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WEIGHTED CONE-VOLUME MEASURES OF PSEUDO-CONES
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作者 Rolf SCHNEIDER 《Acta Mathematica Scientia》 2025年第1期40-51,共12页
A pseudo-cone in ℝ^(n) is a nonempty closed convex set K not containing the origin and such thatλK⊆K for allλ≥1.It is called a C-pseudo-cone if C is its recession cone,where C is a pointed closed convex cone with i... A pseudo-cone in ℝ^(n) is a nonempty closed convex set K not containing the origin and such thatλK⊆K for allλ≥1.It is called a C-pseudo-cone if C is its recession cone,where C is a pointed closed convex cone with interior points.The cone-volume measure of a pseudo-cone can be defined similarly as for convex bodies,but it may be infinite.After proving a necessary condition for cone-volume measures of C-pseudo-cones,we introduce suitable weights for cone-volume measures,yielding finite measures.Then we provide a necessary and sufficient condition for a Borel measure on the unit sphere to be the weighted cone-volume measure of some C-pseudo-cone. 展开更多
关键词 pseudo-cone surface area measure cone-volume measure weighting Minkowski type problem
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RECONSTRUCTION PROBLEMS OF CONVEX BODIES FROM EVEN L_(p)SURFACE AREA MEASURES
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作者 Juewei HU Gangsong LENG 《Acta Mathematica Scientia》 2025年第1期126-142,共17页
We build a computer program to reconstruct convex bodies using even L_(p)surface area measures for p≥1.Firstly,we transform the minimization problem Pi,which is equivalent to solving the even L_(p)Minkowski problem,i... We build a computer program to reconstruct convex bodies using even L_(p)surface area measures for p≥1.Firstly,we transform the minimization problem Pi,which is equivalent to solving the even L_(p)Minkowski problem,into a convex optimization problem P4 with a finite number of constraints.This transformation makes it suitable for computational resolution.Then,we prove that the approximate solutions obtained by solving the problem P4 converge to the theoretical solution when N and k are sufficiently large.Finally,based on the convex optimization problem P_(4),we provide an algorithm for reconstructing convex bodies from even L_(p)surface area measures,and present several examples implemented using MATLAB. 展开更多
关键词 reconstruction problem even L_(p)surface area measures spherical harmonic
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HealthMeasures患者报告结局报告清单的解读
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作者 臧娴 宗旭倩 +4 位作者 袁长蓉 王玲 吴傅蕾 张雯 黄青梅 《护士进修杂志》 2024年第10期1088-1092,共5页
美国匹兹堡大学和HealthMeasures指导委员会及PROMIS健康组织标准委员会共同发表了HealthMeasures患者报告结局报告清单,旨在促进不同患者报告结局测量工具的标准化报告,帮助研究人员提高工具报告质量及结果解释的准确性,进一步改善跨... 美国匹兹堡大学和HealthMeasures指导委员会及PROMIS健康组织标准委员会共同发表了HealthMeasures患者报告结局报告清单,旨在促进不同患者报告结局测量工具的标准化报告,帮助研究人员提高工具报告质量及结果解释的准确性,进一步改善跨研究间的比较分析。本文对HealthMeasures患者报告结局报告清单的主要内容进行介绍和解读,以期为中国患者报告结局研究者提供参考和借鉴。 展开更多
关键词 患者报告结局 报告清单 测量工具 标准化 解读
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Whole petroleum system in Jurassic coal measures of Taibei Sag in Tuha Basin,NW China
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作者 ZHI Dongming LI Jianzhong +6 位作者 YANG Fan CHEN Xuan WU Chao WANG Bo ZHANG Hua HU Jun JIN Jikun 《Petroleum Exploration and Development》 SCIE 2024年第3期519-534,共16页
Based on the latest results of near-source exploration in the Middle and Lower Jurassic of the Tuha Basin,a new understanding of the source rocks,reservoir conditions,and source-reservoir-cap rock combinations of the ... Based on the latest results of near-source exploration in the Middle and Lower Jurassic of the Tuha Basin,a new understanding of the source rocks,reservoir conditions,and source-reservoir-cap rock combinations of the Jurassic Shuixigou Group in the Taibei Sag is established using the concept of the whole petroleum system,and the coal-measure whole petroleum system is analyzed thoroughly.The results are obtained in three aspects.First,the coal-measure source rocks of the Badaowan Formation and Xishanyao Formation and the argillaceous source rocks of the Sangonghe Formation in the Shuixigou Group exhibit the characteristics of long-term hydrocarbon generation,multiple hydrocarbon generation peaks,and simultaneous oil and gas generation,providing sufficient oil and gas sources for the whole petroleum system in the Jurassic coal-bearing basin.Second,multi-phase shallow braided river delta–shallow lacustrine deposits contribute multiple types of reservoirs,e.g.sandstone,tight sandstone,shale and coal rock,in slope and depression areas,providing effective storage space for the petroleum reservoir formation in coal-measure strata.Third,three phases of hydrocarbon charging and structural evolution,as well as effective configuration of multiple types of reservoirs,result in the sequential accumulation of conventional-unconventional hydrocarbons.From high structural positions to depression,there are conventional structural and structural-lithological reservoirs far from the source,low-saturation structural-lithological reservoirs near the source,and tight sandstone gas,coal rock gas and shale oil accumulations within the source.Typically,the tight sandstone gas and coal rock gas are the key options for further exploration,and the shale oil and gas in the depression area is worth of more attention.The new understanding of the whole petroleum system in the coal measures could further enrich and improve the geological theory of the whole petroleum system,and provide new ideas for the overall exploration of oil and gas resources in the Tuha Basin. 展开更多
