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51.
The energy of a mass of liquid is evaluated asymptotically in powers of the range of the intermolecular potential divided by a typical dimension of the liquid. The leading term is the internal energy, proportional to the liquid volume. The second term is the energy of surface tension, proportional to the area of the liquid surface. The third term is proportional to an integral over this surface of the square of the mean curvature of the surface minus one-third of its Gaussian curvature. This new term has exactly the form of the bending energy of a thin elastic plate. Comparing it with the bending energy yields expressions for the flexural rigidity and the Poisson ratio of the liquid surface. This flexural rigidity of the surface leads to new terms in the equation of equilibrium of the liquid surface, in addition to the usual surface tension terms. 相似文献
52.
In this paper it is shown that various existing constructions of ‘Hopf invariant’ are equivalent to each other. In consequence
one gets that the oneToda-Hopf invariant enjoys various properties.
Both authors supported in part by the NSF. 相似文献
53.
E. Todd Brown Karen Karp Joseph M. Petrosko Jane Jones Gloria Beswick Carrie Howe Kathy Zwanzig 《School science and mathematics》2007,107(3):102-116
This study investigated K‐12 teachers' beliefs and reported teaching practices regarding calculator use in their mathematics instruction. A survey was administered to more than 800 elementary, middle and high school teachers in a large metropolitan area to address the following questions: (a) what are the beliefs and practices of mathematics teachers regarding calculator use? and (b) how do these beliefs and practices differ among teachers in three grade bands? Factor analysis of 20 Likert scale items revealed four factors that accounted for 54% of the variance in the ratings. These factors were named Catalyst Beliefs, Teacher Knowledge, Crutch Beliefs, and Teacher Practices. Compared to elementary teachers, high school teachers were significantly higher in their perception of calculator use as a catalyst in mathematics instruction. However, the higher the grade level of the teacher, the higher the mean score on the perception that calculator use may be a way of getting answers without understanding mathematical processes. The mean scores for teachers in all three grade bands indicated agreement that students can learn mathematics through calculator use and using calculators in instruction will lead to better student understanding and make mathematics more interesting. The survey results shed light on teachers' self reported beliefs, knowledge, and practices in regard to consistency with elements of the National Council of Teachers of Mathematics Principles and Standards for School Mathematics (2000) technology principle and the NCTM use of technology position paper (2003). This study extended previous research on teachers' beliefs regarding calculator use in classrooms by examining and comparing the results of teacher surveys across three grade bands. 相似文献
54.
55.
Nadeem Saeed Basant K Puri Angela Oatridge Joseph V Hajnal Ian R Young 《Magnetic resonance imaging》1998,16(10):1237-1247
Two semi-automated methods for quantification of ventricular volume change from baseline and follow-up magnetic resonance imaging scans have been developed. Technique 1 employs direct segmentation of the ventricles from both the scans using thresholding and contour extraction. Technique 2 operates on difference images produced by voxel based intensity subtraction of the baseline from the registered follow-up images. Here, all voxels with intensities above a noise threshold and in a restricted area are monitored to compute volumetric changes. In phantom measurements the first technique was accurate to 0.0046%, the second to 0.167% of the phantom volume. Results from normal volunteers was that the average ventricular volume changed by 1.52% and 1.54% for images acquired within 9 months using techniques 1 and 2, respectively. With schizophrenic patients mean change of 10.78% and 9.43% were found employing the first and second procedures, respectively. All measurements agreed with a radiologist’s visual grading of the changes. Robust, objective, fast, easy-to-use, and fairly accurate procedures have been developed and validated to quantify volumetric changes. 相似文献
56.
Strong, low-energy two-photon absorption in extended amine-terminated cyano-substituted phenylenevinylene oligomers 总被引:8,自引:0,他引:8
Chung SJ Rumi M Alain V Barlow S Perry JW Marder SR 《Journal of the American Chemical Society》2005,127(31):10844-10845
Three quadrupolar oligophenylenevinylenes with five rings in the conjugated backbone, terminal donor groups, and various acceptors and/or donors along the backbone were synthesized and their two-photon spectroscopic properties investigated. These chromophores exhibit large two-photon absorption cross sections over a wide wavelength range and two distinct peaks, the strongest of which (deltamax > 3600 GM) is observed at 960-970 nm, a wavelength close to twice the value of the linear absorption maximum (2lambda(1)max). The findings on these chromophores are compared with those for analogous molecules with shorter conjugation length, for which the main two-photon band is at significantly shorter wavelength than 2lambda(1)max. 相似文献
57.
The silanization/hydrosilation method is used to bond an alkyne (1-octyne) to a silica hydride surface. The new bonded material is characterized by elemental analysis and diffuse reflectance infrared Fourier transform spectroscopy. The hydrophobic behavior of this material was determined by the retention characteristics of aromatic solutes and the shape selectivity as well as phase classification (monomeric or polymeric) was measured by the polycyclic aromatic hydrocarbon mixture standard reference material 869. The presence of residual silanols on the bonded phase was probed by several basic solutes at pH 7. Long-term stability studies were conducted by measuring retention and peak symmetry of basic compounds over several thousand column volumes at pH 10. 相似文献
58.
Desulfurization of dibenzothiophene, two methyldibenzothiophenes, and phenanthro[4,5-bcd]-thiophene to give 60-80% yields of hydrocarbon products was effected by means of a sulfided molydena catalyst plus methanol at 450° and a pressure of ca. one atmosphere. The methanol functions both as an in situ hydrogen donor and as a methylating agent. 相似文献
59.
Kommareddi Nagesh S. Tata Murthy Karayigitoglu Cigdem John Vijay T. McPherson Gary L. Herman Michael F. O'Connor Charles J. Lee Young-Sook Akkara Joseph A. Kaplan David L. 《Applied biochemistry and biotechnology》1995,51(1):241-252
Applied Biochemistry and Biotechnology - Horseradish peroxidase has been used as a biocatalyst to synthesize a polymeric material from alkyl-substituted phenols. The synthesis is carried out in a... 相似文献
60.
Li C Lee D Graf TN Phifer SS Nakanishi Y Burgess JP Riswan S Setyowati FM Saribi AM Soejarto DD Farnsworth NR Falkinham JO Kroll DJ Kinghorn AD Wani MC Oberlies NH 《Organic letters》2005,7(25):5709-5712
[chemical reaction: see text]. Three new ent-trachylobane diterpenoids (1-3) were isolated and structures elucidated from Mitrephora glabra Scheff. (Annonaceae). Mitrephorone A (1) possesses a hexacyclic ring system with adjacent ketone moieties and an oxetane ring, both of which are unprecedented among trachylobanes. All compounds were evaluated for cytotoxicity against a panel of cancer cells, where 1 displayed the most potent and broadest activity, and against a battery of antimicrobial assays, where all compounds were approximately equipotent. 相似文献