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...In this book the authors for the first time study special type of Euclid squares in the real plane, complex plane, neutrosophic plane, dual number plane and their specializations. This study can be visualized as a blend of algebra, geometry and analysis. There are six such planes and they behave d...

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... 2CONTENTSPreface 5Chapter OneSPECIAL TYPES OF SQUARES IN REAL PLANE 7Chapter TwoSQUARES OF NETROSOPHIC PLANE ... ...E In this book for the first time the authors study the new typeof Euclid squares in various planes like real plane, complexplane, dual number plane,... ...and they behave distinctly. Fromthe study it is revealed that each type of squares behave in adifferent way depending on the plane. We define several... ...em.Such study is new, innovative and interesting. However forsome types of squares; one is not in a position to define product.Further under addition ... ... same size square associated with it. We will give the graph of all the four squares in thefollowing. I ... ...2, –4I) and (–12, 4I) respectively. We give the graph of these four neutrosophic squares. I ... ...P = {(–1, I), (1, I), (–1, 3I), (1, 3I)}. We give the graph of all the four squares in the neutrosophic plane. ... ...es not intersect any of the complex squares. However all the four complex squares A + P, P – A, A and A – P have the size of the si... ... given in Figure 3.18. M, A + M, A – M and M – A. Clearly all the four square intersect or have a point incommon.148 Euclid Squares on In...

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...The Square Root Spiral ( or “Spiral of Theodorus” or “Einstein Spiral” ) is a very interesting geometrical structure in which the square roots of all natural numbers have a clear defined orientation to each other. This enables ...

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...Another striking property of the Square Root Spiral is the fact, that the square roots of all square numbers ( 4, 9, 16, 25, 36… ) lie on 3 highly symmetrical spiral graphs which divide the square root spiral into 3 equal areas. ( see FIG.1 : graphs Q1, Q2 ...

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... The Distribution of Prime Numbers on the Square Root Spiral - Harry K. Hahn - ... ...Abstract :Prime Numbers accumulate on defined spiral graphs, which run through the Square Root Spiral.These spiral graphs can be assigned to different... ...ic polynomials. For example the well known Euler Polynomial x2+x+41 appears on the SquareRoot Spiral in the form of three spiral-graphs, which are def... ...ers, divisible by a certain prime factor, also lie on defined spiral graphs on the SquareRoot Spiral ( or “Spiral of Theodorus”, or “Wurzelspirale” ).... ...iral-Graphs have a 2. Differential of 20 !! Æ see difference calculation for the four exemplary spiralarms D8, F2, G5 and I5 On the shown 12 Prime... ... in red ). Note, that there are only around 10 spiralarms drawn for each of these four spiral-systems. Note, that the other 7 Prime Number Spiral S... ...t the periodic occurrence of numbers sequences form a periodic sequence of four numbers which recur ad infinitum.divisible by 3 or 5 in the nu... ...factors in these sequences.Then I picked out a longer section at the beginning and four sections out of the Here the sequence B33 was developed, ... ... number-sequence K5 was chosen, because it contains many small prime-For the other four sections I picked sections of 8 numbers out of the number ...

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...Here for the first time we introduce the semi open square using modulo integers. Authors introduce several algebraic structures on them. These squares under addition modulo ‘n’ is a group and however under product × this semi open square is only a semigroup as under × the squ...

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...Algebraic Structures on Real and Neutrosophic Semi Open Squares W. B. Vasantha Kandasamy Florentin Smarandache ... ... 5Chapter OneALGEBRAIC STRUCTURES USINGSEMI OPEN REAL SQUARE {(a, b) | a, b  [0, n)} 7Chapter TwoALGEBRAIC STRUCTURES USI... ...b  [0, n)} 7Chapter TwoALGEBRAIC STRUCTURES USING REALNEUTROSOPHIC SQUARES 81Chapter ThreeSEMIRINGS AND PSEUDO RINGS USINGR... ... 81Chapter ThreeSEMIRINGS AND PSEUDO RINGS USINGREAL NEUTROSOPHIC SQUARES 147 3FURTHER READING ... ..., y) | x, y  [0, 4)} be the semi openreal square of side length less than four. Let Y = (0.378, 1.37) and X = (3.622, 2.63)  A. We see X + Y = (0.... ...der product. P = {(1, 1), (1, 8), (8, 1), (8, 8)}  M is a group of order four given by the following table.  (1,1) (1,8) (8,1) (8,8... ... z, max {y, z} = z Thus {(0, 0), x, y, z}  M is a subsemiring of order four. Likewise we can get subsemirings of any desired order. Further ... ...nder max operation. W has finite subsemigroup of order one, two, three, fourand so on. All these finite subsemigroups of W are not ideals of W.E... ...bsemigroup but is notan ideal. P has subsemigroups of order two, three, four and so on. Now we propose the following problems for this chapter.P...

