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Rationally designed amyloid inhibitors based on amyloid-related structural studies
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作者 Jinjian Hu Yufen Zhao Yanmei Li 《Chinese Chemical Letters》 SCIE CAS CSCD 2023年第2期7-17,共11页
Amyloid proteins correlate with a series of degenerative diseases. Targeting amyloid aggregation has remained a hot topic in therapeutic studies. Numerous inhibitors have been developed, but very few have been approve... Amyloid proteins correlate with a series of degenerative diseases. Targeting amyloid aggregation has remained a hot topic in therapeutic studies. Numerous inhibitors have been developed, but very few have been approved for marketing. Meanwhile, the growing knowledge of amyloid structural characteristics provides a basis for the rational design of inhibitors. Here we introduce the high-resolution structural findings of amyloid fibrils in recent years and discuss the reported strategies toward rationally designed inhibitors based on amyloid-related structural studies. 展开更多
关键词 AMYLOID Amyloid structure Degenerative disease Amyloid inhibitor Rational design
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Harnessing Interactional Sensory Genes for Rationally Reprogramming Chaotic Metabolism
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作者 Chunlin Tan Ping Xu Fei Tao 《Research》 SCIE EI CSCD 2023年第3期295-308,共14页
Rationally controlling cellular metabolism is of great importance but challenging owing to its highly complex and chaotic nature.Natural existing sensory proteins like histidine kinases(HKs)are understood as“sensitiv... Rationally controlling cellular metabolism is of great importance but challenging owing to its highly complex and chaotic nature.Natural existing sensory proteins like histidine kinases(HKs)are understood as“sensitive nodes”of biological networks that can trigger disruptive metabolic reprogramming(MRP)upon perceiving environmental fluctuation.Here,the“sensitive node”genes were adopted to devise a global MRP platform consisting of a CRISPR interference-mediated dual-gene combinational knockdown toolbox and survivorship-based metabolic interaction decoding algorithm.The platform allows users to decode the interfering effects of n×n gene pairs while only requiring the synthesis of n pairs of primers.A total of 35 HK genes and 24 glycine metabolic genes were selected as the targets to determine the effectiveness of our platform in a Vibrio sp.FA2.The platform was applied to decode the interfering impact of HKs on antibiotic resistance in strain FA2.A pattern of combined knockdown of HK genes(sasA_8 and 04288)was demonstrated to be capable of reducing antibiotic resistance of Vibrio by 108-fold.Patterns of combined knockdown of glycine pathway genes(e.g.,gcvT and ltaE)and several HK genes(e.g.,cpxA and btsS)were also revealed to increase glycine production.Our platform may enable an efficient and rational approach for global MRP based on the elucidation of high-order gene interactions.A web-based 1-stop service(https://smrp.sjtu.edu.cn)is also provided to simplify the implementation of this smart strategy in a broad range of cells. 展开更多
关键词 METABOLISM RATIONAL programming
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Community perspectives on the effectiveness of watershed management institutions in the Himalayas
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作者 Nisha SILWAL Nabin DHUNGANA +2 位作者 Rajan SUBEDI Suraj UPADHAYA Chun-Hung LEE 《Journal of Mountain Science》 SCIE CSCD 2024年第4期1119-1139,共21页
The sustainability of environmental management initiatives,such as watershed management programs,relies on the presence of effective institutions at the watershed level.However,there needs to be more empirical evidenc... The sustainability of environmental management initiatives,such as watershed management programs,relies on the presence of effective institutions at the watershed level.However,there needs to be more empirical evidence from evaluating the effectiveness of watershed-level institutions.Therefore,this study presents a pioneering effort to evaluate the effectiveness of Nepal’s first watershed conservation committee at the watershed scale,focusing on the case of the Khageri Khola watershed in Central Nepal.The study involved conducting a household survey,key informant interviews,focus group discussions,and field observations to collect and analyze the data.Descriptive analysis,index value calculation,and chi-square statistics were then employed to summarize the results regarding local respondents’perceptions of twelve institutional characteristics,their rationalities,and their association with socio-demographic variables.The results reveal that the watershed conservation committee was perceived as performing well in managing the watershed.Specifically,good interaction,appropriate scale,technical,environmental,social,organizational,and government rationality were perceived as highly effective,with an average index value of less than 0.36.In contrast,clarity of objectives and economic rationality showed moderate effectiveness,with an average index value ranging from 0.36 to 0.65.However,the results suggested that adaptiveness,compliance capacity,and financial rationality merit increased attention,intending to improve their performance.Further,the results showed the association of socio-demographics with respondents’perceptions of various indicators of institutional characteristics and their rationalities.Therefore,the study provides valuable insights for policymakers,researchers,and development practitioners charged with designing sustainable and effective programs and institutions.To enhance the effectiveness and sustainability of watershed management programs,we recommend establishing a policy-guided institutional mechanism at the watershed scale.This mechanism should be based on various institutional characteristics and rationalities and should consider the extant variability in the socio-demographic and topographic characteristics of the watershed. 展开更多
关键词 WATERSHED Watershed institutions INDICATORS Institutional characteristics Rationalities Nepal.
