On the Rates of Approximation of Bernstein Type Operators

Asymptotic behavior of two Bernstein-type operators is studied in this paper. In the first case, the rate of convergence of a Bernstein operator for a bounded function f is studied at points x where f(x+) and f(x−) exist. In the second case, the rate of convergence of a Szász operator for a function f whose derivative is of bounded variation is studied at points x where f(x+) and f(x−) exist. Estimates of the rate of convergence are obtained for both cases and the estimates are the best possible for continuous points.     

地震栓波器假频本质的动力稳定性解释

地震栓波器是用来栓测竖向地震波的仪器.本文根据它的实际结构,提出了一个较精确的力学模型——双层三悬丝模型.把悬丝作为曲杆,用动力稳定性理论进行分析,揭示了地震仪栓波器由于竖向地震波以外的因素而产生输出的所谓假频现象产生的原因:位于悬丝所在水平面内的激励在一定条件下将导致悬丝在面外动力失稳而产生强烈振动,从而引起虚假输出.计算结果说明了影响假频的诸因素,为激励速度峰值、激励相对于栓波器的方向和曲杆面内振动的固有频率等的作用,并与实验值作了比较.     

Automated synthesis of symmetric integrin αvβ3-targeted radiotracer [18F]FP-PEG3-β-Glu-RGD2

A automated synthesis of symmetric integrin α_vβ₃-targeted radiotracer [¹⁸F]FP-PEG₃-β-Glu-RGD₂ was carried out by multi-step procedure on the modified PET-MF-2V-IT-I synthesizer. Firstly, the prosthetic group of 4-nitrophenyl 2-[¹⁸F]fluoropropionate ([¹⁸F]NFP) was automated synthesized by a convenient three-step, one-pot procedure. Secondly, [¹⁸F]FP-PEG₃-β-Glu-RGD₂ was synthesized by coupling [¹⁸F]NFP with the symmetric RGD-peptide (PEG₃-β-Glu-RGD₂) and purified by a solid-phase extraction cartridge. The radiochemical yields of [¹⁸F]NFP were 35 ± 5 % (n = 10, decay-corrected) based on [¹⁸F]fluoride in 80 min. [¹⁸F]FP-PEG₃-β-Glu-RGD₂ was obtained with yield 40 ± 10 % (n = 5, decay-corrected) from [¹⁸F]NFP within 20 min. The radiochemical purity of [¹⁸F]FP-PEG₃-β-Glu-RGD₂ was greater than 98 %.     

NMR-based metabonomic analyses of the effects of ultrasmall superparamagnetic particles of iron oxide (USPIO) on macrophage metabolism

The metabonomic changes in murine RAW264.7 macrophage-like cell line induced by ultrasmall superparamagnetic particles of iron oxides (USPIO) have been investigated, by analyzing both the cells and culture media, using high-resolution NMR in conjunction with multivariate statistical methods. Upon treatment with USPIO, macrophage cells showed a significant decrease in the levels of triglycerides, essential amino acids such as valine, isoleucine, and choline metabolites together with an increase of glycerophospholipids, tyrosine, phenylalanine, lysine, glycine, and glutamate. Such cellular responses to USPIO were also detectable in compositional changes of cell media, showing an obvious depletion of the primary nutrition molecules, such as glucose and amino acids and the production of end-products of glycolysis, such as pyruvate, acetate, and lactate and intermediates of TCA cycle such as succinate and citrate. At 48 h treatment, there was a differential response to incubation with USPIO in both cell metabonome and medium components, indicating that USPIO are phagocytosed and released by macrophages. Furthermore, information on cell membrane modification can be derived from the changes in choline-like metabolites. These results not only suggest that NMR-based metabonomic methods have sufficient sensitivity to identify the metabolic consequences of murine RAW264.7 macrophage-like cell line response to USPIO in vitro, but also provide useful information on the effects of USPIO on cellular metabolism.     

