An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

Adaptive sampling for geometric problems over data streams

Geometric coordinates are an integral part of many data streams. Examples include sensor locations in environmental monitoring, vehicle locations in traffic monitoring or battlefield simulations, scientific measurements of earth or atmospheric phenomena, etc. This paper focuses on the problem of summarizing such geometric data streams using limited storage so that many natural geometric queries can be answered faithfully. Some examples of such queries are: report the smallest convex region in which a chemical leak has been sensed, or track the diameter of the dataset, or track the extent of the dataset in any given direction. One can also pose queries over multiple streams: for instance, track the minimum distance between the convex hulls of two data streams, report when datasets A and B are no longer linearly separable, or report when points of data stream A become completely surrounded by points of data stream B, etc. These queries are easily extended to more than two streams.

In this paper, we propose an adaptive sampling scheme that gives provably optimal error bounds for extremal problems of this nature. All our results follow from a single technique for computing the approximate convex hull of a point stream in a single pass. Our main result is this: given a stream of two-dimensional points and an integer r, we can maintain an adaptive sample of at most 2r+1 points such that the distance between the true convex hull and the convex hull of the sample points is O(D/r²), where D is the diameter of the sample set. The amortized time for processing each point in the stream is O(logr). Using the sample convex hull, all the queries mentioned above can be answered approximately in either O(logr) or O(r) time.     

Implicitly representing arrangements of lines or segments

Anarrangement ofn lines (or line segments) in the plane is the partition of the plane defined by these objects. Such an arrangement consists ofO(n ²) regions, calledfaces. In this paper we study the problem of calculating and storing arrangementsimplicitly, using subquadratic space and preprocessing, so that, given any query pointp, we can calculate efficiently the face containingp. First, we consider the case of lines and show that with (n) space¹ and (n ^3/2) preprocessing time, we can answer face queries in (n)+O(K) time, whereK is the output size. (The query time is achieved with high probability.) In the process, we solve three interesting subproblems: (1) given a set ofn points, find a straight-edge spanning tree of these points such that any line intersects only a few edges of the tree, (2) given a simple polygonal path , form a data structure from which we can find the convex hull of any subpath of quickly, and (3) given a set of points, organize them so that the convex hull of their subset lying above a query line can be found quickly. Second, using random sampling, we give a tradeoff between increasing space and decreasing query time. Third, we extend our structure to report faces in an arrangement of line segments in (n ^1/3)+O(K) time, given(n ^4/3) space and (n ^5/3) preprocessing time. Lastly, we note that our techniques allow us to computem faces in an arrangement ofn lines in time (m ^2/3 n ^2/3+n), which is nearly optimal.The first author is pleased to acknowledge the support of Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862 and National Science Foundation Grant CCR-8714565. Work on this paper by the fifth author has been supported by Office of Naval Research Grant N00014-87-K-0129, by National Science Foundation Grant NSF-DCR-83-20085, by grants from the Digital Equipment Corporation, and the IBM Corporation, and by a research grant from the NCRD—the Israeli National Council for Research and Development. The sixth author was supported in part by a National Science Foundation Graduate Fellowship. This work was begun while the non-DEC authors were visiting at the DEC Systems Research Center.     

Solution-phase parallel synthesis of hexahydro-1H-isoindolone libraries via tactical combination of Cu-catalyzed three-component coupling and Diels-Alder reactions

Parallel solution-phase synthesis of combinatorial libraries of hexahydro-1 H-isoindolones exploiting a novel "tactical combination" of Cu-catalyzed three-component coupling and Diels-Alder reactions was accomplished. Three distinct libraries consisting of 24 members (library I), 60 members (library II), and 32 members (library III) were constructed. Variation of three substituents on the isoindolone scaffold in library I was exclusively achieved by the choice of the building blocks. In the syntheses of libraries II and III, sublibraries of isoindolone scaffolds were prepared initially in a one-pot/two-step process and were further diversified via Pd-catalyzed Suzuki cross-coupling reaction with boronic acids at two different diversification points. The Lipinski profiles and calculated ADME properties of the compounds are also reported.     

