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An analytical study for detonation wave boundary layer interactions under reflections
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作者 Hao YAN Xin HAN +2 位作者 Haochen XIONG Chongguang SHI Yancheng YOU 《Chinese Journal of Aeronautics》 2026年第2期178-201,共24页
Numerical simulations and theoretical models are developed in this paper for the Detonation-Wave/Boundary-Layer Interactions(DWBLIs)under reflections.Transient flow fields demonstrate the highly non-stationarity of th... Numerical simulations and theoretical models are developed in this paper for the Detonation-Wave/Boundary-Layer Interactions(DWBLIs)under reflections.Transient flow fields demonstrate the highly non-stationarity of the DWBLIs when Mach Reflection(MR)occur,and subsequent analyses show that the subsonic region introduced by the boundary layer exacerbates the instability.Further quantitative analyses show that viscosity has little effect on propulsive performance and the separation wave can be considered as an oblique detonation wave.Influence parameters to DWBLIs such as combustion chamber height,incoming Mach number,equivalence ratio,and inlet channel length are categorized and studied.Besides simulations,theoretical analytical modeling is established for Regular Reflection(RR)and MR of DWBLIs.Multiple formulas for the separation zone length are obtained according to the mass conservation under different transformation type between inviscid and viscid reflections.Comparison with the numerical simulations verifies the validity of the model and it can be further generalized to the curved DWBLIs.The developed model makes the theoretical solution process of DWBLIs possible and provides the key foundation for further analysis and solution. 展开更多
关键词 Boundary layer interaction Detonation wave Hypersonic flow reflectION VISCOSITY
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On U_(S)-admitting Reflections of T_(0) Spaces
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作者 Liqun LIN Jinbo YANG 《Journal of Mathematical Research with Applications》 2025年第6期800-812,共13页
U_(S)-admitting spaces,which were introduced by Heckmann,enjoy many nice properties similar to those of the extensively studied well-filtered spaces.In this paper,we present a direct construction of the U_(S)-admittin... U_(S)-admitting spaces,which were introduced by Heckmann,enjoy many nice properties similar to those of the extensively studied well-filtered spaces.In this paper,we present a direct construction of the U_(S)-admitting reflections by using U_(S)-admitting determined sets. 展开更多
关键词 well-filtered space reflective subcategory sober space U_(S)-admitting space
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Metacognition Inspired Reflective Chain-of-Thought for Knowledge-Based VQA
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作者 Zhongfan Sun Kan Guo +1 位作者 Yongli Hu Yong Zhang 《Computers, Materials & Continua》 2026年第4期1909-1933,共25页
Knowledge-based VisualQuestion Answering(VQA)requires the integration of visual information with external knowledge reasoning.Existing approaches typically retrieve information from external corpora and rely on pretra... Knowledge-based VisualQuestion Answering(VQA)requires the integration of visual information with external knowledge reasoning.Existing approaches typically retrieve information from external corpora and rely on pretrained language models for reasoning.However,their performance is often hindered by the limited capabilities of retrievers and the constrained size of knowledge bases.Moreover,relying on image captions to bridge the modal gap between visual and language modalities can lead to the omission of critical visual details.To address these limitations,we propose the Reflective Chain-of-Thought(ReCoT)method,a simple yet effective framework inspired by metacognition theory.ReCoT effectively activates the reasoning capabilities ofMultimodal Large LanguageModels(MLLMs),providing essential visual and knowledge cues required to solve complex visual questions.It simulates a metacognitive reasoning process that encompasses monitoring,reflection,and correction.Specifically,in the initial generation stage,an MLLM produces a preliminary answer that serves as the model’s initial cognitive output.During the reflective reasoning stage,this answer is critically examined to generate a reflective rationale that integrates key visual evidence and relevant knowledge.In the final refinement stage,a smaller language model leverages this rationale to revise the initial prediction,resulting in amore accurate final answer.By harnessing the strengths ofMLLMs in visual and knowledge grounding,ReCoT enables smaller language models to reason effectively without dependence on image captions or external knowledge bases.Experimental results demonstrate that ReCoT achieves substantial performance improvements,outperforming state-of-the-art methods by 2.26%on OK-VQA and 5.8%on A-OKVQA. 展开更多
关键词 Knowledge-based VQA METACOGNITION reflective chain-of-thought answer refinement