关键词 Tuha Basin Taibei Sag Middle and Lower Jurassic whole petroleum system coal measure tight oil and gas coal rock gas shale oil
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Measurement of emissivity with a new grey body and novel IR thermal sensor dubbed TMOS
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作者 Moshe Avraham Shlomi Bouscher +2 位作者 Jonathan Nemirovsky Yael Nemirovsky 《红外与毫米波学报》 北大核心 2025年第1期17-24,共8页
The concept of emissivity has been with the scientific and engineering world since Planck formulated his blackbody radiation law more than a century ago.Nevertheless,emissivity is an elusive concept even for ex⁃perts.... The concept of emissivity has been with the scientific and engineering world since Planck formulated his blackbody radiation law more than a century ago.Nevertheless,emissivity is an elusive concept even for ex⁃perts.It is a vague and fuzzy concept for the wider community of engineers.The importance of remote sensing of temperature by measuring IR radiation has been recognized in a wide range of industrial,medical,and environ⁃mental uses.One of the major sources of errors in IR radiometry is the emissivity of the surface being measured.In real experiments,emissivity may be influenced by many factors:surface texture,spectral properties,oxida⁃tion,and aging of surfaces.While commercial blackbodies are prevalent,the much-needed grey bodies with a known emissivity,are unavailable.This study describes how to achieve a calibrated and stable emissivity with a blackbody,a perforated screen,and a reliable and linear novel IR thermal sensor,18 dubbed TMOS.The Digital TMOS is now a low-cost commercial product,it requires low power,and it has a small form factor.The method⁃ology is based on two-color measurements,with two different optical filters,with selected wavelengths conform⁃ing to the grey body definition of the use case under study.With a photochemically etched perforated screen,the effective emissivity of the screen is simply the hole density area of the surface area that emits according to the blackbody temperature radiation.The concept is illustrated with ray tracing simulations,which demonstrate the approach.Measured results are reported. 展开更多
关键词 BLACKBODY grey body graybody cavity blackbody extended area blackbody EMISSIVITY IR thermometry remote temperature measurement
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A pure quantum secret sharing scheme based on GHZ basis measurement and quantum entanglement exchange
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作者 Bai Liu Jun Zhang +1 位作者 Shupin Qiu Mingwu Zhang 《Chinese Physics B》 2025年第3期95-102,共8页
At present,most quantum secret sharing(QSS)protocols are more or less designed with the incorporation of classical secret sharing schemes.With the increasing maturity of quantum technology,QSS protocols based on pure ... At present,most quantum secret sharing(QSS)protocols are more or less designed with the incorporation of classical secret sharing schemes.With the increasing maturity of quantum technology,QSS protocols based on pure quantum mechanics are becoming more important.Classical secret sharing schemes cannot achieve absolute security,and their involvement can compromise the security of QSS protocols.This paper proposes a QSS scheme based on Greenberger-Horn-Zeilinger(GHZ)basis measurement and quantum entanglement exchange.In this protocol,the secret sender stores the secret information using Pauli operations.Participants obtain their shares by measuring the product state sequentially.Finally,participants complete the secret reconstruction through quantum entanglement exchange and other related quantum operations.In addition,the particles held by participants in the protocol do not contain any secret information.Each participant's particles are in a state of maximum entanglement,and no participant can deduce the particle information of other participants through their own particles.At the same time,the protocol is based on pure quantum mechanics and does not involve classical schemes,which avoids the problem of reduced security of the protocol.Security analysis indicates that the protocol is not vulnerable to retransmission interception and collusion attacks.Moreover,it is capable of detecting and terminating the protocol promptly when facing with attacks from dishonest participants. 展开更多
