Showing papers on "Magic square published in 2010"

Method for sensing electronic magic square, electronic magic square and magic square game system

Abstract: The embodiment of the invention discloses a method for sensing an electronic magic square, the electronic magic square and a magic square game system. The method comprises the following steps: acquiring sensing data of the electronic magic square, wherein the sensing data comprises any one or more of acceleration sensing data, geomagnetic field sensing data, gyro sensing data and touch screen sensing data; acquiring motion information and/or positioning information of the electronic magic square according to the acquired sensing data, wherein the motion information comprises the motion information of the whole body of the electronic magic square and relative motion information of each sub square, and the positioning information comprises the positioning information of the whole body of the electronic magic square and the relative positioning information of each sub square; and sending the acquired motion information and/or the positioning information of the electronic magic square in a wireless transmission mode. The embodiment of the invention achieves the effective interactions between the electronic magic square and the electronic magic square, and between the electronic magic square and other game terminals or devices, thereby greatly strengthening the interactivity and the entertainment of a magic square game.

A cryptographic algorithm based on hybrid cubes

Abstract: Cryptographic algorithms are important to ensure the security of data during transmission or storage. Many algorithms have been proposed based on various transformation and manipulation of data. One of which is using magic cube. However, the existing approaches are based on a transformation of magic cube’s face values. In this paper, we propose a new cryptographic algorithm based on combinations of hybrid magic cubes which are generated from a magic square and two orthogonal Latin squares. Using two random functions, i.e., random selection of thirteen magic cubes and random key selection from layers of hybrid, the generated chipertexts are free from any predicted pattern which might be used by cryptanalyst to decipher the original message.

Decomposable functors and the exponential principle, ii

Abstract: We develop a new setting for the exponential principle in the context of multisort species, where indecomposable objects are generated intrinsically instead of being given in advance. Our approach uses the language of functors and natural transformations (composition operators), and we show that, somewhat surprisingly, a single axiom for the composition already suffices to guarantee validity o the ex- ponential formula. We provide various illustrations of our theory, among which are applications to the enumeration of (semi-)magic squares.

E7 groups from octonionic magic square

Abstract: In this paper we continue our program, started in [2], of building up explicit generalized Euler angle parameterizations for all exceptional compact Lie groups. Here we solve the problem for E7, by first providing explicit matrix realizations of the Tits construction of a Magic Square product between the exceptional octonionic algebra J and the quaternionic algebra H, both in the adjoint and the 56 dimensional representations. Then, we provide the Euler parametrization of E7 starting from its maximal subgroup U=(E6 x U(1))/Z3. Next, we give the constructions for all the other maximal compact subgroups.

Method for disordering, splitting, storing, combining and mutually validating files

Abstract: The invention provides a method for disordering, splitting, storing, combining and mutually validating files. The method is characterized in that the method includes the following steps: A. file disordering; B. magic square encryption; C. file restoration and mutual validation. The method has good security and high efficiency, and is provided with the function of mutual validation. The method has the following advantages: the disorder of split files, the high security of the magic square encryption algorithm and the validation of self integrity and mutual integrity of combined files.

An Information Hiding Scheme Using Magic Squares

Abstract: In this paper, a data hiding scheme has been proposed to efficiently hide the data at the LSBs of a host image. Two operations used in the encryption and decryption processes, transposition and substitution, are performed to disarrange and replace the data stream. First, data are exchanged by the transposition square which is reordered by a sequential of magic squares. The secret data are replaced by matching, encoding and substituting from a constructed table. The hidden data are embedded into the LSBs of the host images. The stego images with embedded data are imperceptible. The needed parameters formed a private key are encrypted and sent to the receiver by the RSA method in the Internet. Moreover, if any one of them is incorrect, it is very difficult to find the correct texts. The averaged error hamming distances are near to 50% of the host image size. These results are the same with those by guessing.

Six little squares and how their numbers grow

Abstract: We find the numbers of 3 � 3 magic, semimagic, and magilatin squares, as functions either of the magic sum or of an upper bound on the entries in the square. Our results on magic and semimagic squares differ from previous ones in that we require the entries in the square to be distinct from each other and we derive our results not by ad hoc reasoning but from the general geometric and algebraic method of our paper "An enumer- ative geometry for magic and magilatin labellings". Here we illustrate that method with a detailed analysis of 3 � 3 squares.

