Another refinement of the right-hand side of the Hermite–Hadamard inequality for simplices

We establish a new refinement of the right-hand side of the Hermite–Hadamard inequality for convex functions of several variables defined on simplices.     

Efficient synthesis of 3,4-dihydropyrano[3,2-c]chromenes catalyzed by Ni(II)-functionalized Li<Superscript>+</Superscript>-Montmorillonite in a one-pot fashion under solvent-free conditions

A family of 3,4-dihydropyrano[3,2-c]chromenes were synthesized from 4-hydroxycoumarin and malononitrile via a one-pot reaction under solvent-free conditions at 100 °C catalyzed by Ni@Imine-Li⁺-MMT. This methodology tolerates most of the substrates and has the merits of lower loading of the catalyst, absence of solvents, excellent yields and reusability of the catalyst. A reasonable mechanism is also proposed. This catalytic system can be reused for at least five times with a negligible loss of activity. The prepared catalyst was characterized by using FTIR, TGA, SEM, TEM, uv-DRS, EDX and XRD.     

Evolving groups

The class of evolving groups is defined and investigated, as well as their connections to examples in the field of Galois cohomology. Evolving groups are proved to be Sylow Tower groups in a rather strong sense. In addition, evolving groups are characterized as semidirect products of two nilpotent groups of coprime orders where the action of one on the other is via automorphisms that map each subgroup to a conjugate.     

Undersampled Windowed Exponentials and Their Applications

We characterize the completeness and frame/basis property of a union of under-sampled windowed exponentials of the form

$$ {\mathcal{F}}(g): =\bigl\{ e^{2\pi i n x}: n\ge 0\bigr\} \cup \bigl\{ g(x)e^{2\pi i nx}: n< 0\bigr\} $$

for \(L^{2}[-1/2,1/2]\) by the spectra of the Toeplitz operators with the symbol \(g\). Using this characterization, we classify all real-valued functions \(g\) such that \({\mathcal{F}}(g)\) is complete or forms a frame/basis. Conversely, we use the classical non-harmonic Fourier series theory to determine all \(\xi \) such that the Toeplitz operators with the symbol \(e^{2\pi i \xi x}\) is injective or invertible. These results demonstrate an elegant interaction between frame theory of windowed exponentials and Toeplitz operators. Finally, we use our results to answer some open questions in dynamical sampling, and derivative samplings on Paley-Wiener spaces of bandlimited functions.

     

Monodisperse Six-Armed Starbursts based on Truxene-Cored Multibranched Oligofluorenes: Design,Synthesis, and Stabilized Lasing Characteristics

A series of monodisperse six-armed conjugated starbursts ( Tr1F , Tr2F , and Tr3F ) containing a truxene core and multibranched oligofluorene bridges capped with diphenylamine (DPA) units has been designed, synthesized, and investigated as robust gain media for organic semiconductor lasers (OSLs). The influence of electron-rich DPA end groups on their optoelectronic characteristics has been discussed at length. DPA cappers effectively raise HOMO levels of the starbursts, thus enhancing the hole injection and transport ability. Solution-processed electroluminescence devices based on the resulting six-armed starbursts exhibited efficient deep-blue electroluminescence with clear reduced turn-on voltages (3.2–3.5 V). Moreover, the resulting six-armed molecules showed stabilized electroluminescence and amplified spontaneous emission with low thresholds (27.4–63.9 nJ pulse⁻¹), high net gain coefficients (80.1–101.3 cm⁻¹), and small optical loss (2.6–4.4 cm⁻¹). Distributed feedback OSLs made from Tr3F exhibited a low lasing threshold of 0.31 kW cm⁻² (at 465 nm). The results suggest that the construction of truxene-centered six-armed conjugated starbursts with the incorporation of DPA units can effectively enhance EL properties by precisely regulating the HOMO energy levels, and further optimizing their optical gain properties.     

EicC对撞光学设计

EicC是中国科学院近代物理研究所计划建造的中国电子-离子对撞机装置,该对撞机质心能位于20 GeV附近,是研究海夸克的最佳能量窗口,同时还可研究胶子和价夸克。EicC对撞粒子为高极化率质子和电子束团,质子环pRing采用八字环设计方案,可以更好地保持极化质子束团极化率,电子环eRing采用跑道形环设计方案,可以更好地利用隧道空间。该装置电子束流能量中心值为3.5 GeV,电子束RMS发射度为水平方向60 nm·rad,垂直方向60 nm·rad,对撞点b函数为水平方向0.4 m,垂直方向0.12 m;质子束流能量中心值20 GeV,质子束RMS发射度为水平方向300 nm·rad,垂直方向180 nm·rad,对撞点b函数为水平方向0.08 m,垂直方向0.04 m,设计亮度2×1033 cm–2s–1。EicC采用双对撞区非对称光学设计,通过对EicC不同色品补偿方案的研究,最终确定了弧区加短直线节共同补偿的色品补偿方案;通过研究对撞点处b函数以及对撞点间相移对动力学孔径的影响,最终得到pRing动力学孔径大于8 s(s为束团RMS尺寸)、eRing动力学孔径大于20 s,满足大于束团尺寸6 s的要求。     

