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Articles 1921 - 1950 of 2013
Full-Text Articles in Physical Sciences and Mathematics
Generalised Bhaskar Rao Designs Of Block Size 3 Over The Group Z4, Warwick De Launey, Dinesh G. Sarvate, Jennifer Seberry
Generalised Bhaskar Rao Designs Of Block Size 3 Over The Group Z4, Warwick De Launey, Dinesh G. Sarvate, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We show that the necessary conditions (i) 2tv(v-l) ≡ O(mod 3) (ii) v ≥ 3 (iii) t ≡ 1,5 (mod 6) => v ≠ 3 are sufficient for the existence of a GBRD(v,3,4t;Z4) except possibly when (v,t) = (27,1) or (39,1).
A Subliminal Channel In Codes For Authentication Without Secrecy, Jennifer Seberry
A Subliminal Channel In Codes For Authentication Without Secrecy, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
G.J. Simmons has advanced the concept of using authentication in an open channel to actually convey information. We review the use of the knapsack problem for public codes and explore the use of Shamir's method for a signature only knapsack to convey messages.
Generalized Bhaskar Rao Designs With Block Size Three, Jennifer Seberry
Generalized Bhaskar Rao Designs With Block Size Three, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We show that the necessary conditions λ = 0 (mod IGI), λ(v-l)=0 (mod2), λv(v 1) = [0 (mod 6) for IGI odd, (0 (mod 24) for IGI even, are sufficient for the existence of a generalized Bhaskar Rao design GBRD(v,b,r,3,λ;G) for the elementary abelian group G, of each order IGI.
Regular Group Divisible Designs And Bhaskar Rao Designs With Block Size Three, Jennifer Seberry
Regular Group Divisible Designs And Bhaskar Rao Designs With Block Size Three, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
Some recursive constructions are given for Bhaskar Rao designs. Using examples of these designs found by Shyam J. Singh, Rakesh Vyas and new ones given here we show the necessary conditions λ = 0 (mod 2), λv(v-1) = 0 (mod 24) are sufficient for the existence of Bhaskar Rao designs with one association class and block size 3. This result is used with a result of Street and Rodger to obtain regular partially balanced block designs with 2v treatments, block size 3, λ,-0, group size 2 and v groups.
Maximal Ternary Codes And Plotkin's Bound, Conrad Mackenzie, Jennifer Seberry
Maximal Ternary Codes And Plotkin's Bound, Conrad Mackenzie, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
The analogue of Plotkin's bound is developed for ternary codes with high distance relative to length. Generalized Hadamard matrices are used to obtain codes which meet these bounds. The ternary analogue of Levenshtein's construction is discussed and maximal codes constructed.
On Bhaskar Rao Designs Of Block Size Four, Warwick De Launey, Jennifer Seberry
On Bhaskar Rao Designs Of Block Size Four, Warwick De Launey, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We show that Bhaskar Rao designs of type BRD(v, b, r, 4, 6) exist for v = 0,1 (mod 5) and of type BRD (v, b, r, 4,12) exist for all v ≥ 4.
Generalized Bhaskar Rao Designs, Clement Lam, Jennifer Seberry
Generalized Bhaskar Rao Designs, Clement Lam, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
Generalized Bhaskar Rao designs with non-zero elements from an abelian group G are constructed. In particular this paper shows that the necessary conditions are sufficient for the existence of generalized Bhaskar Rao designs with k=3 for the following groups: │G│ is odd, G=Zr2, and G=Zr2 X H where 3+│H│ and r ≥ l. It also constructs generalized Bhaskar Rao designs with v=k, which is equivalent to v rows of a generalized Hadamard matrix of order n where v ≤ n.
The Directed Packing Numbers Dd(T, V ,V), T ≥ 4, J E. Dawson, Jennifer Seberry, D B. Skillicorn
The Directed Packing Numbers Dd(T, V ,V), T ≥ 4, J E. Dawson, Jennifer Seberry, D B. Skillicorn
Faculty of Informatics - Papers (Archive)
A directed packing is a maximal collection of k-subsets, called blocks, of a set of cardinality v having the property that no ordered t-subset occurs in more than one block. A block contains an ordered t-set if its symbols appear, left to right, in the block. The cardinality of such a maximal collection is denoted by DD(t, k, v). We consider the special case when k=v and derive some results on the sizes of maximal collections.
