Full Text Search Details
...ty, privacy, or moral rights may limit how you usethe material.Author: Choo, Yan Min.Title: H2 Mathematics Textbook.ISBN: 978-981-11-0383-4 (e-book).P... ... www.EconsPhDTutor.com The first thing to understand is that mathematics is an art. Paul Lockha... ...ideas. ... Beauty is the first test: there is no permanent place in the world for ugly mathematics. - G.H. Hardy (1940 [1967], A ... ...stead these resources,which are provided with the efficient Type #1 student in mind:• The H2 Mathematics CheatSheet, which contains all t... ... y ∈ C . . . . . . . . . . . 63 3.3 Real-Valued Functions of a Real Variable . . .... .... . . . . . . . . . . . . . . . . . . . . . 57059 Random Variables: Introduction ... ... 571 59.1 A Random Variable vs. Its Observed Valu... ... . . . . . . . . . . . 573 59.3 The Probability Distribution of a Random Variable ... ... . . . . . . . . . . . . . . . 574 59.4 Random Variables Are Simply Functions ...

Description Details
...arrant neither to a claim of comprehensiveness nor of context. It represents the beginning of an odyssey toward realization of the classical ideal in mathematics education at the doctoral level....

Full Text Search Details
...Sketch of a Doctoral Program in Classical Mathematics, With an Emphasis Upon Primary Sources ... ... Program Introductory Essay I am a mathematician and philosopher of mathematics with interests in classical puremathematics (especially the Arc... ...ed topics in formal epistemology. As a classical educator and professor of mathematics, myacademic trajectory has brought me into extensive contact wi... ...was dismayed when, in the course of my early academiccareer, I encountered mathematics courses taught as if to inculcate mere computation, as opposed ... ... career from 2009 to present has focused uponthe construction of classical mathematics courses at the undergraduate level. These courses haveincluded ... ...scartes, Kant, Poincare, Hardy 3c. Analysis and synthesis: function and variableArchimedes, Descartes, Newton, Locke, Whitehead3d. Symbols and form... ...e scope of mathematical inquiry3c. Analysis and synthesis: function and variable3d. Symbols and formulas: the attainment of generality 4. Mathemat... ...Descartes, Newton, Whitehead3d. Calculus: the measurement of irregular and variable motionsArchimedes, Kepler, Galileo, Pascal, Newton, Whitehead 3. ...

Description Details
...This book presents the fundamental scientific developments in mathematics, physics and astronomy from the Classic Greek Era to the present time. It discusses and illustrates the 2,000-year history in the development of the great ideas, concepts and laws that revolutionized our scient...

Full Text Search Details
... The Renaissance of Science The Story of the Atom Mathematics, Astronomy and PhysicsThe Magnificent Scientists and their Fab... ...ream and Journey into the Past, Present and FutureIn the World of the Atom, Mathematics, Astronomy and Physics Albert Martini, Ph.D.The Ren... ...am and Journey into the Past, Present and Future In the World of the Atom, Mathematics, Astronomy and Physics Albert Martini, Ph.D. ... ... RENE DESCARTES. III THE FOUNDERS OF MATHEMATICS, PHYSICS AND COSMOLOGY GALILEO GALILEI ... ... the branch of MATHEMATICS that uses CONSTANTS (usuallyNUMBERS) and VARIABLES or UNKNOWNS (usually LETTERS) to characterize theSTATIC and DYNA... ...terize theSTATIC and DYNAMIC properties of NUMERICAL RELATIONSHIPS. The VARIABLES may be regarded as DEPENDENT or INDEPENDENT. In the EQUATION... ...ded as DEPENDENT or INDEPENDENT. In the EQUATION: X = 2Y + 3 The VARIABLE X is the DEPENDENT VARIABLE. This means that the VALUEof X is DET... ...LE. This means that the VALUEof X is DETERMINED by the VALUE of Y. The VARIABLE Y is the INDEPENDENT VARIABLE. This means that theVALUE ... ...ith HEAT andTEMPERATURE and their relationships to ENERGY and WORK, and the VARIABLESof INTERNAL ENERGY, ENTROPY (or DEGREE OF DISORDER) and PRESSURE....

