quite elementary, it is still valuable probe by researchers, especially, thoseofm... ...entable surfaces are enumerated in this chapter. The last section gives an elementary classification for the closed s-manifolds by maps. Thelastchapter... ...ntribution of combinatorics to classical mathematics, such as, the Riemann geometry and Smarandache geometries is realized. Those are the wish of mine... ...able, 2−g(S)−k(S). if Sis non−orientable. 1.1.2 Definition of a Smarandache geometry By the history, we know that classical geometries include the Eucl... ... that classical geometries include the Euclid geom- etry, the hyperbolical geometry and the Riemann’s geometry. Each of the later two is proposed by d... ..., Science Publisher Press, Beijing, 1999. [72] H.X.Wu, C.L.Shen and Y.L.Yu,Elementary Riemann Geometry, Peking Uni- versity Press, 1989. [73] M.Y.Xu,I... ...lying a graph on orientable and non-orientable surfaces are discovered. An elementary classification for the closed s-manifolds is found. Open problems...

Description Details
...ughout the history, starting from the Near East Bronze Age until our days. The reader is expected to be familiar with basics of the Flower of Life geometry. Elementary knowledge of the ancient Near East history and history of mathematics is helpful. Knowledge of visual arts, geometry, and comparative religion studies are also useful. I hope that my independent resear...

Description Details
...inal research papers and survey articles in all aspects of Smarandachemulti-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces...

Excerpt Details
... generating the group or hsgg in short. In this paper we prove some results on hsggs of a group. Order class of a group are special halfsubgroupoids. Elementary abelian groups are characterized as groups with maximum special halfsubgroupoids. Order class of a group with unity forms a typical halfsubgroup. Key words: halfsubgroup, hsgg, order class of an element. AMS(20...

Description Details
...nal research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces,...

Excerpt Details
...was first intiated by Vasantha Kandasamy. The objective of this paper is to present the concept of bicoset of a bivector space and obtain some of its elementary properties. Key Words: bigroup, bivector space, bicoset, bisum, direct bisum, inner biproduct space, biprojection. ...

Description Details
... the usage of the symbol roughly from 1600 BC to 1600 AD. The reader of this document is expected to be familiar with basics of the Flower of Life geometry1. Elementary knowledge of the ancient Near East history and history of mathematics is helpful. Knowledge of visual arts, geometry, and comparative religion studies are also useful. I hope my independent research p...

Description Details
...nal research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces,...

Table of Contents Details
... . . . . . . . . . . 20 Supermagic Coverings of Some Simple Graphs BY P.JEYANTHI AND P.SELVAGOPAL . . . . . . . . . . . . . . . . . . . . . . . 33 Elementary Abelian Regular Coverings of Cube BY FURONG WANG AND LIN ZHANG. . . . . . . . . . . . . . . . . . . . . .49 Super Fibonacci Graceful Labeling of Some Special Class of Graphs BY R.SRIDEVI, S.NAVANEETHAKRISHNAN AN...

Table of Contents Details
...Contents Preface 5 Foreword 6 1 Unsolved Problems in Theoretical Physics 8 1.1. Problems related to elementary particles 8 1.2. Problems related to Unmatter 11 1.3 Some unresolved problems, questions and applications of the Brightsen nucleon cluster model 21 2 Unsolved Problems in Mathematics 24 2.1. Maximum number of...

Table of Contents Details
...ce-Time concept – M. Pitkanen 44 3. Prediction and calculation of New Energy development – Fu Yuhua 111 4. Some unsolved problems in the physics of elementary particle – V. Christianto & F. Smarandache (PiP, vol. 3 no. 4, 2007) 127 5. About some unsolved problems in physics – M. Pitkanen 132 Beyond Standard Model, Unmatter and Yang-Mills Field 6. Bifurcations and patt...

