Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original 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,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical 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 gravitatio...

x4: Radio labeling of P3n for n is less than or equal to 5 or n = 7 In this section we determine radio numbers of cube path of small order as a special case....

The Hale Kuamoo–Hawaiian Language Center supports and encourages expansion of Hawaiian language as the medium of education, business, government, and other contexts of social life in Hawaii. The Center provides professional and material resources necessary to address this goal including educational support in the development of curriculum materials for Hawaiian medium education, teacher training, Na Maka O Kana Hawaiian language newspaper, and the Mamaka Kaiao dictionary of contemporary Hawaiian terms....

He Alii nui o Lonoikamakahiki no ka mokupuni o Hawaii ma hope iho o ko Keawenuiaumi make ana; he kanaonokumamaha hanauna maia Wakea mai. O Keawenuiaumi kona makua kane, a o Kaihalawai kona makuahine; ma Napoopoo kona wahi i hanau ai, a ma laila no o ia i hanai ia ai a nui, e kona mau kahu, e Hauna laua me Loli, a me ka laua wahine o Kohenemonemo. I ko Lonoikamakahiki wa opiopio, oiai ua hoomaka ae kona noonoo ana, i ia manawa nana aela o Lonoikamakahiki, e kau ana na mea lealea a kona makua kane he nui ma loko o ka hale alii. Ike aela o ia e kau ana na ihe pahee. Nana loihi aela o ia, a liuliu, a laila, ninau akula o ia i kona mau kahu: “He aha keia mau mea loloa e kau nei i luna o ka hale”...

Kona Ao ia ana i ka Wa Opiopio. 1 -- Ko Lonoikamakahiki Imi ana i na Hana Oi o ka Waiwai. 6 -- Ka Ili Mua ana o ka Aina ia Lonoikamakahiki. 10 -- Ka Holo ana o Lonoikamakahiki i Oahu; Ko Ohaikawiliula Hiki ana mai; Ko Lonoikamakahiki Hoopaa ana me Kakuhihewa. 13 -- Ka Pili Ana O Kakuhihewa Me Lonoikamakahiki. 7 -- Ka Hoopapa Alua ana, Akolu, Aha, a me ka Lima, a me ka Hiki ana mai o Kaikilani. 6 -- Ka Hoopapa hou ana o Kakuhihewa me Lonoikamakahiki no Hauna. 41 -- Ka Hoike ana a Lonoikamakahiki i ka Iwi o na Alii i Make ia Keawenuiaumi. 45 -- Na Hoouka Kaua a Lonoikamakahiki. 52 -- Ka Hee ana o Kanaloakuakawaiea me na Kipi; Ka Lanakila ana o Lonoikamakahiki. 55 -- Ka Holo ana o Lonoikamakahiki i Maui e Ike me Kamalalawalu. 58 -- Ka Hoi ana o Kauhipaewa a me Kihapaewa i Hawaii; Ka Holo ana o Kamalalawalu i Hawaii. 63 -- Ka Hoouka Kaua ana ma Waimea; Ka Lanakila ana o Lonoikamakahiki; Auhee o Kamalalawalu me Kona Make ana. . 68 -- Ka Hooponopono Hou ana o Lonoikamakahiki i ke Aupuni; Kona Holo ana i Kauai; Haalele ia o Lonoikamakahiki e ka Lehulehu. 74 -- Hoonoho ia o Kapaihiahilina i Kuhina Nui; Ka Imihala ia ana; Kana Mele Aloha. 77...

Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original 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,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical 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 gravitatio...

Contents Tangent Space and Derivative Mapping on Time Scale BY EMIN ¨OZYILMAZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 01 Basic Properties Of Second Smarandache Bol Loops BY T.G.JA´IY´E O. L´A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11 Smarandachely Precontinuous maps and Preopen Sets in Topological Vector Spaces BY SAYED ELAGAN. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Path Double Covering Number of Product Graphs BY A. NAGARAJAN, V. MAHESWARI, S. NAVANEETHAKRISHNAN. . . . . . 27 Some Remarks on Fuzzy N-Normed Spaces BY SAYED ELAGAN. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 σ-Coloring of the Monohedral Tiling BY M. E. BASHER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 The Forcing Domination Number of Hamiltonian Cubic Graphs BY H.ABDOLLAHZADEH AHANGAR AND PUSHPALATHA L. . . . . . . . . . 53 Permutation Polynomials modulo n, n 6= 2w and Latin Squares BY VADIRAJA BHATTA G. R. and SHANKAR B. R. . . . . . . . . . . . . . . . . 58 Graphoidal Tree d - Cover BY S.SOMASUNDARAM, A.NAGARAJAN AND G.MA...