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Rational Engineering of Secondary Metabolic Pathways in a Heterologous Host to Enable the Biosynthesis of Hibarimicin Derivatives with Enhanced Anti-Melanomic Activity
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作者 Xiangyang Liu Fei-Peng Zhao +9 位作者 Tian Tian Wei-Chen Wang Zaizhou Liu Qiang Zhou Xian-Feng Hou Jing Wang Wenli Guo Shuangjun Lin Yasuhiro Igarashi Gong-Li Tang 《Engineering》 SCIE EI CAS CSCD 2024年第7期113-123,共11页
A 61-kb biosynthetic gene cluster(BGC),which is accountable for the biosynthesis of hibarimicin(HBM)B from Microbispora rosea subsp.hibaria TP-A0121,was heterologously expressed in Streptomyces coelicolor M1154,which ... A 61-kb biosynthetic gene cluster(BGC),which is accountable for the biosynthesis of hibarimicin(HBM)B from Microbispora rosea subsp.hibaria TP-A0121,was heterologously expressed in Streptomyces coelicolor M1154,which generated a trace of the target products but accumulated a large amount of shunt products.Based on rational analysis of the relevant secondary metabolism,directed engineering of the biosynthetic pathways resulted in the high production of HBM B,as well as new HBM derivates with improved antitumor activity.These results not only establish a biosynthetic system to effectively synthesize HBMs-a class of the largest and most complex Type-Ⅱpolyketides,with a unique pseudo-dimeric structure-but also set the stage for further engineering and deep investigation of this complex biosynthetic pathway toward potent anticancer drugs. 展开更多
关键词 Hibarimicin BIOSYNTHESIS Heterologous expression Biosynthetic gene cluster Rational engineering Type-II polyketide
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Gate Tunable Labyrinth Domain Structures in a van der Waals Itinerant Ferromagnet Cr_(7)Te_(8)
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作者 Kui Meng Zeya Li +11 位作者 Yicheng Shen Xiangyu Bi Junhao Rao Yuting Qian Zhansheng Gao Peng Chen Caiyu Qiu Feng Qin Jinxiong Wu Feng Luo Junwei Huang Hongtao Yuan 《Chinese Physics Letters》 SCIE EI CAS CSCD 2024年第9期122-132,共11页
Manipulating magnetic domain structure plays a key role in advanced spintronics devices.Theoretical rationale is that the labyrinthine domain structure,normally appearing in ferromagnetic thin films with strong magnet... Manipulating magnetic domain structure plays a key role in advanced spintronics devices.Theoretical rationale is that the labyrinthine domain structure,normally appearing in ferromagnetic thin films with strong magnetic anisotropy,shows a great potential to increase data storage density for designing magnetic nonvolatile memory and logic devices.However,an electrical control of labyrinthine domain structure remains elusive.Here,we demonstrate the gate-driven evolution of labyrinthine domain structures in an itinerant ferromagnet Cr_(7)Te_(8).By combining electric transport measurements and micromagnetic finite difference simulations,we find that the hysteresis loop of anomalous Hall effect in Cr_(7)Te_(8)samples shows distinct features corresponding to the generation of labyrinthine domain structures.The labyrinthine domain structures are found to be electrically tunable via Li-electrolyte gating,and such gate-driven evolution in Cr_(7)Te_(8)originates from the reduction of the magnetic anisotropic energy with gating,revealed by our micromagnetic simulations.Our results on the gate control of anomalous Hall effect in an itinerant magnetic material provide an opportunity to understand the formation and evolution of labyrinthine domain structures,paving a new route towards electric-field driven spintronics. 展开更多
关键词 RATIONAL ELECTROLYTE FERROMAGNETIC
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Approximate solution of Volterra-Fredholm integral equations using generalized barycentric rational interpolant
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作者 Hadis Azin Fakhrodin Mohammadi 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第2期220-238,共19页
It is well-known that interpolation by rational functions results in a more accurate approximation than the polynomials interpolation.However,classical rational interpolation has some deficiencies such as uncontrollab... It is well-known that interpolation by rational functions results in a more accurate approximation than the polynomials interpolation.However,classical rational interpolation has some deficiencies such as uncontrollable poles and low convergence order.In contrast with the classical rational interpolants,the generalized barycentric rational interpolants which depend linearly on the interpolated values,yield infinite smooth approximation with no poles in real numbers.In this paper,a numerical collocation approach,based on the generalized barycentric rational interpolation and Gaussian quadrature formula,was introduced to approximate the solution of Volterra-Fredholm integral equations.Three types of points in the solution domain are used as interpolation nodes.The obtained numerical results confirm that the barycentric rational interpolants are efficient tools for solving Volterra-Fredholm integral equations.Moreover,integral equations with Runge’s function as an exact solution,no oscillation occurrs in the obtained approximate solutions so that the Runge’s phenomenon is avoided. 展开更多
