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...rst time define a special type of fixed points using MOD rectangular matrices as operators. In this case the special fixed points or limit cycles are pairs which is arrived after a finite number of iterations. Such study is both new and innovative for it can find lots of applications in mathematical modeling. Such study is new innovative and certainly lead to several speci...

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... Special Type of Fixed Point Pairsusing MOD Rectangular Matrix Operators W. B. Vasantha Kand... ... Ilanthenral K Florentin Smarandache 2016This book can be ordered from:EuropaNova ASBLClos du Parnasse, 3E1000, BruxellesBelgium... ... 5Chapter OneINTRODUCTION 7Chapter TwoMOD-FIXED POINT PAIRS OFMOD-RECTANGULAR REALMATRIX OPERATORS 9 ... ...OPERATORS 9 3Chapter ThreeMOD FIXED POINT PAIRS USING MODRECTANGULAR MATRIX OPERATORSWITH ENTRIES FROM 〈Zn ∪ I〉 ... ...matrices as operators. Inthis case the special fixed points or limit cycles are pairs whichis arrived after a finite number of iterations. Such study ... ... n IC (Z ) are all of finite order we are sure to arrive at a MOD fixed npoint pair or a MOD limit cycle pair after a finite number ofiterations. It...

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...iv–archive under my author name and the following title : Æ “ The Ordered Distribution of Prime Numbers on the Square Root Spiral ” ... ...tems ( PNS ) P18-A, P18-C and P18-C , the prime numbers are located on pairs of spiral arms, which are separated by 3 numbers in between. And t... ... are separated by 3 numbers in between. And two spiral arms of one such pair of spiral arms, are separated by 1 number in between. All spi... ... 15-F Æ K5 = F(x) = 11x2 + 25x + 13 ( or 11x2 + 3x – 1 )Æ see my study “ The Ordered Distribution of Prime Numbers on the Square Root Spiral ”Prof. E... ... derivatives mentioned by Mr. Hahn is certainlyvisible.If are pairwise different, and if , then accordingto a mean val...

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...aps (NRMs) model using the MOD rectangular or relational matrices. The advantage of using these models is that we are sure to get the MOD fixed point pair or a MOD limit cycle pair after a finite number of iterations. However we as in case of FRMs or NRMs need not at each stage threshold the resultant state vectors. We do updating when the on state which we started becomes...

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... Ilanthenral K Florentin Smarandache 2016This book can be ordered from:EuropaNova ASBLClos du Parnasse, 3E1000, BruxellesBelgiumE-m... ...dvantage of using these models is that we are sure toget the MOD fixed point pair or a MOD limit cycle pair after afinite number of iterations. Howeve... ... of using thesenewly constructed models. Finally the resultant state vector pair can be real MOD valuesor finite complex or neutrosophic or a dual nu... ...various types of natural neutrosophicnumbers or indeterminacies as resultant pairs. 7 This will address all practical problems as we c... ... MOD rectangular matrix operator contribute to special type of fixed point pair. This study is also carried out in [66]. The special features e... ...e after a finite number of iterations to arrive at aMOD realized fixed point pair or a MOD realized limit cycle pair. Let x = (0, 1, 0, 0, 0) ∈ X; to...

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...e. The Apes of Eden is Written in Rhymed Iambic Pentameter Thus Falling Into the Category Called Heroic Couplets. Each Line Has 10 Syllables and the Pairs of Lines Rhyme. While Many Lines Were Written in 10 Syllables in Very Early Latin, It Was Geoffrey Chaucer Who Added the Meter and Originated Iambic Pentameter in the English Language Which Was Further Immortalized in ...