This book aims to assist social scientists to analyze their problems using fuzzy models. The basic and essential fuzzy matrix theory is given. The book does not promise to give the complete properties of basic fuzzy theory or basic fuzzy matrices. Instead, the authors have only tried to give those essential basically needed to develop the fuzzy model. The authors do not present elaborate mathematical theories to work with fuzzy matrices; instead they have given only the needed properties by way of examples. The authors feel that the book should mainly help social scientists who are interested in finding out ways to emancipate the society. Everything is kept at the simplest level and even difficult definitions have been omitted. Another main feature of this book is the description of each fuzzy model using examples from real-world problems. Further, this book gives lots of references so that the interested reader can make use of them. This book has two chapters. In Chapter One, basic concepts about fuzzy matrices are introduced. Basic notions of matrices are given in section one in order to make the book self contained. Section two g...

Preface 4 Dedication 6 Chapter One BASIC MATRIX THEORY AND FUZZY MATRIX THEORY 7 1.1 Basic Matrix Theory 7 1.2 Basic Concepts on Fuzzy Matrices 33 1.3 Basic Concepts on Graphs 47 Chapter Two DESCRIPTION OF SIMPLE FUZZY MODELS AND THEIR APPLICATIONS TO REAL WORLD PROBLEMS 71 2.1 Description of Simple Fuzzy Matrix Model 72 2.2 Definition of Fuzzy Cognitive Maps with real world model representation 146 2.3 Definition and Illustration of Fuzzy Relational Maps 205 2.4 Introduction to Bidirectional Associative Memories (BAM) Model and their Application 238 2.5 Description of Fuzzy Associative Memories (FAM) model and their illustrations 264 2.6 Fuzzy Relational Equations (FRE) and their application 277 REFERENCE 317 INDEX 345 ABOUT THE AUTHORS 352...

Progress in Physics has been created for publications on advanced studies in theoretical and experimental physics, including related themes from mathematics. All submitted papers should be professional, in good English, containing a brief review of a problem and obtained results. All submissions should be designed in LATEX format using Progress in Physics template. This template can be downloaded from Progress in Physics home page http://www.geocities.com/ptep_online. Abstract and the necessary information about author(s) should be included into the papers. To submit a paper, mail the file(s) to Chief Editor. All submitted papers should be as brief as possible. Short articles are preferable. All that has been accepted for the online issue of Progress in Physics is printed in the paper version of the journal. To order printed issues, contact Chief Editor. This journal is non-commercial, academic edition. It is printed from private donations....

According to the Dictionary of Mathematics (Borowski and Borwein, 1991 [1]), the paradox is “an apparently absurd or self-contradictory statement for which there is prima facie support, or an explicit contradiction derived from apparently unexceptionable premises”....

Backgammon is one of the oldest board games for two players. The playing pieces are moved according to the roll of dice, and a player wins by removing all of his pieces from the board before his opponent. Backgammon is a member of the tables family, one of the oldest classes of board games in the world. Although luck is one of the determining factors in the outcome, strategy plays a more important role in the long run.[1] With each roll of the dice, players must choose from numerous options for moving their checkers and anticipate possible counter-moves by the opponent. In variants that originate from early 20th century New York, players may raise the stakes during the game. There is an established repertoire of common tactics and occurrences. Like chess, backgammon has been studied with great interest by computer scientists. Owing to this research, backgammon software has been developed capable of beating world-class human players. ...

ELT teachers' personal philosophy statements and reflections on the issue of classroom discipline.

Teaching or imposing discipline? A teacher's dilemma.