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Heterolayered Carbonized MXene/Polyimide Aerogel for Low-Reflection Electromagnetic Interference Shielding and Multi-Spectrum Compatible Protection
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作者 Shan Zhang Chen‑Ming Liang +5 位作者 Lu Zhou Juntao Wu Martin CKoo Zongxin Wu Yun‑Tian Chen Guang‑Sheng Wang 《Nano-Micro Letters》 2026年第6期702-716,共15页
The advancement of next-generation high-frequency communication systems and stealth detection technologies necessitate the development of efficient,multi-spectrum compatible shielding materials.However,the achievement... The advancement of next-generation high-frequency communication systems and stealth detection technologies necessitate the development of efficient,multi-spectrum compatible shielding materials.However,the achievement of simultaneous high efficiency and low reflectivity across microwave,terahertz,and infrared spectra remains a formidable challenge.Herein,a carbonized MXene/polyimide(C-MXene/PI)aerogel material integrating a spatially coupled hierarchically anisotropic structure with stepwise conductivity gradients was constructed.Electromagnetic waves propagate through the top-down vertical disordered horizontal architecture and progressive conductivity gradient of C-MXene/PI aerogel,undergoing stepwise absorption-dissipation-re-dissipation processes.The C-MXene/PI aerogel exhibits an average electromagnetic interference(EMI)shielding effectiveness of91.0 dB in X-band and a reflection coefficient of 0.40.In the terahertz frequency band,the average EMI shielding performance reaches66.2 dB with a reflection coefficient of 0.33.Furthermore,the heterolayered porous architecture of C-MXene/PI aerogels exhibits low thermal conductivity and reduced infrared emissivity,enabling exceptional infrared stealth capability across the 2-16μm wavelength spectrum.This study provides an feasible strategy for constructing low-reflectivity multi-spectrum compatible shielding materials. 展开更多
关键词 Heterolayered Electromagnetic interference shielding Multi-spectrum Low reflection High efficiency
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Collaborative Assessment of Reflectivity Consistency between FY-3G Precipitation Measurement Radar and Ground-Based Radars
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作者 Chunyan ZHANG Heng HU +4 位作者 Jiashan ZHU Qinqiang ZHOU Lei WU Jianyong LI Xuan ZHU 《Advances in Atmospheric Sciences》 2026年第5期1065-1078,共14页
FY-3G is the first polar-orbiting satellite equipped with a precipitation measurement radar(PMR)operating at Ku-andKa-band frequencies in China.In this study,we compare the reflectivity data from the FY-3G PMR Ku prod... FY-3G is the first polar-orbiting satellite equipped with a precipitation measurement radar(PMR)operating at Ku-andKa-band frequencies in China.In this study,we compare the reflectivity data from the FY-3G PMR Ku product and groundbasedradars(GRs)during 2024.Also,the FY-3G PMR is used as a third-party reference to evaluate the reflectivityconsistency among different GRs.The FY-3G PMR and GRs share similarities in their general distribution,characteristics,and intensity of reflectivity in strong precipitation cloud systems,though the former presents less detailed system structure.Systematic deviations between the FY-3G PMR and GRs and between GRs are comparable,albeit the reflectivity of the FY-3G PMR is generally slightly stronger than that of GRs(especially X-band GRs),with a mean bias ranging from 0.7 to 1.7dB.S-band GRs exhibit the smallest systematic deviation(STD=3.09 dB)from the FY-3G PMR,whereas the X-band GRsshow the largest(STD=3.61 dB),indirectly indicating the highest internal consistency among S-band GRs and the lowestamong X-band GRs.Besides,both S-and C-band GRs display similar deviations when paired with the FY-3G PMR as wellas when paired with their adjacent S/C-band GRs,suggesting good consistency between these two bands.In contrast,XbandGRs exhibit relatively poor consistency with S-band GRs and the FY-3G PMR,showing a deviation ranging from 3.0to 4.6 dB. 展开更多
关键词 reflectIVITY deviation CONSISTENCY FY-3G PMR ground-based radars
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A conceptual analysis of reflective supervision for creating a positive intensive care practice environment
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作者 Mpho Grace Chipu 《International Journal of Nursing Sciences》 2026年第1期88-95,共8页
Objectives This study aimed to explore and clarify the concept of reflective supervision as a professional self-care strategy to create a positive Intensive Care Unit(ICU)practice environment.Methods Walker and Avant... Objectives This study aimed to explore and clarify the concept of reflective supervision as a professional self-care strategy to create a positive Intensive Care Unit(ICU)practice environment.Methods Walker and Avant’s eight-step concept analysis approach was utilized to identify and define the attributes,antecedents,and consequences of reflective supervision in the ICU.An extensive literature search was conducted across various databases,including Google Scholar,CINAHL,PubMed.Articles published from 2005 to 2025 were identified.We followed the Preferred Reporting Items for