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1.
This paper compares the attitudes about mathematics of students from traditionally taught calculus classes and those from a “reformed” calculus course. The paper is based on three studies, which together present a consistent picture of student attitudes about calculus reform. The reformed course appeared to violate students' deeply held beliefs about the nature of mathematics and how it should be learned. Although during their first months in the reformed course most students disliked it, their attitudes gradually changed. One and 2 years after, reform students felt significantly more than the traditionally taught students that they better understood how math was used and that they had been required to understand math rather than memorize formulas. 相似文献
2.
David P. Dobkin Steven J. Friedman Kenneth J. Supowit 《Discrete and Computational Geometry》1990,5(1):399-407
LetS be any set ofN points in the plane and let DT(S) be the graph of the Delaunay triangulation ofS. For all pointsa andb ofS, letd(a, b) be the Euclidean distance froma tob and let DT(a, b) be the length of the shortest path in DT(S) froma tob. We show that there is a constantc (≤((1+√5)/2) π≈5.08) independent ofS andN such that $$\frac{{DT(a,b)}}{{d(a,b)}}< c.$$ 相似文献
3.
The dam problem with general geometry is considered. Fluid is drawn from the bottomS
1 at a ratek where 0 k N,
S
1
k M; the objective is to minimize the total pressure of the fluid in the dam. A bang-bang principle is established for any optimal controlk
0, that is,k
0 = 0 on a setA andk
0 =N on the complement setS
1
A. In the case of a rectangular dam the structure ofA is determined and the uniqueness of the minimizerk
0 is established.This work is partially supported by National Science Foundation Grants DMS-8501397 and DMS-8420896. 相似文献
4.
We report simultaneous observation of coherent resonance Raman scattering and incoherently broadened resonance fluorescence following excitation of cytochrome c in the α(0, 0) region. The influence of incoherent broadening processes on resonance Raman scattering experiments is considered. 相似文献
5.
L. Margulies N. Friedman M. Sheves Y. Mazur M.E. Lippitsch M. Riegler F.R. Aussenegg 《Tetrahedron》1985,41(1):191-195
Linear dichroism spectra of several retinoids and related polyenes incorporated in stretched polyethylene films were determined. It is suggested that the retinoids are oriented with the plane of the ring parallel to the stretching direction of the film, the long polyene chain being displaced from that direction. 相似文献
6.
Michael Stavola J.M. Friedman R.A. Stepnoski Mark G. Sceats 《Chemical physics letters》1981,80(1):192-194
Cooperative vibronic spectra involving Gd3+ electronic transitions and the vibrational transitions of nearby water molecules are used to determine the stretching spectrum for isotopically dilute OH in a solution of GdCl3 in D2O. The OH stretching spectrum of water molecules in the first hydration sphere is shifted to lower energy than that of the bulk liquid. 相似文献
7.
Friedman LA You F Sabat M Harman WD 《Journal of the American Chemical Society》2003,125(49):14980-14981
The rhenium furan complexes TpRe(CO)(MeIm)(eta2-2-methylfuran) (1) and TpRe(CO)(MeIm)(eta2-2,5-dmethylfuran) (2) undergo Lewis acid-promoted cyclopentannulation reactions with enones and enals to generate 3-acetylcyclopentene complexes. During the reaction, a rearrangement occurs such that the alpha and beta carbons of the enone are incorporated into the new carbocycle. Treatment of these complexes with an oxidant (H2O2 or silver triflate) liberates the acetylcyclopentene. When a resolved form of the rhenium complex is used, the acetylcyclopentenes can be obtained enantioselectively. 相似文献
8.
Friedman M 《Journal of chromatography. A》2004,1054(1-2):143-155
Potatoes and tomatoes, members of the Solanaceae plant family, serve as major, inexpensive low-fat food sources providing for energy, high-quality protein, fiber, vitamins, pigments, as well as other nutrients. These crops also produce biologically active secondary metabolites, which may have both adverse and beneficial effects in the diet. This limited overview, based largely on our studies with the aid of HPLC, TLC, ELISA, GC-MS, and UV spectroscopy, covers analytical aspects of two major potato trisaccharide glycoalkaloids, alpha-chaconine and alpha-solanine, and their hydrolysis products (metabolites) with two, one, and zero carbohydrate groups; the potato water-soluble nortropane alkaloids calystegine A3 and B2; the principal potato polyphenolic compound chlorogenic acid; potato inhibitors of digestive enzymes; the tomato tetrasaccharide glycoalkaloids dehydrotomatine and alpha-tomatine and hydrolysis products; the tomato pigments beta-carotene, lycopene, and chlorophyll; and the anticholinergic alkaloids atropine and scopolamine present in Datura stramonium (jimson weed) seeds that contaminate grain and animal feed. Related studies by other investigators are also mentioned. Accurate analytical methods for these food ingredients help assure the consumer of eating a good-quality and safe diet. 相似文献
9.
Brooks BC Meiere SH Friedman LA Carrig EH Gunnoe TB Harman WD 《Journal of the American Chemical Society》2001,123(15):3541-3550
The mechanisms for the interconversion of facial diastereomers of a variety of TpRe(CO)(L)(eta(2)-L(Ar)) complexes [L = (t)BuNC, pyridine (py), PMe(3), or 1-methylimidazole (MeIm); L(Ar) = benzene, anisole, naphthalene, 1-methylpyrrole, furan, or thiophene; Tp = hydridotris(pyrazolyl)borate] have been investigated by (1)H NMR spin saturation experiments. In addition, the rates and free energies of activation for these processes were calculated from spin saturation experiments and T(1) measurements. The operative mechanisms for interconversion of the pi diastereomers were found to be nondissociative, undergoing either an interfacial or intrafacial linkage isomerization. A comparison of the kinetic parameters for isomerization of related eta(2)-olefin complexes of the [TpRe(CO)(PMe(3))] and [CpRe(NO)(PPh(3))](+) fragments is also presented. 相似文献
10.
An interesting energy cascade is observed in the phosphorescence spectra of 1% biphenyl-h10 in biphenyl-d10 (2–15 K); strongly perturbed host sites, with energy levels below that of the protonated guest, quench the guest sites at higher temperatures (11–15 K). The identification of the perturbed sites is based on vibrational characteristics (both intensity and frequency), obtained with the help of phosphorescence spectra of biphenyl-h10 and biphenyl-d10 in an argon matrix, indicating an isotope dependent vibronic structure. A partial vibrational analysis is presented, resulting in confirmation of the first triplet state of biphenyl as orbitally ungerade. The dynamics of the triplet excitation are discussed, including several possible mechanisms explaining the non-Boltzmann nature of the low-temperature steady state. 相似文献