Contents Introduction page 1 Enhancing student self-discipline through a process of promoting positive achievement and behaviour by Eleni Aliataki 3 “Stir and Settle”: the key points for a successful classroom by Eleni Chatziandreou 13 Classroom management: mix and match and be prepared to adjust by Ioanna Chioni 18 Teaching: a mission never accomplished? by Dimitra Chioti 25 The art of classroom discipline: tricks and tips for teachers by Dimitra Dalpanagioti 30 The Holy Grail of classroom management by Marika Dimitriadou 35 Teaching or imposing discipline? a teacher’s dilemma by Zacharenia Dimitriadou 46 My personal philosophy statement on classroom management by Maria Koukourikou 51 Does a teacher possess the power to make a child’s life miserable or joyous? by Chryssoula Lazou 58 Keep calm, be aware and teach on! by Sophia Petridou 67 Abbreviations 73 ...

Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original 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,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical 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 gravitatio...

On (∈ vq)-Fuzzy Bigroup Abstract: In this paper, we introduce the concept of fuzzy singleton to bigroup, and uses it to define (∈ v q)- fuzzy bigroup and discuss its properties. We investigate whether or not the fuzzy point of a bigroup will belong to or quasi coincident with its fuzzy set if the constituent fuzzy points of the constituting subgroups both belong to or quasi coincident with their respective fuzzy sets, and vise versa. We also prove that a fuzzy bisubset μ is an (∈ vq)-fuzzy subbigroup of the bigroup G if its constituent fuzzy subsets are (∈ vq)-fuzzy subgroups of their respective subgroups among others. Key Words: Bigroups, fuzzy bigroups, fuzzy singleton on bigroup, (∈ vq)- fuzzy subgroups, (∈ vq)- fuzzy bigroup ...

Contents On (∈ vq)- Fuzzy Bigroup BY AKINOLA L.S. and AGBOOLA A.A.A. . . . . . . . . . . . . . . . . . . . . . . . . . . 01 Connectivity of Smarandachely Line Splitting Graphs BY B.BASAVANAGOUD and VEENA MATHAD . . . . . . . . . . . . . . . . . . . . . . 08 Separation for Triple-Harmonic Di?erential Operator in Hilbert Space BY E.M.E.ZAYED and S.A.OMRAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Classification of Differentiable Graph BY A. El-Abed . . . . . . . . . . . . . . . . . 24 On Equitable Coloring of Helm Graph and Gear Graph BY KALIRAJ.K and VERNOLD VIVIN.J . . . . . . . . . . . . . . . . . . . . . . . . . . 32 On the Roman Edge Domination Number of a Graph BY K. EBADI, E. KHODADADI and L. PUSHPALATHA. . . . . . . . . . . . . . . . . . 38 The Upper Monophonic Number of a Graph BY J.JOHN and S.PANCHALI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Some Results on Pair Sum Labeling of Graphs BY R. PONRAJ, J.VIJAYA XAVIER PARTHIPAN and R.KALA . . . . . . . . . . . . . . 53 Weierstrass Formula for Minimal Surface in the Special Three-Dimensional Kenmotsu Manifold K with _-...

This book will take you on a journey, through the eyes and minds of two unlikely heroes. These two amazing, inventive & creative young souls find adventure & create solutions through the use of mathematics, "Om technology", and sharo-logical edutainment as well as creating a multitude of "Harmless but helpful inventions that assist themselves & those that they meet. These heroes make friends where ever they may go while solving many of what some may call "the worlds problems" along the way. This dynamic duo as well as their amazing group of friends find as much joy in Action sports as they do in listening to all of the great adventures of people that have been alive many more years then them. Love, respect, caring, self-confidence,responsibility and joy are the tools of their trade, and they believe that all people can be truly amazing! Get your copy of "An Essential Book of Good" here today so you can feel, and be even more amazing today!...

"There were no great walls that could stop a free thinking minds path". One just has to simply do the math, create a plan and then just actually commit, and then do whatever the task". "If one was to study the magic of Mathematics or the physics of lifting off, one could create solutions to even inventing a flying skate-snow or surfboard that levitates effortlessly without even the slightest of sounds"....

