An Arc as the Inverse Limit of a Single Bonding Map of Type N on [0,1]

Let I = [0, 1], c ₁, c ₂ ∈ (0, 1) with c ₁ < c ₂ and f : I⊸I be a continuous map satisfying: are both strictly increasing and is strictly decreasing. Let A = {x ∈ [0, c ₁]∣f(x) = x}, a=max A, a ₁ =max(A\{a}), and B = {x ∈ [c ₂, 1]∣f(x) = x}, b=minB, b ₁ =min(B\{b}). Then the inverse limit (I, f) is an arc if and only if one of the following three conditions holds: (1) If c ₁ < f (c ₁) ≤ c ₂ (resp. c ₁ ≤ f (c ₂) < c ₂), then f has a single fixed point, a period two orbit, but no points of period greater than two or f has more than one fixed point but no points of other periods, furthermore, if A≠φ and B≠φ, then f (c ₂) > a (resp. f (c ₁) < b). (2) If f (c ₁) ≤ c ₁ (resp. f (c ₂) ≥ c ₂), then f has more than one fixed point, furthermore, if B≠φ and A\ {a} ≠φ, f (c ₂) ≥ a or if a ₁ < f (c ₂) < a, f ² (c ₂) > f (c ₂), (resp. f has more than one fixed point, furthermore, if A≠φ and B\{b}≠φ, f (c ₁) ≤ b or if b < f (c ₂) < b ₁, f ² (c ₁) < f (c ₁)). (3) If f (c ₁) > c ₂ and f (c ₂) < c ₁, then f has a single fixed point, a single period two orbit lying in I\(u, v) but no points of period greater than two, where u, v ∈ [c ₁, c ₂] such that f (u) = c ₂ and f (v) = c ₁. Supported by the National Natural Science Foundation of China (No. 19961001, No. 60334020) and Outstanding Young Scientist Research Fund. (No. 60125310)     

An improved palladium-based DMFCs cathode catalyst

A novel carbon-supported palladium-rich Pd3Pt1/C catalyst prepared by a modified polyol process showed a better cell performance than Pt/C in direct methanol fuel cells, which may be attributed to palladium's inactivity to methanol electro-oxidation while exhibiting good performance to oxygen reduction reaction.     

Molality as a unit of measure for expressing 1H MRS brain metabolite concentrations in vivo

Absolute concentrations of cerebral metabolite in in vivo 1H magnetic resonance spectroscopy studies (1H-MRS) are widely reported in molar units as moles per liter of tissue, or in molal units as moles per kilogram of tissue. Such measurements require external referencing or assumptions as to local water content. To reduce the scan time, avoid assumptions that may be invalid under specific pathologies, and provide a universally accessible referencing procedure, we suggest that metabolite concentrations from 1H-MRS measurements in vivo be reported in molal units as moles per kilogram of tissue water. Using internal water referencing, a two-compartment water model, a simulated brain spectrum for peak identification, and a spectroscopic bi-exponential spin-spin relaxation segmentation technique, we measured the absolute concentrations for the four common 1H brain metabolites: choline (Cho), myo-inositol (mIno), phosphocreatine + creatine (Cr), and N-acetyl-aspartate (NAA), in the hippocampal region (n = 26) and along the Sylvian fissure (n = 61) of 35 healthy adults. A stimulated echo localization method (20 ms echo time, 10 ms mixing time, 4 s repetition time) yielded metabolite concentrations, uncorrected for metabolite relaxation or contributions from macromolecule resonances, that were expectantly higher than with molar literature values. Along the Sylvian fissure the average concentrations (coefficient of variation (CV)) in mmoles/kg of tissue water were 17.6 (12%) for NAA, 14.2 (9%) for Cr, 3.6 (13%) for Cho, and 13.2 (15%) for mIno. Respective values for the hippocampal region were 15.7 (20%), 14.7 (16%), 4.6 (19%), and 17.7 (26%). The concentrations of the two regions were significantly different (p 相似文献   