Magic square coding-based median filter method

Abstract: The invention discloses a magic square coding-based median filter method comprising the following steps of: firstly, reading the coordinates and the gray value of each pixel in an image; secondly, traversing the image and judging whether each pixel is a noise pixel or positioned in a linear detail area or not by using a magic square coding-based method; and thirdly, maintaining the gray value of a non-noise image unchanged and removing the noise of the noise pixel by amending the gray value of the noise pixel The invention can be used for judging whether the pixel processed as the noise pixel is positioned in the linear detail area or not without generating pixel loss in the linear detail area, thereby ensuring the integrity of image information; the pixels in the linear detail area are judged by using the magic square coding-based method with small calculated quantity; and a proper value is selected to replace the noise pixel according to the difference condition between the gray median value and the mean value of the maximum gray value and the minimum gray value so as to reduce the fuzzy phenomenon caused during the the image noise removing processing

The Magic of Permutation Matrices: Categorizing, Counting and Eigenspectra of Magic Squares

Abstract: Permutation matrices play an important role in understand the structure of magic squares. In this work, we use a class of symmetric permutation matrices than can be used to categorize magic squares. Many magic squares with a high degree of symmetry are studied, including classes that are generalizations of those categorized by Dudeney in 1917. We show that two classes of such magic squares are singular and the eigenspectra of such magic squares are highly structured. Lastly, we prove that natural magic squares of singly-even order of these classes do note exist.

Enumeration of $4 \times 4$ Magic Squares

Abstract: A magic square is an n x n array of distinct positive integers whose sum along any row, column, or main diagonal is the same number. We compute the number of such squares for n = 4, as a function of either the magic sum or an upper bound on the entries. The previous record for both functions was the n = 3 case. Our methods are based on inside-out polytopes, i.e., the combination of hyperplane arrangements and Ehrhart's theory of lattice-point enumeration.

Magic Square Construction Algorithms and Their Applications

Abstract: In recreational mathematics, a magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the sum of n numbers in all rows, all columns and both diagonals is the same constant called the magic number. The magic square in normal is represented using n x n matrix. A normal magic square contains the integers from 1 to n2. Normal magic squares exist for all orders n is greater than or equal to 1, except n = 2. The magic constant for normal magic squares of order n is given by n(n2 + 1)/2. There are several methods for constructing the magic square of any given order. This paper proposes algorithms to obtain the magic square of any given order n. Some of the algorithms are straight forward and others are designed using the divide and conquer technique.

Upside Down Numerical Equation, Bimagic Squares, and the day September 11

Abstract: In this short note we have given an equation based on the date 11.09.2001 and presented some magic squares. The magic squares presented are of order 3x3, 4x4, 5x5, 9x9, 16x16 and 25x25. While the magic square of higher order 9x9, 16x16 and 25x25 are bimagic. These magic squares are based on the digits, 1-6-9, 0-1-2, 0-1-2-9 and 0-1-2-6-9. The interesting fact in all these magic squares is that if we gave them a rotation of 180 degrees, they remain again the magic squares. In order to have this rotation, we have used the numbers in digital forms. Moreover, the day of submission of this work (20.10.2010) has only the digits 0, 1 and 2. Using only these three digits, we have presented magic squares of order 3x3 and 9x9.

Equivalent Versions of "Khajuraho" and "Lo-Shu" Magic Squares and the day 1st October 2010 (01.10.2010)

Abstract: In this short note we shall give connection between the most perfect "Khajuraho" magic square of order 4x4 discovered in 10th century and the "Lo-Shu" magic square of order 3x3 with the day October 1, 2010, i.e., 01.10.2010. The day has only three digits 0, 1 and 2. Here we have given an equivalent version of Khajuraho magic square using only three digits 0, 1 and 2. If we write the above date in two parts, 0110 2010, interestingly, the sum of new magic square is the first part, i.e., 0110, and the numbers appearing in the magic square are from the second part. An equivalent version of "Lo-Shu" magic square of order 3x3 is also given

On Multiplicative Magic Squares

Abstract: In this note, we give a lower bound for the distance between the maximal and minimal element in a multiplicative magic square of dimension $r$ whose entries are distinct positive integers.