Introduction 1) Essential Fabric & Style 2) Fish Faith 3) Life Keys for you & me 4) A Gift for you 5) Then and Now 6) Strange Days 7) Dream Seeds 8) The Great Storm 9) A Brand New Day 10) A friend in Need is a Friend Indeed 11) Success with Persistence ~ The Golden Envelope...

ഇന്ത്യയിൽ ഇന്ന് ഇങ്ഗ്ളിഷ് പഠിപ്പിക്കുന്നതിൽ പലപ്രശ്നങ്ങളും നേരിടുന്നുണ്ട്. അതിൽ അതീവ പ്രധാനപ്പെട്ടതും, അതേ സമയം ആരും സൂചിപ്പിക്കാത്തതുമായ കാര്യം, ഇന്ത്യൻ ഭാഷകളിലെ ഫ്യൂഡൻ ഉച്ചനീചത്വ കോഡുകൾ ഇങ്ഗ്ളിഷിലേക്ക് കടന്നുവരുന്നതിനെക്കുറിച്ചാണ്. ഇത് അതി ഭയാനകമായ ഒരു ഭവഷ്യത്താണ് ഇങ്ഗ്ളിഷിൽ കൊണ്ടുവരുന്നത്. തന്നെക്കാൾ താഴ്ന്നവരോട് മാത്രം ഇങ്ഗ്ളിഷിലെ പൊതുവായ വാക്കുകൾ ഉപയോഗിക്കാൻ പാടുള്ളു എന്ന ഒരു ചിന്താഗതി വളർത്തിയെടുക്കുകയാണ് ഇത് ചെയ്യുന്നത്. ഇതിനെക്കുറിച്ച് പലതും പറയാനുണ്ടെങ്കിലും, ഇവിടെ ഇതുമാത്രം പറയാം. ഇങ്ഗ്ളിഷിലെ YOU എന്ന പദത്തെ ‘നീ’ യെന്നും, HE എന്ന പദത്തെ ‘അവൻ’ എന്നും, SHE എന്ന പദത്തിനെ ‘അവൾ’ എന്നും തർജ്ജമചെയ്ത് പഠിക്കുന്ന ഇങ്ഗ്ളിഷ്, ഉയർന്ന മാനവിക നിലവാരങ്ങളിൽ നിന്നും താഴെവീണ് ദുഷിച്ചുപോയൊരു ഇങ്ഗ്ളിഷാണ്. ഈ ഇങ്ഗ്ളിഷ് അല്ല പഠിക്കേണ്ടത്. മറിച്ച്, സമൂഹത്തെ ഉന്നതനിലവാരത്തിലേക്ക് നയിക്കുന്ന കലർപ്പില്ലാത്ത ഇങ്ഗ്ളിഷാണ് പഠിക്കേണ്ടത്. ഈ ഇങ്ഗ്ളിഷ്പഠനം ഒരുക്കിയിട്ടുള്ളത് VED from VICTORIA INSTITUTIONS എന്ന തൂലികാനാമം പേറുന്ന എഴുത്തുകാരനാണ്. ഇദ്ദേഹം, ഭാഷകളെപ്പറ്റിയും, ഭാഷാകോഡുകളെപ്പറ്റിയും, യാഥാർത്ഥ്യത്തിന്റെ കോഡുകളെപ്പറ്റിയും മറ്റും നീരീക്ഷണ പരീക്ഷണങ്ങൾ നടത്തിയിട്ടുള്ള വ്യക്തിയും, അവയുമായി ബന്ധപ്പെട്ട് അനവധി പുസ്തകങ്ങൾ എഴുതിയിട്ടുള്ള ആളും ആണ...

Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original 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,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical 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 gravitatio...

Extending Homomorphism Theorem to Multi-Systems Abstract: The multi-laterality of WORLD implies multi-systems to be its best candidate model for ones cognition 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 systems, and shows how to extend the homomorphism theorem in abstract algebra to multi-systems or combinatorial systems. All works in this paper are motivated by a combinatorial speculation of mine which is reformed on combinatorial systems and can be also applied to geometry. Key Words: Homomorphism theorem, multi-system, combinatorial system. ...