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... War occurred; of that there’s little doubt,since apes cannot be brusquely ordered out.Apparently the Tribe was put to flight,but surely not without a... ...ply not only lungs aboveinside your human ribcage, but, we know,the larger pair of equine lungs below.It's puzzling, how you folks coordinateyour hors... ...one set of lungs breathes fast, the other slow.Regardless what you do, one pair will berelaxed, the other breathing heavily.If all four Bronchi are co... ...ped to work--though now quite doubtfully.It soon became apparent that this pairof Creatures planned to make a landing there.Our tribesman dropped his ... ...or do.The gangrel beings who had landed therewere not a very prepossessing pair.As he'd expected, they were human Things,quite typical except for batt... ...ndscame hunting apes through gullies, gaps and glens.They liked to hunt in pairs, or groups of three,uprooting shrubs and shaking every tree,no more a...

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...I ordered staples and stores without any trouble, and went back outside to find a florid fellow questioning the wagon driver. The slave put his deed back in a pocket, and his questioner nodded and strolled over to me. "New in...

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...sure." * * * The second passenger car tucked a pair of sleeping quarters into a pair of corners, as well as asmall chamber... ...ew miles an hour, the train's rhythm lagged. The sound of rolling from one pairof rails to the next took far longer than usual. Ka-chunk…ka-chunk…ka-c... ...ssistance." The moment he spoke, I said, "Are, perchance, either of the pair of you yclept Martin?" The nondescript one said, "Uhhhh…" I said... ...and a heavily made-up woman wearing aturban thrust her head from between a pair of black curtains. "Wait," she said in an exotic accent, anddisappeare... ...oss the street," she said softly. I glanced over, and saw nothing but a pair of idlers. Then I looked past the ordinary clothes,sharpened my gaze, ... ...ey might waylay me,I told the slave to wait, and went into the store. I ordered staples and stores without any trouble, and went back outside to fi... ..., and stuttered, "Th—The inspection is completed.You may go." He left, and ordered his men as they came out to pick up the sergeant and return to theb... ...t," said Rackell. "Keep yer eyes sharp, boys." A couple of paces later, he ordered, "Fixbayonets." He glanced at me and said, "Still no sense shooting... ... "Oh, without a doubt," I said. "But don't people sometimes resent being ordered about by thisunseen figure?" "I suppose," she said. "But anyone ...

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...r current copyright, patent, and trademark laws. In a series of fascinating case studies, Boyle explains why gene sequences, basic business ideas and pairs of musical notes are now owned, why jazz might be illegal if it were invented today, why most of 20th century culture is legally unavailable to us, and why today's policies would probably have smothered the World Wide W...

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...nkler puts it, Alice Randall, an African American woman, was ordered by a government official not to publish her criticism ... ...s the right and the limitations on the right as an inseparable pair. One cannot discuss them in isolation. Kapla... ... discipline. The DNA we are familiar with, for example, has four “base pairs”— A, C, G, and T. Scientists have developed genetic alpha... ...ists have developed genetic alphabets that involve twelve base pairs. Not only is the result not found in nature, but the very language in... ... that a standard biological part should be well specified and able to be paired with other parts into subassemblies and whole systems. Once t... ...y strangers, shared on comparatively open sites worldwide, and ordered by search engines? What about Wikipedia? I think not. ...

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...hey define as linguistic matrices. The authors build linguistic matrices only for those linguistic variables which yield a linguistic continuum or an ordered linguistic set. This book is organised into three chapters. The first chapter is introductory, in which we introduce all the basic concepts of linguistic variables and the associated linguistic set to make this book s...

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...pyright 2022 by Editorial Global knowledge and the AuthorsThis book can be ordered from:Editorial Global Knowledge848 BRICKELL AVE STE 950 MIAMI, FLOR... ...nly for those linguistic variableswhich yield a linguistic continuum or an ordered linguistic set. This book is organised into three chapters. The fi... ...f linguistic terms or be a linguisticcontinuum. We define on these totally ordered linguistic termsthe two binary operation min and max. At this jun... ...nd so on. Now suppose we try to order them; will it be a totally ordered set or a partially ordered set. It is important in order to make ... ...his book a self-contained one we just recall the definition of a totally ordered set and a partially ordered set and illustrate them with some exa... ... 1.1. Let S be a set of elements. We say S is totally ordered if for any pair of elements a, b S we have a b (or b a). Thus {S, } is a ... ...a). It is to be noted that unlike the totally ordered set inwhich every pair should be comparable in a partially orderedset where at least two dist... ...lly ordered set. However P(S) is not a totally ordered set as we have pairs of distinct elements which do not satisfy containment relation. ... ...ition of a partially orderedsets which demands that there which at least a pair of distinctelements in S which are ordered. Hence the claim.Result 1.2...