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...The Square Root Spiral ( or “Spiral of Theodorus” or “Einstein-Spiral” ) is a very interesting geometrical structure, in which the square roots of all natural numbers have a defined (spatial ) position to each other. The Squa...

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...vident that the numbers divisible by 2 ( marked in yellow ) lie on defined spiral graphs which have their starting point in or near the centre of the square root spiral. These spiral graphs have either a positive or a negative rotation direction. A spiral graph which has a clockwise rotation direction shall be called negative (N) and a spiral graph which has an coun...

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...atural numbers divisible by 2, 3, 5, 11, 13 and 17 on the Square Root Spiral - Harry K. Hahn - ... ...ors 2, 3, 5, 11, 13 and 17 lie on defined spiral-graphs, whichrun through the Square Root Spiral. And a mathematical analysis shows that these spiral ... ...ocument represents a supplementation to my detailed introduction study to the Square Root Spiral,and it contains the missing diagrams and analyses for... ...distribution of the natural numbers divisible by2, 3, 5, 11, 13 and 17 on the Square Root Spiral. My introduction study can be found in the ArXiv–arc... ...itle of the study : “ The ordered distribution of the natural numbers on the Square Root Spiral ” ( This study also contains diagram & analysis for n... ... These spiral arms are drawn in light grey and they lie between the other four spiral graph systems which are drawn in color. ...

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...In this book authors build algebraic structures on fuzzy unit semi open square UF = {(a, b) | a, b ε [0, 1)} and on the fuzzy neutrosophic unit semi open square UN = {a + bI | a, b ε [0, 1)}. This study is new and we define, develop and describe several interesting and innovative theories about t...

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... Algebraic Structures on Fuzzy Unit Square andNeutrosophic Unit Square W. B. Vasantha Kandasamy ... ... 5Chapter OneALGEBRAIC STRUCTURES ON THE FUZZYUNIT SQUARE UF = {(a, b) | a, b  [0, 1)} 7Chapter TwoFUZZY NEUTROSOP... ...FACE In this book authors build algebraic structures on fuzzy unitsemi open square UF = {(a, b) | a, b  [0, 1)} and on the fuzzyneutrosophic unit se... ...re UF = {(a, b) | a, b  [0, 1)} and on the fuzzyneutrosophic unit semi open square UN = {a + bI | a, b  [0, 1)}. This study is new and we define, d... ....3, 0.2), (0, 0.7), (0.9, 0.2), (0.7, (0.111)}  P is asubsemigroup of order four and is not an ideal of P.18 Algebraic Structures on Fuzzy Unit Squar... ...x we can havemax or min as operation of multiplying by a scalar. Thus we get four types of semivector spaces over the fuzzyunit square semiring S = {U... ...}, max, 1  i  4}and M4 = {(a1, a2, a3, a4) | ai  {UF}, min, 1  i  4} be foursemivector over the semiring S = {UF, min, max}.72 Algebraic Structu... ...0.8, 0.71), (0.8, 0.3), (0.8, 0.5), (0.8, 0.5))  M4 … IV We see all the four operations for the same set of elements yield different elements i... ...d different elements in Mi; 1  i  4. Hence the claim. Thus we have four types of semivector spaces using the special fuzzy unit square. ...