关键词 Barycentric rational interpolation Volterra-Fredholm integral equations Gaussian quadrature Runge's phenomenon
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Blockchain-Based Key Management Scheme Using Rational Secret Sharing
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作者 Xingfan Zhao Changgen Peng +1 位作者 Weijie Tan Kun Niu 《Computers, Materials & Continua》 SCIE EI 2024年第4期307-328,共22页
Traditional blockchain key management schemes store private keys in the same location,which can easily lead to security issues such as a single point of failure.Therefore,decentralized threshold key management schemes... Traditional blockchain key management schemes store private keys in the same location,which can easily lead to security issues such as a single point of failure.Therefore,decentralized threshold key management schemes have become a research focus for blockchain private key protection.The security of private keys for blockchain user wallet is highly related to user identity authentication and digital asset security.The threshold blockchain private key management schemes based on verifiable secret sharing have made some progress,but these schemes do not consider participants’self-interested behavior,and require trusted nodes to keep private key fragments,resulting in a narrow application scope and low deployment efficiency,which cannot meet the needs of personal wallet private key escrow and recovery in public blockchains.We design a private key management scheme based on rational secret sharing that considers the self-interest of participants in secret sharing protocols,and constrains the behavior of rational participants through reasonable mechanism design,making it more suitable in distributed scenarios such as the public blockchain.The proposed scheme achieves the escrow and recovery of personal wallet private keys without the participation of trusted nodes,and simulate its implementation on smart contracts.Compared to other existing threshold wallet solutions and keymanagement schemes based on password-protected secret sharing(PPSS),the proposed scheme has a wide range of applications,verifiable private key recovery,low communication overhead,higher computational efficiency when users perform one-time multi-key escrow,no need for trusted nodes,and personal rational constraints and anti-collusion attack capabilities. 展开更多
关键词 Blockchain smart contract rational secret sharing key management
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Smoking of Carica papaya in Nigeria:The rationale,the public health effects and policies for intervention
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作者 Abolaji Paul Adekeye 《Asian Pacific Journal of Tropical Medicine》 SCIE CAS 2024年第3期95-96,共2页
Psychoactive substance use is characterized by the habitual use of substances that have significant effects in altering the activities of neurotransmitters in certain regions of the brain.Consequently,these alteration... Psychoactive substance use is characterized by the habitual use of substances that have significant effects in altering the activities of neurotransmitters in certain regions of the brain.Consequently,these alterations manifest as cognitive,emotional,perceptual and behavioural changes in affected individuals[1]. 展开更多
关键词 RATIONAL behaviour EMOTIONAL
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Scientific principles for accelerating the Sustainable Development Goals
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作者 Bojie Fu Xutong Wu +1 位作者 Shuai Wang Wenwu Zhao 《Geography and Sustainability》 CSCD 2024年第2期157-159,共3页
The Sustainable Development Goals(SDGs)are significantly off-course as we reach the midpoint of their 2030 deadline.From a scientific perspective,the critical challenge in achieving the SDGs lies in the need for more ... The Sustainable Development Goals(SDGs)are significantly off-course as we reach the midpoint of their 2030 deadline.From a scientific perspective,the critical challenge in achieving the SDGs lies in the need for more scientific principles to understand the complex socio-ecological systems(SES)and their interactions influencing the 17 SDGs.Here,we propose a scientific framework to clarify the common scientific principles and the rational treatment of diversity under these principles.The framework’s core is revealing the complex mechanisms underlying the achievement of each Sustainable Development Goal(SDG)and SDG interactions.Building upon the identified mechanisms,complex SES models can be established,and the implementation of SDGs can be formulated as a multi-objective optimization problem,seeking a compromise in competition between essential costs and desired benefits.Our framework can assist countries,and even the world in accelerating progress towards the SDGs. 展开更多