On Orthogonal Matrices With Constant Diagonal, Jennifer Seberry, Clement Wh Lam
On Orthogonal Matrices With Constant Diagonal, Jennifer Seberry, Clement Wh Lam
Faculty of Informatics - Papers (Archive)
In connection with the problem of finding the best projections of k-dimensional spaces embedded in n-dimensional spaces Hermann Konig asked: Given mER and nEN, are there n X n matrices C={c,,), i, i = 1,... ,n, such that c,,= m for all i, │C'ii│=l for i ≠ i, and C2={m2+n-l)ln? Konig was especially interested in symmetric C, and we find some families of matrices, satisfying this condition. We also find some families of matrices satisfying the less restrictive condition CCT = (m2 + n -1)1".
Some Families Of Partially Balanced Incomplete Block Designs, Jennifer Seberry
Some Families Of Partially Balanced Incomplete Block Designs, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
Bhaskar Rao designs with elements from abelian groups are defined and it is shown how such designs can be used to obtain group divisible partially balanced incomplete block designs with group size g, where g is the order of the abelian group. This paper studies the group Z3 and shows, using recursive constructions given here, that the necessary conditions are sufficient for the existence of generalized Bhaskar Rao designs. These designs are then used to obtain families of partially balanced designs.
Some Remarks On The Permanents Of Circulant (0,1) Matrices, Peter Eades, Cheryl E. Praeger, Jennifer Seberry
Some Remarks On The Permanents Of Circulant (0,1) Matrices, Peter Eades, Cheryl E. Praeger, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
Some permanents of circulant (0,1) matrices are computed. Three methods are used. First, the permanent of a Kronecker product is computed by directly counting diagonals. Secondly, Lagrange expansion is used to calculate a recurrence for a family of sparse circulants. Finally, a "complement expansion" method is used to calculate a recurrence for a permanent of a circulant with few zero entries. Also, a bound on the number of different permanents of circulant matrices with a given row sum is obtained.
The Skew - Weighing Matrix Conjecture, Jennifer Seberry
The Skew - Weighing Matrix Conjecture, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We review the history of the skew-weighing matrix conjecture and show that there exist skew-symmetric weighing matrices W (21.2t, k) for all k=0,l,.....,21.2t - I, t ≥ 4 a positive integer. Hence there exist orthogonal designs of type l(l,k) for all k=O,l,..., 21.2t - 1, t ≥ 4 a positive integer, in order 21.2t.
Higher Dimensional Orthogonal Designs And Hadamard Matrices, Joseph Hammer, Jennifer Seberry
Higher Dimensional Orthogonal Designs And Hadamard Matrices, Joseph Hammer, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
When n2 elements are given they can be arranged in the form of a square, similarly when ng elements (g ≥ 3 an integer) are given they can be arranged in the form of a g-dimensional cube of side n (in short a g-cube). The position of the elements can be indicated by g suffixes.
Higher Dimensional Orthogonal Designs And Applications, Joseph Hammer, Jennifer Seberry
Higher Dimensional Orthogonal Designs And Applications, Joseph Hammer, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
When n2 elements are given, they can be arranged in the form of a square; similarly, when n8 elements (g ≥ 3 an integer) are given, they can be arranged in the form of a g-dimensional cube of side n (in short, a g-cube). The position of the elements can be indicated by g suffixes.
Complex Weighing Matrices And Orthogonal Designs, Jennifer Seberry, Albert L. Whiteman
Complex Weighing Matrices And Orthogonal Designs, Jennifer Seberry, Albert L. Whiteman
Faculty of Informatics - Papers (Archive)
Galois fields G,F(q2) are used to obtain a new infinite family of complex weighing matrices. CW(q+l,q), q =1 (mod 8), and type P = [R – S S* - R*] where R and S are symmetric complex circulants. These matrices are used to construct orthogonal designs. Some unsolved cases of Geramita and Geramita are also settled.