Description Details
...This book presents the fundamental scientific developments in mathematics, physics and astronomy from the Classic Greek Era to the present time. It discusses and illustrates the 2,000-year history in the development of the great ideas, concepts and laws that revolutionized our scient...

Table of Contents Details
...TABLE OF CONTENTS THE STORY OF THE ATOM MATHEMATICS, ASTRONOMY AND PHYSICS 1 INTRODUCTION 1 THE FOUR FUNDAMENTAL COMPONENTS OF OUR UNIVERSE 9 OUR MIND AND ITS ADVENTURE INTO THE WORLD OF KNOWLEDGE 12 MATTER - ENERGY - SPACE - TIME 14 WHAT IS MATTER ? 1...

Full Text Search Details
... The Renaissance of Science The Story of the Atom Mathematics, Astronomy and Physics1s The Magnificent Sc... ...ream and Journey into the Past, Present and Future In the World of the Atom, Mathematics, Astronomy and Physics Albert M... ...tastic Dream and Journey into the Past, Present and Future In the World of the Atom, Mathematics, Astronomy and Physics Albert Martini, Ph.... ...EATED AND THERE WAS MATTER, ENERGY, SPACE, TIME, AND THE FABULOUS SCIENCES OF MATHEMATICS, PHYSICS, CHEMISTRY AND BIOLOGYTHE ATOM IS THE ESSEN... ...LGEBRA is the branch of MATHEMATICS that uses CONSTANTS (usuallyNUMBERS) and VARIABLES or UNKNOWNS (usually LETTERS) to characterize theSTATI... ... to characterize theSTATIC and DYNAMIC properties of NUMERICAL RELATIONSHIPS. The VARIABLES may be regarded as DEPENDENT or INDEPENDENT. In th... ...y be regarded as DEPENDENT or INDEPENDENT. In the EQUATION: X = 2Y + 3 The VARIABLE X is the DEPENDENT VARIABLE. This means that the VALUEo... ...ENT VARIABLE. This means that the VALUEof X is DETERMINED by the VALUE of Y. The VARIABLE Y is the INDEPENDENT VARIABLE. This means that ... ...oncerned with HEAT andTEMPERATURE and their relationships to ENERGY and WORK, and the VARIABLESof INTERNAL ENERGY, ENTROPY (or DEGREE OF DISORDER) and...

Description Details
...This volum includes 37 papers of mathematics or applied mathematics written by the author alone or in collaboration with the following co-authors: Cătălin Barbu, Mihály Bencze, Octavian Cira, Marian Niţu, Ion Pătraşcu, Mircea E. Şelariu, Rajan Alex, Xingsen ...

Full Text Search Details
...s, V Florentin Smarandache Papers of Mathematics or Applied mathematics ... ... Collected Papers Vol. V Papers of Mathematics or Applied mathematics EuropaNova ... ...adutescu, University of Craiova, Craiova, RomaniaMumtaz Ali, Department of Mathematics, Quaid-i-Azam University, Islamabad, PakistanSiad Broumi, Facul... ...Florentin SmarandacheRatio Estimators in Simple Random Sampling when Study Variable is anAttribute 2... ... 303Florentin SmarandacheRecreational Mathematics: Puzzle Me! 3... ... stack is done with the vector that con- tains the number 229. The variable k has the initial value of 51 be- cause the index of the 229... ... in linear numerical eccen- tricity domain s 2 [ 1; 1], or of centric variable , which are continuous for any value of s. This means that s... ...tions (CE-SMF), because the eccentric derivative function of eccentric variable can express exactly this rectangular function (Figure 3 N top) o... ...e area near the origin. By the CE-SMF eccentric amplitude of eccentric variable (7) F ( ) = 1:57 aex[ ; S(0:6; 0)]; as shown ...

Description Details
...I have met the Smarandache's world for the first time about one year ago reading some articles and problems published in the Journal of Recreational Mathematics. From then on I discovered the interesting American Research Press web site dedicated to the Smarandache notions and held by Dr. Perez (address: http://www.gallup.unm.edu/~smarandache/), the Smarandache Notions Jo...