Systematic Reviews and Meta-Analyses(PRISMA)2020 statement to indicate the included articles and extract related data based on relevance.Results Forty articles were included in the analysis.The identified attributes included the supervisor-supervisee relationship,effective communication,teamwork,collaborations,reflection,competencies,feedback,continuous support,and autonomous choice.The identified antecedents included participation,supportive supervision,flexibility,open-door policy,training,and motivation.Consequences impacting the success of reflective supervision were identified as promotion of resiliency,autonomy,work-life balance,self-awareness,increased self-esteem,professional development,critical thinking,increased job satisfaction,and enhanced commitment.Conclusions Reflective supervision is a complex professional self-care strategy that enhances ICU practice,by promoting nurses’well-being,self-awareness,therapeutic skills,and professional development. 展开更多
关键词 Concept analysis Intensive Care Unit NURSING Positive environment reflective supervision
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Quantifying the impact of dust retention on maize canopy spectral reflectance and vegetation indices in dust belt regions:A case study in southern Xinjiang,China
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作者 MA Baodong GAO Shuxian +2 位作者 KANG Ting CHE Defu SHU Yang 《Journal of Arid Land》 2026年第1期101-130,共30页
Sand dust belts span approximately one-fifth of the global land surface.In these regions,dust tends to settle on vegetation surfaces,altering the observed reflectance and affecting remote sensing detections.To enhance... Sand dust belts span approximately one-fifth of the global land surface.In these regions,dust tends to settle on vegetation surfaces,altering the observed reflectance and affecting remote sensing detections.To enhance the accuracy of maize growth monitoring in dust-affected regions,this study aims to quantify the effect of sand dust retention on maize during the tasseling stage in the Kashgar Prefecture,Xinjiang Uygur Autonomous Region,China,by analyzing changes in canopy reflectance and vegetation indices.First,field sampling was conducted to measure the key canopy structure parameters and dust retention levels of maize,and laboratory spectral measurements were performed on leaf spectral properties under gradient dust retention.The measured data were then used to drive the LargE-Scale remote sensing data and image Simulation framework(LESS)model for simulating realistic maize canopy spectra across different dust levels,with validation against Sentinel-2 imagery.Second,on the basis of the simulated and satellite-derived spectra,the dust resistance of 36 common vegetation indices was systematically evaluated,and new robust dust-resistant indices were developed.The results showed that compared with dust-free maize,the canopy reflectance of dust-retained maize followed an increase–decrease–increase pattern,with critical turning points at 735 and 1325 nm.The maximum reflectance difference of–0.11755(change rate:29.002%)occurred within the 735–1325 nm range at 24 g/m^(2)dust retention,and the minimum reflectance difference of 0.04285(change rate:148.950%)was observed in the 350–735 nm range under the same dust retention level.Among the 36 vegetation indices,only the global environment monitoring index(GEMI)and the ratio of transformed chlorophyll absorption in reflectance index to optimized soil-adjusted vegetation index(TCARI/OSAVI)exhibited dust resistance,with GEMI being effective below 6 g/m^(2)and TCARI/OSAVI remaining stable across all levels(average ratio:0.970).The newly developed indices in this study,(RE3–RE2)/(NIR–RE2),(RE3–RE2)/(RE4–RE2),and(NIR–RE2)/(RE4–RE2),retained values within the predefined dust-resistant range over the full dust retention levels of 0–24 g/m^(2),thus showing a more stable dust resistance compared with the commonly used 36 vegetation indices.Specially,(RE3–RE2)/(RE4–RE2)performed the most robustly in Sentinel-2 imagery,that is,58.020%of pixels were within the dust-resistant range,and an average ratio of 0.937 was obtained for the original-spectra index.This study provides a scientific basis for crop monitoring and management in dust-affected regions. 展开更多
关键词 sand dust retention canopy spectral reflectance LargE-Scale remote sensing data and image Simulation framework(LESS)model dust-resistant vegetation indices tasseling-stage maize Sentinel-2 imagery
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Reflections on Non-English Major Postgraduate English Teaching Reform 被引量:2
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作者 郁仲莉 《Sino-US English Teaching》 2006年第8期12-15,31,共5页
This paper presents some reflections on non-English major postgraduate English teaching reform. The author points out some understandings on the English proficiency of non-English major postgraduate students and curri... This paper presents some reflections on non-English major postgraduate English teaching reform. The author points out some understandings on the English proficiency of non-English major postgraduate students and curriculum changes in the reform. The author thinks that postgraduate English teaching reform is a systematic project, with a goal to meet the practical needs of postgraduate students and improve their ability to use English in their study and work. Hence, every effort of the reform should be made to satisfy the practical needs of the students and to make their English study contribute to their achievements in their own subject area. 展开更多
