In this paper we prove that for any prime power q equivalent to 3 (mod 8) there exist 4 - {q(2); k, k, k, k; lambda} supplementary difference sets (SDSs) with k = q(q - 1)/2, lambda 4k - q(2), and Hadamard matrices of...In this paper we prove that for any prime power q equivalent to 3 (mod 8) there exist 4 - {q(2); k, k, k, k; lambda} supplementary difference sets (SDSs) with k = q(q - 1)/2, lambda 4k - q(2), and Hadamard matrices of order 4q(2), and give several constructions of these SDSs. Moreover, combining the results of reference [1], we conclude that for any prime p equivalent to 3 (mod 8) and integer r greater than or equal to 1 there exists an Hadamard matrix of order 4p(2r).展开更多
Rotatability is a desirable quality of fitting response surface experimental designs. The propertystates that the variance of the estimated response made from the Taylor’s series expansion areconstant on circles, sph...Rotatability is a desirable quality of fitting response surface experimental designs. The propertystates that the variance of the estimated response made from the Taylor’s series expansion areconstant on circles, spheres and hyper-spheres about the centre of the design. In this article,a measure of rotatability of modified second-order rotatable design is presented. The variancefunction of a second-order response design and an infinite class of supplementary difference setsis used in coming up with the design.展开更多
An infinite family of is obtained, that is,(ν)≠￠ forυ ∈ N=N1UN2 U N3 where Using(υ),we give 2-(2υ;k1,k2;k1 + k2 -υ} supplementary difference sets withυ=(k1-υ)2 + (k2 - υ)2. Finally. we prove that if there ...An infinite family of is obtained, that is,(ν)≠￠ forυ ∈ N=N1UN2 U N3 where Using(υ),we give 2-(2υ;k1,k2;k1 + k2 -υ} supplementary difference sets withυ=(k1-υ)2 + (k2 - υ)2. Finally. we prove that if there exists an orthogonal design OD(4t;t,t,t,t) and(υ) ≠￠ then a Hadamard rnatrix of order 4tυ can be constructed.展开更多
文摘In this paper we prove that for any prime power q equivalent to 3 (mod 8) there exist 4 - {q(2); k, k, k, k; lambda} supplementary difference sets (SDSs) with k = q(q - 1)/2, lambda 4k - q(2), and Hadamard matrices of order 4q(2), and give several constructions of these SDSs. Moreover, combining the results of reference [1], we conclude that for any prime p equivalent to 3 (mod 8) and integer r greater than or equal to 1 there exists an Hadamard matrix of order 4p(2r).
文摘Rotatability is a desirable quality of fitting response surface experimental designs. The propertystates that the variance of the estimated response made from the Taylor’s series expansion areconstant on circles, spheres and hyper-spheres about the centre of the design. In this article,a measure of rotatability of modified second-order rotatable design is presented. The variancefunction of a second-order response design and an infinite class of supplementary difference setsis used in coming up with the design.
文摘An infinite family of is obtained, that is,(ν)≠￠ forυ ∈ N=N1UN2 U N3 where Using(υ),we give 2-(2υ;k1,k2;k1 + k2 -υ} supplementary difference sets withυ=(k1-υ)2 + (k2 - υ)2. Finally. we prove that if there exists an orthogonal design OD(4t;t,t,t,t) and(υ) ≠￠ then a Hadamard rnatrix of order 4tυ can be constructed.