Contents Extending Homomorphism Theorem to Multi-Systems BY LINFAN MAO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 01 A Double Cryptography Using the Smarandache Keedwell Cross Inverse Quasigroup BY T. G. JA´IY´EOL´A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 On the Time-like Curves of Constant Breadth in Minkowski 3-Space BY SUHA YILMAZ AND MELIH TURGUT. . . . . . . . . . . . . . . . . . . . . 34 On the Basis Number of the Strong Product of Theta Graphs with Cycles BY M.M.M. JARADAT, M.F. JANEM AND A.J. ALAWNEH. . . . . . . . . . . .40 Smarandache Curves in Minkowski Space-time BY MELIH TURGUT AND S¨UHA YILMAZ . . . . . . . . . . . . . . . . . . . . . 51 The Characterization of Symmetric Primitive Matrices with exponent n − 3 BY LICHAO, HUANGFU AND JUNLIANG CAI . . . . . . . . . . . . . . . . . . 56 The Crossing Number of the Circulant Graph C(3k − 1; {1, k}) BY JING WANG AND YUANQIU HUANG. . . . . . . . . . . . . . . . . . . .79 On the Edge Geodetic and k-Edge Geodetic Number of a Graph BY A.P. SANTHAKUMARAN AND S.V. ULLAS CHANDRAN. . . . . . . . . .85 Simple Path Cove...

In a world of chaotic alignments, traditional logic with its strict boundaries of truth and falsity has not imbued itself with the capability of reflecting the reality. Despite various attempts to reorient logic, there has remained an essential need for an alternative system that could infuse into itself a representation of the real world. Out of this need arose the system of Neutrosophy, and its connected logic, Neutrosophic Logic. Neutrosophy is a new branch of philosophy that studies the origin, nature and scope of neutralities, as well as their interactions with different ideational spectra. This was introduced by one of the authors, Florentin Smarandache. A few of the mentionable characteristics of this mode of thinking are [90-94]: It proposes new philosophical theses, principles, laws, methods, formulas and movements; it reveals that the world is full of indeterminacy; it interprets the uninterpretable; regards, from many different angles, old concepts, systems and proves that an idea which is true in a given referential system, may be false in another, and vice versa; attempts to make peace in the war of ideas, and to make w...

Chinese checkers is a strategy board game which can be played by two, three, four, or six people, playing individually or with partners. The game is a modern and simplified variation of the game Halma. The objective is to be first to race one's pieces across the hexagram-shaped gameboard into "home"—the corner of the star opposite one's starting corner—using single-step moves or moves which jump over other pieces. The others continue playing to establish 2nd, 3rd, 4th, 5th, and last place finishers. Like other skill-based games, Chinese checkers involves strategy. The rules are simple, so even young children can play. ...

This book has five chapters. In Chapter I, we give a brief description of the sixteen sutras invented by the Swamiji. Chapter II gives the text of select articles about Vedic Mathematics that appeared in the media. Chapter III recalls some basic notions of some Fuzzy and Neutrosophic models used in this book. This chapter also introduces a fuzzy model to study the problem when we have to handle the opinion of multiexperts. Chapter IV analyses the problem using these models. The final chapter gives the observations made from our study....

We then remove the common factor if any from each and we find x + 1 staring us in the face i.e. x + 1 is the HCF. Two things are to be noted importantly. (1) We see that often the subsutras are not used under the main sutra for which it is the subsutra or the corollary. This is the main deviation from the usual mathematical principles of theorem (sutra) and corollaries (subsutra). (2) It cannot be easily compromised that a single sutra (a Sanskrit word) can be mathematically interpreted in this manner even by a stalwart in Sanskrit except the Jagadguru Puri Sankaracharya. We wind up the material from the book of Vedic Mathematics and proceed on to give the opinion/views of great personalities on Vedic Mathematics given by Jagadguru. Since the notion of integral and differential calculus was not in vogue in Vedic times, here we do not discuss about the authenticated inventor, further we have not given the adaptation of certain sutras in these fields. Further as most of the educated experts felt that since the Jagadguru had obtained his degree with mathematics as one of the subjects, most of the results given in book on Ve...

