Showing papers on "Magic square published in 2008"

Magic N = 2 supergravities from hyper-free superstrings

Abstract: We show by explicit construction the existence of various four dimensional models of type II superstrings with N = 2 supersymmetry, purely vector multiplet spectrum and no hypermultiplets. Among these, two are of special interest, at the field theory level they correspond to the two exceptional N = 2 supergravities of the magic square that have the same massless scalar field content as pure N = 6 supergravity and N = 3 supergravity coupled to three extra vector multiplets. The N = 2 model of the magic square that is associated to N = 6 supergravity is very peculiar since not only the scalar degrees of freedom but all the bosonic massless degrees of freedom are the same in both theories. All presented hyper-free N = 2 models are based on asymmetric orbifold constructions with = (4, 1) world-sheet superconformal symmetry and utilize the 2d fermionic construction techniques. The two exceptional N = 2 models of the magic square are constructed via a ``twisting mechanism" that eliminates the extra gravitini of the N = 6 and N = 3 extended supergravities and creates at the same time the extra spin-½ fermions and spin-1 gauge bosons which are necessary to balance the numbers of bosons and fermions. Theories of the magic square with the same amount of supersymmetry in three and five space-time dimensions are constructed as well, via stringy reduction and oxidation from the corresponding four-dimensional models.

Video game apparatus, method for proceeding video game and program

Abstract: PROBLEM TO BE SOLVED: To improve strategic characteristic by reflecting the skill of a player to a battle between a player character and an enemy character. SOLUTION: In the battle between the player character 101 and the enemy character 102, when the player selects a magic as a behavior of the player character, a puzzle battle is started. In the puzzle battle, a magic square (block frame) 121 is displayed on a display 15 according to the kind of a selected magic, and the player operates an input device to move/rotate blocks 122 falling from the upper part of the display 15 and stops the block at a desired position to fill the magic square 121. When all the squares in the magic square 121 is filled with the blocks 122 before a prescribed time passes after the time of starting the puzzle battle shown in a passing time gauge 124, the magic selected by the player is actuated to damage the enemy character 102. The effect of the magic corresponds to overlapping of the blocks 122 and projecting of them from the magic square 121. COPYRIGHT: (C)2008,JPO&INPIT

A Generalization of Magic Squares with Applications to Digital Halftoning

Abstract: A semimagic square of order n is an n×n matrix containing the integers 0,…,n 2−1 arranged in such a way that each row and column add up to the same value. We generalize this notion to that of a zero k×k -discrepancy matrix by replacing the requirement that the sum of each row and each column be the same by that of requiring that the sum of the entries in each k×k square contiguous submatrix be the same. We show that such matrices exist if k and n are both even, and do not if k and n are relatively prime. Further, the existence is also guaranteed whenever n=k m , for some integers k,m≥2. We present a space-efficient algorithm for constructing such a matrix. Another class that we call constant-gap matrices arises in this construction. We give a characterization of such matrices. An application to digital halftoning is also mentioned.

Polytopes of Magic Labelings of Graphs and the Faces of the Birkhoff Polytope

Abstract: In this article, we construct and enumerate magic labelings of graphs using Hilbert bases of polyhedral cones and Ehrhart quasi-polynomials of polytopes. This enables us to generate and enumerate perfect matchings of a graph via magic labelings of the graph. We explore the correspondence of magic labelings of graphs with magic squares and define polytopes of magic labelings to give a description of the faces of the Birkhoff polytope as polytopes of magic labelings of digraphs.

Freudental magic square and its dimensional implication for α¯0≃137 and high energy physics

Abstract: Modern theories of high energy physics are based in one way or another on Lie symmetry group’s considerations. In particular the exceptional family plays a pivotal role in superstring and E-infinity theory. For a long time the very existence of the famous 5 exceptional Lie groups G2, F4, E6, E7 and E8 with dimensions 14; 52, 78, 133 and 248 was bizarre. Freudental magic square gives some reasons to believe that the exceptional groups are not that exceptional. In the present work we elaborate this point further still and show that the sum of the dimension of E8, E7 and E6 when adding the dimensions of the two grand unification groups SO(10) and SU(4) to them amounts to the number of states in Witten’s p = 5 Brane model, namely 528. Furthermore when taking the standard model SU(3) SU(2) U(1) and an eight degrees of freedom Higgs field into account, the number rises to 4 multiplied with 137 of the inverse electromagnetic fine structure constant 528 + 12 + 8 = 4 α ¯ 0 = ( 4 ) ( 137 ) = 548 . The general implications of these results for high energy physics are briefly discussed.

