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ENTRANCE LAWS FOR DAWSON-WATABE SUPERPROCESSES WITH NONLOCAL BRANCHING
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作者 李增沪 《Acta Mathematica Scientia》 SCIE CSCD 1998年第4期449-456,共8页
This paper proves a 1-1 correspondence between minimal probability entrance laws for the superprocess and entrance laws for its underlying process. From this the author deduces that an infinitely divisible probability... This paper proves a 1-1 correspondence between minimal probability entrance laws for the superprocess and entrance laws for its underlying process. From this the author deduces that an infinitely divisible probability entrance law for the superprocess is uniquely determined by an infinitely divisible probability measure on the space of the underlying entrance laws. Under an additional condition, a characterization is given for all entrance laws for the superprocess, generalizing the results of Dynkin (1989). An application to immigration processes is also discussed. 展开更多
关键词 SUPERPROCESS entrance law 1-1 correspondence.
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The Lynx and Hare Data of 200 Years as the Nonlinear Conserving Interaction Based on Noether’s Conservation Laws and Stability
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作者 Hiroshi Uechi Lisa Uechi Schun T. Uechi 《Journal of Applied Mathematics and Physics》 2021年第11期2807-2847,共41页
We applied <em>n</em>-variable conserving nonlinear differential equations (<em>n</em>-CNDEs) to the population data of the 10-year cycles of Canadian lynx (1821-2016) and the snowshoe hare (18... We applied <em>n</em>-variable conserving nonlinear differential equations (<em>n</em>-CNDEs) to the population data of the 10-year cycles of Canadian lynx (1821-2016) and the snowshoe hare (1845-1921). Modeling external effects as perturbations to population dynamics, recovering and restorations from disintegrations (or extinctions), stability and survival strategies are discussed in terms of the conservation law inherent to dynamical interactions among species. The 2-variable conserving nonlinear interaction (2CNIs) is extended to 3, 4, ... <em>n</em>-variable conserving nonlinear interactions (<em>n</em>-CNIs) of species by adjusting minimum unknown parameters. The population cycle of species is a manifestation of conservation laws existing in complicated ecosystems, which is suggested from the CNDE analysis as <em>a standard rhythm</em> of interactions. The ecosystem is a consequence of the long history of nonlinear interactions and evolutions among life-beings and the natural environment, and the population dynamics of an ecosystem are observed as approximate CNIs. Physical analyses of the conserving quantity in nonlinear interactions would help us understand why and how they have developed. The standard rhythm found in nonlinear interactions should be considered as a manifestation of the survival strategy and the survival of the fittest to the balance of biological systems. The CNDEs and nonlinear differential equations with time-dependent coefficients would help find useful physical information on the survival of the fittest and symbiosis in an ecosystem. 展开更多
关键词 The 10-year Population Cycles of Canadian Lynx and Snowshoe Hare The Standard Rhythm of Interactions Noether’s Conservation law Conserving Nonlinear Interactions of Species
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CONVERGENCERATESIN THESTRONG LAWSOFASYMPTOTICALLY NEGATIVELY ASSOCIATEDRANDOM FIELDS 被引量:53
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作者 Zhang Lixin\ Wang Xiuyun 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1999年第4期406-416,共11页
In this paper, a notion of negative side ρ \|mixing ( ρ\+- \|mixing) which can be regarded as asymptotic negative association is defined, and some Rosenthal type inequalities for ρ\+- \|mixing random fields are est... In this paper, a notion of negative side ρ \|mixing ( ρ\+- \|mixing) which can be regarded as asymptotic negative association is defined, and some Rosenthal type inequalities for ρ\+- \|mixing random fields are established. The complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are also discussed for ρ\+-\| mixing random fields. The results obtained extend those for negatively associated sequences and ρ\+*\| mixing random fields. 展开更多
关键词 Rosenthal-type inequality strong law of large num bers ρ- -m ixing ρ-m ixing asym p-totic negative association random fields
