On hybrid moments of $$\Delta _2(x)$$ Δ 2 ( x ) and $$\Delta _3(x)$$ Δ 3 ( x )

The Ramanujan Journal - Let $$k\geqslant 2$$ be a fixed natural number and $$d_k(n)$$ denote the number of ways n can be written as a product of k positive integers. We use $$\Delta _k(x)$$ to...     

Manin’s conjecture for a class of singular cubic hypersurfaces

Let l > 2 be a fixed positive integer and Q(y) be a positive definite quadratic form in l variables with integral coefficients. The aim of this paper is to count rational points of bounded height on the cubic hypersurface defined by u³ = Q(y)z. We can get a power-saving result for a class of special quadratic forms and improve on some previous work.     

Synthetic [FeFe]-H2ase models bearing phosphino thioether chelating ligands

Through the oxidation-reduction combination procedure, the neutral tri-substituted {2Fe3S} complex 2 was synthesized by replacing the CO ligand in 1 with phosphine. This substitution leads to the Fe-Fe bonds in 1 and 2 with large Lewis basicity difference, i.e. △pK_a^MeCN~10.     

Enhanced Harvesting of <Emphasis Type="Italic">Chlorella vulgaris</Emphasis> Using Combined Flocculants

In this study, a novel flocculation strategy for harvesting Chlorella vulgaris with combined flocculants, poly (γ-glutamic acid) (γ-PGA) and calcium oxide (CaO), has been developed. The effect of flocculant dosage, the order of flocculant addition, mixing speed, and growth stage on the harvesting efficiency was evaluated. Results showed that the flocculation using combined flocculants significantly decreases the flocculant dosage and settling time compared with control. It was also found that CaO and γ-PGA influenced microalgal flocculation by changing the zeta potential of cells and pH of microalgal suspension. The most suitable order of flocculant addition was CaO first and then γ-PGA. The optimal mixing speed was 200 rpm for 0.5 min, followed by 50 rpm for another 4.5 min for CaO and γ-PGA with the highest flocculation efficiency of 95 % and a concentration factor of 35.5. The biomass concentration and lipid yield of the culture reusing the flocculated medium were similar to those when a fresh medium was used. Overall, the proposed method requires low energy input, alleviates biomass and water contamination, and reduces utilization of water resources and is feasible for harvesting C. vulgaris for biofuel and other bio-based chemical production.     

Promoting Surface Electric Conductivity for High-Rate LiCoO2

The cathode materials work as the host framework for both Li⁺ diffusion and electron transport in Li-ion batteries. The Li⁺ diffusion property is always the research focus, while the electron transport property is less studied. Herein, we propose a unique strategy to elevate the rate performance through promoting the surface electric conductivity. Specifically, a disordered rock-salt phase was coherently constructed at the surface of LiCoO₂, promoting the surface electric conductivity by over one magnitude. It increased the effective voltage (V_eff) imposed in the bulk, thus driving more Li⁺ extraction/insertion and making LiCoO₂ exhibit superior rate capability (154 mAh g⁻¹ at 10 C), and excellent cycling performance (93 % after 1000 cycles at 10 C). The universality of this strategy was confirmed by another surface design and a simulation. Our findings provide a new angle for developing high-rate cathode materials by tuning the surface electron transport property.     

Highly luminescent carbon nanodots by microwave-assisted pyrolysis

Carbon nanodots (CDs) with a low cytotoxicity have been synthesized by one-step microwave-assisted pyrolysis of citric acid in the presence of various amine molecules. The primary amine molecules have been confirmed to serve dual roles as N-doping precursors and surface passivation agents, both of which considerably enhanced the fluorescence of the CDs.     

化学激光器1/4环柱型增益发生器

设计并搭建了化学激光器1/4环柱型增益发生器的实验系统。按设计流量进行了出光实验,功率计探测到的出光功率在60 W左右。测量了燃烧室温度及压力,与Alpha激光器HL911-3实验数据类似,燃烧室温度及压力曲线都存在一个爬升阶段。环柱型增益发生器沿角向扩张的特点使得光腔区压力很低,仅为0.5 kPa左右。为验证环柱状增益区的有效形成,对3对取光孔分别进行了出光实验,结果表明每对取光孔都有功率输出,证明设计的增益发生器运行正常。     

Ga~(3+)对Eu~(2+)掺杂钡长石结构和发光特性的影响

在弱还原气氛下采用高温固相法制备Ba0.955A l2-xGaxS i2O8:Eu2+(x=0~1.0)系列荧光粉,研究Ga3+置换A l3+对晶体结构和光谱特性的影响。Ga3+与A l3+以类质同相替代进入BaA l2S i2O8晶格形成连续固溶体,晶胞参数a,b,c,β和晶胞体积V均随Ga3+置换量呈线性增加。宽带激发光谱,覆盖范围为230~400 nm,可拟合成4个峰,表观峰值位于330 nm,基本不随Ga3+置换量变化;随着Ga3+置换量的增加,半高宽从93 nm减小至83 nm。发射光谱位于375~560 nm,可由422和456 nm两峰拟合而成,表观峰值位于434 nm,两拟合峰峰位均随Ga3+置换量呈线性红移,且拟合峰强度比呈线性递减。     

Atomic scale control of catalytic process in oxidation of Pb thin films

Using scanning tunneling microscopy (STM), we demonstrate that oxidation on Pb films is greatly enhanced by atomic Cs catalysts. With only a minute concentration of isolated Cs substitutional atoms in the surface layer (0.004 ML coverage), surface oxidation rates are greatly enhanced. First-principles density functional theory (DFT) calculations reveal that a substitutional Cs atom strongly increases O₂ binding on the surface. Then, with additional oxygen exposure this substitutional Cs-initiated oxidation process results in growth of PbO layers in an auto-catalytic manner. Furthermore, we investigate the role of temperature in the oxidation of the Pb films with and without Cs, and we explore the overall morphology of the resultant oxide layers.     

Residual symmetry,nth Bäcklund transformation,and soliton-cnoidal wave interaction solution for the combined modified KdV–negative-order modified KdV equation

This paper is concerned with the nth Bäcklund transformation (BT) related to multiple residual symmetries and soliton-cnoidal wave interaction solution for the combined modified KdV–negative-order modified KdV (mKdV-nmKdV) equation. The residual symmetry derived from the truncated Painlevé expansion can be extended to the multiple residual symmetries, which can be localized to Lie point symmetries by prolonging the combined mKdV-nmKdV equation to a larger system. The corresponding finite symmetry transformation, ie, nth BT, is presented in determinant form. As a result, new multiple singular soliton solutions can be obtained from known ones. We prove that the combined mKdV-nmKdV equation is integrable, possessing the second-order Lax pair and consistent Riccati expansion (CRE) property. Furthermore, we derive the exact soliton and soliton-cnoidal wave interaction solutions by applying the nonauto-BT obtained from the CRE method.