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Feeding ecology and interactions with mammal hosts in a symbiotic genus of birds(Buphagus spp.)in Namibia

Avian Research 2024年第3期15卷 336-344页

作者： Michael S.Lukubwe Daniel Velarde-Garcéz Fernando Sequeira Susana Lopes Adrian j.F.K.Craig Vanessa A.Mata Department of zoology and Entomology Rhodes UniversityMakhandaSouth Africa Department of Wildlife Management and Tourism Studies University of NamibiaKatima Mulilo CampusNamibia Departamento de Biologia Faculdade de CiênciasUniversidade do PortoPortoPortugal CIBIO Centro de Investigação em Biodiversidade e Recursos GenéticosInBIO Laboratório AssociadoCampus de VairãoVairãoPortugal BIOPOLIS Program in Genomics Biodiversity and Land PlanningCIBIOCampus de VairãoVairãoPortugal

As the sole obligate symbiotic birds in Africa,oxpeckers offer a unique model for studying symbiotic *** to the multitrophic level they occupy and the context dependent foraging behavior they exhibit,the type of symbiotic relationship can be *** addition to providing a cleaning service to the host by removing ticks,oxpeckers frequently feed on blood,mucus,and saliva,inflicting potential damage on the ***,we used DNA metabarcoding on faecal samples to analyze the taxonomic composition of the trophic interactions of the Yellow-billed Oxpecker(Buphagus africanus)and Red-billed Oxpecker(***)in northeastern *** contrast to conventional methods,DNA metabarcoding allows for a detailed identification of dietary resources encompassing both mammal hosts and consumed arthropods within the same *** this information,we examined differences in the diet composition between oxpecker species and localities,as well as the co-occurrence between host and arthropod *** findings revealed that oxpeckers predominantly source their diet from mammals,ticks,and flies;however,ticks and flies rarely co-occur in the diet of an *** observed variability among individuals in their feeding ecology,which is strongly correlated with locality and,to a lesser extent,with the mammal *** noted a high degree of mobility between hosts within relatively short periods,with 32%of the samples showing traces of at least two mammal *** study illustrates the dynamic foraging behavior of these specialized symbiotic birds,shedding light on their potential role in pest control services and disease transmission.

关键词： Commensalism Diet DNA metabarcoding Oxpeckers Parasitism Trophic ecology

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Morphological disruption and visual tuning alterations in the primary visual cortex in glaucoma(DBA/2j.mice

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Neural Regeneration Research 2024年第1期19卷 220-225页

作者： Yin Yang zhaoxi Yang Maoxia Lv ang j.a j.nj.n Li Baitao Liao j.ng’an Chen zhengzheng Wu Yi Shi Yang Xia Dezhong Yao Ke Chen Department of Ophthalmology Sichuan Provincial People’s HospitalMedical SchoolUniversity of Electronic Science and Technology of ChinaChengduSichuan ProvinceChina The Clinical Hospital of Chengdu Brain Science Institute MOE Key Lab for NeuroInformationSchool of Life Science and TechnologyUniversity of Electronic Science and Technology of ChinaChengduSichuan ProvinceChina Research Unit of NeuroInformation Chinese Academy of Medical SciencesChengduSichuan ProvinceChina Institute of Basic Medical Sciences Chinese Academy of Medical Sciences School of Basic Medicine Peking Union Medical CollegeBeijingChina Health Management Center Sichuan Provincial Key Laboratory for Human Disease Gene StudySichuan Provincial People’s HospitalUniversity of Electronic Science and Technology of ChinaChengduSichuan ProvinceChina Research Unit for Blindness Prevention of Chinese Academy of Medical Sciences(2019RU026) Sichuan Academy of Medical SciencesChengduSichuan ProvinceChina School of Electrical Engineering Zhengzhou UniversityZhengzhouHenan ProvinceChina