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... protect her vulnerable mind. Her current anchor, Colonel Jeremy Lingley, is nearing burnout. An alien race is seeking an alliance with Earth and the pair are assigned the mission of discovering the aliens' secrets. Crown Prince Dex LoudRoar is a Gatoan warrior and a royal with a terrible secret. His people wage a constant war against their enemy, the Lupinious empire....

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...ieutenant, we want only verbal conversation from here on out,” the President ordered.He banged his cybernetic hand on the desk. Jewels jumped guiltil... ...t was better left alone.She knew they would regret this. * * * After the pair left, the four men silently regarded each other. The quiet was broke... ...is a dedicated and decorated Psi-Ops officer in his own right. That's why we paired them in thefirst place." The President steepled his fingers and s... ...er third anchor partner and a very secretive man. It wasn’t untilthey’d been paired for a year that his true nature surfaced. Cruel and murderous, he ... ...d the medical crew sprang into action. Jeremy was shoved back and brusquely ordered to a corner. He didn't wait to be told anything else.He stood at ... ...ly closed. Dex removed his paw and stepped back. “Reach her now, Human,” he ordered. Jeremy bristled at the alien's tone. He gently touched Jewels' ... ...I was just about to take the Lieutenant to her quarters to rest as Dr.Cosmit ordered.” “Good, she's going to need it.” Jeremy stiffened, not liking ... ...is ludicrous!" "Colonel, you will compose yourself and sit down," the judge ordered sternly. "Please," Jewels begged and she saw Jeremy's anger vani... ...ightened and walked to the two waiting men. She stopped a foot away from the pair. “Lt.Jewels Enbran reporting as ordered.” She snapped to attention a...

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...atorial 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 Neutrosoph...

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...ations not including in above topics arealso welcome. It is also available in microfilm format and can be ordered online from: Books on Demand ProQu... ...tific Information (PA, USA), Library of Congress Subject Headings (USA).Subscription A subscription can be ordered by a mail or an email directly to th... ... Flexibility of Embeddings of a Halin Graph on the Projective Plane 9of them. Those four paths are pairwise inner disjoint. It is easy for o... ...hose four paths are pairwise inner disjoint. It is easy for one to see that those pathstogether with a pair of segments (which are determined by... ...athstogether with a pair of segments (which are determined by the four leaves) of the leaf-cycleform a pair of inner disjoint paths connecting x ... ...is determined by making a twist ata vertex of a Halin graph. On the other hand, by making a twist at each pair of corners aroundevery vertex of a Hali... ... v. Let P1 be path from v to x3 on ∂f2. Thecycle C′ = Q1vP1x3y2 is also non-contractible. Notice that any pair of non-contractible cycles(curves) on N... ...opy of the journal included his or her paper(s) are provided to the authorsfreely. Additional sets may be ordered at the time of proof correction. ...

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...ectics: 104 II. Basic Principles of Materialist Dialectics The Principle of General Relationships: 107 Principle of Development: 119 III. Basic Pairs of Categories of Materialist Dialectics Private and Common: 128 Reason and Result: 138 Obviousness and Randomness: 144 Content and Form: 147 Essence and Phenomenon: 156 Possibility and Reality: 160 IV. Basic La...