Lipase TL-mediated kinetic tesolution of 5-benzyloxy-1-tert-butyldimethylsilyloxy-2-pentanol at low temperature: concise asymmetric synthesis of both enantiomers of a piperazic acid derivative

Lipase TL-mediated kinetic resolution of (+/-)-5-benzyloxy-1-tert-butyldimethylsilyloxy-2-pentanol (5) at low temperature proceeded to give the corresponding (S)-alcohol 5 and (R)-acetate 6 in quantitative yields with high enantiomeric purity. The addition of bases such as pyridine, DMAP, 2,4- and 2,6-lutidines, or triethylamine considerably enhanced the rate of kinetic resolution. The alcohol (S)-5 and the acetate (R)-6 were converted to piperazic acid derivatives (R)- and (S)-3, respectively, via the intramolecular Mitsunobu reaction as a key step.     

Novel synthesis of highly active Pt/C cathode electrocatalyst for direct methanol fuel cell

A 40 wt% Pt/C cathode electrocatalyst with controlled Pt particle size of approximately 2.9 nm showing better performance than commercial catalyst for direct methanol fuel cell was prepared by a polyol process with water but without using stabilizing agent.     

Synthesis of a new insoluble polymer-supported chiral alcohol auxiliary and its first application to nucleophilic addition to ketenes

The preparation of a new optically active alcohol with a carboxylic function that allowed its attachment to an amine-functionalized insoluble polymer is described. Its first use as a polymer supported chiral auxiliary is demonstrated by asymmetric transformation of two racemic aryl propionic acids via ketene formation (95-96% ee).     

Synthesis of main‐chain poly(carbazole)s via CuAAC

The synthesis and characterization of a novel family of main‐chain carbazole‐containing polymers using copper‐catalyzed azide‐alkyne cycloaddition chemistry is reported. The reactions were performed under mild conditions using readily available copper catalysts and ligands, which afforded polymeric products with M_ws up to 18 kDa. Using a range of techniques, the polymers were found to exhibit a glass transition temperature (T_g) of 85 °C, high thermal stability (T_d = 274 °C), and high photoluminescent quantum efficiency (?_f = 0.29; λ_em = 448 nm), which underscore their potential for use in organic light‐emitting diodes or other emissive devices, particularly where efficient blue emission is of value. The approach described offers practical advantages over other synthetic methods used to prepare main‐chain carbazole‐containing polymers, especially with regard to the lack of need for rigorously inert conditions and the absence of byproducts generated during the polymerization reaction. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Mode decomposition of a noise suppressed mixing layer

Noise is generated in atwo-dimensional mixing layer due to the growing of instability waves and vortex pairings. The adjoint-based control methodology has shown to be arobust tool to suppress noise radiation. The mode decomposition algorithms such as the compressible versionof proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are employed toanalyze thespatial/spatial-temporal coherent structures for a consecutive data sets of the controlled mixing layer and itsuncontrolled counterpart. The analyses of POD indicate that the y-direction body forcecontrol mainly modify themost energetic spatialstructures, and increase the uniformity of the flow. The analyses of DMD show us prevalent frequencies andcorresponding mode structures, and the stability characteristics of each mode can be obtained fromDMD-spectrum. The spectral signatures illustrate that a lot of neutral/slightly damping modesemerging in uncontrolled flow within the frequency range (ω < 0.4) are suppressed due to control, relevant spatial-temporal structures are also varied, which iscoincident with the change of far-field noise spectra. From the view of mode decomposition, the action of control redistribute the energy forfrequency components of ω < 0.4 by weakening nonlinearities and regularizing corresponding dynamicstructures in streamwise direction, and thus suppress the noise radiation. Moreover, the POD- and DMD-analysis in this studydemonstrate that DMD can serve as an important supplement for POD in analyzing a time-resolved physicalprocess.