关键词 quantum secret sharing projection measurement quantum entanglement exchange THRESHOLD
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Measurement and Analysis of Radar-Cross-Section of UAV at 21-26 GHz Frequency Band
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作者 AN Hao LIU Ting +2 位作者 HE Danping MA Yihua DOU Jianwu 《ZTE Communications》 2025年第1期107-114,共8页
With the emergence of the 6G technology,integrated sensing and communication(ISAC)has become a hot-spot vertical application.The low-altitude scenario is considered to be a significant use case of the ISAC.However,the... With the emergence of the 6G technology,integrated sensing and communication(ISAC)has become a hot-spot vertical application.The low-altitude scenario is considered to be a significant use case of the ISAC.However,the existing channel model is hard to meet the demands of the sensing function.The radar-cross-section(RCS)is a critical feature for the sensing part,while accurate RCS data for the typical frequency band of ISAC are still lacking.Therefore,this paper conducts measurements and analysis of the RCS data of the unmanned aerial vehicles(UAVs)under multiple poses and angles in real flying conditions.The echo from a UAV is acquired in an anechoic chamber,and the RCS values are calculated.The results of different flying attitudes are analyzed,providing RCS features for the ISAC applications. 展开更多
关键词 unmanned aerial vehicle radar-cross-section integrated sensing and communication anechoic chamber measurement
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MODIFIED BRASCAMP-LIEB INEQUALITIES AND LOG-SOBOLEV INEQUALITIES FOR ONE-DIMENSIONAL LOG-CONCAVE MEASURE
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作者 Denghui WU Jiazu ZHOU 《Acta Mathematica Scientia》 2025年第1期104-117,共14页
In this paper,we develop Maurey’s and Bobkov-Ledoux’s methods to prove modified Brascamp-Lieb inequalities and log-Sobolev inequalities for one-dimensional log-concave measure.To prove these inequalities,the harmoni... In this paper,we develop Maurey’s and Bobkov-Ledoux’s methods to prove modified Brascamp-Lieb inequalities and log-Sobolev inequalities for one-dimensional log-concave measure.To prove these inequalities,the harmonic Prékopa-Leindler inequality is used.We prove that these new inequalities are more efficient in estimating the variance and entropy for some functions with exponential terms. 展开更多
关键词 Brunn-Minkowski inequality Prékopa-Leindler inequality Brascamp-Lieb inequality log-Sobolev inequality log-concave measure
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Precision storage lifetime measurements of highly charged heavy ions in the CSRe storage ring using a Schottky resonator
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作者 Qian Wang Xin-Liang Yan +13 位作者 Guang-Yu Zhu Shahab Sanjari Li-Jun Mao He Zhao Yuri ALitvinov Rui-Jiu Chen Meng Wang Yu-Hu Zhang You-Jin Yuan Jun-Xia Wu Hong-Yang Jiao Yue Yu Zu-Yi Chen Yin-Fang Luo 《Nuclear Science and Techniques》 2025年第1期150-160,共11页
Schottky mass spectrometry utilizing heavy-ion storage rings is a powerful technique for the precise mass and decay half-life measurements of highly charged ions.Owing to the nondestructive ion detection features of S... Schottky mass spectrometry utilizing heavy-ion storage rings is a powerful technique for the precise mass and decay half-life measurements of highly charged ions.Owing to the nondestructive ion detection features of Schottky noise detectors,the number of stored ions in the ring is determined by the peak area in the measured revolution frequency spectrum.Because of their intrinsic amplitude-frequency characteristic(AFC),Schottky detector systems exhibit varying sensitivities at different frequencies.Using low-energy electron-cooled stored ions,a new method is developed to calibrate the AFC curve of the Schottky detector system of the Experimental Cooler Storage Ring(CSRe)storage ring located in Lanzhou,China.Using the amplitude-calibrated frequency spectrum,a notable refinement was observed in the precision of both the peak position and peak area.As a result,the storage lifetimes of the electron-cooled fully ionized^(56)Fe^(26+)ions were determined with high precision at beam energies of 13.7 and 116.4 MeV/u,despite of frequency drifts during the experiment.When electron cooling was turned off,the effective vacuum condition experienced by the 116.4 MeV/u^(56)Fe^(26+)ions was determined using amplitude-calibrated spectra,revealing a value of 2×10^(−10)mbar,which is consistent with vacuum gauge readings along the CSRe ring.The method reported herein will be adapted for the next-generation storage ring of the HIAF facility under construction in Huizhou,China.It can also be adapted to other storage ring facilities worldwide to improve precision and enhance lifetime measurements using many ions in the ring. 展开更多