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............................................................. 119 III. Basic Pairs of Categories of Materialist Dialectics 1. Private and Common........ .......................................... 239Appendices Appendix A: Basic Pairs of Categories Used in Materialist Dialectics ............... 246 A... ...refers to how matter exists in our universe. Form comes from the category pair [see Basic Pairs of Categories of Materialist Dialec- tics, p. 126] of... ...ness to physical processes. Example: a gambler who comes to believe that a pair of diceis “spiteful” or “cursed” is attributing conscious motivation t... ...nception of the world. Note: Materialist Dialectics contains Twelve Basic Pairs of Categories, Two Basic Princi- ples and Three Universal Laws. These... ...edge is that it is systematic, i.e., it is a set of information which is ordered according to certain theoretical principles. A collection of unsy...

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...AND NURAL YUKSEL . . 98 Respectable Graphs BY A.SATYANARAYANA REDDY. . . . . . . . . . . . . . . . . . . . . . . . . . 104 Common Fixed Points for Pairs of Weakly Compatible Mappings BY RAKESH TIWARI AND S.K.SHRIVASTAVA . . . . . . . . . . . . . . . . . . 111 Some Results on Generalized Multi Poly-Bernoulli and Euler Polynomials BY HASSAN JOLANY, HOSSEIN MOHEBBI AND ...

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...tific Information (PA, USA), Library of Congress Subject Headings (USA).Subscription A subscription can be ordered by a mail or an email directly to L... ... other. This graph can be shown as a tree. Because of each non-end vertexwith a rotation and end vertices pairwise with binary indices, this tree itse... ...two of its edgesintersect. The crossing number cr(G) of a graph G is the least number of intersections of pairsof edges in any embedding of G in the p... ...vertex. If not, let a, b, c and dbe the vertices of G adjacent to v. Then there exist paths between every pair of vertices of a, b, cand d not contain... ... is a graph with vertex set V1 ∪V2, where V1 ∩V2 = ∅, |V1| = mand |V2| = n; and with edge set of all pairs of vertices with one element in V1 ... ...f generality, by renaming the vertices, supposethat crD(ai) = 2q − 1 for i ≤ x.Case 1.1 There exists a pair of (i, j), 1 ≤ i < j ≤ x, such that crD... ...th vertex set V = {v1, v2, . . . , vn} and edgeset E = {e1, e2, . . . , em}. Assume that the vertices are ordered such that d1 ≥ d2 ≥ . . . ≥ dn,where...

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...he 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 _-Parallel Ric...

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...tific Information (PA, USA), Library of Congress Subject Headings (USA).Subscription A subscription can be ordered by a mail or an email directly to L... ... is m-connected. Theorem B([2]) A graph G is n-connected if and only if every pair of vertices are joinedby at least... ..., i = 1, 2, ..., n.12 B.Basavanagoud and Veena MathadAlso by Case 1, every pair of xi and yi are joined by ... ...finition 2([1,2,4,7,8]) A loop is an edge whose endpoints are equal. Multiple edges are edgeshave the same pair of endpoints.Definition 3([2,6]) A simpl... ...es . We specifya simple graph by its vertex set and edge set, treating the edge set as a set of unordered pairsof vertices and writing e = uv (or e = ... ...h G is a triple consisting of a vertex set V (G), anedge set E(G) , and a function assigning each edge an ordered pair of vertices. the first vertexof ... ...ts. We say that an edge is an edge from its tail to its head.Definition 5([2]) A digraph is simple if each ordered pair is the head and tail of at most... ...graph consists of numerical jvertices VN which represent the numerical solutions yj of (I.V.P.), and ordered numerical edge 1 2 n j... ...vertex set consistsof a set of graphs (digraphs) i.e. V (G) = {G1, G2, ...} and an edge set of unordered (ordered )pairs of this graphs i.e. E(G) = {(...

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...t was almost a girl, and she came out of A god can do so. But tell me how a man Raise no gravestone. Only let the rose Praising, that’s it! As one ordered to praise, Only one who has raised the lyre But you now, you whom I knew like a flower O this is the creature that has never been. Will transformation. O long for the flame, Be in front of all parting, as though ...