Glaucoma is a leading cause of irreve rsible blindness wo rldwide,and previous studies have shown that,in addition to affecting the eyes,it also causes abnormalities in the ***,it is not yet clear how the primary visual cortex(V1)is altered in *** study used DBA/2j.mice as a model for spontaneous secondary *** aim of the study was to compare the electrophysiological and histomorphological chara cteristics of neurons in the V1between 9-month-old DBA/2j.mice and age-matched C57BL/6j.*** conducted single-unit recordings in the V1 of light-anesthetized mice to measure the visually induced responses,including single-unit spiking and gamma band *** morphology of layerⅡ/Ⅲneurons was determined by neuronal nuclear antigen staining and Nissl staining of brain tissue ***-seven neurons from eight DBA/2j.mice and eighty-one neurons from eight C57BL/6j.mice were *** with the C57BL/6j.group,V1 neurons in the DBA/2j.group exhibited weaker visual tuning and impaired spatial *** r,fewer neuro ns were observed in the V1 of DBA/2j.mice compared with C57BL/6j.*** findings suggest that DBA/2j.mice have fewer neurons in the VI compared with C57BL/6j.mice,and that these neurons have impaired visual *** findings provide a better understanding of the pathological changes that occur in V1 neuron function and morphology in the DBA/2j.mouse *** study might offer some innovative perspectives regarding the treatment of glaucoma.

关键词： DBA/2j degeneration gamma band oscillations glaucoma primary visual cortex(V1) retina single-unit recording tuning curve

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Distributed fixed-time observers for linear time-invariant systems

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Kongzhi yu j.ece/Control and Decision 2024年第11期39卷 3664-3672页

作者： z.ang T. Wu H.-Y. zhu z.-H. zheng X.-j. Guan z.-H. Engineering Research Center for Metallurgical Automation and Measurement Technology of Ministry of Education Wuhan University of Science and Technology Wuhan 430081 China Institute of Robotics and Intelligent Systems Wuhan University of Science and Technology Wuhan 430081 China School of Artificial Intelligence and Automation Huazhong University of Science and Technology Wuhan 430074 China

A class of distributed fixed-time convergent observers is designed based on the bi-limit weighted homogeneous approximation theory and observability decomposition for the distributed state estimation of linear time-invariant systems. Firstly, for a single-input-single-output integrating chain system, a centralized fixed-time observer is designed for the system using bi-limit weighted homogeneous estimation. Then, the linear time-invariant system is decomposed into observable and unobservable subsystems based on the observability decomposition. Each agent in the sensor network reconstructs local observable sub-states in a fixed time based on the centralized observer by using only the system output measurements, and then state information between the agents is used to construct a consistent algorithm to estimate the local unobservable sub-states in a fixed time, thus realizing state omniscience in a fixed time. Unlike previous works, this paper does not need to construct a specific Lyapunov function to give an expression for the convergence time. Finally, the effectiveness of the designed observer is verified by simulations. © 2024 Northeast University. All rights reserved.

关键词： distributed estimation fixed-time observer linear systems observability decomposition sensor networks weighted homogeneity

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A new class of crystalline X-ray induced photochromic materials assembled from anion-directed folding of a flexible cation

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Chinese Chemical Letters 2024年第8期35卷 554-557页

作者： Hong-j.n Liao zhu zhuo Qing Li Yoshihito Shiota j.nathan P.Hill Katsuhiko Ariga zi-Xiu Lu Lu-Yao Liu zi-ang Nan Wei Wang You-Gui Huang CAS Key Laboratory of Design and Assembly of Functional Nanostructures and Fujian Provincial Key Laboratory of NanomaterialsFujian Institute of Research on the Structure of MatterChinese Academy of SciencesFuzhou 350002China College of Chemistry and Materials Science Fujian Normal UniversityFuzhou 350007China Xiamen Key Laboratory of Rare Earth Photoelectric Functional Materials Xiamen Institute of Rare Earth MaterialsHaixi InstitutesChinese Academy of SciencesXiamen 361021China Fuj.an Science&Technology Innovation Laboratory for Optoelectronic Information of China Fuzhou 350108China Institute for Materials Chemistry and Engineering Kyushu UniversityFukuoka 819-0395Japan World Premier International(WPI)Center for Materials Nanoarchitectonics(MANA) National Institute for Materials Science(NIMS)Ibaraki 305-0044Japan

