一类变号(k,n-k)共轭边值问题正解的存在性

通过构造一个特殊的锥,利用范数形式的锥拉伸锥压缩不动点定理,在允许非线性项变号无下界且没有任何单调性假设的条件下,得出了一类高阶(k,n-k)共轭两点边值问题方程组正解的存在性结论.     

Electrochemical C–H/N–H cross-coupling of 2-phenylindolizines with phenothiazines to synthesize novel N-aryl phenothiazine derivatives

A facile and elegant method for synthesis of novel N–aryl phenothiazine derivatives from 2-phenylindolizines and phenothiazines through direct electrochemical oxidation has been developed. This approach was performed smoothly at room temperature without external oxidant and catalyst. Cyclic voltammetry and in situ FTIR techniques were applied to analyze the cross-coupling process of phenothiazines and 2-phenylindolizines, which helped to select the appropriate reaction potential. Under the optimized conditions, a broad range of substrates were well tolerated, affording the desired products in moderate to excellent isolated yields (up to 91%) with high regioselectivity. Meanwhile, a plausible mechanism involving a radical pathway has been proposed.     

Platinum nanoparticles as recyclable heterogeneous catalyst for selective methylation of amines and imines with formic acid: Indirect utilization of CO2

N-methylation of amines and imines with formic acid as C1 source by easily prepared Pt NPs as heterogeneous catalyst is reported here. Primary, secondary amines and imines were successfully methylated in good to excellent yields under mild conditions. Both aromatic and aliphatic amines could be applied as substrates. Meanwhile, the heterogeneous Pt NPs were capable to be recylcled and reused for 7 times without significant decrease of reactivity. This protocol provided an indirect utilization pathway of CO₂ by using formic acid as C1 source.     

Research on the Solid State Fermentation of Jerusalem Artichoke Pomace for Producing <Emphasis Type="Italic">R</Emphasis>,<Emphasis Type="Italic">R</Emphasis>-2,3-Butanediol by <Emphasis Type="Italic">Paenibacillus polymyxa</Emphasis> ZJ-9

R,R-2,3-butanediol (R,R-2,3-BD) was produced by Paenibacillus polymyxa ZJ-9, which was capable of utilizing inulin without previous hydrolysis. The Jerusalem artichoke pomace (JAP) derived from the conversion of Jerusalem artichoke powder into inulin extract, which was usually used for biorefinery by submerged fermentation (SMF), was utilized in solid state fermentation (SSF) to produce R,R-2,3-BD. In this study, the fermentation parameters of SSF were optimized and determined in flasks. A novel bioreactor was designed and assembled for the laboratory scale-up of SSF, with a maximum yield of R,R-2,3-BD (67.90 g/kg (JAP)). This result is a 36.3% improvement compared with the flasks. Based on the same bath of Jerusalem artichoke powder, the total output of R,R-2,3-BD increased by 38.8% for the SSF of JAP combined with the SMF of inulin extraction. Overall, the utilization of JAP for R,R-2,3-BD production was beneficial to the comprehensive utilization of Jerusalem artichoke tuber.     

A free boundary problem for Aedes aegypti mosquito invasion

An advection–reaction–diffusion model with free boundary is proposed to investigate the invasive process of Aedes aegypti mosquitoes. By analyzing the free boundary problem, we show that there are two main scenarios of invasive regime: vanishing regime or spreading regime, depending on a threshold in terms of model parameters. Once the mortality rate of the mosquito becomes large with a small specific rate of maturation, the invasive mosquito will go extinct. By introducing the definition of asymptotic spreading speed to describe the spreading front, we provide an estimate to show that the boundary moving speed cannot be faster than the minimal traveling wave speed. By numerical simulations, we consider that the mosquitoes invasive ability and wind driven advection effect on the boundary moving speed. The greater the mosquito invasive ability or advection, the larger the boundary moving speed. Our results indicate that the mosquitoes asymptotic spreading speed can be controlled by modulating the invasive ability of winged mosquitoes.     

