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...Papers concerning any of the Smarandache type functions, sequences, numbers, algorithms, inferior/superior f-parts, magic squares, palindromes, functional iterations, semantic paradoxes, Non-Euclidean geometries, manifolds, conjectures, open problems, algebraic structures, neutrosophy, neutrosophic logic/set/probability, hypothesis that th...

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...nction, f-inferior part function, k-k additive relationships, 2-2 subtractive relationships, sequences, coprime functions, double factorial function, magic squares, problems, conjectures, equations, partitions, paradoxes, series, algebraic structures, pseodo-smarandache function, erdos-smarandache moments numbers; and in physics: related to smarandache hypothesis that ther...

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...he municipal workers came and pasted funereal announcements onto his concrete pole and the magic was all but gone. My grandma withered, dilapidated... ... Fatigue-glued to my chair I find it hard to stoop and place the wagers on the fluctuating squares of the roulette board. Eli wobbles towards me, h... ... there unannounced or uninvited. Moonlight transforms brickwork chateaux into the stuff of magic. They take your breath away and hurl it back at you... ...platinum tie clip and pair of cufflinks, the betting stopped. A tangled web of avenues and squares, the foliaged daubs of green and orange, the ash... ...ances (she buried them among her lingerie until they all evaporated). At the bottom of his magic chest lay booklets with titillating tales of sizzl... ... white. I proudly presented my paper loot. We used a ruler and scissors to divide them into squares. And all that protracted time I prayed that Shal... ...ht all around. I have a predilection towards "key phrases", the kind that, not unlike some magic spells, capture the entire world in its embryonic ... ...e would beg, mother mother, more and she graciously consented and those were afternoons of magic and I felt no need to read, only to listen to the ...

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...pect of our lives. A friend of mine, Steve Crothers, calls attitude the "Magic Word." It's important to realize, though, that you create the magic ... ...you can do, or dream you can, begin it. Boldness has 77 genius, power and magic in it. Only engage and the mind grows heated, begin and then the tas... ...ion or lack of commitment can be. 1m, mediately below the title were nine squares, each with a picture of a light bulb and a quote above each bulb.... ...ht be helpful to remember Goethe's words, "Boldness has genius, power and magic in it. Only engage and the mind grows heated, begin and then the ta... ...y one of the most power, ful words in the English language. It can bring magic and instant gratification in your life. If I have any secrets, tappi...

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...All people loved him and went to him for help. And he helped them with his magic powers. Just with a look he could see into their hearts. And he could... ...o draw with his walking stick in the dust of the road. Triangles, circles, squares were interlacing, weaving symmetric forms. And soon these forms beg...

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...n angel, but Satan himself; of whom Antichrist shall learn all kinds of divinations and magic, by which he shall perform prodigies in the world. Othe... ...pocalypse and other parts of scripture, we find not a single word concerning sorceries, magic, or that power of doing miracles, which the doctors att... ...nd joined themselves to the house and kingdom of Judah. And what if nothing of all this squares with as certainly it doth not, but manifestly contrad...

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...t is known that SSC(r) = I Now consider the number r -'- 1. Since perfect squares are not sequential, r + I cannot also be a perfect square Therefor... ...at M > d, V d E D. Proof: Apply the reasoning of theorem 3, replacing all squares by cubes. D Corollary 2: There are no positive integers M and k su... ...h is composed of prime factors. Clearly, nand n+ I cannot both be perfect squares or perfect cubes so it is not the case that SSC(n) = I = SSC(w-l) o... ...ore, the only remaining possibility is when both nand n-I are not perfect squares( cubes) Clearly, nand n, I have distinct prime factors And so, whe... ...t do not involve sequences. Problems relating the Smarandache function to magic squares have also been posed by \1ike \1udge in his regular ':\'umbe... ...ular ':\'umbers Count' column in Personal Computer World Definition 33: A magic square is a collections of numbers a], a2, ., ak such that k = n*n i... ... 7 12 ,4 15 14 I such that the common sum is 34. It is well-known that magic squares can be constructed using only primes, so it is also known th... ...ing Smarandache Numbers Seal), S(a2), . , SCad can be used to construct a magic square. For example, consider the 3 x 3 magic square 101 29 83 53 ... ... S(p) = P for p a prime, the Smarandache values would form the same 3 x 3 magic square. A logical extension of this problem places a restriction on ...