Electron-deficient viologens are widely used as ligands or structure-directing agents(SDAs)to synthesize crystalline X-ray induced photochromic ***,a new rational strategy of anion-directed fold-ing a flexible cation(H_(2)imb)^(2+)((H_(2)imb)^(2+)=di-protonated 2,3-bis(imidazolin-2-yl)-2,3-dimethylbutane)has been ***-donating Cl−and(znCl4)2−are used to direct folding a flexible electron-deficient(H_(2)imb)^(2+)*** complexes(H_(2)imb)(NO_(3))2(1),(H_(2)imb)Cl2·H_(2)O(2),and(H_(2)imb)znCl4(3)have been synthesized in which(H_(2)imb)^(2+)crystallize in an anti-conformation,88.8°-gauche,and 51.8°-gauche,*** contrary to X-ray silent complex 1,X-ray induced photochromism has been achieved in both complex 2 and *** intermolecular charge-transfer mechanism has been elucidated and the anion directed folding of(H_(2)imb)^(2+)has been validated to be critical to yield colored long-lived charge-separated states.

关键词： Supramolecular Photochromic X-ray induced Anion-directed folding Electron-deficient viologens

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Development,validation,and transportability of several machine-learned,non-exercise-based VO_(2max)prediction models for older adults

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j.urnal of Sport and Health Science 2024年第5期13卷 611-620页

作者： Benj.min T.Schumacher Michael j.LaMonte Andrea z.LaCroix Eleanor M.Simonsick Steven P.Hooker Humberto Parada j.. j.hn Bellettiere Arun Kumar Herbert Wertheim School of Public Health and Human Longevity Science University of California San DiegoLa JollaCA 92093USA Department of Epidemiology and Environmental Health School of Public Health and Health ProfessionsUniversity at BuffaloState University of New YorkBuffaloNY 14214USA Translational Gerontology Branch Intramural Research ProgramNational Institute on AgingNational Institutes of HealthBaltimoreMD 21225USA College of Health and Human Services San Diego State UniversitySan DiegoCA 92182USA Division of Epidemiology and Biostatistics School of Public HealthSan Diego State UniversitySan DiegoCA 92182USA University of California San Diego Moores Cancer Center La JollaCA 92093USA Computer Science and Engineering and Halicioglu Data Science Institute University of California San DiegoLa JollaCA 92093USA

Background:There exist few maximal oxygen uptake(VO_(2max))non-exercise-based prediction equations,fewer using machine learning(ML),and none specifically for older *** direct measurement of VO_(2max)is infeasible in large epidemiologic cohort studies,we sought to develop,validate,compare,and assess the transportability of several ML VO_(2max)prediction ***:The Baltimore Longitudinal Study of Aging(BLSA)participants with valid VO2_(max)tests were included(n=1080).Least absolute shrinkage and selection operator,linear-and tree-boosted extreme gradient boosting,random forest,and support vector machine(SVM)algorithms were trained to predict VO_(2max)*** developed these algorithms for:(a)the overall BLSA,(b)by sex,(c)using all BLSA variables,and(d)variables common in aging ***,we quantified the associations between measured and predicted VO_(2max)and ***:The age was 69.0±10.4 years(mean±SD)and the measured VO_(2max)was 21.6±5.9 mL/kg/*** absolute shrinkage and selection operator,linear-and tree-boosted extreme gradient boosting,random forest,and support vector machine yielded root mean squared errors of 3.4 mL/kg/min,3.6 mL/kg/min,3.4 mL/kg/min,3.6 mL/kg/min,and 3.5 mL/kg/min,*** quartiles of measured VO_(2max)showed an inverse gradient in mortality *** VO_(2max)variables yielded similar effect estimates but were not robust to ***:Measured VO_(2max)is a strong predictor of *** ML can improve the accuracy of prediction as compared to simpler approaches but estimates of association with mortality remain sensitive to *** studies should seek to reproduce these results so that VO_(2max),an important vital sign,can be more broadly studied as a modifiable target for promoting functional resiliency and healthy aging.