关键词 reflectION non-English major postgraduate English teaching reform
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Reflections on Communicative Language Teaching Approach Based on Observation of Management Course
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作者 侯香勤 《大学英语教学与研究》 2014年第3期11-13,共3页
Communicative language teaching approach is effective in cultivating students' communicative competence. It has changed the way of teaching as well as learning. This paper, based on class observation of one semest... Communicative language teaching approach is effective in cultivating students' communicative competence. It has changed the way of teaching as well as learning. This paper, based on class observation of one semester's "management"course,reflects on the teaching approach employed by the teacher, discusses its benefits and problems within the class, and explores the underlying principles of the approach adopted. 展开更多
关键词 大学 英语学习 学习方法 阅读知识 阅读材料
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Reflections on Humanity from the Modern Vampirism 被引量:1
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作者 张志国 《海外英语》 2011年第10X期308-309,共2页
Vampirism is a very popular theme in modern novels, movies or other forms of literature genres. This paper tries to explore the development of vampirism literatures and by doing so makes some deep reflections on human... Vampirism is a very popular theme in modern novels, movies or other forms of literature genres. This paper tries to explore the development of vampirism literatures and by doing so makes some deep reflections on humanity from the modern vampirism. 展开更多
关键词 HUMANITY Vampirism reflections
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High-accuracy self-mixing interferometer based on multiple reflections using a simple external reflecting mirror 被引量:2
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作者 WANG Xiu-lin1 WEI Zheng2 +1 位作者 WANG Rui2 HUANG Wen-cai2 《Optoelectronics Letters》 EI 2018年第3期161-163,共3页
A self-mixing interferometer(SMI)with resolution twenty times higher than that of a conventional interferometer is developed by multiple reflections.Only by employing a simple external reflecting mirror,the multiple-p... A self-mixing interferometer(SMI)with resolution twenty times higher than that of a conventional interferometer is developed by multiple reflections.Only by employing a simple external reflecting mirror,the multiple-pass optical configuration can be constructed.The advantage of the configuration is simple and easy to make the light re-injected back into the laser cavity.Theoretical analysis shows that the resolution of measurement is scalable by adjusting the number of reflections.The experiment shows that the proposed method has the optical resolution of approximateλ/40.The influence of displacement sensitivity gain(G)is further analyzed and discussed in practical experiments. 展开更多
关键词 HIGH-ACCURACY SELF-MIXING INTERFEROMETER mul-Liple reflections
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A Free Surface Frequency Domain Green Function with Viscous Dissipation and Partial Reflections from Side Walls 被引量:3
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作者 Hongde Qin Jing Shen Xiaobo Chen 《Journal of Marine Science and Application》 2011年第3期259-264,共6页
The free-surface Green function method is widely used in solving the radiation or diffraction problems caused by a ship or ocean structure oscillating on the waves. In the context of inviscid potential flow, hydrodyna... The free-surface Green function method is widely used in solving the radiation or diffraction problems caused by a ship or ocean structure oscillating on the waves. In the context of inviscid potential flow, hydrodynamic problems such as multi-body interaction and tank side wall effect cannot be properly dealt with based on the traditional free-surface frequency domain Green function method, in which the water viscosity is omitted and the energy dissipation effect is absent. In this paper, an open-sea Green function with viscous dissipation was presented within the theory ofvisco-potential flow. Then the tank Green function with a partial reflection from the side walls in wave tanks was formulated as a formal sum of open-sea Green functions representing the infinite images between two parallel side walls of the source in the tank. The new far-field characteristics of the tank Green function is vitally important fur improving the validity of side-wall effects evaluation, which can be used in supervising the tank model tests. 展开更多
关键词 Green function viscous dissipation side wall effect partial reflection
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Reflections on Tools and Methods for Differentiated Assessments of Individual Scientists, Groups of Scientists and Scientific Journals 被引量:2