Some Remarks On Amicable Orthogonal Designs, Jennifer Seberry
Some Remarks On Amicable Orthogonal Designs, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We present some new results on amicable orthogonal designs. We obtain amicable Hadamard matrices of order 24 .211 and a skew Hadamard matrix of order 24.295 which were previously not known.
All Directed Bibds With K = 3 Exist, Jennifer Seberry, David Skillicorn
All Directed Bibds With K = 3 Exist, Jennifer Seberry, David Skillicorn
Faculty of Informatics - Papers (Archive)
A directed BIBD with parameters (v,b,r,k,λ*) is a BIBD with parameters (v, b, r, k, 2λ*) in which each ordered pair of varieties occurs together in exactly λ* blocks. It is shown that λ*v(v - 1) = 0 (mod 3) is a necessary and sufficient condition for the existence of a directed (v, b, r, k, λ*) BIBD with k = 3.
An Infinite Family Of Skew-Weighing Matrices, Jennifer Seberry
An Infinite Family Of Skew-Weighing Matrices, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We show that orthogonal designs of type (l,k) exist for all k = 0,1,...,2 .15-1, in order 2t .15, t ≥ 4 a positive integer. Hence there exist skew-symmetric weighing matrices W(2t .15,k) for all k = 0,1,... ,2t .15-1.
A Construction For Generalized Hadamard Matrices, Jennifer Seberry
A Construction For Generalized Hadamard Matrices, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We prove that if pv and pr -1 are both prime powers then there is a generalized Hadamard matrix of order pr(pr -1) with elements from the elementary abelian group Zp x...x Zp. This result was motivated by results of Rajkundlia on BIBD's. This result is then used to produce pr -1 mutually orthogonal F-squares F(pr(pr -1); pr -1).
Some Infinite Classes Of Hadamard Matrices, Jennifer Seberry
Some Infinite Classes Of Hadamard Matrices, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
A recursive method of A. C. Mukhopadhay is used to obtain several new infinite classes of Hadamard matrices. Unfortunately none of these constructions give previously unknown Hadamard matrices of order <40,000.
All Dbibds With Block Size Four Exist, Deborah J. Street, Jennifer Seberry
All Dbibds With Block Size Four Exist, Deborah J. Street, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
A directed balanced incomplete block design with parameters (v,b,r,k,λ*), is a balanced incomplete block design with parameters (v,b,r,k,2λ*), in which the blocks are regarded as ordered k-tuples and in which each ordered pair of elements occurs in λ* blocks. By generalizing results of Hanani, we show that the necessary conditions for the existence of these designs, when k = 4, are sufficient.
Higher Dimensional Orthogonal Designs And Hadamard Matrices, Jennifer Seberry
Higher Dimensional Orthogonal Designs And Hadamard Matrices, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We construct n-dimensional orthogonal designs of type (1, 1)n, side 2 and propriety (2,2,...,2). These are then used to show that orthogonal designs of type (2t, 2t)n, side 2t+1 and propriety (2,2,...,2) exist.
On The Distribution Of The Permanent Of Cyclic (0,1) Matrices, Evi Nemeth, Jennifer Seberry, Michael Shu
On The Distribution Of The Permanent Of Cyclic (0,1) Matrices, Evi Nemeth, Jennifer Seberry, Michael Shu
Faculty of Informatics - Papers (Archive)
Some results are obtained on the permanent of cyclic (0,1) matrices which support the conjecture that for such matrices of prime order p the number of distinct values the permanent attains is of order p. Writing e(r) for the number of distinct values the permanent of cyclic (0,1) matrices of order n can attain we found e(5) = 6, e(6) = 12, e(7) = 9, e(8) = 11, e(9) = 21, e(10) ≤ 44, and e(11) ≤ 30. It is easy to show e(p) ≤ 1/p(2p-2)+2, p prime, but these answers are considerably smaller. We obtain formulae for the permanent …
Ordered Partitions And Codes Generated By Circulant Matrices, R Razen, Jennifer Seberry, K Wehrhahn
Ordered Partitions And Codes Generated By Circulant Matrices, R Razen, Jennifer Seberry, K Wehrhahn
Faculty of Informatics - Papers (Archive)
We consider the set of ordered partitions of n into m parts acted upon by the cyclic permutation (I2 ... m). The resulting family of orbits P(n, m) is shown to have cardinality p(n, m) = (l/n) ∑d│m φ(d) (::.'!~) where φ is Euler's φ-function. P(n, m) is shown to be set-isomorphic to the family of orbits ℓ(n, m) of the set of all m-subsets of an n-set acted upon by the cyclic permutation (12 ... n). This isomorphism yields an efficient method for determining the complete weight enumerator of any code generated by a circulant matrix.
