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...eps through the wormhole, older but not aged, his gray-green eyes betray his youth. A sense of weightlessness fills his body every time he rips. The cube glows a florescent green. The journey although less than 5 seconds is 13 years across 1 universe. He looks at the familiar beige wall that stands before him. Water dripping into one of the many drains that kept the la...

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... - 8 1.1. ADVENTURES and VARIATIONs IN MURPHY’s LAW (Preface) - 9 1.2. What and Why Florentin’s law - 11 1.3. Florentin’s Laws / !An Author to the Cube! - 13 1.3.1. Florentin’s Laws: To hell with Murphy, deviate! - 14 1.3.2. Florentin’s Laws: Relax Peter’s! - 16 1.3.3. Florentin’s Interdisciplinary Laws - 18 1.3.4. More Variations in Florentin’s Law - 20 2. FLORENT...

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...instant photovideo journal Nopțile Polare Inuite (Inuit Polar Nights), published by Agora Editions, Romania, 2018. 2,565,000,000,000,000 Tonne Ice Cube sits on top of Greenland, weighting 2.565 quadrillion tonnes, with its mean height of over 2 km, and over 3 km at its thickest point. The global sea levels would raise by 23 feet if the ice of Greenland were to melt....

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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 f...

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...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....

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...rings of Some Simple Graphs BY P.JEYANTHI AND P.SELVAGOPAL . . . . . . . . . . . . . . . . . . . . . . . 33 Elementary Abelian Regular Coverings of Cube BY FURONG WANG AND LIN ZHANG. . . . . . . . . . . . . . . . . . . . . .49 Super Fibonacci Graceful Labeling of Some Special Class of Graphs BY R.SRIDEVI, S.NAVANEETHAKRISHNAN AND K.NAGARAJAN. . . . . . . . 59 Surface...

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...andache Identities 59 Muneer Jebreel Karama On the integer part of a positive integer’s k -th root 61 Yang Hai , Fu Ruiqin Smarandache Friendly Cube Numbers 67 Muneer Jebreel Karama Some Expressions of the Smarandache Prime Function 71 Sebastian Martin Ruiz An Improved Algorithm for Calculating the Sum-of-Factorials Function 75 Jon Perry On the Smarandche fu...

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...er set F(2 X ), the set of all fuzzy subsets of X, look like? It looks like a cube, What does a fuzzy set look like? A fuzzy subsets equals the unit... ...cube, What does a fuzzy set look like? A fuzzy subsets equals the unit hyper cube I n = [0, 1] n . The fuzzy set is a point in the cube I n . Vert... ... I n = [0, 1] n . The fuzzy set is a point in the cube I n . Vertices of the cube I n define a non-fuzzy set. Now with in the unit hyper cube I n ... ...nd fuzziness of a fuzzy set and more fundamentally to a measure. Thus within cube theory directly extends to the continuous case when the space X i... ...ce X is a subset of R n . The next step is to consider mappings between fuzzy cubes. This level of abstraction provides a surprising and fruitful a... ...or statistical techniques directly from problem domain sample data. Between cube theory is fuzzy-systems theory. A fuzzy set defines a point in a ... ...uzzy set defines a point in a cube. A fuzzy system defines a mapping between cubes. A fuzzy system S maps fuzzy sets to fuzzy sets. Thus a fuzzy sy... ...zzy system S is a transformation S: I n → I P . The n-dimensional unit hyper cube I n houses all the fuzzy subsets of the domain space or input un... ... (FAMs) are transformation. FAMs map fuzzy sets to fuzzy sets. They map unit cubes to unit cubes. In simplest case the FAM system consists of a sin...

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...ites) with lowest potential at maximum distance ―the corners of the nuclear cube. 11. This indicates the noble elements, (Column 8A, Periodic Table)...

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...lity is arranged for every single person. To understand this, let us picture a cube with about seven billion layers, approximately the number of peop... ...one is integrated. Moreover, each of the other cells has its own layer in the cube, and that layer, too, is now awakened. In fact, when a single per... ...ges in the aware- ness of all people. Such interactions between layers in the cube promote all of humanity toward correction and wholeness. We shoul...

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...g at Dan’s Place Dan dipped the flowery kitchen towel in a bowl of cluttering ice cubes and applied it to my bloated face. “They didn’t have to do...

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...eful tour of speckles premises. Toddlers in flowery pyjamas amuse themselves with ligneous cubes and plastic toys. I can't remember if I have never...

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...6) was a Danish polymath (mathematician, inventor, designer, game inventor, poet). Hex, Tangloids, Morra, Tower, Polytaire, TacTix, Pyramystery, Soma cube are creative games developed by Hein. He created a new form of poetry, 'Grook' ("gruk" in Danish, short for 'GRin & sUK' - "laugh & sigh", in Danish), characterized by irony, paradox, brevity. He wrote over 10,000 of gro...

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... blender and belnd until you get a green juice. Take a big glass and add 1-2 tablespoons of sugar, the basil juice and some lime juice. Add some ice cubes and cold water. Very refreshing. ...

