A Room Design of Order 14

1968 ◽  
Vol 11 (2) ◽  
pp. 191-194 ◽  
Author(s):  
C D. O'Shaughnessy
Keyword(s):  
Positive Integer ◽  
Unordered Pair ◽  
Room Design ◽  
The Right ◽  
Square Array ◽  
Being Moved

A Room design of order 2n, where n is a positive integer, is an arrangement of 2n objects in a square array of side 2n - 1, such that each of the (2n - 1)2 cells of the array is either empty or contains exactly two distinct objects; each of the 2n objects appears exactly once in each row and column; and each (unordered) pair of objects occurs in exactly one cell. A Room design of order 2n is said to be cyclic if the entries in the (i + l) th row are obtained by moving the entries in the i th row one column to the right (with entries in the (2n - l)th column being moved to the first column), and increasing the entries in each occupied cell by l(mod 2n - 1), except that the digit 0 remains unchanged.

A Room Design of Order 10

1964 ◽  
Vol 7 (3) ◽  
pp. 377-378 ◽  
Author(s):  
Louis Weisner
Keyword(s):  
Positive Integer ◽  
Unordered Pair ◽  
Room Design

A Room design of order 2n, where n is a positive integer, is an arrangement of 2n objects in a square of side 2n - 1, so that each of the (2n - 1)2 cells of the array is either empty or contains just two distinct objects; each of the 2n objects occurs just once in each row and in each column; and each (unordered) pair of objects occurs in just one cell.

An Existence Theorem for Room Squares*

1969 ◽  
Vol 12 (4) ◽  
pp. 493-497 ◽  
Author(s):  
R. C. Mullin ◽  
E. Nemeth
Keyword(s):  
Positive Integer ◽  
Existence Theorem ◽  
Prime Power ◽  
Unordered Pair ◽  
Room Squares ◽  
Square Array

It is shown that if v is an odd prime power, other than a prime of the form 22n + 1, then there exists a Room square of order v + 1.A room square of order 2n, where n is a positive integer, is an arrangement of 2n objects in a square array of 2 side 2n - 1, such that each of the (2n - 1)2 cells of the array is either-empty or contains exactly two distinct objects; each of the 2n objects appears exactly once in each row and column; and each (unordered) pair of objects occurs in exactly one cell.

Automorphisms of a Family of Cubic Graphs

2013 ◽  
Vol 20 (03) ◽  
pp. 495-506 ◽  
Author(s):  
Jin-Xin Zhou ◽  
Mohsen Ghasemi
Keyword(s):  
Automorphism Group ◽  
Positive Integer ◽  
Cayley Graph ◽  
Regular Representation ◽  
Cayley Graphs ◽  
Cubic Graphs ◽  
Full Automorphism Group ◽  
Vertex Set ◽  
The Right ◽  
Normal Cayley Graphs

A Cayley graph Cay (G,S) on a group G with respect to a Cayley subset S is said to be normal if the right regular representation R(G) of G is normal in the full automorphism group of Cay (G,S). For a positive integer n, let Γn be a graph with vertex set {xi,yi|i ∈ ℤ2n} and edge set {{xi,xi+1}, {yi,yi+1}, {x2i,y2i+1}, {y2i,x2i+1}|i ∈ ℤ2n}. In this paper, it is shown that Γn is a Cayley graph and its full automorphism group is isomorphic to [Formula: see text] for n=2, and to [Formula: see text] for n > 2. Furthermore, we determine all pairs of G and S such that Γn= Cay (G,S) is non-normal for G. Using this, all connected cubic non-normal Cayley graphs of order 8p are constructed explicitly for each prime p.

Ramanujan's Continued Fraction and the Bauer-Muir Transformation

1961 ◽  
Vol 57 (1) ◽  
pp. 76-79 ◽  
Author(s):  
V. N. Singh
Keyword(s):  
Positive Integer ◽  
Gamma Function ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Gamma Functions ◽  
Image Position ◽  
The Right ◽  
Basic Analogue ◽  
Ramanujan's Continued Fraction

Ramanujan's Continued Fraction may be stated as follows: Let where there are eight gamma functions in each product and the ambiguous signs are so chosen that the argument of each gamma function contains one of the specified number of minus signs. Then where the products and the sums on the right range over the numbers α, β, γ, δ, ε: provided that one of the numbers β, γ, δ, ε is equal to ± ±n, where n is a positive integer. In 1935, Watson (3) proved the theorem by induction and also gave a basic analogue. In this paper we give a new proof of Ramanujan's Continued Fraction by using the transformation of Bauer and Muir in the theory of continued fractions (Perron (1), §7;(2), §2).