Full Text Search Details
...st time about one year ago reading somearticles and problems published in the Journal of Recreational Mathematics.From then on I discovered the intere... ...ndache papers" special collections at: theArizona State University (Tempe, USA), Archives of American Mathematics(University of Texas at Austin, USA),... ...universe is undoubtedly very fascinating and is halfway betweenthe number theory and the recreational mathematics. Even though sometime this universe ... ...randache notions and problems, Erhus Univ. Press, 1996[3] E. Weisstein, CRC Concise Encyclopedia of Mathematics, CRC Press, 1999[4] F. Smarandache, ... ...duct sequences, Smarandache Notions Journal, Nov. 1999[5] E. Weisstein, CRC Concise Encyclopedia of Mathematics, CRC Press, 1999[6] N. Sloane, Encyc... ...so 25/5/99 1030 ' ************************************** 1040 ' 1050 ' The sub return the value of variable PASS. 1060 ' If pass is equal to 1 the... ...st prime smaller than the previous one. On the contrary if thesum is smaller than n+r we increase the variable p to the next prime. This loopcontinues... ...next prime. This loopcontinues untill p is lower than q. If this is not the case then we increase the variable rto the next prime and we restart again... ...Russo 25/5/99 340 ' ************************************** 350 ' 360 ' The sub return the value of variable PASS. 370 ' If pass is equal to 1 then...

Full Text Search Details
...ue, generalmodel of utility that is independent of spatio-temporal and behavioral variables. The problem of utility is best illustrated by the probl... ...l wealth at time t = T, Z0 is the initial wealth attime t = 0, x is a random loss variable, I(x) is the indemnification function, C(x) is thecost of i... ...f solutions toconstrained optimization problems. Both economic and physical state variables come inintensive/extensive variable pairs and the one such... ...itive models, our approach is predominantly numerate andsubstantiated by rigorous mathematics rather than being merely normative or speculative. The... ...ispricings in the options market are somewhatunique as the only non-deterministic variable in option pricing theory is volatility.Moreover, given the ... ...ssments. While countless research papers have been written and published on the mathematicsof option pricing formulation, surprisingly little work h... ... 83(1). W0=0(2). Wt-Ws is a random variable that is normally distributed with mean 0 and variance t-s(3... ...S. Nash. Numerical Methods and Software. Prentice-Hall Series in Computational Mathematics, New Jersey: Prentice-Hall, 1989.Khoshnevisan, M., S. Bh... ...1978: 551-578.Lyuu, Yuh-Dauh. Financial Engineering and Computation – Principles, Mathematics, Algorithms. Cambridge University Press, U.K., 2002.M...

Full Text Search Details
...(Print) ISSN 2380-3517 (Online)Critical Review A Publication of Society for Mathematics of Uncertainty ... ... Volume XII, 2016 Editors: Paul P. Wang John N. Mordeson Mark J. Wierman Publisher: Center for Mathematics of Uncertainty Creig... ...ark J. Wierman Publisher: Center for Mathematics of Uncertainty Creighton University A Publication of Society for Mathematics of Uncertainty ... ... John N. Mordeson Mark J. Wierman Publisher: Center for Mathematics of Uncertainty ... ...to solve only problems where the number of posynomialterms of the objective function was one more than the number of variables,and the function was no... ... and reliable when they areapplied to a convex problem, and also avoid difficulties with derivativesingularities, as variables raised to fractional po... ...proach zero, since logsof such variables will approach −∞ , and large negative lower bounds shouldbe placed on those variables. ... ...sociated with dual-based algorithms.Li and Tsai (2005) proposed a technique for treating (positive, zero or negative)variables in SGP. Most existing m... ... Unconstrained Geometric ProgrammingDefinition 2.1Let 𝑋 be the set of all fuzzy neutrosophic variable vectors 𝑥 , 𝑖 = 1,2, …...

Full Text Search Details
...lements of the symmetric sequences for an arbitrary base, which is stored in the base1 variable. All elements will be sequentially constructed up to... ...t=new BigInteger("3");/* The elements will first be created as strings. The base1String variable will store the left side of the element and the base... ...his program will create the elements of the Mirror Sequence for the base stored in the variable base1. It will then determine if the number is prime.... ... 4 will generate the elements of the Natural Sequence for the basevalue assigned to the variable base1.Listing 4/* This program will compute the eleme... ...eger theLimit=new BigInteger(theInput.toString());// The BigInteger theIncrement is the variable that will by multiplied with the// accumulator.// The... ... Florentin Smarandache is truly a Renaissance man, having produced quality work in art, mathematics andliterature. This is my fifth book where I expan...