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...n the sequence are 1,2,3,1,5,6,7,2,10,11,3,14,15,1,17, 0 28. Smarandache Cube Complements Definition 2: For each integer n, the Smarandache Cube Co... ...ube Complement SCC(n) is the smallest integer k such that nk is a perfect cube. The first few numbers in this sequence are 1,4,9,2,25,36,49,1,3,100... ... integer n Output SCqn), the smallest integer k such that kn is a perfect cube Step 1. If n = I return k = 1 Else Step 2 Factor n into the product... ...orm 3j+2 then set k = k * Pi Step 5 Return k. Clearly, if n is a perfect cube, SCqn) = 1 The set of fixed points of SCqn) is decidedly different fr... ... 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 such that • ... ...ime 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) or SCC(n) = I = SCC... ...SSC(w-l) or SCC(n) = I = SCC(n-1) If either n or n+ I is a perfect square(cube) the other is not and therefore not equal to I Therefore, the only re... ...only remaining possibility is when both nand n-I are not perfect squares( cubes) Clearly, nand n, I have distinct prime factors And so, when SSC(n) ... ...f squares exist 0 Problem (74) in [5] is similar. 74) Smarandache Pseudo-Cubes of the Third Kind Definition 5: A number is a Smarandache Pseudo-Cub...

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...s of rye bread coated with water by a wide brush emitted steam and particular fragrances that Walter relished. He also remembered how he placed sugar cubes outside on the windowsill; Walter badly wanted a brother or sister. He was told that sugar cubes would help bring about his wish. Although he tried a lot, brother and sister never arrived. His parents gave him a used t...

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...quence Have in Common …………………. 120 2.20 Smarandache Patterned Perfect Cube Sequences ………………… 121 2.21 The Smarandache Additive Cube Sequence ... ...andache n2n Sequence ………………… 126 2.25 The Smarandache Fermat Additive Cube Sequence ………………… 128 2.26 The Smarandache nn 2 Sequence Contains ... ...es With a Given Valid Digit Sum ………………….. 155 3.3 Fabricating Perfect Cubes With a Given Valid Digit Sum …………………… 157 3.4 Smarandache Perfect... ...e to derive T n = 2 n-2 * ( n+3)(n)/ 2. 6) Smarandache Pascal Derived Cube Sequence Start with the sequence of perfect squares S b : 1, 8, 27, ... ...s in some position. b) A prime in which N appears in some position. c) A cube in which N appears in some position. d) A power in which N appears in... ... the proof of the theorem. Section 20 Smarandache Patterned Perfect Cube Sequences Consider the sequences 10011, 100011, 1000011, 100001... ... ‘n’ zeros followed by 11, or 10 n+3 + 11. The sequence formed by the cubes of the numbers in this sequence is 1003303631331, 1000330036301331... ... Theorem: The two sequences above form a Smarandache patterned perfect cube sequence. Proof: The n th term of (1) is given by T n =10 n+... ... is given by T n =10 n+3 + 11. Hence the n th term of corresponding cube sequence is T n 3 = 10 3n+9 + 33 * 10 3n+6 + 363* 10 n+3 + ...

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...64125216, . . . where element k is formed by concatenating the sequence of cubes on the right side 1(2*2*2)(3*3*3) . . . (k*k*k) The question that was... ...The question that was then posed was: How many of the elements are perfect cubes? 65 A program was also written to search for elements of this seque... ... was also written to search for elements of this sequence that are perfect cubes. That program is similar to the one that searches the Concatenated Sq... ...squares and was used to examine the first 500 elements of the Concatenated Cube sequence. No perfect cubes were found. As was done for the Concatenat... ...m was then altered to examine the differences between the smallest perfect cube that is greater than an element of the Concatenated Cube sequence and ... ...s in the numbers, the general behavior of both graphs for the Concatenated Cube sequence is the same. Since both are increasing, the following conject... ... to be a very safe on. Conjecture: There is no element of the Concatenated Cube sequence which is a perfect cube. Figure 3 66 Figure 4 5) Smarandache... ...gure 9. The Concatenated Cubic sequence, which grows by concatenating the cubes of the integers on the right was used to create the image of figure 1...

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... • Is there any perfect square among the terms of that sequence? A perfect cube? 59 5) Smarandache alternate consecutive and reverse palprimes sequen... ... 1, 8, 125, 512, 1000, 1331, 8000, 19683, 35937, ......... Sequence of cubes which digits sum is a cube too. • Is this sequence finite? • Which is... ...o. • Is this sequence finite? • Which is the maximum number of consecutive cube that are also additive cube? • Evaluate the continued general fraction... ...Conjecture: A finite number. • How many terms in that sequence are perfect cube? • How many terms in that sequence are squarefree? • Evaluate ) ( ) 1... ... perfect square? Conjecture: A finite number. • How many terms are perfect cube? Conjecture: None 23) Smarandache ) (n nf generalized sequence L...

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...on. In a similar interpretation by Lee and Yang the points stand for small cubes in Euclidean space where each cube may or may not be occupied by a... ...1 Graph, 18 H Hamilton path, 33 Hamiltonain cycle, 46-8 Hamiltonian cube graph, 54 Hamiltonian graphs, 46-9 Height of a neutrosophic relati...