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Prevalence and Years Lived with Disability for Dental Caries among Children Aged 0-14 Years in China, 1990-2016 被引量:6
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作者 LIU Wen Zhao SU Ling Yu +3 位作者 XIE Xu Dong XIANG Xue Rong HUANG Jiao JI Ping 《Biomedical and Environmental Sciences》 SCIE CAS CSCD 2018年第5期376-381,共6页
The estimate of dental caries among Chinese children at the microscale level using standard methodology remains unclear. In this study, we assessed and analyzed the disease burden of childhood dental caries in China b... The estimate of dental caries among Chinese children at the microscale level using standard methodology remains unclear. In this study, we assessed and analyzed the disease burden of childhood dental caries in China by extracting data from the Global Burden of Disease, Injuries, and Risk Factors Study 2016 (GBD 2016). In 2016, the number of cases, prevalence, years lived with disability (YLD), and age-standardized YLD rate of dental caries was 93.0 million, 43.0%, 32,200 person years, and 14.8 per 100,000, respectively. Across 33 provincial units, the disease burden was highest in Hubei (YLD rate 28.6 per 100,000), lowest in Macao (9.1 per 100,000), while geographical clustering was not observed. Compared with 1990, the prevalence in 2016 decreased from 46.8% to 43.0%, and the YLD rate decreased from 16.5 per 100,000 to 14.8 per 100,000. Given the slight decrease in dental caries burden, the prevalence and disease burden remained high among Chinese children. Strategies for addressing the spatial inequity of childhood dental caries require geographical targeting. 展开更多
关键词 In Prevalence and years Lived with Disability for Dental Caries among Children Aged 0-14 years in China 1990-2016
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Factors Influencing Preventive Behaviors of Mothers for Diarrhea in Children Aged 1-5 Years in Buol District, Indonesia 被引量:1
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作者 Helmi Rumbo Susheewa Wichaikull Boosaba Sanguanprasit 《Sociology Study》 2016年第12期745-753,共9页
This study aims to determine the factors related with mothers' behaviors in preventing diarrhea in children aged 1-5 years inBuol District. This was a cross-sectional survey design with health belief model as the con... This study aims to determine the factors related with mothers' behaviors in preventing diarrhea in children aged 1-5 years inBuol District. This was a cross-sectional survey design with health belief model as the conceptual framework. A total of 300mothers were selected by using purposive sampling method based on criteria. Mothers were interviewed by using astructured questionnaire during October to November 2015. A chi-square (X^2) test was used to determine a significantassociation between independent variables and dependent variable. The finding showed that 68.3% of mothers hadgood behaviors in preventing diarrhea. The factors significantly related to mothers' behaviors included perceivedsusceptibility to diarrhea, perceived severity of diarrhea, perceived benefits of diarrhea prevention behaviors, and perceivedbarriers of diarrhea prevention behaviors CP 〈 .01, p 〈 .01, p 〈 .01, and p 〈 .01 respectively). Further, mothers had highperception to comply with diarrhea prevention behaviors. Those who perceived that diarrhea prevention behaviors werehighly beneficial to their children had good behaviors in preventing diarrhea. However, taking certain actions must considernegative aspects. 展开更多
关键词 Mothers' PERCEPTIONS and behaviors preventing diarrhea CHILDREN aged 1-5 yearS
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Energy Balance-related Behaviors Are Related to Cardiometabolic Parameters and Predict Adiposity in 8-14-year-old Overweight Chinese Children One Year Later 被引量:1
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作者 LI Liu Bai WANG Nan +4 位作者 WU Xu Long WANG Ling LI Jing Jing YANG Miao MA Jun 《Biomedical and Environmental Sciences》 SCIE CAS CSCD 2016年第10期754-757,共4页