A Note On Orthogonal Graeco-Latin Designs, Jennifer Seberry
A Note On Orthogonal Graeco-Latin Designs, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
It is shown that Graeco-Latin block designs which have treatments totally balanced with respect to blocks in each set and which are pairwise orthogonal with respect to the other set can be constructed with parameters v1 = r2 = p + 1, r1 = v2 = p, b = 2p, k = (p+l)/2 for p a prime power. Moreoever they can be represented in a compact manner and previously ad hoc examples become part of the series.
Some Remarks On Generalised Hadamard Matrices And Theorems Of Rajkundlia On Sbibds, Jennifer Seberry
Some Remarks On Generalised Hadamard Matrices And Theorems Of Rajkundlia On Sbibds, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
Constructions are given for generalised Hadamard matrices and weighing matrices with entries from abelian groups. These are then used to construct families of SBIBDs giving alternate proofs to those of Rajkundlia.
Women In Mathematics In Australia, Jennifer Seberry
Women In Mathematics In Australia, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
Many people believe women cannot "do" mathematics. This is not true, Tables 1, 2 and 3 show us that some women are quite good at mathematics. Also Table 1 which shows Honours degrees, clearly indicates that in recent years the percentage of women obtaining Honours degrees has steadily increased. I attribute this increase to the consciousness raising due to changing community attitudes to to women. It is no longer unfashionable for women to obtain a mathematical education with a view to having a career.
Higher-Dimensional Orthogonal Designs And Hadamard Matrices Ii, J Hammer, Jennifer Seberry
Higher-Dimensional Orthogonal Designs And Hadamard Matrices Ii, J Hammer, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
Higher-dimensional orthogonal designs of type (l,l)n are used to obtain higher-dimensional weighing matrices of type (q)n, side q+l and propriety (2,2,...,2) for q = l(mod 4) a prime power. Next, n-dimensional orthogonal designs of type (l,l,l,l)n, side 4 and propriety (2,2, ...,2) are constructed. These are then used to show that higher-dimensional Hadamard matrices of order (4t)t exist whenever t is the side of 4-Williamson matrices. This establishes the existence of higher-dimensional Hadamard matrices of order (4t) t for t odd, 1 ≤ t ≤ 33 and several infinite families, all of propriety (2,2,...,2). Finally, we establish that if there …
Optimum Trip Level Of M-Out-Of-N Reactor Temperature Trip-Amplifier Systems, J. M. Kontoleon
Optimum Trip Level Of M-Out-Of-N Reactor Temperature Trip-Amplifier Systems, J. M. Kontoleon
Faculty of Informatics - Papers (Archive)
This paper determines the optimum high-trip- level setting of m-out-of-n:G temperature- trip-amplifier systems,used for the protection of nuclear reactors against excess temperatures, which results in the maximum reliability. The bivariate normal distribution is used to simulate the fluctuation of the thermocouple signals and the uncertainties of the trip settings. The thermocouples and the trip amplifiers can fail in two modes of failure: fail-safe and fail-danger. It is shown that by properly selecting the trip levels of the amplifier units the reliability of the protection system is maximized. The optimum trip-level is calculated for various commonly used configurations using a computer …
On The Structure And Existence Of Some Amicable Orthogonal Designs, Peter J. Robinson, Jennifer Seberry
On The Structure And Existence Of Some Amicable Orthogonal Designs, Peter J. Robinson, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
The structure is determined for the existence of some amicable weighing matrices. This is then used to prove the existence and non-existence of some amicable orthogonal designs in powers of two.