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...ation Date: June 3rd 2013 325 Mary WalzThe Four Stones 2Chapter 1 A late afternoon fog had settled over ... ...capital of Cherin, whichis where your suitor is from- then a good three or four weeks,depending on the weather.” I nodded. “Have you been to Corlath... ...ot very talkative. Liara was different, though. She was only twenty-one- four yearsmy senior- so she acted more like a friend than any of the others... ... and dug through her saddlebag. “I brought enough foodto last us for about four days,” she told me as she worked. “It’s nothingglamorous, but it’ll ha... ...l have to do. I wish I knew how to hunt, then we couldeat proper food.” “Four days?” I echoed as I took the food from her. “Is that how longit will ... ... bare outcroppings of rock. To the far south, Icould see flat, patchworked squares; beyond that was a large clusterof tall buildings. “Is that Port Fa... ...t only had two largetriangular sails- one on each mast- instead of several square ones.“That’s a strange ship,” I mumbled. “Indeed,” Liara agreed. “... ...hangs every last one of them in this... mass hanging ceremony inthe public square.” He cringed. “It’s the reason why Gareth alwaysmade certain to be i... ...gly and nodded. “So I did it,” Gareth finally admitted. “I shot William, square in thehead, and killed him. And a few seconds after that, Joseph cam...

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...Description: At the top of an elaborate temple tower a mile up in the sky, a man has waited for four centuries. He watches for an unknown threat from the south, but it has never come...and he begins to doubt. Four Hundred Years in the Sky is a spin-off of my duology, The Long Way and The Forgotten Way. If you like this...

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...n he would see nothing. He had been putting up with thosedreams for nearly four hundred years. They were always different, butalways the same. And the... ...e a man. He recalled thatthere were women, too. Or at least there had been four hundred yearsago. Now, who knew?This musing took him little time, and ... ... great effort. He did not know whythere were so many pages. Only the first four had writing on them.He had been appointed to a position of great respo... ...e were alchemic texts on the third floor,decaying storybooks on the twenty-fourth, and the records in theConnoisseur’s cellar. The Watcher had browsed... ...ith them…Another.And they did construct a wooden bear, ten cubits tall and fourteen anda half cubits long. The length of its nose from nostril to eye ... ...savored the feeling for a moment,and then he pulled the door open.It was a square room, empty except for one corner, in which a figurewas curled. It w...

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...n. They Had No Memories, Only Data. Civilization Continued Normally, But No One Aged. But There Are Still Those Who Have Not Yet Become Machines.. . Fourteen Year Old Xion Forester is One of the Few Remaining Who Have Not Become Androids. Although She Doesnt Know It. Xion Thinks She is Just Like Everyone Else, a Machine. But One Day, She Gets a Mysterious Letter Urging He...

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...12th 2013 9 Fallen AngelTwenty-Four Days Left To Live For Michelle, my best writing buddy ... ... Michelle, my best writing buddy 2Prologue Twenty-Four Days Left To Live ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~... ... . Water pouredout of an abstract structure, cascading down into the large square poolbelow. Around the structure, small blocks shining turquoise ligh...

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... THE COUNTRY OF THE ANIMALS a mute play in four scenes of desperation by Florentin Smarandac... ...ame gestures.Successively, their bodies are merging into only one body with twoheads, four hands. Then his heads and hands are multiplying þ fourheads... ...f the Senior?"(There is a portrait of the Instructor General glued onto the plate ina square frame. Under the portrait is written: "The SeniorSQUAREHE... ...h to children a woman is copulating with adonkey and a man with a goat. These are the four protagonists of thesub-scene. The sexual acts will be styli... ...e is standing up but with his face turned towardsthe wall. - the table is made of four men, staying on the floor,supporting a square board on thei... ...wardsthe wall. - the table is made of four men, staying on the floor,supporting a square board on their heads From time to time people-servants ar... ... the angle of the view at about 3.5 m over the field, thecamera will show the perfect square shape of the field of Indian cornand the identical height... ...eld. Five tall and straight country men rush to the car. One opensthe door, the other four lay a Persian carpet over the hideous mud andsilt. The Inst...

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...rrationality espoused by SS guards, camp doctors, and Nazi jurists. This analysis contributes to global discussions of comparative genocide, semiotic square usage, and post-structuralist identity politics. This study will interest advanced students of political science and human rights professionals interested in genocide prevention....