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...Only let the rose .......................... 33Praising, that’s it! As one ordered to praise, ................. 34Only one who has raised the lyre ...... ...s work,that first had to be accomplished), then he must see them,the quiet pair, mutely following him: 8the god of errands and ... ...n as he goes beyond. 33I, 7Praising, that’s it! As one ordered to praise,he emerged like the ore from the silent stone.His heart, ... ...Only let the rose .......................... 33Praising, that’s it! As one ordered to praise, ................. 34Only one who has raised the lyre ......

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...y and its applications in Algebra, written between 2014-2022 by the author alone or in collaboration with the following 81 co-authors (alphabetically ordered) from 19 countries: E.O. Adeleke, A.A.A. Agboola, Ahmed B. Al-Nafee, Ahmed Mostafa Khalil, Akbar Rezaei, S.A. Akinleye, Ali Hassan, Mumtaz Ali, Rajab Ali Borzooei , Assia Bakali, Cenap Özel, Victor Christianto, Chunxi...

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...e or in collaboration with the following 81 co-authors (alphabetically ordered) from 19 countries: E.O. Adeleke, A.A.A. Agboola, Ahmed B. Al-Nafee... ...9 Florentin Smarandache Refined Neutrosophy and Lattices vs. Pair Structures and YinYang Bipolar Fuzzy Set / 598 Xiaohong ... ... 52. Florentin Smarandache (2019). Refined Neutrosophy and Lattices vs. Pair Structures and YinYang Bipolar Fuzzy Set. Mathematics, 7, 353... ...nuous Function. 1 INTRODUCTION In this case the pair X ,  is called a neutrosophic The idea of "neutrosophic set" wa... ... defined the soft set in the following manner: Definition 2.17. A pair (F, A) is called a soft set over U where F is a mapping given by F... ... If X is self distributive then relation “≤” is a transitive ordered set on X, because if x ≤ y and y ≤ z, then x ∗ z = 1... ...ive self distributive BE-algebra, then relation “≤” is a partial ordered set on X. Proposition 2.2. [6] In a BE-algebra X, the ... ... 1 Preliminaries Definition 2.1 A hypergraph is an ordered pair H = (X, E), where: (1) X = {𝑥1, 𝑥2, … , 𝑥𝑚}... ... Definition 2.6 A single valued neutrosophic hypergraph is an ordered pair H = (X, E), where: (1) X = {𝑥1, 𝑥2, … , 𝑥𝑚}...

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...ion Making, Economics, Statistics, written between 2001-2022 by the author alone or in collaboration with the following 84 co-authors (alphabetically ordered) from 19 countries: Abhijit Saha, Abu Sufian, Jack Allen, Shahbaz Ali, Ali Safaa Sadiq, Aliya Fahmi, Atiqa Fakhar, Atiqa Firdous, Sukanto Bhattacharya, Robert N. Boyd, Victor Chang, Victor Christianto, V. Christy, Dao ...

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..., Florentin Smarandache, Zenonas Turskis The Use of The Pivot Pairwise Relative Criteria Importance Assessment Method for Determ... ...ne or in collaboration with the following 84 co-authors (alphabetically ordered) from 19 countries: Abhijit Saha, Abu Sufian, Jack Allen, Shahb... ...lorentin Smarandache, Zenonas Turskis (2017). The Use of The Pivot Pairwise Relative Criteria Importance Assessment Method for Deter... ...t violates the theory of • Suppose a certain physical process produces a pair relativity and the principle of causality, others support the ... ...and its antimatter counterpart. It was first configuration includes a pair quark-antiquark. Unmatter is generated in the 2015 experiment [1... ...s a surprised stare, a practical people and view the world as logical, ordered and predictable. May blank look and words like, ‘What do you mean,... ... noun, reishit. Also note that in Hebrew, subjects and verbs are usually ordered verb-first (unlike English in which the subject is written first). I... ...noun, reishit. Also note that in Hebrew, subjects and verbs are usually ordered verb-first (unlike English in which the subject is written fir... ...n a distant village was disturbed by voice of a cat in his house, so he ordered his students to tie the cat to a pole in the backyard, so he could...