关键词 PRINCIPLES SUSTAINABLE RATIONAL
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Experimental study of core MHD behavior and a novel algorithm for rational surface detection based on profile reflectometry in EAST
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作者 叶凯萱 周振 +20 位作者 张涛 马九阳 王嵎民 李恭顺 耿康宁 吴茗甫 文斐 黄佳 张洋 邵林明 杨书琪 钟富彬 高善露 喻琳 周子强 向皓明 韩翔 张寿彪 李国强 高翔 the EAST Team 《Plasma Science and Technology》 SCIE EI CAS CSCD 2024年第3期66-75,共10页
Microwave reflectometry is a powerful diagnostic that can measure the density profile and localized turbulence with high spatial and temporal resolution and will be used in ITER,so understanding the influence of plasm... Microwave reflectometry is a powerful diagnostic that can measure the density profile and localized turbulence with high spatial and temporal resolution and will be used in ITER,so understanding the influence of plasma perturbations on the reflect signal is important.The characteristics of the reflect signal from profile reflectometry,the time-of-flight(TOF)signal associated with the MHD instabilities,are investigated in EAST.Using a 1D full-wave simulation code by the Finite-DifferenceTime-Domain(FDTD)method,it is well validated that the local density flattening could induce the discontinuity of the simulated TOF signal and an obvious change of reflect amplitude.Experimental TOF signals under different types of MHD instabilities(sawtooth,sawtooth precursors and tearing mode)are studied in detail and show agreement with the simulation.Two new improved algorithms for detecting and localizing the radial positions of the low-order rational surface,the cross-correlation and gradient threshold(CGT)method and the 2D convolutional neural network approach(CNN)are presented for the first time.It is concluded that TOF signal analysis from profile reflectometry can provide a straightforward and localized measurement of the plasma perturbation from the edge to the core simultaneously and may be a complement or correction to the q-profile control,which will be beneficial for the advanced tokamak operation. 展开更多
关键词 MHD instabilities profile reflectometry rational surface detection convolutional neural network(CNN) EAST tokamak
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Assessing the Efficacy of Wheat-Soybean Based Intercropping System at Different Plant Densities in Bambili, Cameroon
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作者 Lendzemo E. Tatah Jeazet K. Teitiogo +3 位作者 Oben Tom Tabi Tange D. Achiri Njualem D. Khumbah Chi Christopher Tamu 《American Journal of Plant Sciences》 CAS 2024年第4期235-251,共17页
Wheat is one of the most important cereals in the world, serving as a staple for millions globally. In the wake of the geopolitical crisis between Russia and Ukraine, it has become incumbent for many countries to inve... Wheat is one of the most important cereals in the world, serving as a staple for millions globally. In the wake of the geopolitical crisis between Russia and Ukraine, it has become incumbent for many countries to invest in wheat production. Improving cropping systems for wheat production is paramount. Intercropping cereals with legumes has tremendous advantages. Therefore, this study was designed to optimize wheat production by intercropping it with soybean at different densities. Between March and August 2023, a randomized complete block design trial was conducted in Bambili, North West of Cameroon with treatments T1 (wheat monocrop at 200,000 plants ha<sup>−</sup><sup>1</sup>), T2 (soybean monocrop at 250,000 plants ha<sup>−</sup><sup>1</sup>), T3 (200,000 wheat and 125,000 soybean ha<sup>−</sup><sup>1</sup>), T4 (100,000 wheat and 250,000 soybean ha<sup>−</sup><sup>1</sup>), T5 (200,000 wheat and 250,000 soybean ha<sup>−</sup><sup>1</sup>) and T6 (100,000 wheat and 125,000 soybean ha<sup>−</sup><sup>1</sup>). Results revealed that growth parameters of wheat were not significantly influenced by monocrop or intercrop. The yield of wheat was significantly higher in the monocrop than the intercrop treatments, with slight variation amongst the intercrop treatments. Soybean yield was higher in the monocrop than in the intercrop, with no variations amongst the intercrop treatments. Only the land equivalence ratio (LER) for T5 was greater than 1.0. The competitive ratio for T5 was 0.54 for wheat and 1.90 for soybean, comparatively lower than the other monocrop treatments. Intercropping wheat and soybean at 200,000:250,000 ratio is recommended. 展开更多
关键词 Competitive Ration Land Equivalence Ration INTERCROP SOYBEAN WHEAT