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作者 Ronald Rousseau Xiaolin Zhang 《Journal of Data and Information Science》 CSCD 2019年第3期1-5,共5页
Requirements for research assessments There are huge differences in mission, emphasis, inherent capability, and targeted utilization of research among scientific institutions. Hence, when it comes to assessments, a on... Requirements for research assessments There are huge differences in mission, emphasis, inherent capability, and targeted utilization of research among scientific institutions. Hence, when it comes to assessments, a one-size-fits-all approach cannot meet the goal(s) of these assessments. Probably even larger differences exist between individuals, research teams and departments. 展开更多
关键词 reflections TOOLS and METHODS DIFFERENTIATED Assessments of INDIVIDUAL Scientists
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Characteristics of seismic reflections in central region of the South China Sea and their geological significance 被引量:1
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作者 刘建华 金翔龙 《Acta Oceanologica Sinica》 SCIE CAS CSCD 2000年第3期103-113,共11页
More than 4 000 km 48-channel seismic reflection data from the central region of the South China Sea have been interpreted. Five seismic interfaces have been distinguished, named T1, T2, T4, T6 and Tg respectively Mea... More than 4 000 km 48-channel seismic reflection data from the central region of the South China Sea have been interpreted. Five seismic interfaces have been distinguished, named T1, T2, T4, T6 and Tg respectively Meanwhile, five seismic sequences numbered I - V have been divided with the ages of Quaternary and Pliocene, Later Mocene, Earlier and Middle Miocene, Oligocene and Pre- Oligocene separately. Sequences I-II overlie all parts of the area. In the continental slope and island slope, Sequences III-V are mainly found in the grabens. Sequence III is found at moot profiles of the deep-sea basin, and Sequnce IV is seen not only at the margins of the east subbasin but also at the margins of the southwest subbasin. Strong reflection from Moho is found at most profiles of the deep-sea basin. The depth of Moho varies between 10 and 12 km, with a thickness of 6- 8 km for the crust. Calculated by age-basement depth correlation formula, the age of basaltic basement in the southwest subbasin is 51-39 Ma. It is indicated that the evolution of the southwest subbasin is simultaneous with or earlier than that of the east subbasin. 展开更多
关键词 Central region of the South China Sea seismic reflection evolution of the back-arc basin
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The influence of reflections from the train body and the ground on the sound radiation from a railway rail 被引量:1
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作者 David J.Thompson Dong Zhao +3 位作者 Evangelos Ntotsios Giacomo Squicciarini Ester Cierco Erwin Jansen 《Railway Sciences》 2024年第1期1-17,共17页
Purpose – The vibration of the rails is a significant source of railway rolling noise, often forming the dominantcomponent of noise in the important frequency region between 400 and 2000 Hz. The purpose of the paper ... Purpose – The vibration of the rails is a significant source of railway rolling noise, often forming the dominantcomponent of noise in the important frequency region between 400 and 2000 Hz. The purpose of the paper is toinvestigate the influence of the ground profile and the presence of the train body on the sound radiation fromthe rail.Design/methodology/approach – Two-dimensional boundary element calculations are used, in which therail vibration is the source. The ground profile and various different shapes of train body are introduced in themodel, and results are observed in terms of sound power and sound pressure. Comparisons are also made withvibro-acoustic measurements performed with and without a train present.Findings – The sound radiated by the rail in the absence of the train body is strongly attenuated by shieldingdue to the ballast shoulder. When the train body is present, the sound from the vertical rail motion is reflectedback down toward the track where it is partly absorbed by the ballast. Nevertheless, the sound pressure at thetrackside is increased by typically 0–5 dB. For the lateral vibration of the rail, the effects are much smaller. Oncethe sound power is known, the sound pressure with the train present can be approximated reasonably well withsimple line source directivities.Originality/value – Numerical models used to predict the sound radiation from railway rails have generallyneglected the influence of the ground profile and reflections from the underside of the train body on the soundpower and directivity of the rail. These effects are studied in a systematic way including comparisons with measurements. 展开更多
关键词 Rolling noise Sound radiation Railway track Boundary elements Ground reflections DIRECTIVITY
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Reflections on the Criticisms of Mainstream Linguistics
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作者 邵嘉 《海外英语》 2010年第9X期268-269,共2页