To identify target energy balance-related behaviors(ERBs),baseline data from 141overweight or obese schoolchildren(aged 8-14years old)was used to predict adiposity[body mass index(BMI)and fat percentage]one year... To identify target energy balance-related behaviors(ERBs),baseline data from 141overweight or obese schoolchildren(aged 8-14years old)was used to predict adiposity[body mass index(BMI)and fat percentage]one year later.The ERBs included a modified Dietary Approach to Stop Hypertension diet score(DASH score),leisure-time physical activity(PA,days/week),and leisure screen time(minutes/day).Several cardiometabolic variables were measured in the fasting state, including systolic blood pressure (SBP), diastolic blood pressure (DBP), blood glucose (GLU), total cholesterol (TC), triglycerides (TG), low-density lipoprotein (LDL-C), and high-density lipoprotein (HDL-C). 展开更多
关键词 Energy Balance-related Behaviors Are Related to Cardiometabolic Parameters and Predict Adiposity in 8-14-year-old Overweight Chinese Children One year Later BMI body
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Entropy Analysis of Vapor-Compression Refrigeration System by Using the Second Law of Thermodynamics
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作者 杨洪海 《Journal of China Textile University(English Edition)》 EI CAS 1999年第4期42-44,共3页
By means of the Second Law of Thermodynamics,thispaper gives out the entropy analysis method for vapor-comperession refrigeration system.The thermal irrevers-ibility of the system charged with R12 and its hopeful al-t... By means of the Second Law of Thermodynamics,thispaper gives out the entropy analysis method for vapor-comperession refrigeration system.The thermal irrevers-ibility of the system charged with R12 and its hopeful al-ternative refrlgerant R134a have been studied respective-ly.On the basis of all the research results of this paper,the measure used to save energy for vapor-compressionrefrigeration system has been put out. 展开更多
关键词 Vapor - Compression REFRIGERATION System Sec-ond law of THERMODYNAMICS ENTROPY ANALYSIS Alternative REFRIGERANT of CFC’s
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Comparing Coordination Abilities of 10-11 Years Old Girls Practicing Basketball and Rhythmic Gymnastic
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作者 Georgi Venelinov Brestnichki 《Journal of Sports Science》 2015年第3期134-137,共4页
The words---coordination, coordination abilities and coordination training are getting more and more popular among the coaches in different sports. The rhythm makes the movement logical, easy and correct done. The pur... The words---coordination, coordination abilities and coordination training are getting more and more popular among the coaches in different sports. The rhythm makes the movement logical, easy and correct done. The purpose of this study is to determine any difference between the coordination abilities of 10-11 years old gifts practicing basketball and rhythmic gymnastics. In that study, we have tested 40 girls at the age of 10-11 years practicing basketball and rhythmic gymnastic. We have tested them by 7 coordination tests. The results from the tests have been calculated in math-statistic methods and we have used descriptive statistic and t-test by Student with guaranteed probability Pt 〉 95 %. Ten-eleven old girls practicing rhythmic gymnastic have advantage against the girls practicing basketball in all 7 tests examining coordination abilities. The girls practicing rhythmic gymnastic, guaranteed by statistic, have better results in the balance and rhythmic abilities than the girls practicing basketball game. That statement is showing us that at this age the rhythmic gymnastic or elements from rhythmic gymnastic should be used for developing balance and rhythmic ability, which are very important for the basketball game. 展开更多
关键词 comparing COORDINATION 10-11 years old GIRLS BASKETBALL rhythmic GYMNASTICS
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The overview of the language acquisition for Chinese city children aged 0-3 years
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作者 ZHU Jian-xiong 《Sino-US English Teaching》 2009年第8期5-8,21,共5页
This paper examines the language development of Chinese children aged 0-3years in city family. About baby's language development by the time stages accordingly. Paying special attention to the efforts for the parents... This paper examines the language development of Chinese children aged 0-3years in city family. About baby's language development by the time stages accordingly. Paying special attention to the efforts for the parents or caregivers. Infants receive more talking education and speak earlier. Most parents can hardly wait for their baby to say its first word and communicate with their baby. From about 2 years old, the child should be able to use simple phrases, retell simple story and even to sing song. Parents play an important role in this stage. By the 3 years children begin to use most of function words rather than omit them. And acquisition for the second language will help children's language development. The children have a gift for learning language. 展开更多
