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关于ARENS乘积
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作者 张波 《齐齐哈尔师范学院学报(自然科学版)》 1989年第3期14-21,共8页
本文对一类局部凸拓扑代数定义了Arens乘积,推广了Banach代数中关于Arens乘积的若干结果,并给出了这一类局部凸拓扑代数的第二对偶关于Arens乘积具有双连续性的一个刻划。
关键词 拓扑代数 巴拿赫代数 arens乘积
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拓扑代数的Arens正则性
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作者 吴从炘 张波 《Journal of Mathematical Research and Exposition》 CSCD 1992年第1期66-70,共5页
Arens在Banach代数A的第二对偶A^(**)中定义了两种乘积,称为Arens乘积.Gulick和Hennefeld又分别讨论了Arens正则性的刻划.在文[4]中,我们把文[1]中的定义和[2][3]中的结果推广到一类局部凸拓扑代数.本文讨论具有H性质的Z-代数的Arens正... Arens在Banach代数A的第二对偶A^(**)中定义了两种乘积,称为Arens乘积.Gulick和Hennefeld又分别讨论了Arens正则性的刻划.在文[4]中,我们把文[1]中的定义和[2][3]中的结果推广到一类局部凸拓扑代数.本文讨论具有H性质的Z-代数的Arens正则性的问题,得到了Arens正则的充分必要条件。 展开更多
关键词 拓扑代数 arens正则性 Z-代数
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Selective utilization of formaldehyde stabilizing additive and methoxy groups in lignin for the production of high-carbon-number arenes 被引量:1
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作者 Lin Dong Zhiqiang Fang +6 位作者 Qianbo Yuan Yong Fan Yong Yang Ping Wang Shixiong Sheng Yanqin Wang Zupeng Chen 《Chinese Journal of Catalysis》 2025年第1期356-365,共10页
Many strategies have been proposed to produce arenes from lignin as liquid fuel additives.However,the development of these methods is limited by the low yield of products,low atom utilization,and inefficient lignin de... Many strategies have been proposed to produce arenes from lignin as liquid fuel additives.However,the development of these methods is limited by the low yield of products,low atom utilization,and inefficient lignin depolymerization.Herein,we develop an energy-efficient synthetic method for the production of high-carbon-number arenes from sustainable lignin with a total yield of 23.1 wt%.Particularly,high carbon number arenes are obtained by fully utilizing the formaldehyde stabilizing additive and the methoxy group in lignin.The process begins with the reductive depolymerization of formaldehyde-stabilized lignin,followed by transmethylation between lignin monomers over Au/Nb_(2)O_(5) catalyst,and the Ru/Nb2O5-catalyzed hydrodeoxygenation.This work demonstrates the potential of value-added arenes production directly from lignin. 展开更多
关键词 LIGNIN Arene TRANSMETHYLATION HYDRODEOXYGENATION Liquid fuel additive
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Decoding the mechanism of P450-catalyzed aromatic hydroxylation:Uncovering the arene oxide pathway and insights into the regioselectivity 被引量:1
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作者 Qun Huang Xuan Zhang +8 位作者 Guangwu Sun Rui-ying Qiu Lan Luo Cuizhen Wang Longwei Gao Bing Gao Bo Chen Binju Wang Jian-bo Wang 《Chinese Journal of Catalysis》 2025年第3期420-430,共11页
P450 enzymes-catalyzed aromatic hydroxylation plays an important role in detoxification,biosynthesis,and potential carcinogenic effect of aromatic compounds.Though it has been explored for decades,the actual process o... P450 enzymes-catalyzed aromatic hydroxylation plays an important role in detoxification,biosynthesis,and potential carcinogenic effect of aromatic compounds.Though it has been explored for decades,the actual process of aromatic hydroxylation and mechanism of regioselectivity catalyzed by cytochrome P450 monooxygenases remained ambiguous.Here,we have resolved these issues.With a stable chiral organofluorine probe,and especially with X-ray data of two isolated arene oxides derivatives,we demonstrate that an arene oxide pathway is definitely involved in P450-catalyzed aromatic hydroxylation.By the capture,isolation,identification and reactivity exploration of the arene 1,2-oxide and arene 2,3-oxide intermediates,together with advanced QM calculations,the mechanism of how two intermediates go to the same product has been elucidated.In addition to the model substrate,we also confirmed that an arene oxide intermediate is involved in the P450-catalyzed hydroxylation pathway of a natural product derivative methyl cinnamate,which indicates that this intermediate appears to be universal in P450-catalyzed aromatic hydroxylation.Our work not only provides the most direct evidence for the arene oxide pathway and new insights into the regioselectivity involved in P450-catalyzed aromatic hydroxylation,but also supplies a new synthetic approach to achieve the dearomatization of aromatic compounds. 展开更多
关键词 Aromatic hydroxylation Cytochrome P450 Arene oxide Regioselectivity DEAROMATIZATION
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Adsorption and visual detection of nitro explosives by pillar[n]arenes-based host–vip interactions 被引量:1