Topics related to the theory of numbers: integer points close to convex hypersurfaces, associated magic squares and a zeta identity

Abstract: Let C be the boundary surface of a strictly convex d-dimensional body. Andrews obtained an upper bound in terms of M for the number of points on MC, the M-fold enlargement of C. We consider the integer points within a distance 5 of the hypersurface MC. Introducing S requires some uniform approximability condition on the surface C, involving determinants of derivatives. To obtain an asymptotic formula (main term the volume of the search region) requires the Fourier transform with conditions up to the Gd-th derivative. We obtain an upper bound subject to a Curvature Condition that re quires only first and second derivatives, that MC has a tangent hyperplane everywhere, and each two-dimensional normal section has radius of curvature in the range cqM +1/2 3), satisfying the Curvature Condition at size M. Then the total number, N, of integer points lying within a distance 6 of MC is bounded by the sum of two terms, one from Andrews's bound, the other from the hypervolume of the search region, with explicit constant factors involving 6, cq and c . In the body of the thesis, to simplify the notation, we use C for the enlarged surface called MC in this summary. In Part II we enumerate a class of special magic squares. We observe a new identity between values of the zeta functions at even integers.

Special Riemannian geometries and the Magic Square of Lie algebras

Abstract: We investigate nonintegrable Riemannian geometries modelled after certain symmetric spaces related to the Freudenthal-Tits Magic Square. The collection of four such structures found by Nurowski is extended by further eight. A focus is given to those admitting a compatible connection with completely skew torsion.

SUDOKU Puzzle Generates a Minimal Art Sculpture

Abstract: A SUDOKU puzzle is a magic square with 9 rows and 9 columns and 81 squares. Each SUDOKU puzzle that is solved can be used as a source of design parameters for a Minimal Art based Sculpture. 9x9 A SUDOKU puzzle is a magic square with 9 rows and 9 columns and 81 squares. Each row and column contains 9 squares. Each square contains a number between 1 and 9. Each number may appear just once in a row or in a column. Each SUDOKU puzzle that is solved can be used as a source of the design parameters for a minimal art based sculpture. Consider each square of the 81 squares as a cube. The 81 cubes will be the elements of a sculpture. To realize a 3D object each cube must have a position in space. Consider the number on each cube as a height coordinate which determines the third dimension, the level of the cube. The cubes with number 1 stay at the bottom, with number 9 take position at the top. The other cubes hold position at a level in between. The result is an object, with the property that you can see all the 81 cubes in all 6 axis-parallel views. So, no cube is hidden by another cube. Not only the top and bottom view, but also the front and back view as well as the left and right view. In all the 6 views you see a 9 by 9 square! But in a random perspective view you see a mash of cubes, an optical illusion, an anamorphic image. 8x8 I did not develop this principle on a SUDOKU puzzle square. I had never seen a puzzle like that when I was busy with this subject in 2001. My inspiration to realize a Minimal Art Sculpture myself was excited when I visited a Minimal Art Exhibition in the Gemeentemuseum in The Hague. As a result I developed a magic cube with a base of 8 rows and 8 columns and 64 cubes. This is the story: I wondered if it is possible to create a piece of art, which looks, seen from 6 different views, like a chessboard, using only 64 cubes. That is what I asked myself, having visited a Minimal Art Exhibition in the Gemeentemuseum in The Hague in the Netherlands, seeing work from Sol LeWitt, an artist of the Minimal Art movement. I read about LeWitt, that in his vision, the idea behind the art work is much more important than the construction of the work of art itself. In my thoughts I saw my Chessboard "Cube" right in the middle of a roundabout, at the crossing of two rectangular roads. On your way to the roundabout you see in front of you the view of the chessboard; while driving on the roundabout, you experience an optical illusion, because the position of each cube in relation to the other cubes changes constantly. Leaving the roundabout you see in your rear-view mirror again the chessboard, independently whether you leave at 1⁄4, 1⁄2 or 3⁄4 of the full circle. I think it is a good idea, and a good result as well. According to Sol LeWitt's point of view it is a win-winsituation. At that time I became a user of the Program Rhinoceros. A computer program you can easily make 3D models with. I tried to reach a result by trial and error. But I did not succeed. Trial and error is not a good practice to solve the problem. If you look at the number of possibilities of the system you find there are millions of possibilities within billions of impossibilities. It is like searching for a needle in a haystack. I have tried to find out how