Dehydration of Castor Oil over NaHSO4/MCM‐41 Catalyst Modified by n‐Dodecyltriethoxysilane

n‐Dodecyltriethoxysilane (DTEOS) modified NaHSO₄/MCM‐41 catalysts (silanized catalysts) were synthesized by different impregnation sequences and evaluated in the liquid‐phase dehydration of castor oil. The samples were evaluated by X‐ray diffraction, nitrogen adsorption‐desorption, SEM, TEM, FT‐IR spectroscopy, XPS, ²⁹Si MAS NMR spectroscopy, contact angle measurements, NH₃‐TPD, and pyridine‐FT‐IR spectroscopy. The analyses demonstrated that silanization enhanced the hydrophobicity of the catalysts, and the impregnation sequence of silanized catalysts had a significant effect on the NaHSO₄ dispersion, surface area, acid distribution, and hydrophobicity of the silanized catalysts. The catalytic activity of the silanized catalysts was much higher than that of NaHSO₄/MCM‐41. Among the silanized catalysts, the catalyst prepared by simultaneous impregnation with DTEOS and NaHSO₄ showed the highest iodine value of 141.8 [g(I₂) per 100 g] and lowest hydroxyl value of 11.3 [mg(KOH) · g^–1].     

Synthesis and Solution Behavior Studies of a Bifunctional Fluorenyl Dioxotetraamine and Its Copper(II) Complex

The fluorenyl dioxotetraamine L⁴ was designed and prepared. The solution behavior of L⁴ and its interaction with the Cu^II ion were studied by pH potentiometric, fluorimetric and spectrophotometric titration. In the dioxane/water solution, it was found that the molecule L⁴ showed an “off‐on” or “on‐off” fluorescent response in the absence or presence of the Cu^II ion with the increase of the pH value. Moreover, influenced by the Cu^II ion, the fluorescence of the dioxotetraamine L⁴ can be almost quenched when the pH value was slightly higher than 4.0, which is rarely reported and useful to detect the Cu^II ion under acidic condition.     

Electrochemical detection of quantum dots by stabilization of electrogenerated copper species

The determination of quantum dots is of particular interest as they are frequently used as labels in electrochemical biosensors. In this paper, we describe a method for the detection of very low concentrations of quantum dots using the voltammetric response of copper in ammonia solution. Copper species electrogenerated on the electrode surface are stabilized by the nanoparticles, preventing their oxidation by dissolved oxygen, and a relationship between the concentration of the nanoparticles and the copper voltammetric response can thus be obtained. The reported method shows a linear range between 0.05 and 2 nM of quantum dots, with a limit of detection in the order of 9 × 10⁷ nanoparticles. This method could be employed to improve the detection limit of electrochemical biosensors using quantum dots as labels.     

A sustainable synthesis of biomass carbon sheets as excellent performance sodium ion batteries anode

Biomass-derived carbon (BMC) materials have attracted much attention due to their high performance and properties of abundant source. Herein, biomass carbon sheets (BMCS) from wheat straws had been successfully synthesized via a facile high temperature carbonization and expansion processes. The morphology of BMCS keeps the natural honeycomb-like shape of the cross section and the hollow tubular array structure of the vertical section with rich pores, which provides low-resistant ion channels to support fast diffusion. The (002) crystal plane reveals that the intercalation distance of carbon sheets is 0.383 nm larger than that graphite (0.335 nm), which benefits the larger sodium ion de/intercalation. By comparing different carbonization temperatures, wheat straws carbonized at 1200 °C (BMCS-1200) with well graphite microcrystallites show more excellent sodium ion storage performance than that of 900 °C (BMC-900). BMCS-1200 shows a stable reversible capacity of 221 mAh g^?1 after 200 cycles at 0.05 A g^?1, while BMC-900 is 162 mAh g^?1 after 100 cycles. And it also exhibits better rate capability (220, 109 mAh g^?1) than that of BMC-900 (125, 77 mAh g^?1) at 0.2 and 1 A g^?1, respectively. Finally, it delivers 89 mAh g^?1 stable capacity after 1400 cycles at 1 A g^?1 to prove its excellent long-term cycling stability.

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Graphical abstract High temperature carbon sheets with well graphite microcrystallites synthesized from wheat straw forexcellent sodium ion storage performance