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作者 Xueru Zhao Aopu Wang +3 位作者 Shimin Wang Zhijie Song Li Ma Li Shao 《Chinese Chemical Letters》 2025年第4期211-215,共5页
Aromatic nitro compounds present substantial health and environmental concerns due to their toxic nature and potential explosive properties.Consequently,the development of host–vip molecular recognition systems for... Aromatic nitro compounds present substantial health and environmental concerns due to their toxic nature and potential explosive properties.Consequently,the development of host–vip molecular recognition systems for these compounds serves a dual-purpose:enabling the fabrication of high-performance sensors for detection and guiding the design of efficient adsorbents for environmental remediation.This study investigated the host–vip recognition behavior of perethylated pillar[n]arenes toward two aromatic nitro molecules,1-chloro-2,4-dinitrobenzene and picric acid.Various techniques including^(1)H NMR,2D NOESY NMR,and UV-vis spectroscopy were employed to explore the binding behavior between pillararenes and aromatic nitro vips in solution.Moreover,valuable single crystal structures were obtained to elucidate the distinct solid-state assembly behaviors of these vips with different pillararenes.The assembled solid-state supramolecular structures observed encompassed a 1:1 host–vip inclusion complex,an external binding complex,and an exo-wall tessellation complex.Furthermore,based on the findings from these systems,a pillararene-based test paper was developed for efficient picric acid detection,and the removal of picric acid from solution was also achieved using pillararenes powder.This research provides novel insights into the development of diverse host–vip systems toward hazardous compounds,offering potential applications in environmental protection and explosive detection domains. 展开更多
关键词 Pillar[n]arenes Host–vip interactions Aromatic nitro compounds Adsorptive separation Explosive detection
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A Pillar[5]arene-Based π-Conjugated Dye Used for Fluorescence Sensing of L-Arginine
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作者 Ling Xiaopeng Tao Shaoping +4 位作者 Lin Qi Shi Bingbing Yao Hong Wei Taibao Chen Jinfa 《有机化学》 北大核心 2025年第7期2480-2485,共6页
In the past decade,people have conducted extensive research on the synthesis and application properties of various functionalized pillararenes.Pillararenes show good application prospects in the field of sensors due t... In the past decade,people have conducted extensive research on the synthesis and application properties of various functionalized pillararenes.Pillararenes show good application prospects in the field of sensors due to the rich host-vip recognition in their rigid electron-rich cavities.However,most reported pillararenes are functionalized by alkoxy modification,which results in poor charge transfer nature and weak fluorescence response.A π-conjugated charge-transfer system P5BN was obtained by introducing electron-donating triarylamine(Ar_(3)N)and electron-deficient triarylborane(Ar_(3)B)into pillar[5]arene skeleton,which significantly improved its luminescence behavior and was further used for fluorescence detection applications.The molecular structure showed that P5BN provided a good macrocyclic cavity to encapsulate amino acids molecules of suitable size.It was found that P5BN,as a fluorescent sensor,showed a highly sensitive and selective response to L-arginine(L-Arg),resulting in a significant enhancement of the fluorescence at 408 nm of P5BN with the lowest detection concentration being 2.21×10^(-8) mol/L.The recognition mechanism was demonstrated through experiments and DFT theoretical calculations. 展开更多
关键词 fluorescent sensor host-vip recognition arene L-ARGININE density functional theory(DFT)calculations
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Visible light-induced deuteration of arenes via thianthrenation
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作者 Jia Peng Guo-Ping Luo +1 位作者 Chao Wu Congyang Wang 《Chinese Chemical Letters》 2025年第8期3-4,共2页
Deuterium(D),a stable and non-radioactive isotope of hydro-gen,is naturally present in the environment and is distinguishedfrom hydrogen by its greater mass.This mass difference resultsin a reduced stretching frequenc... Deuterium(D),a stable and non-radioactive isotope of hydro-gen,is naturally present in the environment and is distinguishedfrom hydrogen by its greater mass.This mass difference resultsin a reduced stretching frequency of the carbon-deuterium(C-D)bond,leading to lower ground state energy and higher bond dis-sociation energy compared to the carbon-hydrogen(C–H)bond. 展开更多