Full Text Search Details
...n, but which is not completely proven as a paradox. We present herein four elementary quantum quasi-paradoxes and their corresponding quantum Sorites ... ... some degree under the “determinist principle”, is formed by a totality of elementary particles, which are under Heisenberg’s “indeterminacy principle... ...le”. 2.3.1 Unstable Quasi-Paradox: “Stable” matter is formed by “unstable” elementary particles (elementary parti- cles decay when free). 2.3.2 Unstab... ...N PHYSICS April, 2005 living” matter is formed by very “short-time-living” elementary particles. 2.4.2 Short-Time-Living Sorites Paradox: Similarly, t... ...lved and Unsolved Problems, Conjectures, and Theorems in Number Theory and Geometry (edited by M. L. Perez), Xiquan Pub- lishing House, Phoenix, 2000.... ...itional potential energy which manifests the fractal and nondifferentiable geometry. 2 Non relativistic quantum mechanics 2.1 Quantum potential In the... ...established as a mere manifestation of the nondifferen- tiable and fractal geometry instead of being deduced from a postulated Schr¨ odinger equation.... ...e energy- momentum tensor, one solves the Einstein feld (i. e. space- time geometry) equations for the metric potentials, then one writes the geodesic... ...riable force is given bymg(τ) and the maximal proper force sustained by an elementary particle of massm P (a Planckton) is assumed to be F max =m Plan...

Full Text Search Details
...United States of America JULY 2005 VOLUME 2 CONTENTS S. J. Crothers On the Geometry of the General Solution for the Vacuum Field of the Point-Mass. . ... ...ed from private donations. July, 2005 PROGRESS IN PHYSICS Volume 2 On the Geometry of the General Solution for the Vacuum Field of the Point-Mass Ste... ...wing unjustifed assumptions, ta- citly or otherwise; S J. Crothers. On the Geometry of the General Solution for the Vacuum Field of the Point-Mass 3 ... ...ired by Einstein’s theory. Mere assumption is not permissible. 2 The basic geometry of the simple point-mass The usual metric g s of the spacetime man... ...cuum Field of the Point-Mass July, 2005 PROGRESS IN PHYSICS Volume 2 this elementary geometrical fact. Consequently, they have managed to attribute t... ...le spatial indices are Latin . As it is well-known [1], dS=m 0 cds is an elementary action to displace a free mass-bearing particle of rest-mass m 0... ...ng the spur of the deformation rate tensor, is the rate of expansion of an elementary volume. Actually, the obtained Lorentz condition (48) implies th... ...Actually, the obtained Lorentz condition (48) implies that the value of an elementary volume flled with a time density feld remains unchanged under it... ...without sources According to §27 of The Classical Theory of Fields [1], an elementary action for a whole system consisting of an electromagnetic feld ...

Full Text Search Details
...literary critics who did not pass through mathematics could not detect but an elementary and heavy scientific vocabulary (G.Calinescu, 15 Istoria... ...stem of symbols that make cognoscible the world of spirit through a superior geometry....But the postulate proposed is not also demonstrated 3) . Th... ...some of them essentially. Thus, at Ion Barbu, the mathematics, especially the geometry, began to join ,at a moment, the art thinking, particularly t... ... he discovered that in a high and bright place the mathematics (especially the geometry) meets the poetry, that the abstract god of the world’s orde... ...cian of the mathematics and only in the measure in what his poetry reminds of geometry” 10) , Smarandache will remain faithfully perhaps all his life... ... from the loxodromic siege/ had pull out the hart invertor / and in a Riemann geometry / had put the Brocard’s point”. Through the absurd of the sit...

Full Text Search Details
...trix representation of the system of linear biequations. Now we can define elementary row operations on the bimatrix AX = Y i.e., A 1 X 1 ∪ A 2 ... ...of operations they can be carried out in the following ways. (1) Uniform elementary row operations means the operations is done similarly on both... ... the operations is done similarly on both the matrices A 1 ∪ A 2 . Type I elementary operations mean only elementary row operations on A 1 and Ty... ...ementary operations mean only elementary row operations on A 1 and Type II elementary operations mean only elementary row operations on A 2 . 9... ... row biequivalent to A if B can be obtained from A by a finite sequence of elementary row operations. Let A = A 1 ∪ A 2 be a bimatrix A is cal... ... Princeton, 1960. 20. KOSTRIKIN, A.I, and MANIN, Y. I., Linear Algebra and Geometry, Gordon and Breach Science Publishers, 1989. 21. LANG, S., Alg... ...bus. In mathematics his research papers are in number theory, non-Euclidean geometry, synthetic geometry, algebraic structures, statistics, and mult...