关键词 OVERVIEW LEARNING language acquisition aged 0-3 years
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Pesticide Residue Control in the Years 1983-1985
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作者 IVANO CAMONI ALFONSO DI MUCCIO +2 位作者 MARIA SANDRA BELLISAI MARIO BERSACCHI PAOLO CITTI 《Biomedical and Environmental Sciences》 SCIE CAS CSCD 1989年第3期287-294,共8页
Levels of organochlorinated, organophosphate, dithiocarbamic, benzimidazolic, and phthalimidic compounds, as well as some other pesticide residues obtained from Regional Laboratories in the years 1983-1985, were assem... Levels of organochlorinated, organophosphate, dithiocarbamic, benzimidazolic, and phthalimidic compounds, as well as some other pesticide residues obtained from Regional Laboratories in the years 1983-1985, were assembled and presented as a part of a study aimed at evaluating food contamination. Approximately 2000 samples of vegetables, fruits, cereals, and food of animal origin were analyzed by local laboratories during the years 1983, 1984, and 1985. Samples were randomly obtained from the market, at production levels, or sometimes at custom sites. Approximately 10,000 determinations of single compounds or classes of compounds were carried out. The analytical results are presented and compared with the Italian maximum residue limits. In the majority of the samples analyzed, either there were no residues or the residues were below the permitted level for the specific pesticide in each commodity. High levels of residues were present in a few cases, mainly with respect to some fungicides in fruits and vegetables and chlorinated compounds in some animal products. (c)1989 Academic Press, Inc. 展开更多
关键词 Pesticide Residue Control in the years 1983-1985
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Pesticide Residue Control in the Years 1986-1987
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作者 IVANO CAMONI ALFONSO DI MUCCIO +1 位作者 MARIA SANDRA BELLISAI PAOLO CITTI 《Biomedical and Environmental Sciences》 SCIE CAS CSCD 1991年第4期415-422,共8页
Results of analytical surveys on pesticide residue levels in foods for the years 1986-1987 are presented. Analytical data obtained from regional laboratories are tabulated in terms of various commodity groups (vegetab... Results of analytical surveys on pesticide residue levels in foods for the years 1986-1987 are presented. Analytical data obtained from regional laboratories are tabulated in terms of various commodity groups (vegetables, fruit, cereals, processed or derived foodstuffs, other commodities, legumes, environmental samples, others) and are compared with maximum legal tolerances established by the ministerial ordinance (Italian Ministry of Health) 6.6. 1985.On a total number of 4715 determinations of classes of compounds or of single compounds made on 1601 commodities samples, only N 53 (1.1 %) violative results appeared. No residue was found at levels exceeding regulatory limits or found in commodities where a tolerance had not been established for a specific pesticide/commodity combination. 展开更多
关键词 Pesticide Residue Control in the years 1986-1987
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Pesticide Residue Control in the Years 1988-1989 in Italy
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作者 IVANOCAMONIALFONSODIMUCCIO PAOLOCITTI MARIASANDRABELLISAI 《Biomedical and Environmental Sciences》 SCIE CAS CSCD 1993年第2期161-171,共11页
The paper reports the monitoring for pesticide residue contamination of foodstuffs carried out in the years 1988-1989 by the Italian peripheral laboratories officially commissioned for the task. The tables show the an... The paper reports the monitoring for pesticide residue contamination of foodstuffs carried out in the years 1988-1989 by the Italian peripheral laboratories officially commissioned for the task. The tables show the analytical data for each class of substrate versus the limits in force at the time. 2506 food samples and 555 samples from the environment were analysed and a total of 16259 determinations made.The residues were absent in 90% of the cases; the percentage of irregularities was 1.52%. These results confirm the data obtained in previous years, which is particularly significant considering the much larger number of analytical determinations performed this time.It has been deemed convenient to survey specific types of foodstuffs (for example, cereals and animal products) by examining a larger number of samples. 展开更多