关键词： Cardiorespiratory fitness Prediction algorithms Epidemiology Mortality

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Negative enthalpy alloys and local chemical ordering:a concept and route leading to synergy of strength and ductility

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National Science Review 2024年第4期11卷 172-184页

作者： zibing An Tao Yang Caij.an Shi Shengcheng Mao Lihua Wang ang Li Wei Li Xianmeng Xue Ming Sun Yifan Bai Yapeng He Fuzeng Ren zhouguang Lu Ming Yan Yang Ren Chain-Tsuan Liu ze z.ang Xiaodong Han Beij.ng Key Lab of Microstructure and Property of Advanced Materials College of Materials Science &Engineering Beijing University of Technology Department of Materials Science and Engineering City University of Hong Kong Key Laboratory of Partial Acceleration Physics& Technology Institute of High Energy PhysicsChinese Academy of Sciences Department of Materials Science &Engineering Southern University of Science and Technology Department of Physics City University of Hong Kong State Key Laboratory of Silicon Materials Department of Materials Science and Engineering Zhejiang University

Solid solutions are ubiquitous in metals and alloys. Local chemical ordering(LCO) is a fundamental sub-nano/nanoscale process that occurs in many solid solutions and can be used as a microstructure to optimize strength and ductility. However, the formation of LCO has not been fully elucidated, let alone how to provide efficient routes for designing LCO to achieve synergistic effects on both superb strength and ductility. Herein, we propose the formation and control of LCO in negative enthalpy alloys. With engineering negative enthalpy in solid solutions, genetic LCO components are formed in negative enthalpy refractory high-entropy alloys(RHEAs). In contrast to conventional ‘trial-and-error' approaches, the control of LCO by using engineering negative enthalpy in RHEAs is instructive and results in superior strength(1160 MPa) and uniform ductility(24.5%) under tension at ambient temperature, which are among the best reported so far. LCO can promote dislocation cross-slip, enhancing the interaction between dislocations and their accumulation at large tensile strains; sustainable strain hardening can thereby be attained to ensure high ductility of the alloy. This work paves the way for new research fields on negative enthalpy solid solutions and alloys for the synergy of strength and ductility as well as new functions.

关键词： negative enthalpy alloys local chemical ordering strength ductility dislocation

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Generation of polarized electron beams through self-inj.ction in the interaction of a laser with a pre-polarized plasma

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High Power Laser Science and Engineering 2024年第3期12卷 62-68页

作者： L.R.Yin X.F.Li Y.j.Gu N.Cao Q.Kong M.Büscher S.M.Weng M.Chen z.M.Sheng Key Laboratory of Nuclear Physics and Ion-beam Application(MoE) Institute of Modern PhysicsDepartment of Nuclear Science and TechnologyFudan UniversityShanghaiChina State Key Laboratory of High Field Laser Physics Shanghai Institute of Optics and Fine MechanicsChinese Academy of SciencesShanghaiChina SANKEN(Institute of Scientific and Industrial Research) Osaka UniversityOsakaJapan Sichuan Research Institute Shanghai Jiao Tong UniversityChengduChina Peter Grünberg Institut(PGI-6) Forschungszentrum JülichJülichGermany Institut für Laser-und Plasmaphysik Heinrich-Heine-Universität DüsseldorfDüsseldorfGermany Key Laboratory for Laser Plasmas(MoE) School of Physics and AstronomyShanghai Jiao Tong UniversityShanghaiChina Collaborative Innovation Center of IFSA Shanghai Jiao Tong UniversityShanghaiChina Tsung-Dao Lee Institute Shanghai Jiao Tong UniversityShanghaiChina