Magic square digital antifake method and its antifake system

Abstract: The present invention discloses a magic square digital anti-counterfeiting method and an anti-counterfeiting system thereof. The anti-counterfeiting method comprises the following steps: a unique number is generated for each commodity; a magic square more than seven orders is randomly generated for each commodity, the magic square is divided into two complementary defect magic squares (M1, M2)through a random shuffle square matrix of which each of the elements is 0 or 1, numbers in the defect magic squares M1 and M2 form a truth checking vector V2 in sequence, and the truth checking vector V2 is stored in an anti-counterfeiting data center; the shuffle square matrix is converted into a decimal number, and the decimal number is used as the anti-counterfeiting code of the identity of the commodity; a label containing the commodity number and the anti-counterfeiting code is manufactured for the commodity, and the anti-counterfeiting code is masked; a user sends the commodity number and the anti-counterfeiting code to a truth checking device through a query code input device to restore the magic square, if the magic square can be restored, the query belongs to the first query, and the commodity is a real commodity, else, the commodity is a counterfeit. The magic square digital anti-counterfeiting method has the characteristics of disclosable encoding algorithm, high security intensity, easy implementation, etc. The invention relates to a magic square number fake prevention method and system. Its steps are as follows: generate an exclusive number for each commodity; generate a magic square over seven ranks for each commodity at random, the magic square is divided into two complement lacuna magic squares (M1,M2) by passing random riffle matrix whose element is 0 or 1 and true or false check vector V2 is orderly composed by numbers in lacuna magic squares M1 and M2 and memorized into fake prevent data center; Riffle matrix is converted into tens digits as fake prevent code of the commodity; label containing commodity number and fake prevent code is made for commodity and covers the fake prevent code; through query code inputting equipment, user inputs commodity and fake prevent code into true or false check equipment to recover magic square, if it can be recovered and it is the first query, the commodity is true, or it is false. Characters of the invention are that its coding arithmetic can be disclosed, security is high and it is easy to implement.

Numerical game apparatus and method

Abstract: A game apparatus and method of playing a game for forming magic squares is provided. The game apparatus provides for various means for forming a magic square in a N×N matrix. The method provides for various means for performing a formation of a magic square in a N×N matrix.

Ball-type magic square toy

Abstract: The utility model provides a ball-type magic square toy which comprises a magic square body composed of at least two independent unit blocks and fastenings used for connecting every two adjacent unit blocks, wherein the unit blocks can be rotated correspondingly; the unit blocks are designed into transparent hollow bodies; through holes are formed on one or more unit blocks of the magic square body; and at least one ball is arranged in the magic square body. The through hole on the unit block can be in butt joint with the through hole on another unit block by rotating the unit block where the ball is located; and the ball passes through the through hole so as to enter another unit block, and finally reaches to a specific unit block or rolls out of the magic square body. The ball-type magic square toy breaks the traditional design and combines the magic square playing way and the ball playing way, has the advantages of novel and unique playing ways, creativeness and interestingness, can practice the brain, the hand flexibility and the perception capability of a player, and can be widely applied to magic square toys with various steps or shapes.

Orthogonal Latin squares of Choi Seok-Jeong

Abstract: A latin square of order n is an array with entries from a set of n numbers arrange in such a way that each number occurs exactly once in each row and exactly once in each column. Two latin squares of the same order are orthogonal latin square if the two latin squares are superimposed, then the cells contain each pair consisting of a number from the first square and a number from the second. In Europe, Orthogonal Latin squares are the mathematical concepts attributed to Euler. However, an Euler square of order nine was already in existence prior to Euler in Korea. It appeared in the monograph Koo-Soo-Ryak written by Choi Seok-Jeong(1646-1715). He construct a magic square by using two orthogonal latin squares for the first time in the world. In this paper, we explain Choi' s orthogonal latin squares and the history of the Orthogonal Latin squares.

Magic square and using method thereof

Abstract: The invention relates to a magic square and a using method thereof, and belongs to the technical field of toys. The magic square is characterized in that a corner square has three surfaces, a clampedsquare has two color surfaces, a middle square has one color surface, and the corner square, the clamped square and the middle square are assembled together by a connecting device; and the square surfaces are provided with protrusions or grooves. The using method for the magic square comprises that the square is treated in an order of a top layer, a middle layer and a bottom layer in turn, whereinthe top layer adjustment comprises the following steps: determining the middle square as a center, homing corner squares with consistent colors on the top surfaces and the related lateral surfaces tofour corners, and adjusting four clamped squares; the middle layer adjustment comprises the following steps: aligning four middle squares once, and adjusting the four clamped squares; and the bottomlayer adjustment comprises the following steps: adjusting the colors of the bottom surface of the bottom layer clamped square, the lateral surfaces of the bottom middle square and the bottom layer clamped square and the connected middle layer to be same, positioning the bottom layer corner squares, and adjusting the surfaces of the bottom layer corner squares to form the magic square. The magic square has the advantages of simple structure, flexible use and obvious hand feel, is convenient for the blind to operate and use, and integrates interest, brain strengthening and body building.