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Erratum regarding Declaration of Competing Interest statements in previously published articles
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《Materials Reports(Energy)》 EI 2024年第1期123-124,共2页
Declaration of Competing Interest statements were incorrectly included in the published version of the following articles that appeared in previous issues of Materials Reports:Energy.The appropriate Declaration of Com... Declaration of Competing Interest statements were incorrectly included in the published version of the following articles that appeared in previous issues of Materials Reports:Energy.The appropriate Declaration of Competing Interest statements,provided by the authors,are included below. 展开更多
关键词 statements RATION SHE
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Practice of Perioperative Rational Use of Antibacterial Drugs Based on Drug Pathway
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作者 Changkai ZHOU Fanbo JING +1 位作者 Haijun QU Jing GAO 《Medicinal Plant》 2024年第2期57-60,64,共5页
[Objectives]To establish a new management model for rational use of perioperative antibacterial drugs in surgical departments.[Methods]Based on evidence-based medicine,the department s drug pathway was formulated,and ... [Objectives]To establish a new management model for rational use of perioperative antibacterial drugs in surgical departments.[Methods]Based on evidence-based medicine,the department s drug pathway was formulated,and the new mode of rational drug use control was established by using fine pharmaceutical technology intervention,and the intervention effect was evaluated by the intensity of antibacterial drug use,per capita drug costs and the proportion of drugs.[Results]After adopting drug pathway in departments,the intensity of antibacterial drug use,per capita drug costs and the proportion of drugs decreased significantly,and the effect of rational drug use control was remarkable.[Conclusions]The drug pathway provides a new management and control mode for the rational use of perioperative antibacterial drugs in surgical departments of hospitals.Thus,it is worthy of popularization and application. 展开更多
关键词 Perioperative period Antibacterial drugs Drug pathway Rational drug use Management model
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Exact controllability of rational expectations model with multiplicative noise and input delay
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作者 Wenjing Wang Juanjuan Xu +1 位作者 Huanshui Zhang Minyue Fu 《Journal of Automation and Intelligence》 2024年第1期19-25,共7页
This paper considers the rational expectations model with multiplicative noise and input delay,where the system dynamics rely on the conditional expectations of future states.The main contribution is to obtain a suffi... This paper considers the rational expectations model with multiplicative noise and input delay,where the system dynamics rely on the conditional expectations of future states.The main contribution is to obtain a sufficient condition for the exact controllability of the rational expectations model.In particular,we derive a sufficient Gramian matrix condition and a rank condition for the delay-free case.The key is the solvability of the backward stochastic difference equations with input delay which is derived from the forward and backward stochastic system. 展开更多
关键词 Rational expectations model Exact controllability Exactly null controllability Multiplicative noise Input delay
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The Global Security Initiative: Its Relevance, Rationale and Delivery
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作者 Liu Shiqiang 《Contemporary World》 2024年第2期34-38,共5页
Today,our world is undergoing profound changes unseen in a century.Global security landscape is becoming ever more unstable and uncertain.In the face of growing deficits in security,Chinese President Xi Jinping put fo... Today,our world is undergoing profound changes unseen in a century.Global security landscape is becoming ever more unstable and uncertain.In the face of growing deficits in security,Chinese President Xi Jinping put forward the Global Security Initiative(GSI),offering a clear answer to the question of the times:what kind of security concept does the world need,and how can we achieve common security?It is of great significance to fully grasp the relevance of and the rationale for the GSI,and push for its strategic delivery,so as to contribute to the long-term peace and stability of the world. 展开更多
关键词 RATIONAL offering RATIONAL
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Rationally connected varieties -On a conjecture of Mumford
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作者 LAZIC Vladimir PETERNELL Thomas 《Science China Mathematics》 SCIE CSCD 2017年第6期1019-1028,共10页
We establish a conjecture of Mumford characterizing rationally connected complex projective manifolds in several cases.