Polarized electron beam production via laser wakefield acceleration in pre-polarized plasma is investigated by particlein-cell *** evolution of the electron beam polarization is studied based on the Thomas±Bargmann±Michel±Telegdi equation for the transverse and longitudinal self-inj.ction,and the depolarization process is found to be influenced by the inj.ction *** the case of transverse self-inj.ction,as found typically in the bubble regime,the spin precession of the accelerated electrons is mainly influenced by the ***,in the case of longitudinal inj.ction in the quasi-1D regime(for example,*** et al.,***.110,135002(2013)),the direction of electron spin oscillates in the laser *** the electrons move around the laser axis,the net influence of the laser field is nearly zero and the contribution of the wakefield can be ***,an ultra-short electron beam with polarization of 99%can be obtained using longitudinal self-inj.ction.

关键词： laser wakefield acceleration longitudinal self-inj.ction particle-in-cell simulation polarized electron beam

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STCF conceptual design report (Volume 1): Physics & detector

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Frontiers of physics 2024年第1期19卷 1-154页

作者： M.Achasov X.C.Ai L.P.An R.Aliberti Q.An X.z.Bai Y.Bai O.Bakina A.Barnyakov V.Blinov V.Bobrovnikov D.Bodrov A.Bogomyagkov A.Bondar I.Boyko z.H.Bu F.M.Cai H.Cai j.j.Cao Q.H.Cao X.Cao z.Cao Q.Chang K.T.Chao D.Y.Chen H.Chen H.X.Chen j.F.Chen K.Chen L.L.Chen P.Chen S.L.Chen S.M.Chen S.Chen S.P.Chen W.Chen X.Chen X.F.Chen X.R.Chen Y.Chen Y.Q.Chen H.Y.Cheng j.Cheng S.Cheng T.G.Cheng j.P.Dai L.Y.Dai X.C.Dai D.Dedovich A.Denig I.Denisenko j.M.Dias D.z.Ding L.Y.Dong W.H.Dong V.Druzhinin D.S.Du Y.j.Du z.G.Du L.M.Duan D.Epifanov Y.L.Fan S.S.Fang z.j.Fang G.Fedotovich C.Q.Feng X.Feng Y.T.Feng j.L.Fu j.Gao Y.N.Gao P.S.Ge C.Q.Geng L.S.Geng A.Gilman L.Gong T.Gong B.Gou W.Gradl j.L.Gu A.Guevara L.C.Gui A.Q.Guo F.K.Guo j.C.Guo j.Guo Y.P.Guo z.H.Guo A.Guskov K.L.Han L.Han M.Han X.Q.Hao j.B.He S.Q.He X.G.He Y.L.He z.B.He z.X.Heng B.L.Hou T.j.Hou Y.R.Hou C.Y.Hu H.M.Hu K.Hu R.j.Hu W.H.Hu X.H.Hu Y.C.Hu j.Hua G.S.Huang j.S.Huang M.Huang Q.Y.Huang W.Q.Huang X.T.Huang X.j.Huang Y.B.Huang Y.S.Huang N.Hüsken V.Ivanov Q.P.j. j.j.j.a S.j.a z.K.j.a H.B.j.ang j.j.ang S.z.j.ang j.B.j.ao z.j.ao H.j.j.ng X.L.Kang X.S.Kang B.C.Ke M.Kenzie A.Khoukaz I.Koop E.Kravchenko A.Kuzmin Y.Lei E.Levichev C.H.Li C.Li D.Y.Li F.Li G.Li G.Li H.B.Li H.Li H.N.Li H.j.Li H.L.Li j.M.Li j.Li L.Li L.Li L.Y.Li N.Li P.R.Li R.H.Li S.Li T.Li W.j.Li X.Li X.H.Li X.Q.Li X.H.Li Y.Li Y.Y.Li z.j.Li H.Liang j.H.Liang Y.T.Liang G.R.Liao L.z.Liao Y.Liao C.X.Lin D.X.Lin X.S.Lin B.j.Liu C.W.Liu D.Liu F.Liu G.M.Liu H.B.Liu j.Liu j.j.Liu j.B.Liu K.Liu K.Y.Liu K.Liu L.Liu Q.Liu S.B.Liu T.Liu X.Liu Y.W.Liu Y.Liu Y.L.Liu z.Q.Liu z.Y.Liu z.W.Liu I.Logashenko Y.Long C.G.Lu j.X.Lu N.Lu Q.F.Lü Y.Lu Y.Lu z.Lu P.Lukin F.j.Luo T.Luo X.F.Luo Y.H.Luo H.j.Lyu X.R.Lyu j.P.Ma P.Ma Y.Ma Y.M.Ma F.Maas S.Malde D.Matvienko z.X.Meng R.Mitchell A.Nefediev Y.Nefedov S.L.Olsen Q.Ouyang P.Pakhlov G.Pakhlova