关于(?)-拟微分核的连续性

Supposa that f(x) is a quasidifferentiable function, defined on S(?)R~n where S is an open set, with a -equivalent bounded quasidifferential subfam ily. Lenma I     

Intended Treatments of Arithmetic Average in U.S. and Asian School Mathematics Textbooks

This study examined how selected U.S. and Asian mathematics curricula are designed to facilitate students' understanding of the arithmetic average. There is a consistency regarding the learning goals among these curriculum series, but the focuses are different between the Asian series and the U.S. reform series. The Asian series and the U.S. commercial series focus the arithmetic average more on conceptual and procedural understanding of the concept as a computational algorithm than on understanding the concept as a representative of a data set; however, the two U.S. reform series focus the concept more on the latter. Because of the different focuses, the Asian and the U.S. curriculum series treat the concept differently. In the Asian series, the concept is first introduced in the context of “equal‐sharing” or “per‐unit‐quantity,” and the averaging formula is formally introduced at a very early stage. In the U.S. reform series, the concept is discussed as a measure of central tendency, and after students have some intuitive ideas of the statistical aspect of the concept, the averaging algorithm is briefly introduced.     

Solid-state Electrochemistry of Gadolinium Hexacyanoferrate Modified Electrode and Electrocatalytic Properties of Gadolinium Hexacyanoferrate

A new electroactive polynuclear inorganic compound of rare earth metal, gadolinium hexacyanoferrate (GdHCF), was prepared and characterized using the techniques of FTIR spectroscopy, thermogravimetric analysis (TG), UV-Vis spectrometry, X-ray photoelectron spectroscopy (XPS), ICP atomic emission spectroscopy, and EDX. The results of ICP atomic emission spectroscopy, EDX, and TGA indicated that the prepared GdHCF sample had a stoichiometry of NaGdFe(CN)₆·12H₂O (when GdHCF was prepared in NaCl solution). The FTIR spectrum of GdHCF showed that there were two types of water molecules in the structure of GdHCF: one was the interstitial water (5 H₂O), which resulted from the association of water due to H-bonding, and the other was water coordinated with Gd (7 H₂O). The results obtained using XPS showed that the oxidation state of Fe and Gd in the GdHCF sample was +2 and +3, respectively. GdHCF was immobilized on the surface of spectroscopically pure graphite (SG) electrode forming the GdHCF/SG electrode, and the solid-state electrochemistry of the resultant electrode was studied using cyclic voltammetry. The cyclic voltammetric results indicated that the GdHCF/SG electrode exhibited a pair of well-defined and stable redox peaks with the formal potential of E^0′=(197±3) mV. The effects of the concentration of the supporting electrolyte on the electrochemical characteristics of GdHCF were studied, and the results showed that the value of E^0′ increased linearly with the activity of the cationic ion of the supporting electrolyte (lga_Na⁺), with a slope of 54.1 mV, which may become a novel method for determining the activity of Na⁺ in solution. Further experimental results indicated that GdHCF had electrocatalytic activities toward the oxidation of dopamine (DA) and ascorbic acid (AA), and the electrocatalytic current increased linearly with the concentration of DA (or AA) in the range of 1.0–10.0 mmol·L^?1 (for DA) or 0.5–20.0 mmol·L^?1 (for AA).     

Crystallographic report: Diiodo[tris(2‐pyridyl)amine]mercury(II), [(C5H4N)3N]HgI2

In mononuclear HgI₂[(C₅H₄N)₃N], mercury is tetrahedrally coordinated by two nitrogen atoms of a tris(2‐pyridyl)amine ligand and two iodides. The coordination moieties are connected by weak intermolecular Hg(II)···I interactions to give a one‐dimensional structure. Copyright © 2003 John Wiley & Sons, Ltd.     