关键词 carbon deuterium bond DEUTERIUM thianthrenation DEUTERATION bond dissociation energy ground state energy visible light ARENES
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Efficient cytosolic delivery of protein by preorganized amidiniums on pillar[5]arene
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作者 Shuwen Guo Haipeng Xu +3 位作者 Zijun Cheng Leyong Wang Peng Yang Ruibing Wang 《Chinese Chemical Letters》 2025年第10期306-311,共6页
Intracellular protein delivery is vital for the development of therapeutic proteins that act on intracellular targets.Although numerous carriers based on polymers and nanomaterials have been reported to facilitate cel... Intracellular protein delivery is vital for the development of therapeutic proteins that act on intracellular targets.Although numerous carriers based on polymers and nanomaterials have been reported to facilitate cellular internalization of membrane impermeable proteins,it is still a great challenge to intracellularly deliver proteins with different sizes and isoelectric points through small molecule-based protein carrier.Herein,amidinium functionalized pillar[5]arene(AP5)was used as a small molecular carrier to facilitate intracellular delivery of proteins with different sizes and isoelectric points.The densely preorganized amidinium groups on pillar[5]arene skeleton could not only glue proteins together to form AP5@protein complex through multiple salt-bridges,but also promote cellular internalization AP5@protein complex.The bioactivities of the internalized proteins were well-maintained.This study provides a novel,versatile and macrocyclic-molecule based intracellular protein delivery carrier through the preorganization of amidiniums on pillar[5]arene. 展开更多
关键词 Proteins delivery arene Amidinium SELF-ASSEMBLY PREORGANIZATION
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Pillar[5]arene based prodrug as a GSH-responsive SO_(2) nanogenerator for effective gas cancer therapy
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作者 Lintao Wu Yujia Meng +6 位作者 Xumei Zheng Yiqiao Bai Chun Han Zhijun Wang Jie Yang Xiaobi Jing Yong Yao 《Chinese Chemical Letters》 2025年第9期334-337,共4页
Sulfur dioxide(SO_(2)),being one of the therapeutic gaseous molecules,has been widely utilized in cancer therapy because of its high therapeutic efficacy and biosafety.Nevertheless,the in situ-triggered and efficient ... Sulfur dioxide(SO_(2)),being one of the therapeutic gaseous molecules,has been widely utilized in cancer therapy because of its high therapeutic efficacy and biosafety.Nevertheless,the in situ-triggered and efficient transportation of SO_(2)to tumors are the main obstacles that restrict its clinical application.To overcome this impediment,we functionalized pillar[5]arene with 2,4-dinitrobenzene sulfonic acid(DNSB)and then self-assembled it with tetraphenyl-PEG(TPE-PEG)in aqueous media to form fluorescent nanoparticles(PSTPE NPs).Meanwhile,the target vip(NH_(2)-PEG-FA)was encapsulated within the spacious cavity of pillar[5]arene via host-vip interaction.The resulting nanoparticles possess distinctive characteristics:(Ⅰ)dual GSH recognition motifs for enhanced SO_(2)release kinetics;(Ⅱ)incorporation of targeting ligands for selective cytotoxicity towards tumor cells while sparing normal tissues and cells;and(Ⅲ)surface modification of pillar[5]arene with TPE-PEG conferring excellent dispersibility,biocompatibility,and fluorescence properties in aqueous environments.Collectively,this novel nanoparticle represents an innovative approach that utilizes macrocyclics as SO_(2)gas donors to induce cellular apoptosis and provides new insights into gas-based therapy. 展开更多
关键词 arenes THERANOSTICS GSH-responsiveness Host-vip interaction Gas therapy
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Recent advances in supramolecular luminescent materials based on macrocyclic arenes
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作者 Yu-Jie Long Xiao-Ni Han +1 位作者 Ying Han Chuan-Feng Chen 《Chinese Chemical Letters》 2025年第6期78-95,共18页
