Your search

"For each date, a diverse dozen speakers were chosen based on prominence; the quality of the quotation; the uniqueness of the speaker with relation to gender, time period, nationality and vocation; and conflicting social, political, religious or philosophical background. Includes a quotation from each person that allows a glimpse of their personality"--Provided by publisher.

We prove two art gallery theorems in which the guards must guard one another in addition to the gallery. A set G of points (the guards) in a simple closed polygon (the art gallery) is a guarded guard set provided (i) every point in the polygon is visible to some point in G; and (ii) every point in G is visible to some other point in G. We prove that a polygon with n sides always has a guarded guard set of cardinality ⌊(3n-1)/7⌋ and that this bound is sharp (n5); our result corrects an erroneous formula in the literature. We also use a coloring argument to give an entirely new proof that the corresponding sharp function for orthogonal polygons is ⌊n/3⌋ for n≤6; this result was originally established by induction by Hernández-Peñalver. © 2003 Elsevier B.V.

The *-polynomial identities of minimal degree of Mn(F) are determined for n = 2, 4, * the symplectic involution. Copyright © 2004 by Marcel Dekker, Inc.

Contractedness of m-primary integrally closed ideals played a central role in the development of Zariski's theory of integrally closed ideals in two-dimensional regular local rings (R, m). In such rings, the contracted m-primary ideals are known to be characterized by the property that I: m = I: x for some x ∈ m\m2. We call the ideals with this property full ideals and compare this class of ideals with the classes of m-full ideals, basically full ideals, and contracted ideals in higher dimensional regular local rings. The m-full ideals are easily seen to be full. In this article, we find a sufficient condition for a full ideal to be m-full. We also show the equivalence of the properties full, m-full, contracted, integrally closed, and normal, for the class of parameter ideals. We then find a sufficient condition for a basically full parameter ideal to be full. © Taylor & Francis Group, LLC.

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.