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Articles 1 - 9 of 9
Full-Text Articles in Physical Sciences and Mathematics
Some New Orthogonal Arrays Oa (4r;R (1) 2(P);2), Warren F. Kuhfeld, Chung Yi Suen
Some New Orthogonal Arrays Oa (4r;R (1) 2(P);2), Warren F. Kuhfeld, Chung Yi Suen
Mathematics and Statistics Faculty Publications
We developed an algorithm to search for new orthogonal arrays, OA(4rOA(4r, r12pr12p, 2), for odd r . With it, we found new orthogonal arrays with 4r=364r=36 through 124 runs. Many other new arrays can be obtained from these new arrays.
On The Construction Of Mixed Orthogonal Arrays Of Strength Two, Chung Yi Suen, Warren F. Kuhfeld
On The Construction Of Mixed Orthogonal Arrays Of Strength Two, Chung Yi Suen, Warren F. Kuhfeld
Mathematics and Statistics Faculty Publications
The generalized Kronecker sum was used by Wang and Wu (J. Amer. Statist. Assoc. 86 (1991) 450) and Dey and Midha (Statist. Probab. Lett. 28 (1996) 211; Proc. AP Akad. Sci. 5 (2001) 39) to construct mixed orthogonal arrays. We modify their methods to obtain several families of mixed orthogonal arrays. Some new arrays with run size less than 100 are found.
Construction Of M^4 Run Linear Graphs By Finite Geometries, Chung Yi Suen
Construction Of M^4 Run Linear Graphs By Finite Geometries, Chung Yi Suen
Mathematics and Statistics Faculty Publications
Finite projective geometries are used to obtain some series of Taguchi's linear graphs involving m^4 runs, where m is a prime or a prime power. The concept of maximal linear graph is introduced to reduce the number of nonisomorphic linear graphs. Some 81-run maximal linear graphs are given as examples. A table of 27 nonisomorphic 16-run maximal linear graphs, which is believed to be complete, is provided.
A Modular Integer Gcd Algorithm, Kenneth Weber, Vilmar Trevisan, Luiz Felipe Martins
A Modular Integer Gcd Algorithm, Kenneth Weber, Vilmar Trevisan, Luiz Felipe Martins
Mathematics and Statistics Faculty Publications
This paper describes the first algorithm to compute the greatest common divisor (GCD) of two n-bit integers using a modular representation for intermediate values U, V and also for the result. It is based on a reduction step, similar to one used in the accelerated algorithm [T. Jebelean, A generalization of the binary GCD algorithm, in: ISSAC '93: International Symposium on Symbolic and Algebraic Computation, Kiev, Ukraine, 1993, pp. 111–116; K. Weber, The accelerated integer GCD algorithm, ACM Trans. Math. Softw. 21 (1995) 111–122] when U and V are close to the same size, that replaces U by (U-bV)/p, where …
Toric Residue And Combinatorial Degree, Ivan Soprunov
Toric Residue And Combinatorial Degree, Ivan Soprunov
Mathematics and Statistics Faculty Publications
Consider an -dimensional projective toric variety defined by a convex lattice polytope . David Cox introduced the toric residue map given by a collection of divisors on . In the case when the are -invariant divisors whose sum is , the toric residue map is the multiplication by an integer number. We show that this number is the degree of a certain map from the boundary of the polytope to the boundary of a simplex. This degree can be computed combinatorially. We also study radical monomial ideals of the homogeneous coordinate ring of . We give a necessary and sufficient …
Combinatorial Construction Of Toric Residues, Amit Khetan, Ivan Soprunov
Combinatorial Construction Of Toric Residues, Amit Khetan, Ivan Soprunov
Mathematics and Statistics Faculty Publications
In this paper we investigate the problem of finding an explicit element whose toric residue is equal to one. Such an element is shown to exist if and only if the associated polytopes are essential. We reduce the problem to finding a collection of partitions of the lattice points in the polytopes satisfying a certain combinatorial property. We use this description to solve the problem when n=2 and for any n when the polytopes of the divisors share a complete flag of faces. The latter generalizes earlier results when the divisors were all ample
Cyclic Maps In Rational Homotopy Theory, Gregory Lupton, Sam Smith
Cyclic Maps In Rational Homotopy Theory, Gregory Lupton, Sam Smith
Mathematics and Statistics Faculty Publications
The notion of a cyclic map g:A→X is a natural generalization of a Gottlieb element in π n (X). We investigate cyclic maps from a rational homotopy theory point of view. We show a number of results for rationalized cyclic maps which generalize well-known results on the rationalized Gottlieb groups.
Homotopy Actions, Cyclic Maps And Their Duals, Martin Arkowitz, Gregory Lupton
Homotopy Actions, Cyclic Maps And Their Duals, Martin Arkowitz, Gregory Lupton
Mathematics and Statistics Faculty Publications
An action of A on X is a map F: AxX to X such that F|_X = id: X to X. The restriction F|_A: A to X of an action is called a cyclic map. Special cases of these notions include group actions and the Gottlieb groups of a space, each of which has been studied extensively. We prove some general results about actions and their Eckmann-Hilton duals. For instance, we classify the actions on an H-space that are compatible with the H-structure. As a corollary, we prove that if any two actions F and F' of A on X …
Free And Semi-Inert Cell Attachments, Peter Bubenik
Free And Semi-Inert Cell Attachments, Peter Bubenik
Mathematics and Statistics Faculty Publications
Let Y be the space obtained by attaching a finite-type wedge of cells to a simply-connected, finite-type CW-complex. We introduce the free and semi-inert conditions on the attaching map which broadly generalize the previously-studied inert condition. Under these conditions we determine H (QY; R) as an R-module and as an R-algebra, respectively. Under a further condition we show that H. (QY; R) is generated by Hurewicz images. As an example we study an infinite family of spaces constructed using only semi-inert cell attachments.