Supramolecular luminescent materials(SLMs)exhibit exceptional luminescence properties and the ability to be intelligently regulated through diverse assembly approaches,making them highly attractive in the field of lum... Supramolecular luminescent materials(SLMs)exhibit exceptional luminescence properties and the ability to be intelligently regulated through diverse assembly approaches,making them highly attractive in the field of luminescent materials.In recent years,the novel macrocyclic arenes characterized by unique electron-rich structures,ease of derivatization,tunable conformations and even inherent luminescence properties afford much opportunities to create such dynamic smart luminescent materials.The incorporation of macrocyclic arenes into SLMs leads to simple preparation process,diverse photophysical phenomena and sophisticated regulatory mechanisms,which is also currently one of the most frontier and hot topics in macrocyclic and supramolecular chemistry and even luminescent materials.In this review,the research advances in construction and applications of SLMs based on macrocyclic arenes in the last several years will be presented from the different assembly strategies,including host-vip complexes,supramolecular polymers,nanoparticles,and other assemblies.Moreover,some insights into future directions for this research area will also be offered. 展开更多
关键词 Supramolecular luminescent materials Macrocyclic arenes Supramolecular assemblies Host-vip complexes Supramolecular polymers Supramolecular nanoparticles
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Metal-coordinate complexes(M=3d,4f)with enhanced circularly polarized luminescence in planar chiral pillar[5]arenes
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作者 Yu Tian Yijun Lin +4 位作者 Siyu Deng Yinghe Tan Xuanyi Bie Zhaoyang Chen Pangkuan Chen 《Chinese Journal of Structural Chemistry》 2025年第8期12-17,共6页
Metal-complexed chiral macrocyclic architectures have attracted increasing research interests in circularly polarized luminescence owing to their distinctive structural and functional attributes.The method of metal co... Metal-complexed chiral macrocyclic architectures have attracted increasing research interests in circularly polarized luminescence owing to their distinctive structural and functional attributes.The method of metal coordination has emerged as a robust methodology for chirality induction in many systems.In this work,we engineered two rigid and flexible chiral organic ligands(L_(1) and L_(2))by synergizing the inherent planar chirality of pillar[5]arenes with tailored metal-coordination moieties.They demonstrate versatile coordination capabilities toward both 3d-and 4f-block metals,enabling modulation of luminescent characteristics with blue,green and red emissions.Four planar chiral complexes exhibiting CPL activity were synthesized through systematic coordination of L_(1)/L_(2) with Zn^(2+),Eu^(3+),and Tb^(3+).The coordination processes effectively rigidify molecular conformations,leading to an enhanced CPL performance.Particularly,the Tb-L_(2) complex displays superior lanthanide-centered emission with a fluorescence quantum yield of~55%and an emission dissymmetry factor glum=5.5×10^(-3).By engineering the substitution on pillar[5]arene scaffolds,we have established a metal-coordination platform with CPL characteristics,which paves the way in the design of new metal-based luminescent materials. 展开更多
关键词 Circularly polarized luminescence arenes Metal-coordination LANTHANIDES
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Ultrasensitive electrochemical sensor based on para-sulfonatocalix[4]arene functionalized gold nanoparticles for sulfamethazine detection
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作者 Zhijuan Niu Peizhe Sun +1 位作者 Kwangnak Koh Changping Li 《Chinese Chemical Letters》 2025年第11期213-217,共5页
In order to realize the simple and rapid detection of antibiotic contaminants in environmental water,the para-sulfocalix[4]arene(pSC_(4))functionalized gold nanoparticles(Au NPs)composites(pSC_(4)-Au NPs)were prepared... In order to realize the simple and rapid detection of antibiotic contaminants in environmental water,the para-sulfocalix[4]arene(pSC_(4))functionalized gold nanoparticles(Au NPs)composites(pSC_(4)-Au NPs)were prepared by sodium borohydride reduction.Here,a rapid and sensitive electrochemical sensor for the detection of antibiotic contaminants in water was constructed.The detection mechanism and the signaling changes of the different sulfamethazine(SMZ)concentrations were further explored based on pSC_(4)-Au NPs/SMZ modified glassy carbon electrode through aggregation of gold nanoparticles induced by host-vip recognition of SMZ and pSC_(4).The results suggested that this method achieved rapid and ultrasensitive detection of SMZ with a limit of detection of 0.0038 ng/m L(linear detection range of 1.0-1.0×10^(4)ng/m L).The recoveries ranged from 91.1%to 97.0%with relative standard deviations(RSDs)of1.5%-3.5%.The accurate detection of SMZ in recovery rate of spiking assay proved the potential practical application of the sensor.Host-vip recognition induced Au NPs aggregation results in dramatic signal enhancement for electrochemical impedimetric detection assay of SMZ.This detection method provides a new concept for developing sensitive electrochemical sensors for simple and sensitive detection of small molecules in water. 展开更多