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...Tables and Semiotic Squares Introduction Chapter I. Conditions of Transformation Chapter II. The Fluid Legality of Nazism Chapter III. Homo Viator & Formalized Social Rejections Chapter IV. Transience Chapter V. Semiotic Squares Chapter ...

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... Table of ContentsTables and Semiotic Squares . . . 2Introducti... ... . . . 44Chapter IV. Transience . . . 66Chapter V. Semiotic Squares . . . 94Chapter V... ...ic Squares . . . 94Chapter VI. Nazi (Ir)Rationality & Semiotic Squares . . . 105Chapter VII. (Ir)rati... ... populations established in eastern Europe . . . 17 Semiotic SquaresChart I: Nazi Jurist Rationality/Irrationality in... ...sion of Poland, Jews …numbered in the…millions. After the campaign against France, there were four million Jews (in)1941. (There were) 11 million Jews... ...the ghettos. These early speeches wereconfined to exploiting conditions of possibility within four basis ideas: first,that Germany suffered from force... ...val andgrowth by uniting with Austria and acquiring the additional lands of the Slavicpeople; fourth, in order to achieve this national greatness and ... ... in Nazi Germany, (Oxford: Oxford University Press, 1998),171.95 T.S. Eliot, ‘Little Gidding” Four Quartets, pt. 5, quoted in Roger Friedland & Deirdr... ...a completeliquidation was in August 1944 - meaning that the ghetto had inexplicablylasted for four years and four months.202III. Auschwitz: For th...

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...es, formulae, conjectures, examples, mathematical criteria, etc. on integer sequences, numbers, quotients, residues, exponents, sieves, pseudo-primes squares cubes factorials, almost primes, mobile periodicals, functions, tables, prime square factorial bases, generalized factorials, generalized palindromes, so on, have been extracted from the Archives of American Mathemati...

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...sequences, numbers, quotients, residues, expo-nents, sieves, pseudo-primes squares cubes factorials, almost primes, mobileperiodicals, functions, tabl... ...bes factorials, almost primes, mobileperiodicals, functions, tables, prime square factorial bases, generalized factori-als, generalized palindromes, s... ...rior and Superior Fractional Prime Part . . . . . . . . . . . . . 69 2.19 Square Part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... .... . . . . . . . . . . . . . . . . . . . 70 2.19.1 Inferior and Superior Square Part . . . . . . . . . . . . . . . . . . . 70 2.19.2 Inferior and... ...ncate-nated sequences, permutation sequence, combinatorial sequences. The fourth chapter discusses special numbers. The first section presentsnume... ...n primes of third rank? 4. There are an infinite number of Luhn primes of fourth rank? 5. There are Luhn prime numbers of o rank, o > 4?1.4 Ending... ... To note that for n ∈ N∗, n ≤ 106 we don’t have Narcissistic numbers in fourdifferent bases, where b ∈ N∗ and 2 ≤ b ≤ 100.2.4.2 Inverse Narcissist... ...y other even number, not exceeding it, is the sum of two of the first 4 (four) odd primes 3, 5, 7, 11; 6 = 3+3, 8 = 3+5, 10 = 3+7, 12 = 5+7, 14 = ... ... number ≥ 9, not ex- ceeding it, is the sum of three of the first 4 (four) odd prime, i.e. the odd primes 3, 5, 7, 11; v5 = ... . Thus we h...

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...Description: Quadrilaterals are four-sided figures. They appear many places in the world. This book will describe the hierarchical order of quadrilaterals....