In this paper,the author starts with a discussion of what mainstream linguistics is,in aim of clearly defining mainstream linguistics.Then the author further makes a distinction and comparison between mainstream lingu... In this paper,the author starts with a discussion of what mainstream linguistics is,in aim of clearly defining mainstream linguistics.Then the author further makes a distinction and comparison between mainstream linguistics and non-mainstream linguistics.In the third part of the paper,the author probes into and reflects on the main criticisms of mainstream linguistics. 展开更多
关键词 MAINSTREAM LINGUISTICS reflectION
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Conversion hip arthroplasty for failed nailing of intertrochanteric fracture: Reflections on some important aspects 被引量:1
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作者 Fu-Chun Yang 《World Journal of Orthopedics》 2024年第10期997-1000,共4页
In this editorial,I present my comments on the article by Solarino et al.Conversion hip arthroplasty,which is an optional salvage procedure performed following unsuccessful fixation of intertrochanteric femur fracture... In this editorial,I present my comments on the article by Solarino et al.Conversion hip arthroplasty,which is an optional salvage procedure performed following unsuccessful fixation of intertrochanteric femur fractures in elderly pati-ents,entails more complex processes and higher rates of operative complications than primary arthroplasty.Hence,it is important to consider the appropriateness of the primary treatment choice,as well as the adequacy of nailing fixation for intertrochanteric fractures.This article briefly analyzes the possible factors contributing to the nailing failure of intertrochanteric fractures and attempts to find corresponding countermeasures to prevent fixation failures.It also analyzes the choice of treatment between nailing fixation and primary arthroplasty for intertrochanteric fractures. 展开更多
关键词 Intertrochanteric femur fracture Femoral nailing fixation Primary hip arthroplasty Conversion hip arthroplasty Failed internal fixation Treatment reflection
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ELECTROMAGNETIC WAVE PROPAGATION IN MAGNETIC MULTILAYERS-NON-RECIPROCAL REFLECTIONS'
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作者 李义兵 《Journal of Electronics(China)》 1994年第4期315-321,共7页
A theory of EM wave propagation through magnetic multilayers and superlattices is presented based on the propagation matrix of a magnetic film. By using the P matrix, the transmission and reflection coefficients of la... A theory of EM wave propagation through magnetic multilayers and superlattices is presented based on the propagation matrix of a magnetic film. By using the P matrix, the transmission and reflection coefficients of layered magnetic media, including: (l)semi-infinite magnetic surfaces, (2) magnetic multilayers, (3) semi-infinite magnetic superlattices are obtained. The numerical results show that the EM modes of a magnetic layer system is excited and manifested as the sharp dips in the S-polarized reflection and the dispersion curves of the magnetic polaritons can be measured by a method similar to the attenuated total reflection (ATR) technique. 展开更多
关键词 Electromagnetic wave propagation MAGNETIC MULTILAYERS EM transmission and reflectION LAYERED media MAGNETIC POLARITONS
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Collisions, or Reflections and Rotations, Leading to the Digits of π
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作者 Franç ois Dubeau 《Applied Mathematics》 2022年第9期705-732,共28页
We analyze a problem of elastic collisions between elements of a system composed of two balls and a wall. Thanks to a change of variables, the problem is reduced to a sequence of reflections and rotations. Moreover, t... We analyze a problem of elastic collisions between elements of a system composed of two balls and a wall. Thanks to a change of variables, the problem is reduced to a sequence of reflections and rotations. Moreover, the total number of collisions is easily found. For specific ratios of ball weights, the number of collisions is related to the first successive digits of π. 展开更多
关键词 Dynamical System Elastic Collisions reflection Rotation Digits of π
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Projections and Reflections in Vector Space
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作者 Kung-Kuen Tse 《Advances in Pure Mathematics》 2016年第6期436-440,共5页
We study projections onto a subspace and reflections with respect to a subspace in an arbitrary vector space with an inner product. We give necessary and sufficient conditions for two such transformations to commute. ... We study projections onto a subspace and reflections with respect to a subspace in an arbitrary vector space with an inner product. We give necessary and sufficient conditions for two such transformations to commute. We then generalize the result to affine subspaces and transformations. 展开更多
关键词 PROJECTION reflectION Commute Inner Product Affine Subspace
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