scholarly journals the coincidence lefschetz number for self-maps of lie groups

2006 ◽  
Vol 3 (3) ◽  
pp. 465-469
Author(s):  
Baghdad Science Journal
Keyword(s):  
Positive Integer ◽  
Lie Group ◽  
Left Translation ◽  
Natural Homomorphism ◽  
Linear Transformations ◽  
Homotopy Classes ◽  
Coincidence Number ◽  
Lefschetz Coincidence Number ◽  
Point G ◽  
The Right

Let/. It :0 ---0 G be any two self maps of a compact connected oriented Lie group G. In this paper, for each positive integer k , we associate an integer with fk,hi . We relate this number with Lefschetz coincidence number. We deduce that for any two differentiable maps f, there exists a positive integer k such that k 5.2+1 , and there is a point x C G such that ft (x) = (x) , where A is the rank of G . Introduction Let G be an n-dimensional com -pact connected Lie group with multip-lication p ( .e 44:0 xG--+G such that p ( x , y) = x.y ) and unit e . Let [G, G] be the set of homotopy classes of maps G G . Given two maps f , f G ---• Jollowing [3], we write f. f 'to denote the map G-.Gdefined by 01.11® =A/WO= fiat® ,sea Given a point g EC and a differ-entiable map F: G G , write GA to denote the tangent space of G at g [4,p.10] , and denote by d x F the linear map rig F :Tx0 T, (x)G induced by F , it is called the differential of Fat g [4,p.22]. Let LA, Rx :0 G be respec-tively the left translation Lx(i)=4..(g,e) , and the right translation Rx(1)./..(gcg). Then there is a natural homomorphism Ad ,the adjoin representation, from G to GL(G•), (the group of nonsingular linear transformations of Qdefined as follows:- Ad(g)= deRe, od,Lx. Note that d xRc, ad.; =d(4,( Lx(e)))0 de; =d.(4, 04)=4(40 Re) = d(4(4, (e)))0 (44, =d ar, o (44, . Since G is connected , the image of Ad belongs to the connected component of G(G)containing the identity,i.e. for each g E 0, detAd(g) > 0 . By Exercise Al • Dr.-Prof.-Department of Mathematics- College of Science- University of Baghdad. •• Dr.-Department of Mathematics- College of Science for Woman- University of Baghdad.

The hit problem for symmetric polynomials over the Steenrod algebra

2002 ◽  
Vol 133 (2) ◽  
pp. 295-303 ◽  
Author(s):  
A. S. JANFADA ◽  
R. M. W. WOOD
Keyword(s):  
Positive Integer ◽  
Polynomial Algebra ◽  
Steenrod Algebra ◽  
Symmetric Polynomials ◽  
Homogeneous Polynomials ◽  
Left Module ◽  
Symmetric Version ◽  
The Right ◽  
Hit Problem ◽  
Prime 2

We cite [18] for references to work on the hit problem for the polynomial algebra P(n) = [ ]2[x1, ;…, xn] = [oplus ]d[ges ]0Pd(n), viewed as a graded left module over the Steenrod algebra [Ascr ] at the prime 2. The grading is by the homogeneous polynomials Pd(n) of degree d in the n variables x1, …, xn of grading 1. The present article investigates the hit problem for the [Ascr ]-submodule of symmetric polynomials B(n) = P(n)[sum ]n , where [sum ]n denotes the symmetric group on n letters acting on the right of P(n). Among the main results is the symmetric version of the well-known Peterson conjecture. For a positive integer d, let μ(d) denote the smallest value of k for which d = [sum ]ki=1(2λi−1), where λi [ges ] 0.

scholarly journals Duplication of Room squares

1972 ◽  
Vol 14 (1) ◽  
pp. 75-81 ◽  
Author(s):  
W. D. Wallis
Keyword(s):  
Unordered Pair ◽  
Room Squares ◽  
Square Array

ARoom squareRof order 2nis a way of arranging 2nobjects (usually 1,2,…, 2n) in a square arrayRof side 2n– 1 so that:(i) every cell of the array is empty or contains two objects;(ii) each unordered pair of objects occurs once inR(iii) every row and column ofRcontains one copy of each object.

scholarly journals Sonyol Megal-Megol

JOGED ◽  
2017 ◽  
Vol 7 (2) ◽  
Author(s):  
Sekar Ayu Oktaviana Sari
Keyword(s):  
The Body ◽  
The Right ◽  
Being Moved