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...of America "...It is just this, which gives the higher arithmetic that magical charm which has made it the favourite science of the greatest mathe... ..., and since x;y;z are integer, the expressions on radicals must be perfect squares of integers. Let xy(x +y +z) =t 2 ; xz(x +y +z) =p 2 ; yz(x +y +z) ... ...n 3 = square, giving z = perfect square. All in all, x;y;z are all perfect squares. Let x = 2 , y = 2 , z = 2 . Then 2 + 2 + 2 =v 2 : (28) From... ...be positive integers. Ifxj(z 2 +1), thenx can be written as the sum of two squares (i.e. x =a 2 +b 2 , where a;b 0) (see e.g. [1], [3]). Lemma 2. (La... ...(m 2 ) m 2 1 m < 2 3 for m > 4, for the composite numbers of the perfect squares we have a very strong improvement. 10) lim n!1 inf (S(n)) n = 0. ... ...her particular cases of (1). 2. First let A =fk 2 : k2 N g = sequence of squares. Let us denote the function obtained from (1) by Q(n) = minfm 2 : m... ...ime number, then with p 1 ;p 2 ;:::p n 2 it is not possible to construct a magic square. Let d be the magic constant of such a square. Then clearly th... ...book [2], by Rouse Ball one can nd that J.N. Muncey in 1913 constructed a magic square of 12th order which involve the rst 143 odd primes and 1, nam...

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... Khalil Raiss discovers a well articulated clownishness, situated close to magic. A Romanian supporter sees in paradoxism “the harmonious anarchy of... ...ate zone and no clement moderation. No and never! Substantially, anti-, magical particle of paradoxism, abolishes the (traditional) literature in ... ...the case of these ones the German translation seemed preferably...), tiny squares - ideal places for some idea, hieroglyphic signs. In order to be k... ...erly speech of sovereign....”). Taking down through linguistic absurd the magic formulas of Power and the propagandistic stereotypes, it is reached ... ...unfolds as a real feat of strength, taking in a hallucinatory vertigo the magical forms of the party mystique and the representatives of its langua... ...ed by totalitarianism. Tempted by trance, paradoxism is fascinated by the magic of the possible. (In the halo of the late paradoxist experiences c...

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...istrict, First Ward, Second Precinct. 6. The names of thoroughfares, parks, squares, blocks, buildings, etc. : Malzzlal of Style: Capitalizatiolz ... ...egelian world of process-how great the contrast !" " ' Process'-that is the magic word of the modem period;" "To be or not to be-that is the questio... ...f &ous mominations 7; of sessions of Congress, 11; of thom$h- fares, parks squares blocks bruldmgs, etc., 6. of( titles icademi'c degrees, orders ... ...of words'den&hg subsechons, m hterary references, loo; rules for, 8a-107. Squares, capitalization of names of, 6. Standard: of measurement in typo...

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...s of the gods, and experience of powers of extra-sensory perception and of magic feats. Following upon these visions there came, as if in complete ref... ...a trance which, according to the spiritual and psychic development of the [magician], is more or less deep and more or less prolonged. The exercise, e... ...ppening in this yoga? Alexandra 38. Alexandra David-Néel, With Mystics and Magicians in Tibet (1931). (Penguin reprint of 1936), pp. 207-8. Hereafter ... ...he West in the practice of yoga. Generally the purpose has been to obtain “magical” powers, or simply to obtain more complete control over the body, r... ...nothing unaccountable about mysticism. It is not in itself myste- rious or magical. As a religious form it simply means feeling that God is present, a... ... the smoker. The medicine man had also left a gourd containing forty small squares of flesh that his grandmother had sacrificed from the surface of he...

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...ld days? How does khaa ta akong differ from Buddhism? They used to draw 12 squares on the ground and there were four signs of the tiger and the rest b... ...ombined. It is Azan Wat who often doubles as sorcerer, he may take care of magic rites which the monks are not keen to perform. Favourable days are st... ... tree seedling, and it is rendered effective by spells or incantations, or magic symbols carved on it. Blowing and measuring with a stick are known al... ...dern generation has retained little knowledge of substances or plants with magic properties.(59 However, almost everybody remembers foods that were fo... ...her phenomenon, who knows the correct incantations and the substances with magic qualities that could cure an illness, for example. With his rites and... ...ritage contain about 150,000 variants of incantations. (65 Substances with magic qualities have varied in different cultural environments, but the log...

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... to explode. It did not explode for no reason at all. It did not explode by magic. In order for it to explode, there had to be a pre-existing Con... ...farthest detectable radiation 13 billion light years away. Now, if you could magically transport the Hubble telescope 13 billion light years to the... ...ut of sight. Whatever goes into a black hole also comes out. There is no magic involved here. The fact that Energy is not destroyed inside a b... ...nsions and Causality The Three dimensions of our Universe did not appear by magic out of nowhere; they were created in a strict causal sequence. ... ...e Actually Infinite. The Three dimensions of our Universe did not appear by magic out of nowhere; they were created in a strict causal sequence. O... ...e middle of hundreds of square miles of natural forests. They buy immaculate squares of land called acres. Sacre acre they buy sacred earth abstr... ...maculate sacred square of abstractly owned land. You can see these immaculate squares of cleared land from the air. They are insane abstract design... ... In stark contrast to the natural beauty of the wild forest all around their squares of raped destroyed earth. Except that most of the natural fore... ...natural grace and beauty of the wild forests all around these weird unnatural squares of artificial ugliness, as destroyed as they are; contrast the...