关键词 Pesticide Residue Control in the years 1988-1989 in Italy
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Preliminary Study on Water Demand Law of 1-0 Rooted Cuttings of Populus szechuanica
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作者 Dabuqiong Haoyu WANG +2 位作者 Huanhuan XIE Zhen XING Yanhui YE 《Meteorological and Environmental Research》 CAS 2021年第4期39-42,共4页
In order to provide theoretical basis and technical support for the afforestation and artificial water supply of P.szechuanica in arid areas,the characteristics of water consumption of P.szechuanica were explored,and ... In order to provide theoretical basis and technical support for the afforestation and artificial water supply of P.szechuanica in arid areas,the characteristics of water consumption of P.szechuanica were explored,and the law of water demand of P.szechuanica was grasped.In this paper,potted seedlings of 1-0 rooted cuttings of P.szechuanica were taken as research objects,and change situation of water consumption under different water control gradients was measured regularly by using weighing method,further analyzing dynamic change of water consumption of P.szechuanica and revealing water demand law of 1-0 rooted cuttings of P.szechuanica.The results showed that total change of water consumption of 1-0 rooted cuttings of P.szechuanica had"slow-fast-slow-fast"double-peak trend in the growth period of the current year,and corresponded with univariate linear relation(R^(2)=0.7137),with significant difference.In whole growth period,water consumption in August was the highest,which was 2.7 times of that in June and July and 1.5 times of that after September.In different water control treatments,the dynamic changes of daily and monthly water consumption were significantly different.In seven water control treatments,monthly water consumption was between(6315.95±1690.70)and(10105.28±3065.30)g/month,and mean was(8211.07±2308.23)g/month.With intensification of water control treatment,water consumption increased,but there was no seedling death due to water shortage.P.szechuanica has great plasticity in water demand,and can survive in both arid and humid environments.Meanwhile,it is revealed that P.szechuanica is the most widely distributed tree species in the region. 展开更多
关键词 Populus szechuanica 1-0 rooted cuttings Water consumption Water demand law
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On the Current Situation of Basic - level Administrative Law Enforcement in China
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作者 Xiaoxing Xie 《International Journal of Technology Management》 2016年第11期36-37,共2页
With the development of economy and society, our country is on the road of rule by law, the legal system is progressing constantly. At the same time, we should also see that the administration according to law is not ... With the development of economy and society, our country is on the road of rule by law, the legal system is progressing constantly. At the same time, we should also see that the administration according to law is not perfect, and its shortcomings exist in different degree and need to be further improved. Based on the analysis of the status quo of grass-roots administrative law enforcement in China, this paper tries to put forward corresponding countermeasures, so as to promote the work of law-based administration for the corresponding study. 展开更多
关键词 grass - roots level administrative law enforcement present situation
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LAW AND LUXURY IN AUGUSTAN ROME (TACITUS, ANNALS 3.53-4)
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作者 Adam Marshall 《Journal of Ancient Civilizations》 2008年第1期97-117,共21页
Introduction: Tacitus on Law and Luxury'quid enim primum prohibere et priscum ad morem recidere adgrediar? villarumne infinita spatia? familiarum numerum et nationes? argenti et auri pondus? aeris tabularumque mir... Introduction: Tacitus on Law and Luxury'quid enim primum prohibere et priscum ad morem recidere adgrediar? villarumne infinita spatia? familiarum numerum et nationes? argenti et auri pondus? aeris tabularumque miracula? promiscas viris et feminis vestis atque illa feminarum propria, 展开更多