Full Text Search Details
...(Print) ISSN 2380-3517 (Online)Critical Review A Publication of Society for Mathematics of Uncertainty ... ... Volume XIII, 2016 Editors: Paul P. Wang John N. Mordeson Mark J. Wierman Publisher: Center for Mathematics of Uncertainty Creig... ... Center for Mathematics of Uncertainty Creighton University Critical ReviewA Publication of Society for Mathematics of Uncertainty ... ... John N. Mordeson Mark J. Wierman Publisher: Center for Mathematics of Uncertainty ... ...gineeringPratt School of EngineeringDuke UniversityDurham, NC 27708-0271ppw@ee.duke.eduJohn N. MordesonDepartment of MathematicsCreighton UniversityOm... ...riu [13] as a number of the form: u = xo +h1x1 + h2x2 + … + hn-1xn-1, (9)where n ≥ 2, and the variables x0, x1, x2, …,xn-1 are ...

Description Details
...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...

Full Text Search Details
... Linfan MAO Institute of Systems Science Academy of Mathematics and Systems Chinese Ac... ...vice) http://wwwlib.umi.com/bod/search/basicPeer Reviewers:F.Tian and X.D.Hu, Academy of Mathematics and Systems, Chinese Academy ofScience... ...s, Chinese Academy ofSciences, Beijing 100080, P.R.China.Y.P.Liu and R.X.Hao, Department of Applied Mathematics, Beijing Jiaotong Uni-versity, Beijing... ... Beijing 100044, P.R.China.S.Bhattacharya, Alaska Pacific University, AK, USA.H.Iseri, Department of Mathematics and Computer Information Science, Mans... ...raph cellularly embedded in asurface. As a linking of combinatorial configuration with the classical mathematics,it fascinates more and more mathematic... ...ions among g[Γ](x), r[Γ](x)eg[Γ](x) or G[Γ](x) are known, and vice via. Denote the variable vector (x1, x2, · · ·) by x, ...

Excerpt Details
...This dual will be studied in a separate paper (in preparation). 2. The additive analogues of the functions 5 and 5. are real variable functions, and have been defined and studied in paper [31. (See also one book [61, pp. 171-174). These functions have been recently further extended, by the use of Euler's gamma function, ill place of the factorial...

Full Text Search Details
... ISSN 1310 - 5132 NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS VOLUME 9 2003 NUMBER 2 CON... ... ANDON 15-TH SMARANDACHE'S PROBLEM 42-45K. Atanassov MATHEMATICSON THE SECOND SMARANDACHE'S PROBLEM ... ...Sandor Department of Mathematics, EDITORIAL BOARD ... ... 102 Lomb Memorial Drive, Rochester, New York 14623-5608, USAA. Bege Faculty of Mathematics, University of Cluj, Str. Koga... ... S{n) = min{rn EN: nlm!}, (1)H. Bustince Dept. of Mathematics and Informatics, Universidad Publica ... ... SOUTH KOREA 2. The additive analogues of the functions 5 and 5. are real variable functions, and ...

Description Details
...This book is inspired by a German theoretical physicist, Sabine Hossenfelder’s publication: “Lost in Mathematics”. Her book seems to question highly mathematical and a lot of abstraction in the development of physics and cosmology studies nowadays. There is clear tendency that in recent decades, the physics science has been ...

Full Text Search Details
... This book is inspired by a German theoretical physicist, in Mathematics Sabine Hossenfelder’s publication: “Lost in Mathematics”. Her... ...ecent decades, the physics science has been predominated by such an advanced mathematics, which at times sounding more like acrobatics approach to a r... ... & is not in superstring theories or other variations of such 26 in Mathematics dimensional bosonic string theory, of which none of those the... ... Indonesia Malang - East Java - Indonesia Lost and Found in Mathematics Dissident cosmologists’s guide to the Universe Victor C... ... 2u . t x x 2 (15)By introducing new variables and after straightforward calculations,we have the automata rul... ...f the time)of gravitational infinitesimals. Gravitational flux density is a variable depending on stellar,interstellar, and intergalactic events. A s... ... of plausiblemechanisms for such a matter-creation process, for instance VMH(variable mass hypothesis) of Narlikar & Arp, and later on C-field modelof... ...ely we can argue if such an entanglement can be explained by certain hidden variable theories or classical physics theories, one thing is certain th... ... im (12) For standard method of separation of variables to solve sphericalSE, see for example [11-13]. The ,  and T ...