关键词 Electrochemical detection Gold nano-nanoparticles arene Host-vip interaction SULFAMETHAZINE
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Separation of toluene-alcohol azeotropes by porous crystals of fluorinated leaning pillar[6]arene
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作者 Jingxiong Jiang Yao Dong +6 位作者 Yuchun Wang Lijuan Qi Zhen-Yu Li Tai-Bao Wei Wen-Juan Qu Qi Lin Bingbing Shi 《Chinese Chemical Letters》 2025年第8期322-325,共4页
Herein we report an environmentally friendly and energy-efficient method for the adsorptive separation of toluene from toluene-alcohol azeotropes using porous crystalline fluorinated leaning pillar[6]arene(FLP6α),ach... Herein we report an environmentally friendly and energy-efficient method for the adsorptive separation of toluene from toluene-alcohol azeotropes using porous crystalline fluorinated leaning pillar[6]arene(FLP6α),achieving up to 100%purity.Moreover,FLP6αdemonstrates rapid adsorption and excellent recyclability. 展开更多
关键词 arene Macrocyclic host Host-vip interactions Porous material Adsorptionand separation
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A chiral supramolecular nanocatcher prepared by D-biotin-pillar[5]arene for the selective capture and targeted delivery of oxaliplatin enantiomers
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作者 Cui-Ting Yang Dan-Dan Wang +7 位作者 Shuai Chen Jian-Mei Yang Jun-Nan He Jun-Hui Zhang Xiao-Qing Liu Jin Zhang Lei Zhang Yan Zhao 《Chinese Chemical Letters》 2025年第9期338-344,共7页
Chiral anticancer drugs are the subject of ongoing research due to their optical characterization and pharmacological effects.Achieving a single enantiomer of a chiral anticancer drug is arduous,but it can significant... Chiral anticancer drugs are the subject of ongoing research due to their optical characterization and pharmacological effects.Achieving a single enantiomer of a chiral anticancer drug is arduous,but it can significantly improve its pharmacokinetics for tumor therapy.Here,the chiral nanocatchers,known as Dbiotin-P5■MCC NCs,were designed and prepared based on host-vip self-assembly between D-biotin anchored pillar[5]arene(D-biotin-P5)and myristoyl chloride choline(MCC).D-Biotin-P5■MCC NCs featuring the chiral separation and enzyme-induced disassemble were evaluated for their ability to selectively capture and subsequently target the release of(R,R)-OXA enantiomers into tumor cells.Furthermore,the use of D-biotin-P5■MCC NCs has demonstrated a significant enhancement in the intracellular uptake of OXA,with the drug being efficiently released to MCF-7 breast cancer cells.This has led to a superior inhibitory effect on MCF-7 cells when compared to free OXA,while also reducing the cytotoxicity of the drug in HEK 293 human embryonic kidney cells.This research not only paves a promising way for the fabrication of chiral supramolecular nanocarriers but also holds the potential to improve the processes of chiral drug separation and targeted therapy. 展开更多
关键词 Chiral supramolecular nanocatcher Selective capture arene Targeted delivery Oxaliplatin enantiomers
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Achieving strong and tunable circularly polarized luminescence through pillar[5]arenes insertion in BINOL-Py-based chromophore
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作者 Xintian Qu Zeen Liu +6 位作者 Zhifan Wang Dongyan Yu Xueqiu Huang Jie Yang Jiecheng Ji Xueqin Wei Cheng Yang 《Chinese Chemical Letters》 2025年第11期270-273,共4页
A series of[1,1-binaphthalene]-2,2-diol-pyrene(BINOL-Py)functionalized pillar[5]arenes with different spacer lengths were synthesized and separated by chiral HPLC to obtain their enantiomers.We elucidated the synergis... A series of[1,1-binaphthalene]-2,2-diol-pyrene(BINOL-Py)functionalized pillar[5]arenes with different spacer lengths were synthesized and separated by chiral HPLC to obtain their enantiomers.We elucidated the synergistic effect of the planar chirality of pillar[5]arenes and axial chirality of BINOL on the circularly polarized luminescence(CPL)behaviors of hybrid chiral BINOL-Py functionalized pillar[5]arenes,achieving high glumup to 1.7×10^(-2).In addition,ascribed to the regulation of chirality information transmission through planar chirality of pillar[5]arenes,the resolved BINOL-Py functionalized pillar[5]arenes reveal unique tunable circular dichroism(CD)and CPL in different aggregation state and upon the addition of vip,providing not only a novel design strategy for developing molecular systems with chiroptical tunability but also an intriguing platform for the construction of CPL luminescent materials based on chiral macrocycles. 展开更多