关键词 Lifetime measurement Schottky mass spectrometry Sensitivity response Highly charged heavy ion RESONATOR UH vacuum Nondestructive diagnostics
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Causes of Mistranslation in English and the Remedial Measures 被引量:1
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作者 翟艳 《海外英语》 2014年第9X期156-157,169,共3页
Mistranslation is a very common phenomenon in the process of English translation.Some translations seem right but actually wrong.It is said that to the Chinese they are right but to the foreigners they do not conform ... Mistranslation is a very common phenomenon in the process of English translation.Some translations seem right but actually wrong.It is said that to the Chinese they are right but to the foreigners they do not conform to their customs.Mistranslation may appear in many fields and the causes of mistranslation are also various.This paper takes some examples of mistranslation in technology and tourism English.It also analyses the causes of mistranslation in English through examples.Finally,the corresponding remedial measures are followed. 展开更多
关键词 TRANSLATION MISTRANSLATION remedial measures
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Current Situation of University Bilingual Teaching and Countermeasures Analysis
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作者 姜有为 《海外英语》 2012年第21期263-265,共3页
The development of education in China has become increasingly international.Therefore,carrying out bilingual teach ing in Universities is of great significance to cultivating international talents.However,the current ... The development of education in China has become increasingly international.Therefore,carrying out bilingual teach ing in Universities is of great significance to cultivating international talents.However,the current bilingual teaching in Universi ties of our country is not optimistic,facing many difficulties and challenges.In order to provide students with advanced interna tional and dynamic culture,educators should continue to explore research and analyze bilingual teaching rationally and work out effective measures. 展开更多
关键词 BILINGUAL TEACHING measurE UNIVERSITY
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Consolidating the Bilingual Education in the Major of Finance:Existing Defects and Corrective Measures
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作者 毛蓓蓓 《海外英语》 2013年第15期279-280,共2页
Under the trend of globalization and international financial integration,Chinese scholars have argued that executing bilingual education in the major of finance is necessary to advance the comprehensive quality and co... Under the trend of globalization and international financial integration,Chinese scholars have argued that executing bilingual education in the major of finance is necessary to advance the comprehensive quality and competitive ability of college students.However,universities attempting to implement bilingual education are procrastinated with many obstacles.To resolve this issue,corrective measures are to be given in the aspects of textbook publishing,professor training and curriculum adjustments. 展开更多
关键词 BILINGUAL education FINANCE CORRECTIVE measures
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WEIGHTED ESTIMATES FOR COMMUTATORS OF MULTILINEAR CALDERóN-ZYGMUND OPERATORS WITH NON-DOUBLING MEASURES 被引量:9
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作者 林海波 孟岩 杨大春 《Acta Mathematica Scientia》 SCIE CSCD 2010年第1期1-18,共18页
Let μ be a nonnegative Radon measure on Rd, which only satisfies the polynomial growth condition. Under this assumption, the authors obtain some weighted weaktype estimates for the commutators generated by the multil... Let μ be a nonnegative Radon measure on Rd, which only satisfies the polynomial growth condition. Under this assumption, the authors obtain some weighted weaktype estimates for the commutators generated by the multilinear CalderSn-Zygmund op- erators and RBMO(μ) functions. 展开更多
关键词 non-doubling measure COMMUTATOR multilinear Calderon-Zygmund opera-tor RBMO(μ) weight
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Green,Sustainable Architectural Bamboo with High Light Transmission and Excellent Electromagnetic Shielding as a Candidate for Energy-Saving Buildings 被引量:7
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作者 Jing Wang Xinyu Wu +5 位作者 Yajing Wang Weiying Zhao Yue Zhao Ming Zhou Yan Wu Guangbin Ji 《Nano-Micro Letters》 SCIE EI CAS CSCD 2023年第1期209-224,共16页