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... 13 Joseph BodnarQuadrilateral Hierarchy May the Fours Be With You 2Quadrilaterals Quadrilateral is the t... ... 2Quadrilaterals Quadrilateral is the term used to describe any four-sided shape. The first distinction we make is based upon how many sets... ...allelogram. Regardless of how many parallel sides there are, thesum of all four angle measurements is 360 degrees in everyquadrilateral. ... ...es and angles. 7Rectangles A parallelogram with four right angles is called a rectangle. Thediagonals of a rectangle are co... ...gle are congruent. 8Rhombi A parallelogram with four congruent sides is called a rhombus.The diagonals of a rhombus are per... ... right angles and four congruent sides is arectobus. Just kidding; it is a square (a rectobus is what you hopethe bus driver doesn't do :) ). A thin... ...nd is that all properties of parallelograms applyto rectangles, rhombi and squares, and all properties of rectangles andrhombi apply to squares. Howev... ...f rectangles andrhombi apply to squares. However, the reverse is not true. Squareshave right angles; rhombi may not. Therefore, all squares are rhombi... ...; rhombi may not. Therefore, all squares are rhombi,but not all rhombi are squares. Likewise, squares have four congruentsides; rectangles may not. Th...

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...t stolen. “Excuse me!” On seeing the booth still empty, she exclaimed, “Oh, thank God!” In a hurry, she climbed onto the red leather cushion on all fours, her mind still on men, not wanting the distraction of them, and on her drunken friend who was probably surrounded by them this very minute. In her haste, up went the hem of her very tight, little black dress. She yelpe...

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Fourteen Chapters

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..., thank God!” In a hurry, she climbed onto the red leathercushion on all fours, her mind still on men, notwanting the distraction of them, and on h... ...t a doubt the mosthandsome she’d ever seen. He had thick, dark, wavyhair, a square jaw and sexy lips parted in surprise. Hewore an expensive suit, com... ...their guest, two of hispack members. The balcony door opened andDontae, the fourth and final member, walked in with 21 Faleena ... ...na Hopkins Dontae said nothing. They were all dressed in suits as all four hadbeen out that night, agreeing to meet back here for alast nightcap... ...ld bedone? They couldn’t install a chimney in a tenth floorflat in a twenty-four-floor high-rise Downtown no 24 Werewolves of New Y... ...olves of New York: Nathanielmatter how good they were at their jobs. The four naturally nocturnal creatures werearchitects by day. Together they ra... ...ablebetween them with fresh lilies that smelled welcomingresting in a clear square vase on top. The receptiondesk was empty with a printed sign on it ... ...inding a purse. “Now!” they ordered Nathaniel. Histemper caught fire and he squared off against themforming a human barrier to his mate. “Nathaniel...

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...J. Wang : Cube-free integers as sums of two squares 1 G. Liu and H. Li : Recurrences for generalized Euler numbers 9 H. Li and Q. Yang : Some properties of the LCM sequence 14 M. Liu : On the generalization of the primitive number function 18 Z. Lv : On the F. Smar...

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..., near the title. References should bementioned in the text by a number in square brackets and should be listedalphabetically. Current address followe... ...untry and will continue to grow. And indeed we are planning toorganize the fourth conference in coming March in Xianyang the famous oldcity which was ... ...dache type problems. They are 1. J. Wang,Cube-free integers as sums of two squares; 2. G. Liu and H. Li, Recurrencesfor generalized Euler numbers; 3. ... ... Contents J. Wang : Cube-free integers as sums of two squares 1 G. Liu and H. Li : Recurrences for gen... ...he function 98 A. Muktibodh : Smarandache mukti-squares 102 xiii Scienti... ...d go to Step2. On the basis of the analysis above, we know that there are four major preparatory stepsrequired to use the genetic algorithm in solvin... ... andeffective to find the optimal. Table 1 Comparison among the four GAs EHGA SGA AGA MGA Global Min... ...at all matters are made of atoms and sub-atomic particles, held togetherby four fundamental forces, i.e., gravity, electromagnetism, strong nuclear fo... ...ory(gravity). The Einstein’s unifying theory of fields wishsto describe the four fundamental forces, i.e., combine Quantum Theory and Relativity Theory...

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...ur Head; All You Need to Learn Are a Few Tricks. You’Ll Be Able to Quickly Multiply and Divide Triple Digits, Compute With Fractions, and Determine Squares, Cubes, and Roots Without Blinking An Eye. No Matter What Your Age or Current Math Ability, Secrets of Mental Math Will Allow You to Perform Fantastic Feats of the Mind Effortlessly. This Is the Math They Never Taught...