关键词 ANNALS 3.53-4 law AND LUXURY IN AUGUSTAN ROME TACITUS
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Risk Factors for Geo-Helminthiasis in Children Aged 6 - 36 Months in a Rural Health District in Cameroon
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作者 Isabelle Mekone Nkwele Monono Naiza +6 位作者 Gervais Talla Kamga Hugues Nana Djeunga Jeannette Epée Ngoue Patricia Epée Eboumbou Suzanne Ngo Um Sap Evelyn Mah Mungeh Joseph Kamgno 《Open Journal of Pediatrics》 2024年第2期391-400,共10页
Introduction and Objectives: Soil-Transmitted-Helminthiasis (STH) is a public health problem in Cameroon. The control strategies currently in place, particularly chemoprevention, has shortcomings linked to the target ... Introduction and Objectives: Soil-Transmitted-Helminthiasis (STH) is a public health problem in Cameroon. The control strategies currently in place, particularly chemoprevention, has shortcomings linked to the target population, which are school-age children. The objective was to determine the prevalence and the risk factors associated with geo-helminthiasis in children aged 0 to 3 years in a rural health district. Method: From December 2020 to May 2021, a descriptive and analytical cross-sectional study of 376 children between 6 and 36 months was carried out in the Akonolinga health district. This was a cluster sampling in 4 health areas. Stool samples were collected and analysed using the mini-FLOTAC method. The results expressed as the number of eggs per gram of stool. A questionnaire on socio-demographic and lifestyle data was administered to the parents. The Chi-squared test was used to measure the association between geo-helminth infection and the data collected. A multivariate analysis using logistic regression was performed (p 0.05). Results: The prevalence of STH was 19.4% (Ascaris lumbricoides: 16% and Trichuris trichiura: 8%). Risk factors were: consumption of contaminated water (AOR = 1.93 [1.03 - 3.6];p = 0.040), early contact of the child with the ground (before age of 4 months) (AOR = 4.9 [2.1 - 11.37];p .001), habit of walking barefoot (AOR = 2.91 [1.1 - 7.97];p = 0.038), and living in a habitat with unpaved ground (AOR = 7.4 [1.55 - 35.7];p = 0.012). Conclusion: The prevalence of STHs in infants was high. Preventive chemotherapy should be extended to this age-group, and other measures intensified. 展开更多
关键词 Akonolinga Soil-Transmitted-Helminths Children Aged 0 - 3 years Risk Factors
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加强高职理论与实践研究,建设高水平政法职业院校--北京政法职业学院“十二五”高职研究工作综述
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作者 李进诚 张景荪 《北京政法职业学院学报》 2016年第2期114-118,共5页
本文在认真总结"十二五"期间北京政法职业学院高职研究工作基础上,深入分析学院高职研究取得的主要成绩、形成的主要经验和主要体会,指出存在的问题与不足,有针对性地提出了今后加强学院高职研究工作的对策建议,这对于加强高... 本文在认真总结"十二五"期间北京政法职业学院高职研究工作基础上,深入分析学院高职研究取得的主要成绩、形成的主要经验和主要体会,指出存在的问题与不足,有针对性地提出了今后加强学院高职研究工作的对策建议,这对于加强高职研究、促进高职研究成果转化、推进"十三五"期间我国高职教育改革创新和发展,具有重要的启示意义。 展开更多
关键词 政法高职教育 “十二五” 高职理论与实践研究 综述
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National Nutrition and Health Systematic Survey for Children 0–17 Years of Age in China 被引量:5
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作者 YANG Zhen Yu ZHANG Qian +13 位作者 ZHAI Yi XU Tao WANG Yu Ying CHEN Bo Wen TANG Xue Jun YUAN Xiao Lin FANG Hong Yun ZHU Yan PANG Xue Hong WANG Shuo XU Juan LI Rui Li SI Xiang ZHAO Wen Hua 《Biomedical and Environmental Sciences》 SCIE CAS CSCD 2021年第11期891-899,共9页
The main purpose of the National Nutrition and Health Systematic Survey for children 0-17 years of age in China(CNHSC)was to collect basic data on the nutrition,development,and health status for children in different ... The main purpose of the National Nutrition and Health Systematic Survey for children 0-17 years of age in China(CNHSC)was to collect basic data on the nutrition,development,and health status for children in different regions across China using evidence-based,reliable,and cost-effective approaches.Children and their parents or guardians from seven regions(south,southwest,north,northwest,eastern,central,and northeast China)in China were recruited.A multi-stage stratified randomized sampling method was used.Two provinces were randomly sampled from each of the seven