Currently,light-transmitting,energy-saving,and electromagnetic shielding materials are essential for reducing indoor energy consumption and improving the electromagnetic environment.Here,we developed a cellulose compo... Currently,light-transmitting,energy-saving,and electromagnetic shielding materials are essential for reducing indoor energy consumption and improving the electromagnetic environment.Here,we developed a cellulose composite with excellent optical transmittance that retained the natural shape and fiber structure of bamboo.The modified whole bamboo possessed an impressive optical transmittance of approximately 60%at 6.23 mm,illuminance of 1000 luminance(lux),water absorption stability(mass change rate less than 4%),longitudinal tensile strength(46.40 MPa),and surface properties(80.2 HD).These were attributed to not only the retention of the natural circular hollow structure of the bamboo rod on the macro,but also the complete bamboo fiber skeleton template impregnated with UV resin on the micro.Moreover,a multilayered device consisting of translucent whole bamboo,transparent bamboo sheets,and electromagnetic shielding film exhibited remarkable heat insulation and heat preservation performance as well as an electromagnetic shielding performance of 46.3 dB.The impressive optical transmittance,mechanical properties,thermal performance,and electromagnetic shielding abilities combined with the renewable and sustainable nature,as well as the fast and efficient manufacturing process,make this bamboo composite material suitable for effective application in transparent,energy-saving,and electromagnetic shielding buildings. 展开更多
关键词 Electromagnetic interference shielding Biomass material TRANSMITTANCE energy-saving BAMBOO
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On Similarity Measures and Distance Measures of Fuzzy Soft Sets 被引量:3
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作者 刘雅雅 秦克云 王玲 《Chinese Quarterly Journal of Mathematics》 2015年第3期349-357,共9页
In this paper we introduce several new similarity measures and distance measures between fuzzy soft sets, these measures are examined based on the set-theoretic approach and the matching function. Comparative studies ... In this paper we introduce several new similarity measures and distance measures between fuzzy soft sets, these measures are examined based on the set-theoretic approach and the matching function. Comparative studies of these measures are derived. By introducing two general formulas, we propose a new method to define the similarity measures and the distance measures between two fuzzy soft sets with different parameter sets. 展开更多
关键词 FUZZY SOFT SET SIMILARITY measurE DISTANCE measurE
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Mechanisms of support failure and prevention measures under double-layer room mining gobs——A case study: Shigetai coal mine 被引量:4
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作者 Defu Zhu Shihao Tu +1 位作者 Hongsheng Tu Zhenqian Yang 《International Journal of Mining Science and Technology》 SCIE EI CSCD 2019年第6期955-962,共8页
In the practice of mining shallow buried ultra-close seams,support failure tends to occur during the process of longwall undermining beneath two layers of room mining goaf(TLRMG).In this paper,the factors causing supp... In the practice of mining shallow buried ultra-close seams,support failure tends to occur during the process of longwall undermining beneath two layers of room mining goaf(TLRMG).In this paper,the factors causing support failure are summarized into geology and mining technology.Combining column lithology and composite beam theory,the key stratum of the rock strata is determined.A finite element numerical simulation is used to analyze the overlying load distribution rule of the main roof for different plane positions of the upper and lower room mining pillars.The tributary area theory(TAT)is adopted to analyze the vertical load distribution of each pillar,and dynamic models of coal pillar instability and main roof fracture are established.Through key block instability analysis,two critical moments are established,of which critical moment A has the greater dynamic load strength.Great economic losses and safety hazards are created by the dynamic load of the fracturing of the main roof.To reduce these negative effects,a method of pulling out supports is developed and two alternative measures for support failure prevention are proposed:reinforcing stope supports in conjunction with reducing mining height,or drilling ground holes to pre-split the main roof.Based on a comprehensive consideration of economic factors and the two categories of support failure causes,the method of reinforcing stope supports while reducing mining height was selected for use on the mining site. 展开更多
关键词 Multiple ROOM MINING GOAF Mechanism of supports FAILURE Numerical simulation Prevention measure
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Review of preventive and constructive measures for coal mine explosions:An Indian perspective 被引量:5
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作者 Santosh Kumar Ray Asfar Mobin Khan +3 位作者 Niroj Kumar Mohalik Debashish Mishra Somu Mandal Jai Krishna Pandey 《International Journal of Mining Science and Technology》 SCIE EI CAS CSCD 2022年第3期471-485,共15页