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...y multiply and divide triple digits, compute with fractions, and determine squares, cubes,and roots without blinking an eye. No matter what your age o... ...ave guy) or one of his pals or associates said, “There are one, two,three, four, five of us here, so we need five pieces of fruit.” Later, “Hey,look,”... ...lly something to be able tofigure that the United States had its first big Fourth of July on aThursday in 1776. April 15, 1912, the day the Titanic sa... ...e numbers in his head faster than mostpeople can with a calculator. He can square two-digit, three-digit, andfour-digit numbers, as well as find squar... ...alculators at their own game! Art next informs the audience that he will square four two-digitnumbers faster than his button-pushers on stage can sq... ...ors at their own game! Art next informs the audience that he will square four two-digitnumbers faster than his button-pushers on stage can square th... ...ers on stage can square them ontheir calculators. The audience asks him to square the numbers 24, 38,67, and 97. Then, in large, bold writing for ever... ... in the palm of his hand, Art now declares that hewill attempt to square a four-digit number. A woman calls out, “1,036,”and Art instantly responds, “... ...city of your mind as you add and subtract two-digit, three-digit, and even four-digit numbers with lightning speed. LEFT-TO-RIGHT ADDITION Most of...

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...d the beach; a strip of sand fifty meters wide separated the water and the trees. Costigan glanced briefly at the locator; his opponent was still two squares away on the grid. The opponent - Costigan thought it was probably the Latino named Roseleaf - would be here within an hour at the outside. He made the rounds of his booby traps, and prepared to wait. It was the last d...

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... trees. Costigan glancedbriefly at the locator; his opponent was still two squares away on the grid.The opponent -- Costigan thought it was probably t... ...t was the sole remaining human being onEarth entered the locator's central square, he dropped the locator, let itfall like a stone to the forest's flo... ...f all living humans. The first timehe had used the locator, there had been four humans within eighty kilometersdistance. Costigan tracked them down an...

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... 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.MAHADEVAN . . . . . . . . 66 Comparing the Number of Acyclic and Totally...

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...ight nucleus of GH denoted by SNρ(GH , ·) = SNρ(GH ) = Nρ(G) ∩ H.GH is called a Smarandache right nuclear square special loop if and only if s2 ∈ SNρ(... ...sT · xT ) · sT = (sx · s)T . Corollary 3.2 Let (GH , ·) be a S2nd BL that is a Smarandache right nuclear square special loop. −1 is a S2nd semi-a... ...Loops : Theory and Applications, Heldermann Verlag, 568pp. [3] J. Dene and A. D. Keedwell (1974), Latin squares and their applications, the English ... ... S. Navaneethakrishnancycles C1 and C2 by Theorem 1.1. Let u ∈ V (Cm ◦ Cn). Since deg(u) = 4, there exist fourvertices v1, v2, v3 and v4 adjacent with... ...neethakrishnanhamilton cycles C1 and C2 by Theorem 1.2. Let v ∈ V (Cm × Cn). Since deg(v) = 4, thereexist four vertices u1, u2, u3 and u4 adjacent wit... ...2, . . . , xn) 7→ kx1, . . . , xnk from X n to [0, ∞) is called ann-seminorm on X if it has the following four properties: 1Received April 14, 2009. A... ...mutually congruent regular convex polygons are the threeregular tilings by equilateral triangles, by squares, or by regular hexagons. A portion ... ... 1 2 1 2 1 2 Fig.4If k = 4, then V (ℑ) colored by four colors, and in this case the 5-mo... ...econd method, if the Ti has the permutation σ = (1234). As we know, each tile surround-ing by eight tiles four tiles adjacent to Ti by edges, and othe...

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...In this book authors introduce the new notion of MOD rectangular planes. The functions on them behave very differently when compared to MOD planes (square). These are different from the usual MOD planes. Algebraic structures on these MOD rectangular planes are defined and developed. These semigroups have special and distinct features. Certainly these finite structures ca...