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..., Unemployment Benefits and Minimum Wages We are all under the spell of magic words such as “mobility”, “globalization” and “flextime”. It seems a... ...ording to these sages, immigration is both inevitable and desirable. This squares nicely with politically correct - yet vague - liberal ideals and s...

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...l relief, just as two years ago. His hands are more than hands, it seems. Magical masseur, he explores yet never gropes: his fingers, padded at the ... ...O VOICES FROM THE PAST 136 Watch the dice in her fingers! She’s a magician of tricks and youth, my Anaktoria and, oddly enough, I can never ... ...eat bronze horse are treasures of mine. Well, his bottega was a place of magic...subtleties in metal and wood. Again it’s late. Francesco is play... ..., the tents and flags reflected in the ice, purple, red, yellow—pen- nants squares gay—men and wenches tippling—musicians trying to keep their feet w... ...ivered. We saw our comradeship, our triumph over slogging days: there was magic flowing through our blood: that fulsomeness, that nothing could tarn... ...ROM THE PAST 482 Stratford I have been thinking of Merlin and his magic ways, the thrall of his immense dabbling: this island should have be...

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... one determine market concentration to start with? The Herfindahl-Hirschmann index squares the market shares of firms in the industry and adds up t... ...nstrate irrational behaviours of economic actors (heuristics, dissonances, biases, magical thinking and so on). The apparent chasm between the rat... ...n a case by case basis. Indeed, this is the greatest lesson of all: There are NO magic bullets, final solutions, right ways and only recipes. Thi... ...ation and injustice. He rebels and rages. Depending upon the pervasiveness of his magical thinking, the narcissist may feel besieged by overwhelm... ...issist, very much the infantile outcome of stunted personal development, engages in magical thinking. He feels omnipotent, that there is nothing he ... ..., or membership of certain groups, that he is above reproach and punishment, that, magically, he is protected and will miraculously be saved at the...

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...sed the brilliance that came to him and felt awe toward the paper that could magically reflect the mood and full realm of his mind. He yearned to embr... ... was separated into two apartments. Sang Huin used his photograph cards like magic tricks to get them to practice tenses and syntax. He liked seeing t... ...aving given to him. It was her hope that the nickname, "Adagio," would, like magic, get him to be calm if not elicit from the child a rather scholasti... ...on on Gabriele, the executioner. She imagined it praying to the earth that magically brought it into life to shrink its size into something so much ... ...to part from continual dreaminess and to end the world of the child that saw magic in a waving leaf on a branch of a tree. He didn't want tedium that ... ...g herself sensing something. It was some type of boxed light or illuminated squares like the pattern of her grandmotherﾁOs quilt and with it was stat...

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...ed, for as the heralds following the buglers proclaim in the market places and squares the death of the sovereign, they also cry aloud, "Long live his... ...hile here and there the most splendid temples rose in grandeur from the city's squares, and there was every indication of extraordinary wealth and the... ...las roared forth the excellence of their wares. On stands in the comers of the squares, fruit dealers displayed their luscious goods and solicited the... ...ey recorded stories of clove-trees fed on dead bodies, of cinnamon produced by magic from human bones; of nutmegs dug up from caves of the sea; of sav... ... the astounding groups filled the streets; evergreen arches were reared in the squares; organs pealed in the churches, choirs sang Te Deums for those ...

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...ht background. As Lermontov said in The Red Shoes: "Not even the greatest magician in the world can pull a rabbit out of a hat if there isn't alread... ...appears to be a static, cluttered diagram with multicoloured, overlapping squares. Really, it is an extremely powerfulway of presenting the dynamics ... ...rships that have formed within each one." Pass your mouse over any of the squares and a virtual floodgate opens - a universe of interconnected and h... ...y people felt that the dot.com era was unrealistic, yet the allure of the magically rising stock prices fueled the eventual conflagration. The same... ...ically well defined prototype, the cybernetic revolution means entering a magical space, much alike that of Alice in Wonderland were laws appear and... ...ully aware of the extension and velocity of the tech-waves. The arena is a magic space, changing abruptly. To survive, the mind of the spiritual man ...

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...untains and cobblestone streets that dated back hundreds of years was still a magical place. The smell of garlic, salami, and sweet bread filled the ... ...ished the chocolate colored liquid and stared into it as if it contained some magic cure -- His mind began flooding with memories: He was born Mich... .... The warm sun, and the exquisite sunsets dipping into the Sea of Cortez, was magical. His good looks were stunning, not pretty or rugged, but aris... ...she asked annoyed, as she whirled pots and pans around with the deftness of a magician's hand. 128 J.Cross/Artemis "Sister Mary Katharine is a... ...d, they will be rounded up like vermin, and their heads severed in the public squares of our cities for all our citizens to see," Oshiro said matchi...