Preface 5 Chapter One INTRODUCTION TO VEDIC MATHEMATICS 9 Chapter Two ANALYSIS OF VEDIC MATHEMATICS BY MATHEMATICIANS AND OTHERS 31 2.1 Views of Prof. S.G.Dani about Vedic Mathematics from Frontline 33 2.2 Neither Vedic Nor Mathematics 50 2.3 Views about the Book in Favour and Against 55 2.4 Vedas: Repositories of Ancient Indian Lore 58 2.5 A Rational Approach to Study Ancient Literature 59 2.6 Shanghai Rankings and Indian Universities 60 2.7 Conclusions derived on Vedic Mathematics and the Calculations of Guru Tirthaji - Secrets of Ancient Maths 61 Chapter Three INTRODUCTION TO BASIC CONCEPTS AND A NEW FUZZY MODEL 65 3.1 Introduction to FCM and the Working of this Model 65 3.2 Definition and Illustration of Fuzzy Relational Maps (FRMS) 72 3.3 Definition of the New Fuzzy Dynamical System 77 3.4 Neutrosophic Cognitive Maps with Examples 78 3.5 Description of Neutrosophic Relational Maps 87 3.6 Description of the new Fuzzy Neutrosophic model 92 Chapter Four MATHEMATICAL ANALYSIS OF THE VIEWS ABOUT VEDIC MATHEMATICS USING FUZZY MODELS 95 4.1 Views of students about the use of Vedic Mathematics in their c...

This book is one of a series originally written by faculty in a Kamehameha reading program. The books were designed to increase students' reading skills and their knowledge of Hawaiian history and culture by focusing on topics such as the Hawaiian monarchy. Some of these books have been translated from their original English into Hawaiian through the efforts of the staff of the Kamehameha Schools Hawaiian Studies Institute. We are pleased at the reception both the English and the Hawaiian editions have received from educational and general audiences....

Try to imagine Hawai’i five hundred years ago. What do you suppose life in the islands was like then? How do you think people survived? From the Mountains to the Sea: Early Hawaiian Life will help answer these questions. It will give us a glimpse of our early Hawaiian ancestors. We will see where they lived and how they lived. We will learn about their close ties to nature. By observing their relationship with this natural environment we will discover that these early Hawaiians were creative, industrious, observant, skillful and wise people....

Prefaceix -- vii -- Acknowledgments -- xi -- Editor's Note -- 1 -- Introduction -- 3 -- Polynesian Discoverers -- 4 -- Marquesans -- 6 -- Tahitians -- 9 -- Umi Divides the Land -- 13 – Ahupuaa -- 18 -- Uka: Mountains and Uplands -- 22 -- Kula: Plains and Fields -- 25 -- Kai: The Sea and the Lands Nearby -- 30 -- Spirits of Nature -- 32 -- Na Akua: The Major Spirits -- 37 -- Heiau: Places of Worship -- 41 -- Na Kapu: The Forbidden or Sacred -- 43 -- Na Kanaka: The People -- 45 -- Na Alii: The Chiefs -- 53 -- Na Kahuna: The Priests and Experts -- 57 -- Na Makaainana: The Working People -- 70 -- Ka Ohana: The Family89 -- Na Mahiai: The Planters -- 94 -- Tools of the Mahiai -- 98 -- Where to Plant -- 100 -- When to Plant -- 102 -- Prayers and Offerings -- 103 -- The Joy of Planting -- 105 -- The Water of Kane -- 109 -- Na Lawaia: The Fishermen -- 110 -- An Honored Profession -- 113 -- Ku ula, Aumakua and Omens -- 117 -- Catching Fish -- 118 -- Conserving the Supply of Fish -- 124 -- Na Poe Hana Noeau: The Craftsmen -- 131 -- Kapa-making 133 -- Featherwork -- 138 -- The First Object Made -- 139 -- Olelo a me Moolelo: Language and Lite...

Reading a Book, a Visual Guide is a Klimers Primers Mind Map on How to Read a Book by Adler and Doren, The Intelligent Guide to Reading. It is a visual guide to all the essential elements of getting the most out of reading any type of book, from novels to history, science to literature, both practical and imaginative texts....

Synchronize TERMS (with the author) or you'll be speaking different languages.

