Your search

Consider a finite r-dimensional projective space PG(r, s) based on the Galois field GF(s) where s is prime or power of a prime. A set of n distinct points in PG(r, s), no t linearly dependent, is said to be maximal or complete if it is not contained in any other set with n* points with n* > n. The number of points in a maximal set is denoted by mt(r + 1, s). The purpose of this paper is to improve the existing bounds for m5(r + 1, s) for r ≥ 5 and s ≥ 5 (odd). The investigation of maximal sets in certain relationships of t, r and s yields parity check matrices of (r + 1) rows and n columns with elements from GF(s) satisfying the condition that no t columns are linearly dependent. This problem has applications to coding theory and also in the theory of fractionally replicated designs. © 1972 Academic Press, Inc.

This investigation was originally motivated by the problem of determining the maximum number of points in finite n-dimensional projective space PG(n, s) based on the Galois field GF(s) of order s=ph (where p and h are positive integers and p is the prime characteristic of the field), such that no t of these chosen points are linearly dependent. A set of k distinct points in PG(n, s), no t linearly dependent, is called a (k, t)-set for k1 >k. The maximum value of k is denoted by mt (n+1, s). The purpose of this paper is to find new upper bounds for some values of n, s and t. These bounds are of importance in the experimental design and information theory problems. © 1971 Institute of Statistical Mathematics.

Cochran’s Q test for differences between related-sample percentages or proportions has generally been incorrectly presented in secondary sources. The most common mistake results from failure to recognize that rows containing only 1’s or only 0’s, i.e., only successes or only failures, do not affect the value of Q. The F test, however, is affected by such rows. The probabilities from the χ2 and F approximations are compared with the exact probabilities in three sets of data. A rule of thumb, based on extensive study of the distribution of 0 in small samples, is given as an aid in judging when the χ2 approximation is satisfactory for practical purposes. © Taylor & Francis Group, LLC.

Kirillov and Reshetikhin introduced rigged configurations as a new way to calculate the entries of the Kostka matrix. Macdonald defined the two-parameter Kostka matrix whose entries generalize. We use rigged configurations and a formula of Stembridge to provide a combinatorial interpretation of in the case where is a partition with no more than two columns. In particular, we show that in this case, has nonnegative coefficients. © 1995 American Mathematical Society.

This paper presents a fresh approach to a general education mathematics course. The basic idea is to turn the customary mathematics class on its head by focusing on applications first, through a reading of articles from magazines and newspapers, and then turning to the technical mathematical details. A description of the topics that were covered in my course, along with references to various publications, is given. A course such as this one is important because it conveys how mathematics is serving the goals of society. © 1994 Taylor and Francis Group, LLC.

One of the problems which many companies face is the distribution of inventory from one or more centrally located distribution centers. The retail, industry, and in particular the women's clothing industry, faces the additional problem that not only does the merchandise have to be distributed but it must be distributed in such a way that every store gets a reasonable spread of colors and sizes. This research attempts to optimize the multi-criteria allocation objective by developing a computer algorithm. In order to be implemented any algorithm developed must be computationally efficient due to the size of the industry and other system related programming constraints. The algorithm which was developed not only provided a solution which was a marked improvement regarding the color spread of the merchandise but was also efficient enough to be immediately implemented on a national basis. © 1992.

Dose-response experiments are crucial in biomedical studies. There are usually multiple objectives in such experiments and among the goals is the estimation of several percentiles on the dose-response curve. Here we present the first non-parametric adaptive design approach to estimate several percentiles simultaneously via generalized Pó lya urns. Theoretical properties of these designs are investigated and their performance is gaged by the locally compound optimal designs. As an example, we re-investigated a psychophysical experiment where one of the goals was to estimate the three quartiles. We show that these multiple-objective adaptive designs are more efficient than the original single-objective adaptive design targeting the median only. We also show that urn designs which target the optimal designs are slightly more efficient than those which target the desired percentiles directly. Guidelines are given as to when to use which type of design. Overall we are pleased with the efficiency results and hope compound adaptive designs proposed in this work or their variants may prove to be a viable non-parametric alternative in multiple-objective dose-response studies. Copyright © 2004 John Wiley & Sons, Ltd.