Three-order hollow magic square

Abstract: The utility model discloses a three-order hollow magic square, which is a 3*3 regular hexahedron construction, but the center of each surface lacks of a combined block. Particularly, the magic square consists of six core components corresponding to six surfaces, twelve intermediate combined blocks and eight angle blocks, wherein the twelve combined blocks are clamped and positioned with the core components by twelve clamping blocks, and can freely rotate along the core components, and the eight angle blocks are clamped and positioned by the twelve clamping blocks and can freely rotate along the core components. The magic square is ingenious in structural design; the combined blocks are connected and positioned by the clamping action of the clamping blocks and can freely rotate around the core components without any fixed part; and in addition, with the novel hollow appearance, the three-order hollow magic square can better attract consumers.

Classical Kloosterman sums: representation theory, magic squares, and Ramanujan multigraphs

Abstract: We study the representation theory of a certain finite group for which Kloosterman sums appear as character values. This leads us to consider a concrete family of commuting hermitian matrices which have Kloosterman sums as eigenvalues. These matrices satisfy a number of "magical" combinatorial properties and they encode various arithmetic properties of Kloosterman sums. These matrices can also be regarded as adjacency matrices for multigraphs which display Ramanujan-like behavior.

Information Security Enhancement to Public–Key Cryptosystem Through Magic Squares

Abstract: The efficiency of a cryptographic algorithm is based on its time taken for encryption and decryption and the way it produces different cipher text from a plain text. The RSA, the widely used public key algorithm and other public key algorithms may not guarantee that the cipher text is fully secured. As an alternative approach to handling ASCII value of the text in the cryptosystem, a magic square of order 16 equivalent to ASCII set generated from two different approaches is thought of in this work. It attempts to enhance the efficiency by providing add-on security to the cryptosystem. Here, encryption/decryption is based on numerals generated by magic square rather than ASCII values. This proposed work provides another layer of security to any public key algorithms. Since, this model is acting as a wrapper to a public-key algorithm, it ensures that the security is enhanced. Further, this approach is experimented in a simulated environment with 2, 4, and 8 processor model using Maui scheduler which is based on back filling philosophy.

Chinese magic square and manufacturing method thereof

Abstract: The invention relates to a Chinese magic square. The Chinese magic square consists of a box body, a chessboard and chess pieces, wherein the box body is a wooden square box body of which the left side and the right side are opened oppositely, and is formed by connecting a box cover and a box base through a hinge arranged on one side; the square chessboard is manufactured by arranging an irony thin plate on a top plate in the box cover; the surface of the chessboard is provided with small check layers of 10*10, a numeral serial number is set in each small check, and the numeral serial number is one of continuous Arabic numbers from 1 to 100; a chess piece is put in each small check, each chess piece is made of a circular permanent magnet which is weakly magnetic in a single surface, and one numeral serial number is adhered to one nonmagnetic surface of each chess piece; and the chessboard manufactured by the square irony thin plate is also arranged in the box base, and the surface of the chessboard is also provided with 10*10 small blank check layers on which the chess pieces are put by players. The Chinese magic square can foster the capability of comprehensive command coordination and organization of the players and make the players associate, and has the advantages of simple and convenient playing, and suitability for both children and adults, and China and foreign countries.

Counting forumula for 3 × 3 generalized magic squares

Abstract: The aim of this article is to explicitly compute the number of generalized magic squares of order 3. Counting functions for (generalized) magic squares of order n with fixed line sum r is known to be a polynomial function in r over ℚ of degree (n−1)2. For higher values of n, it is quite difficult to explicitly write down such counting functions.

Distinguishing quantum channels via magic squares game

Abstract: We study the effect of quantum memory in magic squares game when played in quantum domain. We consider different noisy quantum channels and analyze their influence on the magic squares quantum pseudo-telepathy game. We show that the probability of success can be used to distinguish the quantum channels. It is seen that the mean success probability decreases with increase of quantum noise. Where as the mean success probability increases with increase of quantum memory. It is also seen that the behaviour of amplitude damping and phase damping channels is similar. On the other hand, the behaviour of depolarizing channel is similar to the flipping channels. Therefore, the probability of success of the game can be used to distinguish the quantum channels.

Semi-Magic Squares and Elliptic Curves

Abstract: We show that, for all odd natural numbers $N$, the $N$-torsion points on an elliptic curve may be placed in an $N \times N$ grid such that the sum of each column and each row is the point at infinity.

Symmetric Spaces of Exceptional Groups

Abstract: We address the problem of the reasons for the existence of 12 symmetric spaces with the exceptional Lie groups. The 1 + 2 cases for G2 and F4, respectively, are easily explained from the octonionic nature of these groups. The 4 + 3 + 2 cases on the E6,7,8 series require the magic square of Freudenthal and, for the split case, an appeal to the supergravity chain in 5, 4, and 3 space—time dimensions.