Table of Contents Details
...Combinatorial Speculation and Combinatorial Conjecture for Mathematics BY LINFAN MAO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Structures of Cycle Bases with Some Extremal Properties BY HAN REN an...

Full Text Search Details
...logy; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combi-natorics to mathematics and theoretical physics; Mathem... ...rallel universes; Other applications of Smarandache multi-space and combinatorics. Generally, papers on mathematics with its applications not includ... ...infan Mao The Editor-in-Chief of International Journal of Mathematical Combinatorics Chinese Academy of Mathematics and System Science Beijing, 100... ...ffith University, AustraliaEditor-in-ChiefLinfan MAO Xueliang LiChinese Academy of Mathematics and System Nankai Univer... ...il: anchang@fzh.edu.cn Guiying YanJunliang Cai Chinese Academy of Mathematics and SystemBeijing Normal Univers... ...m, the support of τ ∗ω is τ −1(suppω), which is compact by that of suppω compact. By the usual change of variables formula, since τ ∗ω = (ω ◦ τ)(detτ... ...arly, the integral of n-forms on an n-manifoldis well-defined. Similar to Theorem 4.2 for the change of variables formula of integral in a combinato...

Full Text Search Details
... ISSN 2380-3517 (Online) Critical ReviewA Publication of Society for Mathematics of Uncertainty ... ... Paul P. Wang John N. Mordeson Mark J. Wierman Publisher Center for Mathematics of Uncertainty ... ...eeringPratt School of EngineeringDuke UniversityDurham, NC 27708-0271ppw@ee.duke.eduJohn N. MordesonDepartment of MathematicsCreighton UniversityOmaha... ...ly check that when each distribution from the classF corresponds to n independent, identically distributed random variables, thenthe arithmetic averag... ... θ(x Example. When the sample values are independent, identically distributed random variables, and the measurement error... ... Let us assume that the actual values x1, . . . , xn are independent identically distributed (i.i.d.) normal variables N(µ, σ2) for some unkn... ...esponds to i.i.d. normal distributions, and |xei − xi| ≤ Δi for all i with probability 1. In other words, the variables x1, . . . , xn are i.i.d. ... .... . + an aav = n . Thus, it is natural to define the expected value E[a] of an interval-valued random variable a = [a, a] component-wise, ... ...osophic Sets Said Broumi , 1 Hassan II University Mohammedia- Florentin Smarandache , 2 Department of Mathematics, Casablanca, Hay El Bara...

Full Text Search Details
...(Print) ISSN 2380-3517 (Online)Critical Review A Publication of Society for Mathematics of Uncertainty ... ...me X, 2015 Editors: Paul P. Wang John N. Mordeson Mark J. Wierman Florentin Smarandache Publisher: Center for Mathematics of Uncertainty Creig... ... Center for Mathematics of Uncertainty Creighton University Critical ReviewA Publication of Society for Mathematics of Uncertainty ... ... Mark J. Wierman Florentin Smarandache Publisher: Center for Mathematics of Uncertainty ... ...trosophic axiom schema:[1] Neutrosophic Axiom Scheme for Universal Instantiation.Let Φ(x) be a formula, depending on variable x defined on a domain D,... ...hic Axiomatic System[2] Neutrosophic Axiom Scheme for Existential Generalization.Let Φ(x) be a formula, depending on variable x defined on a domain D,... ...sophic Axiomatic SystemEven more, the neutrosophic component functions 𝑡, 𝑡, 𝑡 may depend, on thetop of these six variables, on hidden parameters a... ...� 𝐴 𝐴 ′ ′ ′and even more 𝑡 , 𝑡 , 𝑡 may depend, on the top of these three variables, ofhidden parameters as... ... chance to find optimalsolutions, hidden patterns and indeterminacies (possibilities) of causalrelationships between variables, which are common in ps...