Abstract:- We provide lower and upper bounds for the domination numbers and the connected domination numbers for outerplanar graphs. We also provide a recursive algorithm that finds a connected domination set for an outerplanar graph. Finally, we show that for outerplanar graphs where all bounded faces are 3-cycles, the problem of determining the connected domination number is equivalent to an art gallery problem, which is known to be NP-hard. Key-Words:- dominating sets, star forests, outerplanar graphs, art gallery 1

In this paper we consider a variation of the Art Gallery Problem. A set of points script G sign in a polygon Pn is a connected guard set for Pn provided that is a guard set and the visibility graph of the set of guards script G sign in Pn is connected. We use a coloring argument to prove that the minimum number of connected guards which are necessary to watch any polygon with n sides is ⌊(n - 2)/2⌋. This result was originally established by induction by Hernández-Peńalver [3]. From this result it easily follows that if the art gallery is orthogonal (each interior angle is 90° or 270°), then the minimum number of connected guards is n/2 - 2. © Springer-Verlag Berlin Heidelberg 2003.

In this paper we consider a variation of the Art Gallery Problem for orthogonal polygons. A set of points in a polygon Pn is a connected guard set for Pn provided that is a guard set and the visibility graph of the set of guards in Pn is connected. The polygon P n is orthogonal provided each interior angle is 90° or 270°. First we use a coloring argument to prove that the minimum number of connected guards which are necessary to watch any orthogonal polygon with n sides is n/2-2. This result was originally established by induction by Hernández-Peñalver. Then we prove a new result for art galleries with holes: we show that n/2-h connected guards are always sufficient to watch an orthogonal art gallery with n walls and h holes. This result is sharp when n = 4h + 4. We also construct galleries that require at least n/2-h-1 connected guards, for all n and h. © Springer-Verlag 2003.

A new theoretical Evans function condition is used as the basis of a numerical test of viscous shock wave stability. Accuracy of the method is demonstrated through comparison against exact solutions, a convergence study, and evaluation of approximate error equations. Robustness is demonstrated by applying the method to waves for which no current analytic results apply (highly nonlinear waves from the cubic model and strong shocks from gas dynamics). An interesting aspect of the analysis is the need to incorporate features from the analytic Evans function theory for purposes of numerical stability. For example, we find it necessary, for numerical accuracy, to solve ODEs on the space of wedge products.

We prove a new theorem for orthogonal art galleries in which the guards must guard one another in addition to guarding the polygonal gallery. A set of points G in a polygon Pn is a k-guarded guard set for Pn provided that (i) for every point x in Pn there exists a point w in G such that x is visible from w; and (ii) every point in G is visible from at least k other points in G: The polygon Pn is orthogonal provided each interior angle is 90° or 270°. We prove that for k ≥ 1 and n ≥ 6 every orthogonal polygon with n sides has a k-guarded guard set of cardinality (Formula Presented.) this bound is best possible. This result extends our recent theorem that treats the case k = 1. © Springer-Verlag Berlin Heidelberg 2001.

In this paper we propose novel algorithms for reconfiguring modular robots that are composed of n atoms. Each atom has the shape of a unit cube and can expand/contract each face by half a unit, as well as attach to or detach from faces of neighboring atoms. For universal reconfiguration, atoms must be arranged in 2×2×2 modules. We respect certain physical constraints: each atom reaches at most unit velocity and (via expansion) can displace at most one other atom. We require that one of the atoms can store a map of the target configuration. Our algorithms involve a total of O(n 2) such atom operations, which are performed in O(n) parallel steps. This improves on previous reconfiguration algorithms, which either use O(n 2) parallel steps [8,10,4] or do not respect the constraints mentioned above [1]. In fact, in the setting considered, our algorithms are optimal, in the sense that certain reconfigurations require Ω(n) parallel steps. A further advantage of our algorithms is that reconfiguration can take place within the union of the source and target configurations. © 2009 Springer-Verlag.