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... MOD PLANES 45 3Chapter FourSEMIGROUPS ON MOD RECTANGULARNATURAL NEUTROSOPHIC NUMBERSAND THEIR PROP... ... The functions on them behave verydifferently when compared to MOD planes (square). Theseare different from the usual MOD planes. Algebraicstructures ... ...r + and  (or ). They are always commutative monoids. In case of 0 square matrices we can have the usual product  and get the infinite orde... ... Figure 2.17 We see the graphs are different in these four planes. So this study is not only innovative and interesting but i... ...5 0.01 x 4 4.5 4.7 y 1 2.25 0.49 There are four zeros in the intervals (1.9, 2), 3, (3.8, 3.9)and (4.6, 4.7). Th... ...  i  4, a 3 a 4  n} be the MOD rectangular square matrix semigroup. (3,5) (4,2) (0,3) (4,8) ... ...0, 11), b  [0, 7), }; 1  i  3, } be the MOD rectangular square matrix semigroup. D is a noncommutative subsemigroup of infinite o... ... questions (i) to (vii) of problem (51) for this S(P[x]5).Chapter FourSEMIGROUPS ON MOD RECTANGULARNATURAL NEUTROSOPHIC NUMBERSAND THEIR PROP... .... Further we cannot have nontrivial idempotents in case of all four types of polynomial semigroups. Finally the nontrivial nilpot...

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.... Meet me on the far side of the tennis courts as soon as the bell rings for lunch.’ The following day, while the other seven hundred and thirty four students were opening their lunch boxes in the quadrangle or under trees on the side lawn, Frankie and Flora were ducking under a wire fence into a scrubby wasteland. A barely visible track led to a concrete wall about t...

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...s as soon as thebell rings for lunch.’ The following day, while the other seven hundred and thirty four students were opening theirlunch boxes in the... ...ral and satisfying way for men and women to copulate is the way all primates do it—thefemale on all fours and the male mounting from behind. The penet... ...abysitting grandparents retired to the Gold Coast, eleven-year-old Ingenio wasappointed guardian of fourteen-year-old Virtue when both parents were at... ...e foray into the lascivious life had been with a pretty, pre-pubescent prostitute when hewas twenty-four, who gave him crabs. Adult women terrified hi... ...ng the garden, he heard a vehicle arrive and stop. He sniffed the air.It sounded and smelled like a four-wheel drive. An adrenalin jolt alerted all se... ...e three-dimensional puzzles. Frankie pointed towhat looked to be the most impossibly wonderful—six, square-section lengths of polished woodabout five ... ...nterior. The key Prosperohad given them fitted a massive wooden door at the rear that opened into a square room with awide, wrought iron spiral stairc... ... again and lunged. Just in time Sylvan leaped back. But the room was small, only about five metres square so shecould stand in the middle, take a ste... ...lowers that, when he saw them, Sylvan reckoned were opium poppies. Another link tempted him with a square stone tower topped by a reddish roof and fr...

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...This is a Bible of four books: The Satanic Book (the mystery of Satanism), Satanic Living (the life of a Satanist), Branches of The Satanic Tree (the growth of a Satanist), and Lessons of Demonic Magic (learning Satanic-Demonic magic.)...

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...eating new, enhanced, sterling things- inventions, is tocombine any two to four things together, as though a soup, with the task of making ittaste goo... ...f water and pray to ademon, or demons your wishes come to fruition.For the fourth stone clench it in your fist tight, and shaking it curse your obstac... ...e. Then take the seventh stone to curse, blaspheme Ya (God.) Thenthrow the fourth and seventh stones outside, away, or into the garbage.Your wishes wi... ...ng-mouse. A thumb stick keyboard, colored light buttons on a controller, a fourthumbstick keyboard- though would take practice, would become an easier... ...le in any way, it is for his poetic, lucid and precise use ofmight, as His Four Horsemen. Striving for a Luciferian PerfectionHe was the seal ... ...bout that and a picture alwayscomes to mind of a crowd staring at a little square on the ground pointing at it,debasing it. I just walk right past it.... ...reoccurring, represents the forever, eternity,reoccurrence, continuity.. A square is grounded, fixes something in place. A rectangle broadens, extends... ...of being. Not as being one among many the same part.So they will take your square peg and try to ram it into a circular hole. When to no avail they wi... ...be a better option than a bell.Demonic Handkerchiefs/ bandanas.Or just any square thin cloth. They are used to wrap within them the magical equipment ...