Description Details
...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....

Full Text Search Details
...logy; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combi-natorics to mathematics and theoretical physics; Mathem... ...rallel universes; Other applications of Smarandache multi-space and combinatorics. Generally, papers on mathematics with its applications not includ... ...infan Mao The Editor-in-Chief of International Journal of Mathematical Combinatorics Chinese Academy of Mathematics and System Science Beijing, 100... ... Email: hiseri@mnsfld.eduEditor-in-ChiefLinfan MAO M.KhoshnevisanChinese Academy of Mathematics and System School of Accounti... ...u.edu.cnEmail: anchang@fzh.edu.cn Guiying YanJunliang Cai Chinese Academy of Mathematics and SystemBeijing Normal Univers... ...egular curve parameterized by time scales and the Jacobian matrix of -completely delta differentiable two variables function. Key Words: Pseudo-Eucli... .... Finally, we write Jacobian matrix and the -derivativemapping of the -completely delta differentiable two variables functions. So our intention is tou... ... (2 − 3) (t,s)→(t s→s Note that in (2 − 1) the function γ2 depends only on the variable s. Setting s = σ1(s0) in(2 − 2) yi... ...us define itand rephrase the conjecture in this setting. The Tutte polynomial T (G; x, y) of a graph G in variables x, y is T (G; x, y) = 1 if G hasno...

Full Text Search Details
...-k ]. * C 37 k=0With the change of variables r – k = w, we get k = 0, w = r and k = r, w = 0. 0 = (1/... ...e sum of the products. As an example, the following is achart for the four variables x , x , x , x . 1 2 3 4 Elementry symmetric func... ...e Smarandache StarFunction", SNJ, Vol.11, No. 1-2-3, 2000.6. Problem 2/31, Mathematics & Informatics Quarterly, 3/99 Volume 9, Sept' 99,Bulgaria.7. Am... ...7, page 240.12. Amarnath Murthy, “On The Infinitude of Prime Numbers”, The MathematicsEducation, India, Vol. XXIX, No. 1, March, 1995.13. Felice Russo...

Description Details
...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....

Full Text Search Details
...che multi-spaces to theoretical physics; Applications of Combi-natorics to mathematics and theoretical physics; Mathematical theory on gravitational ... ...ations of Smarandache multi-space and combinatorics. Generally, papers on mathematics with its applications not including in above topics arealso wel... ...of International Journal of Mathematical Combinatorics Chinese Academy of Mathematics and System Science Beijing, 100190, P.R.China Email: maolinfa... ...itor-in-ChiefLinfan MAO M.KhoshnevisanChinese Academy of Mathematics and System School of Accounting and Finance,Science, P.R.Chi... ... Guiying YanBeijing Normal University, P.R.China Chinese Academy of Mathematics and System Science, P.R.ChinaEmail: cai... ...ion of rooted loopless Eulerianplanar maps with vertex partition and other variables as parameters were investigated by Liu[5,6,7] too. From then on s... ... dynamical system. Iff is any continuous function, then the evolution of a variable x can be given by the formulaxn+1 = f(xn). This equation can also ... ...other words; a dynamic system is a set of equations specifying how certain variableschange over time. The equations specify how to determine (compute)...

Description Details
...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....

Full Text Search Details
...logy; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combi-natorics to mathematics and theoretical physics; Mathem... ...rallel universes; Other applications of Smarandache multi-space and combinatorics. Generally, papers on mathematics with its applications not includ... ...infan Mao The Editor-in-Chief of International Journal of Mathematical Combinatorics Chinese Academy of Mathematics and System Science Beijing, 100... ... Griffith University, AustraliaEditor-in-ChiefLinfan MAO Xueliang LiChinese Academy of Mathematics and System Nankai University,... ...u.edu.cnEmail: anchang@fzh.edu.cn Guiying YanJunliang Cai Chinese Academy of Mathematics and SystemBeijing Normal Univers... ... c) = 0. (11) ds σ ds τ τ Rs Using an exchange variable t = σds in (11), we easily hav... ...′ ′ σ2 H1 + σ ( σ ) H1 + H1 = 0. (21) Rs Using an exchange variable t = σds in (20), ...