X.Pan Y.Pan E.Passemar Y.P.Pei H.P.Peng L.Peng X.Y.Peng X.j.Peng K.Peters S.Pivovarov E.Pyata B.B.Qi Y.Q.Qi W.B.Qian Y.Qian C.F.Qiao j.j.Qin j.j.Qin L.Q.Qin X.S.Qin T.L.Qiu j.Rademacker C.F.Redmer H.Y.Sang Anhui University Hefei 230039China Beihang University Beijing 100191China Budker Institute of Nuclear Physics Novosibirsk 630090Russia CAS Key Laboratory of Theoretical Physics Institute of Theoretical PhysicsChinese Academy of SciencesBeijing 100190China Cavendish Laboratory University of CambridgeJJ Thomson AveCambridge CB30HEUnited Kingdom Central China Normal University Wuhan 430079China Central South University Changsha 410083China China University of Geosciences Wuhan 430074China China University of Mining and Technology Xuzhou 221116China École Polytechnique Fédérale de Lausanne(EPFL) LausanneSwitzerland Fudan University Shanghai 200433China Goethe University Frankfurt D-60325 Frankfurt am MainGermany Guangxi Normal University Guilin 541004China Guangxi Uninversity Nanning 530004China Hangzhou Institute for Advanced Study UCASHangzhou 310024China Hebei Normal University Shijiazhuang 050024China Hebei University Baoding 071002China Hefei University of Technology Hefei 230601China Helmholtz Institute Mainz Staudinger Weg 18D-55099 MainzGermany Henan Normal University Xinxiang 453007China Henan University Kaifeng 475004China High Energy Physics Center Chung-Ang UniversitySeoul 06974Korea Higher School of Economy 11 Pokrovsky Bulvar Moscow 109028Russia Huangshan University Huangshan 245000China Hubei University of Automotive Technology Shiyan 442002China Hunan Normal University Changsha 410081China Hunan University of Science and Technology Xiangtan 411201China Hunan University Changsha 410082China Indiana University BloomingtonIndiana 47405USA Inner Mongolia University Hohhot 010021China Institute of Advanced Science Facilities Shenzhen 518107China Institute of High Energy Physics Chinese Academy of SciencesBeijing 100049China Institute of Modern Physics Chinese Academy of SciencesLanzhou 730000China Institute of Physics Academia SinicaTaipeiTaiwan 11529China Institute of Theoretical Physics Chinese Academy of SciencesBeijing 100190China j.lin University Changch

The superτ-charm facility(STCF)is an electron–positron collider proposed by the Chinese particle physics *** is designed to operate in a center-of-mass energy range from 2 to 7 GeV with a peak luminosity of 0.5×10^(35) cm^(–2)·s^(–1) or *** STCF will produce a data sample about a factor of 100 larger than that of the presentτ-charm factory—the BEPCII,providing a unique platform for exploring the asymmetry of matter-antimatter(charge-parity violation),in-depth studies of the internal structure of hadrons and the nature of non-perturbative strong interactions,as well as searching for exotic hadrons and physics beyond the Standard *** STCF proj.ct in China is under development with an extensive R&D *** document presents the physics opportunities at the STCF,describes conceptual designs of the STCF detector system,and discusses future plans for detector R&D and physics case studies.

