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Melanie Parker 《School science and mathematics》1997,97(8):406-412
Percent is a standardized ratio comparison that is often used to describe relative amounts of increase and decrease. In this paper, the nonsymmetric relationship between percent of increase and percent of decrease is explored in several ways. Beginning with a simple graphical representation of the relationship, the functional relationship is developed, with relative decrease expressed as a function of relative increase. Once expressed in the form f(x) = 100x/(100 + x), an immediate connection is made to two other topics commonly found within the study of rates—the work problem and the harmonic mean. Finally, successive percents of increase or decrease are shown to be everyday applications of the geometric mean. This deeper look at a common mathematical concept has uncovered rich structural relationships between topics that are often isolated in the curriculum. 相似文献
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Christopher A. Luckhurst Ian Millichip Beth Parker James Reuberson Mark Furber 《Tetrahedron letters》2007,48(50):8878-8882
A one-pot reaction of carboxylic acids with sulfonamides to afford sulfonylureas is described. 相似文献
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A. A. Collyer D. W. Clegg M. Morris D. G. Parker G. W. Wheatley G. C. Corfield 《Journal of polymer science. Part A, Polymer chemistry》1991,29(2):193-200
High molecular weight alternating block copolymers of polyethesulphone (PES) and polydimethylsiloxane (PDMS) were prepared by the condensation of dimethylamino-terminated PDMS oligomers and hydroxy-terminated PES oligomers in 1,2-dichlorobenzene. Microphase separation of the block copolymers at exceptionally short block lengths was observed by differential scanning calorimetry (DSC) and transmission electron microscopy (TEM). The Si? O? C intersegment linkage in these materials appeared to display poor hydrolytic stability which is contrary to results obtained for other block copolymers. 相似文献
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Let p a prime, X = SL2(pa) and K = GF(pa). For S a Sylow p-subgroup of X, we explicitly describe the structure of the commutator series of S on each of the irreducible KX-modules.Received: 28 April 2004 相似文献
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Researchers first examined the problem of separable concave programming more than thirty years ago, making it one of the earliest branches of nonlinear programming to be explored. This paper proposes a new algorithm that finds the exact global minimum of this problem in a finite number of iterations. In addition to proving that our algorithm terminates finitely, the paper extends a guarantee of finiteness to all branch-and-bound algorithms for concave programming that (1) partition exhaustively using rectangular subdivisions and (2) branch on the incumbent solution when possible. The algorithm uses domain reduction techniques to accelerate convergence; it solves problems with as many as 100 nonlinear variables, 400 linear variables and 50 constraints in about five minutes on an IBM RS/6000 Power PC. An industrial application with 152 nonlinear variables, 593 linear variables, and 417 constraints is also solved in about ten minutes. 相似文献
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