关键词 rationally connected varieties Mumford conjecture non vanishing conjecture ABUNDANCE
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Green Olympics
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《ChinAfrica》 2024年第10期58-59,共2页
The Double Take column looks at a single topic from an African and Chinese perspective.This month we discuss to what extent the idea of Green Olympics is rational.The organisers of the Paris Olympics took some unusual... The Double Take column looks at a single topic from an African and Chinese perspective.This month we discuss to what extent the idea of Green Olympics is rational.The organisers of the Paris Olympics took some unusual measures such as absence of air conditioning in a quite hot weather and lack of meat in food for athletes in their bid to hold the“greenest-ever”Olympic games this August.This has sparked a discussion on how we should balance a low-carbon lifestyle with other human needs such as comfort and nutrition. 展开更多
关键词 RATIONAL WEATHER UNUSUAL
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The Path,Trends,and Approaches of the Civilization Evolution of Rural Marriage Forms
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作者 Renxiu Chen 《Review of Educational Theory》 2024年第1期6-9,共4页
Rural marriage has characteristics such as close relationship with labor production,deep integration of traditional culture,shy and introverted expression of subjective emotions,and illegal and rough marriage.The civi... Rural marriage has characteristics such as close relationship with labor production,deep integration of traditional culture,shy and introverted expression of subjective emotions,and illegal and rough marriage.The civilization evolution of rural marriage forms is moving towards a path that is conducive to the development of production and the pursuit of happiness for farmers,the construction of rural spiritual civilization,and the comprehensive development of rural society.This study analyzes the direction of the evolution of rural marriage form civilization,predicts the trend of rural marriage form civilization evolution,and proposes the future path of rural marriage form civilization evolution,including adhering to human’s most original value expectations of marriage life,drawing nourishment from excellent traditional Chinese culture,and continuously adjusting marriage and family policy tools to keep up with changes in the world of life. 展开更多
关键词 Rural Marriage Forms Civilization Evolution Marriage Squeeze Civilized Rationality
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The Impact of the“Belt and Road”Initiative on Industrial Structure Upgrading Along the Corridor
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作者 Fangyuan Lou 《Proceedings of Business and Economic Studies》 2024年第3期194-199,共6页
The“Belt and Road”initiative functions as a novel impetus for China’s external economic development within the framework of the new normal of economic growth.By leveraging panel data from 30 provinces and regions a... The“Belt and Road”initiative functions as a novel impetus for China’s external economic development within the framework of the new normal of economic growth.By leveraging panel data from 30 provinces and regions across China for the period of 2010 to 2020,this research assesses the influence of the“Belt and Road”initiative on the enhancement of the industrial structure along its trajectory.The findings indicate that:the most notable influence on the rationalization and progress of the industrial structure is observed in the eastern region,with the central region following suit,whereas the western region has yet to exhibit a significant transformation.The analysis delves into the role of technological innovation,concluding that the initiative primarily catalyzes optimization and upgrading through the effect of technological advancement.The study advances several pertinent policy recommendations to support and enhance these developments. 展开更多
关键词 Belt and Road Industrial structure advancement Industrial structure rationalization
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Whole Perfect Vectors and Fermat’s Last Theorem
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作者 Ramon Carbó-Dorca 《Journal of Applied Mathematics and Physics》 2024年第1期34-42,共9页
A naïve discussion of Fermat’s last theorem conundrum is described. The present theorem’s proof is grounded on the well-known properties of sums of powers of the sine and cosine functions, the Minkowski norm de... A naïve discussion of Fermat’s last theorem conundrum is described. The present theorem’s proof is grounded on the well-known properties of sums of powers of the sine and cosine functions, the Minkowski norm definition, and some vector-specific structures. 展开更多
关键词 Fermat’s Last Theorem Whole Perfect Vectors Sine and Cosine Functions Natural and Rational Vectors Fermat Vectors
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