关键词： electron–positron collider tau-charm region high luminosity STCF detector conceptual design

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创造性执行的定位与调适策略研究——基于z省Q市环境医院项目执行过程的个案分析

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中国行政管理 2024年第5期40卷 28-36页

作者：徐强吴昂中国人民大学生态环境学院北京100872 中国人民大学法学院北京100872

创造性执行是新一届政府提出的施政要求。就其本质而言,创造性执行可被视为政策执行活动的一种细分类型,创造性执行的核心要义是服务高质量发展导向下执行方式的灵活创新,以服务发展目标补充、强化、平衡、修正原政策的形式目标与实质精... 详细信息

创造性执行是新一届政府提出的施政要求。就其本质而言,创造性执行可被视为政策执行活动的一种细分类型,创造性执行的核心要义是服务高质量发展导向下执行方式的灵活创新,以服务发展目标补充、强化、平衡、修正原政策的形式目标与实质精神,追求政策执行效果的整体提升。在创造性执行中,执行主体需注意与目标群体的调适,通过多种调适策略增进目标群体的理解和接受程度。本文基于对z省Q市环境医院项目执行过程的分析,呈现了创造性执行中执行主体与目标群体的调适过程,其中既包含了与企业平等对话交流和主动服务的对话型策略,也有通过严格监管激发企业需求、借势中央生态环保督察的压力型策略。由此可知,采取多样调适策略增进目标群体的理解和接受,对推动创造性执行具有重要意义。

关键词：创造性执行政策执行互适模型调适策略

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Where Is Phase Velocity in Minkowski Space?

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j.urnal of Modern Physics 2024年第10期15卷 1555-1566页

作者： Antony j. Bourdillon Ultra-High Resolution Lithography San Jose CA USA

In the special theory of relativity, massive particles can travel at neither the speed of light c nor faster. Meanwhile, since the photon was quantized, many have thought of it as a point particle. How pointed? The idea could be a mathematical device or physical simplification. By contrast, the preceding notion of wave-group duality has two velocities: a group velocity vg and a phase velocity vp. In light vp = vg = c;but it follows from special relativity that, in massive particles, vp > c. The phase velocity is the product of the two best measured variables, and so their product constitutes internal motion that travels, verifiably, faster than light. How does vp then appear in Minkowski space? For light, the spatio-temporal Lorentz invariant metric is s2=c2t2−x2−y2−z2, the same in whatever frame it is viewed. The space is divided into 3 parts: firstly a cone, symmetric about the vertical axis ct > 0 that represents the world line of a stationary particle while the conical surface at s = 0 represents the locus for light rays that travel at the speed of light c. Since no real thing travels faster than the speed of light c, the surface is also a horizon for what can be seen by an observer starting from the origin at time t = 0. Secondly, an inverted cone represents, equivalently, time past. Thirdly, outside the cones, inaccessible space. The phase velocity vp, group velocity vg and speed of light are all equal in free space, vp = vg = c, constant. By contrast, for particles, where causality is due to particle interactions having rest mass mo > 0, we have to employ the Klein-Gordon equation with s2=c2t2−x2−y2−z2+mo2c2. Now special relativity requires a complication: *** = c2 where vg c and therefore vp > c. In the volume outside the cones, causality due to light interactions cannot extend beyond the cones. However, since vp > c and even vp >> c when wavelength λ is long, extreme phase velocities are then limited in their causal effects by the particle uncertainty σ,

关键词： Event Horizon Scattering Range Wave Packet Phase Velocity Group Velocity Dispersion Dynamics Quantum Physics

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