Modelling of a single drop impact onto liquid film using particle method

The process of single liquid drop impact on thin liquid surface is numerically simulated with moving particle semi‐implicit method. The mathematical model involves gravity, viscosity and surface tension. The model is validated by the simulation of the experimental cases. It is found that the dynamic processes after impact are sensitive to the liquid pool depth and the initial drop velocity. In the cases that the initial drop velocity is low, the drop will be merged with the liquid pool and no big splash is seen. If the initial drop velocity is high enough, the dynamic process depends on the liquid depth. If the liquid film is very thin, a bowl‐shaped thin crown is formed immediately after the impact. The total crown subsequently expands outward and breaks into many tiny droplets. When the thickness of the liquid film increases, the direction of the liquid crown becomes normal to the surface and the crown propagates outward. It is also found that the radius of the crown is described by a square function of time: r_C = [c(t ? t₀)]^0.5. When the liquid film is thick enough, a crown and a deep cavity inside it are formed shortly after the impact. The bottom of the cavity is initially oblate and then the base grows downward to form a sharp corner and subsequently the corner moves downward. Copyright © 2004 John Wiley & Sons, Ltd.     

Photorefractive Four-Wave Mixing Switches Utilizing Pockels Effect -Longitudinal and Lateral Switches-

We carried out detailed calculations for photorefractive wave-mixing switches based on one of three crystals with high electro-optic coefficients, namely, BaTiO₃, Strontium Barium Niobate (SBN (0.75)), and Potasium Sodium Strontium Barium Niobate (KNSBN). A comparison of results for the three crystals shows that a 0_-cut BaTiO³ crystal is suitable for a longitudinal switch and requires a voltage of about 80 for a 2-mm-thick crystal to induce sufficient phase mismatch. The electrodes must be transparent for the incident and diffracted beams. A 45_-cut SBN (0.75) crystal, however, is suitable for a lateral switch and requires a voltage of about 150 for a 1-mm-wide crystal. The electrodes do not need to be transparent.     

Synthesis and characterization of well‐defined diblock and triblock copolymers of poly(N‐isopropylacrylamide) and poly(ethylene oxide)

Well‐defined diblock and triblock copolymers composed of poly(N‐isopropylacrylamide) (PNIPAM) and poly(ethylene oxide) (PEO) were successfully synthesized through the reversible addition–fragmentation chain transfer polymerization of N‐isopropylacrylamide (NIPAM) with PEO capped with one or two dithiobenzoyl groups as a macrotransfer agent. ¹H NMR, Fourier transform infrared, and gel permeation chromatography instruments were used to characterize the block copolymers obtained. The results showed that the diblock and triblock copolymers had well‐defined structures and narrow molecular weight distributions (weight‐average molecular weight/number‐average molecular weight < 1.2), and the molecular weight of the PNIPAM block in the diblock and triblock copolymers could be controlled by the initial molar ratio of NIPAM to dithiobenzoate‐terminated PEO and the NIPAM conversion. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4873–4881, 2004     

Exploitation of introducing of catalytic centers into layer galleries of layered silicates and related epoxy nanocomposites. I. Epoxy nanocomposites derived from montmorillonite modified with catalytic surfactant‐bearing carboxyl groups

Montmorillonite (MMT) was modified with the acidified cocamidopropyl betaine (CAB) and the resulting organo‐montmorillonite (O‐MMT) was dispersed in an epoxy/methyl tetrahydrophthalic anhydride system to form epoxy nanocomposites. The intercalation and exfoliation behavior of the epoxy nanocomposites were examined by X‐ray diffraction and transmission electron microscopy. The curing behavior and thermal property were investigated by in situ Fourier transform infrared spectroscopy and DSC, respectively. The results showed that MMT could be highly intercalated by acidified CAB, and O‐MMT could be easily dispersed in epoxy resin to form intercalated/exfoliated epoxy nanocomposites. When the O‐MMT loading was lower than 8 phr (relative to 100 phr resin), exfoliated nanocomposites were achieved. The glass‐transition temperatures (T_g's) of the exfoliated nanocomposite were 20 °C higher than that of the neat resin. At higher O‐MMT loading, partial exfoliation was achieved, and those samples possessed moderately higher T_g's as compared with the neat resin. O‐MMT showed an obviously catalytic nature toward the curing of epoxy resin. The curing rate of the epoxy compound increased with O‐MMT loading. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1192–1198, 2004