Firedamp and coal dust explosion constitute a lion’s share in mine accidents in a global mining scenario.This paper reports a list of mine explosion disasters since last two decades,a critical review of the different... Firedamp and coal dust explosion constitute a lion’s share in mine accidents in a global mining scenario.This paper reports a list of mine explosion disasters since last two decades,a critical review of the different prevention and constructive measures,and its recent development to avoid firedamp and coal dust explosion.Preventive legislation in core coal-producing countries,viz.China,USA,Australia,South Africa,and India related to firedamp and coal dust explosion are critically analysed.Accidents occurred due to explosion after Nationalisation of Coal Mines(1973)in India are listed.Prevention and constructive measures adopted in India are critically analysed with respect to the global mining scenario.Measures like methane credit concept,classification of mines/seams with respect to explosion risk zone,deflagration index;installation of automatic fire warning devices,canopy air curtain technology,explosion-prevention measures,such as fire-retardant materials,inhibitors,extinguishing agent,dust suppressor,and active explosion barrier are discussed in detail to avoid explosion and thereby adhering to zero accident policy due to coal mine explosion. 展开更多
关键词 Firedamp explosion Coal dust explosion Preventive measures Constructive measures LEGISLATION
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CARLESON MEASURES FOR BESOV-SOBOLEV SPACES WITH APPLICATIONS IN THE UNIT BALL OF C^n 被引量:3
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作者 彭茹 欧阳才衡 《Acta Mathematica Scientia》 SCIE CSCD 2013年第5期1219-1230,共12页
This paper is devoted to give the connections between Carleson measures for Besov-Sobolev spaces Bp^σ(B) and p-Carleson measure in the unit ball of C^n. As applications, we characterize the Riemann-Stieltjes operat... This paper is devoted to give the connections between Carleson measures for Besov-Sobolev spaces Bp^σ(B) and p-Carleson measure in the unit ball of C^n. As applications, we characterize the Riemann-Stieltjes operators and multipliers acting on Bp(B) spaces by means of Carleson measures for Bp^σ(B). 展开更多
关键词 Carleson measures Besov-Sobolev spaces Riemann-Stieltjes operators MULTIPLIERS
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Hardening measures for bipolar transistors against microwave-induced damage 被引量:3
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作者 柴常春 马振洋 +3 位作者 任兴荣 杨银堂 赵颖博 于新海 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第6期637-641,共5页
In the present paper we study the influences of the bias voltage and the external components on the damage progress of a bipolar transistor induced by high-power microwaves. The mechanism is presented by analyzing the... In the present paper we study the influences of the bias voltage and the external components on the damage progress of a bipolar transistor induced by high-power microwaves. The mechanism is presented by analyzing the variation in the internal distribution of the temperature in the device. The findings show that the device becomes less vulnerable to damage with an increase in bias voltage. Both the series diode at the base and the relatively low series resistance at the emitter, Re, can obviously prolong the burnout time of the device. However, Re will aid damage to the device when the value is sufficiently high due to the fact that the highest hot spot shifts from the base-emitter junction to the base region. Moreover, the series resistance at the base Rb will weaken the capability of the device to withstand microwave damage. 展开更多
关键词 bipolar transistor high-power microwave hardening measures
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CASH SUBADDITIVE RISK MEASURES FOR PORTFOLIO VECTORS 被引量:3
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作者 刘红卫 胡亦钧 魏林晓 《Acta Mathematica Scientia》 SCIE CSCD 2018年第1期361-376,共16页
In this paper, from the viewpoint of the time value of money, we study the risk measures for portfolio vectors with discount factor. Cash subadditive risk measures for portfolio vectors are proposed. Representation re... In this paper, from the viewpoint of the time value of money, we study the risk measures for portfolio vectors with discount factor. Cash subadditive risk measures for portfolio vectors are proposed. Representation results are given by two different methods which are convex analysis and enlarging space. Especially, the method of convex analysis make the line of reasoning and the representation result be simpler. Meanwhile, spot and forward risk measures for portfolio vectors are also introduced, and the relationships between them are investigated. 展开更多
关键词 cash subadditivity risk measures convex analysis portfolio vectors
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