Tulang adalah penopang tubuh, tanpa tulang tubuh tidak akan bisa berdiri tegak. Salah satu tulang yang berfungsi sebagai tumpuan badan ketika duduk disebut dengan tulang panggul atau pangkal paha di sebelah belakang. Keunikan yang terjadi ketika tulang panggul digerakkan dengan cara memutar atau bergerak ke kanan dan ke kiri akan berakibat yang disebut dengan istilah Jawa yaitu megal-megol atau pantat yang bergerak ke kanan dan ke kiri.            Melihat fenomena di atas muncul ide untuk menciptakan sebuah karya tari yang bersumber dari gerakan otot bagian panggul. Penata memiliki postur tubuh yang menonjol di bagian panggul, sehingga tampak kurang proposional, hal ini menjadi menarik sehingga terinspirasi untuk menciptakan sebuah koreografi kelompok. Karya tari ini akan fokus pada gerakkan seputaran panggul. Gerakan tersebut sangat menarik karena memiliki keunikan tersendiri. Permainan panggul yang digerakan secara vibrasi mengakibatkan pantat bergetar, sehingga gerakan tersebut menjadi salah satu gerak yang akan dikembangkan.            Karya koreografi Sonyol Megal-Megol ini melibatkan dua puluh delapan orang penari perempuan, dengan delapan penari inti dan duapuluh penari pendukung. Adapun jumlah penari sebagai pertimbangan untuk komposisi koreografi, sedangkan untuk pemilihan jenis kelamin karena yang memiliki panggul atau pantat besar dominan perempuan. Karya koreografi mengangkat konsep tentang salah satu bagian tubuh yang berfungsi sebagai tumpuan badan ketika duduk yaitu panggul atau pantat. Musik yang akan digunakan adalah play recorder. Skull is the supporting of the body, and without it body will not be able to stand upright. Skull which has the function to support the body when in sit position is called hip. When hip is being moved to the right and left side or by the curning way, it will create a movement named megal-megol(the bottom move to the right and left side) in javanese analogy.             Look at the phenomenon stated above, an idea to create a dance work based on the movement muscle in hip arises. Choreographer has a prominent hip therefore it looks less proportional. This interisting fact inspires choreographer to create a group dance. This dance focuses on hip movement which has uniqueness inside it. Hip which is being moved vibratory causes a movement on the bottom, therefore this a dance that will be developed.             Sonyol Megal-Megol choreography involves twenty eight female dancers consist of eight main dancer and twenty supporter dancer. Choreography composition considers the number of dancers. The reason of choosing female as the dancer is because female more likely to have a big hip. The concept of the choreography come up from a part of the body which is used to be a body supporting when in a sit position called hip. The music is being played by recorder.

Effects of Element Density on Segmentation by Luminance, Colour, and Motion

Perception ◽  
1996 ◽  
Vol 25 (1_suppl) ◽  
pp. 106-106
Author(s):  
P Moeller ◽  
A C Hurlbert
Keyword(s):  
Local Maximum ◽  
Broad Distribution ◽  
Global Properties ◽  
Local Extrema ◽  
Monotonically Decreasing Function ◽  
Element Density ◽  
Dot Density ◽  
The Right ◽  
Square Array ◽  
Background Contrast

A target composed of random dots can be easily segmented from a background of random dots when each is defined by a different, broad distribution of dot speeds, colours, or brightnesses, even if these distributions overlap extensively. This shows that segmentation can be based on global properties of the target and background. If average feature value is the relevant global property, segmentation threshold should be a monotonically decreasing function of dot density. Observers viewed a 6.5 deg × 6.5 deg square array of between 512 and 36 864 randomly positioned dots (dot size 4.7 or 1.6 min arc) in which the target was a vertical band of dots defined by a different distribution of luminance, colour, or motion from the background. The task was to indicate whether the target appeared on the left or on the right of midline. The stimulus was displayed for 67 ms, followed after 233 ms by a 67 ms mask. We found that motion segmentation thresholds decrease monotonically as a function of density. For luminance and colour, segmentation thresholds initially decrease toward a local minimum, then increase to a local maximum. Thereafter, thresholds decrease monotonically as density increases further. These results suggest that the integrative segmentation process for motion is qualitatively different from those for luminance and colour. The local extrema for luminance and colour suggests that segmentation in these domains is based on forming clusters by linking together dots with similar feature properties. Only when interdot distance is sufficiently small are all dots within an area included in the cluster. Behaviour is then determined by difference in average feature value or target — background contrast.

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