关键词 CPL arene Planar chirality Chirality transfer π-πstacking
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Near-perfect separation of alicyclic ketones and alicyclic alcohols by nonporous adaptive crystals of perethylated pillar[5]arene and pillar[6]arene
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作者 Jingyu Chen Sha Wu +1 位作者 Yuhao Wang Jiong Zhou 《Chinese Chemical Letters》 2025年第4期205-210,共6页
The separation of alicyclic ketones and alicyclic alcohols is one of the challenges in the field of petrochemical industry. However, traditional separation methods suffer from excessive energy consumption,complicated ... The separation of alicyclic ketones and alicyclic alcohols is one of the challenges in the field of petrochemical industry. However, traditional separation methods suffer from excessive energy consumption,complicated operation, and unsatisfactory separation efficiency for substances with similar boiling points.Herein, we offer an innovative method for the separation of alicyclic ketones and alicyclic alcohols employing nonporous adaptive crystals(NACs) of perethylated pillar[5]arene(EtP5) and perethylated pillar[6]arene(Et P6). NACs of EtP5 cannot adsorb either alicyclic ketones or alicyclic alcohols because of the small cavity size of Et P5. By contrast, NACs of Et P6 can separate cyclopentanone from the vapor mixture of cyclopentanone/cyclopentanol(v:v = 1:1) and cyclohexanone from the vapor mixture of cyclohexanone/cyclohexanol(v:v = 1:1) with purities of 99.1% and 100%, respectively. Density functional theory calculations show that the selectivity comes from the thermodynamic stability of the newly formed crystal structure after adsorption of the preferred vip molecule. Moreover, NACs of Et P6 can be reused without losing selectivity and performance. 展开更多
关键词 Pillar[n]arenes Nonporous adaptive crystals Adsorptive separation Host-vip complexes Supramolecular chemistry
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Functional macrocyclic arenes with active binding sites inside cavity for biomimetic molecular recognition
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作者 Xixian Sun Shengke Li +1 位作者 Ruibing Wang Leyong Wang 《Chinese Chemical Letters》 2025年第4期1-2,共2页
Molecular recognition of bioreceptors and enzymes relies on orthogonal interactions with small molecules within their cavity. To date, Chinese scientists have developed three types of strategies for introducing active... Molecular recognition of bioreceptors and enzymes relies on orthogonal interactions with small molecules within their cavity. To date, Chinese scientists have developed three types of strategies for introducing active sites inside the cavity of macrocyclic arenes to better mimic molecular recognition of bioreceptors and enzymes.The editorial aims to enlighten scientists in this field when they develop novel macrocycles for molecular recognition, supramolecular assembly, and applications. 展开更多
关键词 supramolecular assembly orthogonal interactions introducing active sites active binding sites macrocyclic arenes molecular recognition orthogonal interactions small molecules biomimetic molecular recognition
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格序代数二次序共轭的一个注 被引量:3
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作者 冯颖 《西南师范大学学报(自然科学版)》 CAS CSCD 北大核心 2008年第3期15-18,共4页
主要讨论了格序代数(f-代数,殆f-代数,d-代数)的二次序连续共轭与一次共轭在Arens乘积下的乘积空间的序结构问题.给出了f-代数二次序连续共轭是半素的f-代数的一个充分必要条件.
关键词 arens乘积 f-代数 殆f-代数 d-代数 二次序连续共轭
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The Multiplier Algebra of a Ternary Algebra 被引量:1
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作者 许天周 《Chinese Quarterly Journal of Mathematics》 CSCD 1992年第2期6-11,共6页
In this article, we have given the definition of the relative double multiplier (quasi-multiplier) on a ternary algebra,and studied the isomorphic problem of the multiplier algebra M(A,e) of a ternary algerbra A.
关键词 multiplier algebra ternary algebra relative arens product
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弱基的一些性质(英文)
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作者 高阳 王尚志 《南开大学学报(自然科学版)》 CAS CSCD 北大核心 2010年第6期48-55,共8页
比较了弱基与基的异同,同时还研究了弱基在投影映射下的性质,并以Arens空间S_2为例对一些不成立的命题给出了反例.
关键词 弱基 arens空间 K-空间 序列空间
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