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...er: famous novelist and sometimes spy Ellis Graveworthy, who wants Jack to come with him to England and build him a flying ship. Graveworthy has been ordered to cross the heavily-guarded coast of Australia, the "Dead Isle" which has no Creation, and which sealed itself off from the outside world more than twenty years before. Rumors abound that Australia is building a war ...

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...t any money." "I have." "Clare – " "It's real money," she said, flashing a pair of coins. They twinkled in the sunlight. "Do you want Chocolate ... ...e laughed and stopped in front of a storefront, leaning in the window. While she ordered, he watched: the burlyman who scooped the ice cream, the mist... ...am; it described a perfect arc through theair but fell well short of its mark. A pair of students walking near to the touchdown site stopped and stare... ... I hopenot. My only goal tonight is to see you enjoy yourselves, and to know the pair of you better. I have a commission muchlarger than you imagine, ... ... the griddle and stove as Jacob showed Clarethe enormous wooden table on which a pair of men were deboning chickens and trimming steaks. "Have you g... ...reen swords. He hurried to pull himself up again. "Don't just stand there," he ordered as reached the rail. "More coal!" Graveworthy gaped at him.... ...ivingorders, Clare giving slightly less impressive orders, and Graveworthy being ordered about – established a hierarchyfirmly in her mind. She fitted... ...hore before he could land properly in this wind. "Graveworthy, the boiler," he ordered, and heard the crunch and clank as the older man began to pil... ...iles and the – wow," Jack said, looking stunned. "Wow." "Breathe," Graveworthy ordered. Jack swallowed and inhaled. "We're all in a little bit of sh...

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...Susan Chapter Five: Leaving Home Chapter Six: Reprieve Chapter Seven: Dr Prosperov’s Island Chapter Eight: A Little Chat Chapter Nine: A Tragic pair Chapter Ten: Welcome to Renwick House Chapter Eleven: Beneath the Ashes Chapter Twelve: Down the Rabbit Hole Chapter Thirteen: Wilder Skies Fact or Fiction ...

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............................................................ 107Chapter Nine: A Tragic pair................................................................. ...ou're a d…that you aren't into men.” That brought her face up again. “Shut up,” she ordered. I shut up. She was mad-as. 7 ... ... he was tense now. I walked around the table toward him. “Sit down little c___!” he ordered. Orders don't work on me now. I ran at him. He stood. My k... ...ed him where thebuses went. He didn't know too much about the buses but he soldme a pair of lukewarm pies and an over-priced map. Naturally theydidn't... ...o we set out for school with none of Rewa'squestions answered. We were a thoughtful pair as we followed thefamiliar path to school. “Why do they have ... ...rt people,” I said, remembering. Aimee came up to our table with a nervous smile. I ordered achicken Pho with pickles in my best imitation Saigon Viet... ...e marooned.” Nope! She definitely didn't know the response words. “That's true.” We ordered dessert which involved chocolate for her and Chua forme. T... ...ade no sense to me at all. It may as well havebeen written in Hungol. The other two ordered quickly enough but Iwas stumped. I asked for explanations ... ...changing spindirections you can send a digital signal of zeros and ones. In thisway paired communicators can exchange signals over any distancewithout...

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...ing Twelve Grand in Scottish Hundred-Pound Notes From Under Your Kitchen Sink, Learn to Make Weaponised Plutonium, Fall Asleep on a Push-Bike, Sell a Pair of Rusty Skis, Be Sued Over a Fictional Secret Agent By An Altogether Terrifyingly Real Firm of International Lawyers, Hang Twenty Four Thousand Chickens on a Rack, Be Pursued By the Paparazzi, Attend a Fancy Dress Party...