Enzymatic Extraction of Bioactive and Self‐Assembling Wool Keratin for Biomedical Applications

Keratin is widely recognized as a high‐quality renewable protein resource for biomedical applications. Despite their extensive existence, keratin resources such as feathers, wool, and hair exhibit high stability and mechanical properties because of their high disulfide bond content. Consequently, keratin extraction is challenging and its application is greatly hindered. In this work, a biological extraction strategy is proposed for the preparation of bioactive keratin and the fabrication of self‐assembled keratin hydrogels (KHs). Based on moderate and controlled hydrolysis by keratinase, keratin with a high molecular weight of approximately 45 and 28 kDa that retain its intrinsic bioactivities is obtained. The keratin products show excellent ability to promote cell growth and migration and are conferred with significant antioxidant ability because of their intrinsically high cysteine content. In addition, without the presence of any cross‐linking agent, the extracted keratin can self‐assemble into injectable hydrogels. The KHs exhibit a porous network structure and 3D culture ability, showing potential in promoting wound healing. This enzyme‐driven keratin extraction strategy opens up a new approach for the preparation of keratin that can self‐assemble into injectable hydrogels for biomedical engineering.     

O-Alkyldithiophosphate Nickel Complexes with dcpf Ligand as Efficient Electrocatalysts for Hydrogen Evolution

Six new O-alkyldithiophosphate nickel complexes with dcpf ligand, [(dcpf)Ni(S₂P{O}OR)] (dcpf = 1,1′-bis (dicyclohexylphosphino)ferrocene, R = CH₃ ( 1 ), CH₃CH₂ ( 2 ), Ph ( 3 ), 4-MeC₆H₄ ( 4 ), PhCH₂ ( 5 ) and PhCH₂CH₂ ( 6 )), have been synthesized by the treatment of dcpf with ((RO)₂PS₂)₂Ni in satisfactory yields. These complexes were characterized by elemental analysis, spectroscopy (FTIR, UV–vis, ¹H, ¹³C, and ³¹P NMR), thermogravimetric analysis and single crystal X-ray diffraction. The nickel atom in 1 , 2 ·CH₂Cl₂, 3 ·CH₂Cl₂, 4 ·2CH₂Cl₂·THF, and 2( 5 )·hexane adopts a slightly distorted square-planar coordination environment finished by two phosphorus atoms of dcpf ligand and two sulfur atoms of O-alkyldithiophosphate ligand. Furthermore, the electrochemical properties for complexes 1 – 6 were also investigated by cyclic voltammetry. With the addition of 120 mM trifluoroacetic acid (TFA), the turnover frequency (TOF) values for 1 – 6 are estimated to be 1243.83, 1046.54, 1331.71, 2545.29, 1899.03, and 1191.37 s⁻¹, with the overpotential (η) values of 0.62, 0.58, 0.71, 0.67, 0.60, and 0.56 V, respectively. The result of electrochemical studies indicates that all complexes can be used as efficient molecular eletrocatalysts for the reduction of protons to hydrogen in the presence of TFA in MeCN.     

Peroxidase-Like Platinum Clusters Synthesized by Ganoderma lucidum Polysaccharide for Sensitively Colorimetric Detection of Dopamine

The sensitive and selective detection of dopamine (DA) is very important for the early diagnosis of DA-related diseases. In this study, we reported the colorimetric detection of DA using Ganoderma lucidum polysaccharide (GLP) stabilized platinum nanoclusters (Pt_n-GLP NCs). When Pt₆₀₀-GLP NCs was added, 3,3’,5,5’-tetramethylbenzidine (TMB) was rapidly catalyzed and oxidized to blue oxTMB, indicating the peroxidase-like activity of Pt₆₀₀-GLP NCs. The catalytic reaction on the substrate TMB followed the Michaelis-Menton kinetics with the ping-pong mechanism. The mechanism of the colorimetric reaction was mainly due to the formation of hydroxyl radical (•OH). Furthermore, the catalytic reaction of Pt₆₀₀-GLP NCs was used in the colorimetric detection of DA. The linear range for DA was 1–100 μM and the detection limit was 0.66 μM. The sensitive detection of DA using Pt-GLP NCs with peroxidase-like activity offers a simple and practical method that may have great potential applications in the biotechnology field.     

Size-complementary effects of PEG diamine 1,1’-disubstituted ferrocene on incorporations of β- and γ-cyclodextrins and syntheses of poly(pseudo)rotaxanes with lower coverages therefrom

Journal of Inclusion Phenomena and Macrocyclic Chemistry - Poly(ethylene glycol) diamine 1,1’-disubstituted ferrocene was utilized as a size-com-plementary site to synthesize lower coverage...