Negative-parity states in Pb isotopes: g-factor of the 480 ns,if Jπ = 9− isomer in 200Pb

The g-factor of the 480 ns, 9^? isomer at 2.237 MeV in ²⁰⁰Pb was measured by the time-differential perturbed angular distribution method. The result, g = ?0.0285±0.0011 confirms the rather pure $\text{(}\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{)}$ quasiparticle structure of this state. Half-lives of 480±20 ns, 43±3 ns and 42±4 ns have been measured for the 2237 keV 9^?, 2154 keV 7^? states in ²⁰⁰Pb and the 2208 keV state in ²⁰²Pb, respectively; E2 transitions and g-factors of negative-parity states in even, neutron-deficient Pb isotopes are discussed.     

Microwave spectrum and ring puckering vibration of 4-methyl-2-oxetanone

We have analyzed the microwave spectrum of 4-methyl-2-oxetanone (β-butyrolactone) in the ground vibrational state and in the first three excited states of the ring puckering mode. The smooth variation of the rotational constants with vibrational quantum number indicates that the ring puckering potential is essentially single minima. In addition, the structural parameters derived from a diagnostic least-squares fit indicate that the equilibrium configuration of the ring is planar within about three degrees in the dihedral angle. These results are in agreement with the far-ir data, but the single minimum is surprising in view of the small barrier found in 2-oxetanone. The ground-state rotational constants are 9267.92 ± 0.15, 2698.357 ± 0.006, and 2380.008 ± 0.03 MHz. The dipole moment is 4.40 ± 0.06 D, with all uncertainties being the standard deviations determined by the least-squares-fitting procedure.     

Allene functionalization via bicyclic methylene aziridines

The oxidative functionalization of olefins is a common method for the formation of vicinal carbon-heteroatom bonds. However, oxidative methods to transform allenes into synthetic motifs containing three contiguous carbon-heteroatom bonds are much less developed. This paper describes the use of bicyclic methylene aziridines (MAs), prepared via intramolecular allene aziridination, as scaffolds for functionalization of all three allene carbons.     

Kinetics of the NCCO + NO2 reaction

The kinetics of the NCCO + NO(2) reaction was studied by transient infrared laser absorption spectroscopy. The total rate constant of the reaction was measured to be k = (2.1 ± 0.1) × 10(-11) cm(3) molecule(-1) s(-1) at 298 K. Detection of products and consideration of possible secondary chemistry shows that CO(2) + NO + CN is the primary product channel. The rate constants of the NCCO + CH(4) and NCCO + C(2)H(4) reactions were also measured, obtaining upper limits of k (NCCO + CH(4)) ≤ 7.0 × 10(-14) cm(3) molecule(-1) s(-1) and k (NCCO + C(2)H(4)) ≤ 5.0 × 10(-15) cm(3) molecule(-1) s(-1). Ab initio calculations on the singlet and triplet potential energy surfaces at B3LYP/6-311++G**//CCSD(T)/6-311++G** levels of theory show that the most favorable reaction pathway occurs on the singlet surface, leading to CO(2) + NO + CN products, in agreement with experiment.     

Morphing Simple Polygons

In this paper we investigate the problem of morphing (i.e., continuously deforming) one simple polygon into another. We assume that our two initial polygons have the same number of sides n , and that corresponding sides are parallel. We show that a morph is always possible through an interpolating simple polygon whose n sides vary but stay parallel to those of the two original ones. If we consider a uniform scaling or translation of part of the polygon as an atomic morphing step, then we show that O(n log n) such steps are sufficient for the morph. Furthermore, the sequence of steps can be computed in O(n log n) time. Received May 25, 1999, and in revised form November 15, 1999.