Multifunctional digit anti-fake label

Abstract: The utility model discloses a multifunctional digital anti-counterfeit label, comprising a label body which is provided with identity code, anti-counterfeit code and an unfinished magic square, wherein the anti-counterfeit code is provided with a covering layer; the unfinished magic square selects part of fixed numeral row or column or diagonal numbers from a random magic square and then selects about half of the numbers of the random square to print on the corresponding grids of the unfinished square of the label as the information feature of the label. The utility model which integrates the identity code, the anti-counterfeit code and the unfinished square which are obtained through a code random square on one label realizes the integral multifunctional digital anti-counterfeit label of anti-counterfeit function of commodity, logistic control, lottery promotion and game promotion. The label has multiple anti-counterfeit functions of anti-counterfeit verification before purchase and anti-counterfeit identification after purchase, can combined anti-counterfeit function of a small package and a big package and can increase the query rate through lottery promotion and game promotion and improve the anti-counterfeit and logistic monitoring effects.

On Integer Solutions to Linear Equations

Abstract: A magic square is an n × n matrix with non-negative integer entries, such that the sum of the entries in each row and column is the same. We study the enumeration and P-recursivity of these in the case in which the sum along each row and column is fixed, with the size n of the matrix as the variable. A method is developed that nicely proves some known results about the case when the row and column sum is 2, and we prove new results for the case when the sum is 3.

Super magic square

Abstract: A super magic cube comprises chunks A (3) and chunks B (2), which have the same number and are distinguished by different colors. When the magic cube is combined, the chunks A (3) are connected with the chunks B (2). Magnets (1) are embedded on the six surfaces of the chunks A (3) and the chunks B (2), and the polar of the six surfaces of the chunks A (3) is opposite to that of the six surfaces of the chunks B (2). Due to the action of magnetic force, all small cubes of the utility model are absorbed together with each other, thereby being capable of combining at will. Spelling letters or characters of any language, such as letters, words or etymons of languages of English, French, German, Russian, and the like, Pinyin, characters or phrases of Chinese, and hiragana, katakana, and the like of Japanese, can be stuck to or printed on each surface of the small cube according to requirements. When used as a toy, a schooling apparatus or an instructional instrument, the utility model not only solves the problem that the traditional magic cube has over less surfaces for displaying information (the number of the surfaces for displaying information of the super magic cube is a plurality times of that of the traditional magic cube), but also solves the problem that the letters, the characters or the phrases are reversed when all surfaces are combined.

An Algorithm for Finding the Three-dimension Paths of the S-Shaped intellectual Magic Square

Abstract: The S-shaped intellectual magic square which composes of 27 cubes connected each other is an type of intellectual magic squares. This paper presents a 3D spatial data model based on the concept of computer graphics. We analyze and classify the key little cubes and put forward a recursion formula for all possible coordinate points about every little cube. In the end, All results which gotten from a recursion algorithm and the prospect about this model have been given in the paper.

Noise Effects in Quantum Magic Squares Game

Abstract: In the article we analyse how noisiness of quantum channels can influence the magic squares quantum pseudo-telepathy game. We show that the probability of success can be used to determine characteristics of quantum channels. Therefore the game deserves more careful study aiming at its implementation.

Symmetric Spaces of Exceptional Groups

Abstract: We adress the problem of the reasons for the existence of 12 symmetric spaces with the exceptional Lie groups. The 1+2 cases for $G_2$ and $F_4$ respectively are easily explained from the octonionic nature of these groups. The 4+3+2 cases on the $E_{6,7,8}$ series require the magic square of Freudenthal and, for the split case, an appeal to the supergravity chain in $5, 4$ and 3 spacetime dimensions.

Generalization of the rule counting of the free variables in double-even pandiagonal magic squares

Abstract: In this paper, we generalize the rule of counting the number of the free variables in the double – even pandiagonal magic squares; our method is not based on the direct computation of the solution of the linear system. Instead, We deduce this rule by applying the theorems and methods of linear algebra , finally put algorithm of the solution . ةصلاخلا ةيرحســلا تاــعبرملا يــف ةرــحلا تا رــيغتملا ددــع هــللاخ نــم بســحي يذــلا نوناــقلا ميــمعت مــت ثــحبلا اذــه يــف اـمناو ،ةـيطخلا تلاداـعملا ماـظن لـح ىـلع دـمتعت لا ةمدختسـملا ميـمعتلا ةـقيرط نإ ،ةفعاضـملا ةـيجوزلا ةـيرطقلا ت نم ا ريخأ ،باسحلا يف ىرخلأا يطخلا ربجلا تايرظنو قرط ةدع قيبط لحلل ةيمزراوخ عضو مت .