How to Read a Book. The Text. Reading. Extrinsic Reading Aids. How to Read Imaginative Literature. How to Read History, Math & Science. How to Read Philosophy. How to Read Social Science. Syntopical Reading. Reflections on How to Read a Book....

Aims and Scope: The International J.Mathematical Combinatorics is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 100-150 pages approx. per volume, which publishes original 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,· · · , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretic...

Abstract: Let G be a group having a partially closed subset S such that S contains the identity element of G and each element in S has an inverse in S. Such subsets of G are called halfsubgroups of G. If a halfsubgroup S generates the group G, then S is called a halfsubgroup 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(2000): 20Kxx, 20L05....

Halfsubgroups BY ARUN S. MUKTIBODH. . . . . . . . . . . . . . . . . . . . . . . . . . . . .01 Flexibility of Embeddings of a Halin Graph on the Projective Plane BY HAN REN and YUN BAI. . . . . . . . . . . . . . . . . . . . . . . . . . . .06 Curvature Equations on Combinatorial Manifolds with Applications to Theoretical Physics BY LINFAN MAO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16 A Pair of Smarandachely Isotopic Quasigroups and Loops of the Same Variety BY T. G. JA´IY´EOL´A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36 A Revision to G¨odel’s Incompleteness Theorem by Neutrosophy BY YUHUA FU and ANJIE FU. . . . . . . . . . . . . . . . . . . . . . . . . . . 45 On the basis Number and the Minimum Cycle Bases of the Wreath Product of Two Wheels BY M.M.M. JARADAT and M.K. AL-QEYYAM . . . . . . . . . . . . . . . . . . 52 Theory of Relativity on the Finsler Spacetime BY SHENGLIN CAO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 On the Number of Graceful Trees BY GUANGXUAN WANG. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 ...

Chess is a board game for two players. It is played on a square board, made of 64 smaller squares, with eight squares on each side. Each player starts with sixteen pieces: eight pawns, two knights, two bishops, two rooks, one queen and one king.[2] The goal of the game is for each player to try and checkmate the king of the opponent. Checkmate is a threat ('check') to the opposing king which no move can stop. It ends the game. During the game the two opponents take turns to move one of their pieces to a different square of the board. One player ('White') has pieces of a light color; the other player ('Black') has pieces of a dark color. There are rules about how pieces move, and about taking the opponent's pieces off the board. The player with white pieces always makes the first move.[4] Because of this, White has a small advantage, and wins more often than Black in tournament games. ...

Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original 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,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical 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 gravitatio...

Contents On the Crypto-Automorphism of the Buchsteiner Loops BY J.O.AD´EN´IRN and Y.T.OYEBO. . . . . . . . . . . . . . . . . . . . . . . . .01 Generalizations of Poly-Bernoulli Numbers and Polynomials BY HASSAN JOLANY, M.R.DARAFSHEH AND R.EIZADI ALIKELAYE . . . . 07 Open Alliance in Graphs BY N.JAFARI RAD AND H.REZAZADEH . . . . . . . . . . . . . . . . . . . . . 15 The Forcing Weak Edge Detour Number of a Graph BY A.P.SANTHAKUMARAN AND S.ATHISAYANATHAN . . . . . . . . . . . . . 22 Special Smarandache Curves in the Euclidean Space BY AHMAD T. ALI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 The H-Line Signed Graph of a Signed Graph BY R.RANGARAJAN, M. S. SUBRAMANYA AND P. SIVA KOTA REDDY. . . .37 Min-Max Dom-Saturation Number of a Tree BY S. ARUMUGAM AND S. SUDHA . . . . . . . . . . . . . . . . . . . . . . . 45 Embeddings of Circular graph C(2n + 1, 2) (n ≥ 2) on the Projective Plane BY XINQIU LIU, YUANQIU HUANG AND JING WANG. . . . . . . . . . . . .53 A Note On Jump Symmetric n-Sigraph BY H. A.MALATHI AND H. C.SAVITHRI . . . . . . . . . . . . . . . . . . . . 65 New Families of Mean Graphs ...

Papers concerning any of the Smarandache type functions, sequences, integer algorithms, paradoxes, Non-Euclidean geometries, conjectures, open problems, neutrosophic logic/set/probability, etc. have been selected for this volume. The...