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...er bad rap artist instead, hoping that he might soonbegin to gesticulate a pair of scissors with his fingers and mentionabout pimpin’ bitches and bust... ...ft with twoBetamax video players, an electric drill that didn’t work and a pair ofrusty skis. It was one of the last auctions I ever went to. ... ...hift rota and determining which of usdumb peasants would work where. I was ordered to stand for the nextfour hours at a conveyor belt ensuring that th... ...rd shining inthe ice cold glow of the industrial fluorescent tubing. I was ordered tospend the next hour rinsing out trays and putting chicken giblets... ...a few more weeks ofconversations before one day he arrived, to my surprise ordered a cupof coffee and told me with a keep-it-under-your-hat wink that ...

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...duction gives a good insight into the interdependencies between the natural numbers, which exist in this amazing geometrical structure. Titel : The ordered distribution of the natural numbers on the Square Root Spiral...

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...duction study can be found in the ArXiv–archive : Title of the study : “ The ordered distribution of the natural numbers on the Square Root Spiral ” ... ...al numbers, which exist in this amazing geometrical structure.Æ Titel : “The ordered distribution of the natural numbers on the Square Root Spiral” ... ...se radial rays.( Æ explanation see in my detailed introduction study : “ The ordered distribution of the natural numbers on the square root spiral... ...ms N1 and N6, N2 and N7, N3 and N8, N4 and N9 as well as N5 and N10, form pairs of spiral graph systems which lie approximately point- symmetr... ...r the positive spiral graph systems P1 – P9 don’t form such point-symmetrical pairs. • Calculating the differences of the successive numbers lying o... ...graph systems, the systems P1 and P4, P2 and P5 as well as P3 and P6 form pairs of spiral graph systems which lie approximately point-symmetrical ... ...r the negative spiral graph systems N1 – N7 don’t form such point-symmetrical pairs. 4 • Calculating the differences of th... ...rules which determine the existence of these spiral-graphs.Æ Titel : “The ordered distribution of natural numbers on the square root spiral” ( ... ...in the arXiv – data bank ) 11ReferencesThe ordered distribution of natural numbers on the square root spiralAuthors...

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...blished between 2005-2022 in different scientific journals, by the author alone or in collaboration with the following 110 co-authors (alphabetically ordered) from 26 countries: Abduallah Gamal, Sania Afzal, Firoz Ahmad, Muhammad Akram, Sheriful Alam, Ali Hamza, Ali H. M. Al-Obaidi, Madeleine Al-Tahan, Assia Bakali, Atiqe Ur Rahman, Sukanto Bhattacharya, Bilal Hadjadji, Ro...

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... or in collaboration with the following 110 co-authors (alphabetically ordered) from 26 countries: Abduallah Gamal, Sania Afzal, Firoz Ahmad, ... ... joint [6] Denavit J., Hartenberg RB - A kinematics notation for lower-pair motion of end-effector and the force error ∆XF is given by me... ...f distances of sets. A distance is a measurement of how far apart each pair of elements of a given set is. Distance functions in m... ...re still in its infancy. 1.1. G-Metric Spaces Metric space is a pair of (A, d), where A is a non-empty set and d is a metric which is defin... ...pty set and d be a metric on A, then if the following conditions hold, the pair (A, d) is called a metric space. Let x, y, z E A (1) d(x,y) �... ...X. Then, an intuitionistic fuzzy set (IFS) Y in X is defined by the ordered triplets as follows: e ... ... 410-413. 33. J. Vimala and J. ArockiaReeta. Ideal approach on lattice ordered fuzzy soft group and its application in select- ing best mobi... ...niverse, and Ri (1 ≤ i ≤ m) is a binary NR on U. We call the tuple ordered set (U, R ) the multigranulation neutrosophic approximation space (... ... is called totally  [{(x1  x2I)(a1  a2I) }{(y1  y2I) ordered under inclusion if N(P) and N(Q) are any { x1  x2I)(y...