最小二乘法相关的一类特殊矩阵的代数运算

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Highly efficient solid-state synthesis of carbon-encapsulated ultrafine MoO<Subscript>2</Subscript> nanocrystals as high rate lithium-ion battery anode

A simple and highly efficient method is developed for the one-step in situ preparation of carbon-encapsulated MoO₂ nanocrystals (MoO₂@C) with core-shell structure for high-performance lithium-ion battery anode. The synthesis is depending on the solid-state reaction of cyclopentadienylmolybdenum tricarbonyl dimer with ammonium persulfate in an autoclave at 200 °C for 30 min. The large amount of heat generated during the explosive reaction cleaves the cyclopentadiene ligands into small carbon fragments, which form carbon shell after oxidative dehydrogenation coating on the MoO₂ nanocrystals, resulting in the formation of core-shell structure. The MoO₂ nanocrystals have an equiaxial morphology with an ultrafine diameter of 2–8 nm, and the median size is 4.9 nm. Hundreds of MoO₂ nanocrystals are encapsulated together by the worm-like carbon shell, which is amorphous and about 3–5 nm in thickness. The content of MoO₂ nanocrystals in the nanocomposite is about 69.3 wt.%. The MoO₂@C anode shows stable cyclability and retains a high reversible capacity of 443 mAh g^?1 after 50 cycles at a current density of 3 A g^?1, owing to the effective protection of carbon shell.     

Mechanism of removal of arsenic by bead cellulose loaded with iron oxyhydroxide (beta-FeOOH): EXAFS study

Bead cellulose loaded with iron oxyhydroxide (BCF) with 47 mass% Fe content was prepared and was successfully applied to the elimination of arsenic from aqueous solutions. A clearer understanding of the arsenic removal mechanism will provide accurate prediction of the arsenic adsorptive properties of the new adsorbent. To study the mechanism of the adsorption process, we measured the extended X-ray absorption fine structure (EXAFS) spectra of arsenite and arsenate sorbed onto the adsorbent with different surface coverages. Both arsenite and arsenate were strongly and specifically adsorbed by akaganéite adsorptive centers on BCF by an inner-sphere mechanism. There was no change in oxidation state following interaction between the arsenic species and the BCF surface. The dominant complex of arsenic species adsorbed on akaganéite was bidentate binuclear corner-sharing ((2)C) between As(V) tetrahedra (or As(III) pyramids) and adjacent edge-sharing FeO(6) octahedra. On the basis of the results from EXAFS spectra, the adsorptive characteristics of arsenic, such as the effects of pH and competing anions, were satisfactorily interpreted.     

A glassy carbon electrode modified with gold nanoparticle-encapsulated graphene oxide hollow microspheres for voltammetric sensing of nitrite

Reduced graphene oxide hollow microspheres (rGO HMS) were encapsulated with gold nanoparticles (AuNPs) by spray drying. Scanning electron microscopy, transmission electron microscopy, X-ray diffraction and Raman spectroscopy were used to characterize the AuNP/rGO HMS. When placed on a glassy carbon electrode (GCE), it exhibits excellent electrochemical catalytic properties towards the oxidation of nitrite. The electrocatalytic properties were studied using various electrochemical techniques. Compared to AuNP-decorated graphene sheet based electrodes documented in the literature, the one presented here provides a larger surface area. This enhances the catalytic activity towards nitrite. The electrode, typically operated at a working potential of 0.82 V (vs. SCE), has a linear response in the 5.0 μM to 2.6 mM nitrate concentration range, and a detection limit as low as 0.5 μM (at an S/N ratio of 3).

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Graphical abstract Schematic presentation of the synthesis of graphene hollow microspheres encapsulated with of gold nanoparticles (AuNP/rGO HMS) through a spray drying technique. The material was applied to the electrochemical determination of nitrite.

     

Hydrothermal growth and optical properties of RbBe2BO3F2 crystals

Crystals of RbBe₂BO₃F₂ up to a size of 22×18×5 mm³ have been grown by the hydrothermal method. The growth conditions were optimized mainly by adjusting the mineralizers and growth temperature. The crystals linear and nonlinear optical properties, including its transmittance spectrum and second harmonic generation from 532 to 266 nm, were measured and compared with those of flux grown crystals. A maximum conversion efficiency of 20% was obtained with a 25 ps, 10 Hz laser system. The results indicate that RbBe₂BO₃F₂ crystals grown by the hydrothermal method show similar capability for frequency conversion compared with flux grown crystals and are promising for future deep-UV harmonic generation.     

ICF靶腔曲面光场计算

传统的衍射计算方法都是针对衍射场为平面的计算,对于ICF靶腔衍射场为曲面时,计算困难。通过比较常用衍射计算方法的优缺点,基于层析成像的思想,提出采用快速傅里叶变换分层计算,并根据最相邻原则拟合曲面衍射场光场分布的快速计算方法。该方法可以计算出任意给定空间曲面上的光场分布,且具有计算快速、结果精确的优点。模拟分析表明,当分层数足够大时,采用该方法可有效解决ICF靶腔内壁曲面光场的计算问题。