regions,from which one urban district and one rural country were also randomly sampled,resulting in a total of 28 survey counties/districts.Dietary surveys,health examinations,laboratory testing,and questionnaires were used to collect dietary intake,nutritional status,child development,and health status information.Nutrition,health,and lifestyle assessment of children and their parents was determined using the Knowledge Attitude Practice(KAP)survey.Greater than 100,000 children(38,000 children<6 years of age and 66,000 children6-17 years of age)completed the survey.The survey provided comprehensive data on child nutrition and health status for future studies and will serve as the basis for an integrated nutrition and health improvement strategies proposal for children in China. 展开更多
关键词 Children 0-17 years of age Nutritional status Health status Study protocol
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Universal hierarchical symmetry for turbulence and general multi-scale fluctuation systems 被引量:5
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作者 Zhen-Su She Zhi-Xiong Zhang State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, 100871 Beijing, China 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2009年第3期279-294,共16页
Scaling is an important measure of multi-scale fluctuation systems. Turbulence as the most remarkable multi-scale system possesses scaling over a wide range of scales. She-Leveque (SL) hierarchical symmetry, since i... Scaling is an important measure of multi-scale fluctuation systems. Turbulence as the most remarkable multi-scale system possesses scaling over a wide range of scales. She-Leveque (SL) hierarchical symmetry, since its publication in 1994, has received wide attention. A number of experimental, numerical and theoretical work have been devoted to its verification, extension, and modification. Application to the understanding of magnetohydrodynamic turbulence, motions of cosmic baryon fluids, cosmological supersonic turbulence, natural image, spiral turbulent patterns, DNA anomalous composition, human heart variability are just a few among the most successful examples. A number of modified scaling laws have been derived in the framework of the hierarchical symmetry, and the SL model parameters are found to reveal both the organizational order of the whole system and the properties of the most significant fluctuation structures. A partial set of work related to these studies are reviewed. Particular emphasis is placed on the nature of the hierarchical symmetry. It is suggested that the SL hierarchical symmetry is a new form of the self-organization principle for multi-scale fluctuation systems, and can be employed as a standard analysis tool in the general multi-scale methodology. It is further suggested that the SL hierarchical symmetry implies the existence of a turbulence ensemble. It is speculated that the search for defining the turbulence ensemble might open a new way for deriving statistical closure equations for turbulence and other multi-scale fluctuation systems. 展开更多
关键词 Turbulence. Scaling law. She-Leveque modelHierarchical symmetry Self-organization - Turbulenceensemble
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Analytical solution for the time-fractional heat conduction equation in spherical coordinate system by the method of variable separation 被引量:2
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作者 Ting-Hui Ning Xiao-Yun Jiang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2011年第6期994-1000,共7页
In this paper,using the fractional Fourier law,we obtain the fractional heat conduction equation with a time-fractional derivative in the spherical coordinate system.The method of variable separation is used to solve ... In this paper,using the fractional Fourier law,we obtain the fractional heat conduction equation with a time-fractional derivative in the spherical coordinate system.The method of variable separation is used to solve the timefractional heat conduction equation.The Caputo fractional derivative of the order 0 〈 α≤ 1 is used.The solution is presented in terms of the Mittag-Leffler functions.Numerical results are illustrated graphically for various values of fractional derivative. 展开更多
关键词 Fractional Fourier law Fractional heat conduction equation - Spherical coordinate system - The separation of variables Mittag-Leffler function
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