Partial Fractions via Calculus

The standard technique taught in calculus courses for partial fraction expansions uses undetermined coefficients to generate a system of linear equations; we present a derivative-based technique that calculus and differential equations instructors can use to reinforce connections to calculus. Simple algebra shows that we can use the derivative to calculate coefficients, reinforcing calculus connections. For irreducible quadratic factors, the simple derivative formula with complex arithmetic gives the coefficients, helping students gain facility with complex numbers. For higher multiplicity factors, we can use higher derivative formulas taken from the Laurent expansion. We conclude with examples of using the technique in different courses, highlighting precalculus and calculus classes.     

Factors explaining faculty technology use and productivity

This study examines factors related to technology use in teaching by university faculty. An EFA analysis of multiple questions of technology use in the classroom found two factors: one loaded with Web use and the second with email use. Therefore, three research questions were asked: What factors explain faculty use of the Web or email? Are these factors the same for both Web and email use? What is the relationship of technology use to faculty productivity? The sample included full-time faculty at doctoral and research institutions selected from the National Study of Postsecondary Faculty:1999 (NSOPF:99) dataset. Independent variables included measures of teaching, research, and service productivity, along with other contextual, demographic, and professional variables. Hierarchical regression analysis was used to prepare eight models (email and Web use for Doctoral I, Doctoral II, Research I, and Research II institutions). Results confirmed that age and Internet access were important factors related to faculty technology use. The relationship between email and Web use to teaching productivity in particular is intriguing and may indicate that productive faculty use technology to help them be more productive or that technology use impacts productivity. Research and service productivity also exhibited distinctive patterns with email and Web use.     

Static image compression based on fractal theory

１ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｆｒａｃｔａｌｇｅｏｍｅｔｒｙｗａｓｅｓｔａｂｌｉｓｈｅｄａｔｔｈｅｂｅｇｉｎｎｉｎｇｏｆｔｈｅｃｅｎｔｕｒｙ．Ｍａｎｄｅｌｂｒｏｔｐｒｅｓｅｎｔｅｄｔｗｏｆｒａｃｔａｌｄｅｆｉｎｉｔｉｏｎｓｉｎ１９８２ａｎｄ１９８４...     

Power and Sample Size Calculations for Logistic Regression Tests for Differential Item Functioning

Logistic regression is a popular method for detecting uniform and nonuniform differential item functioning (DIF) effects. Theoretical formulas for the power and sample size calculations are derived for likelihood ratio tests and Wald tests based on the asymptotic distribution of the maximum likelihood estimators for the logistic regression model. The power is related to the item response function (IRF) for the studied item, the latent trait distributions, and the sample sizes for the reference and focal groups. Simulation studies show that the theoretical values calculated from the formulas derived in the article are close to what are observed in the simulated data when the assumptions are satisfied. The robustness of the power formulas are studied with simulations when the assumptions are violated.     

Early identification of developmentally disabled and at-risk preschool children.

This study examined child-centered data (from birth to 7 years) and familial factors as possible predictors of disabilities in adolescence. The sample was taken from original participants in the National Collaborative Perinatal Project in Rhode Island who were also judged as handicapped after school entry. Results of the current study indicated that parental traits (i.e., maternal education) are more accurate predictors of adolescent status than the child's own behavior from birth to 3 years, whereas child-centered skills assessed at 4 and 7 years of age are better predictors than are familial factors. Overall, data suggest that early identification models which focus upon developmental delay or adverse medical events from birth to 3 years of age are inadequate in fully identifying children eventually judged to be handicapped. Screening initiatives must be developed that are multivariate (child and family focused) and account for differential weights of risk factors over time.     

PRACTICAL ANALYSIS OF ORTHOTROPIC PLATES SUPPORTED IN ONE DIRECTION

A practical method for computing the one-way rectangular orthotropicplate(isotropic plate as a special case)is suggested in this paper.The supported condi-tions in two opposite edges may be simply supported,continuous or supportednonsymmetrically and the other two opposite edges are slide-supported or free.A series ofsimplified formulas are given for calculating the bending moments along the cross section(loaded section),in which the acting point of the concentrated load or the center of a rec-tangular uniform load is located.The valid range and accuracy of these formulas were stud-ied and the approximate results were examined and compared extensively with those by thetriangular series solution or finite element method.     

Playing catch up: A term-level investigation of the racial gap in STEM retention

This paper examines differences in STEM retention between minority and non-minority students enrolled at the University of California, Los Angeles (UCLA) from 1980 through 2006. Using detailed administrative records of undergraduate students, we document that minority students and non-minority students take divergent pathways through the STEM major. Specifically, minority students take fewer lower division STEM courses in their early career, which delays their enrollment in upper division STEM courses and leads to lower graduation probability in STEM within four years and higher dropout rates. We investigate the potential reasons (and/or predictors) for this apparent discrepancy. To do so, we first identify a student’s major-specific Individual Performance Potential (IPP) from lower division course regressions. We find that once we control for the heterogeneity in the IPP’s and a rich set of term level controls, the differences in intermediate outcomes (declared major, STEM course load) between minority and non-minority students largely disappear, but that some of the gap in outcomes persist, with the exception being in graduation from STEM within five years, for which minority students are more likely after controlling for these factors. Our findings suggest that minority STEM majors would benefit from additional support such as early career course advising.     

Measuring quality in universities: An approach to weighting research productivity

The aim of the study is to demonstrate, via the use of the discipline of Education, a procedure to identify and weight the importance of various indicators of research productivity which in turn have become significant components in determining quality within and between universities. The methodology allows for the identification of indicators that are most important, and ascertains if there are differences among academics as to the relative weighting of the various research indicators.Highly valued indicators of research productivity amongst the Education academics were refereed journal articles, peer reviewed books, and major competitive research grants. Refereeing was critical in the determination of quality in research productivity, and the findings generalized across many academics regardless of their own personal productivity. It is recommended that the methodology can serve to determine the tacit weights that academics within and across disciplines attach to various research products. At least, this method makes academics and administrators aware of the weightings they are actually using when making decisions about the quality of academic departments.     

求分段函数导数的一个定理

给出利用求导公式及求导法则来判断一个分段函数在分段点处是否可导以及在可导情况下如何求该导数的一个定理,并举例说明该定理的应用及其局限性。     

分工概念与历史唯物主义——恩格斯分工概念述论

分工概念是恩格斯《家庭、私有制和国家的起源》一书中的核心概念之一。恩格斯认为,用分工的观点最容易理解历史唯物主义。虽然生产力的发展是人类产生分工的基础和直接原因,但分工是联系生产力和生产关系的中间环节,并且是私有制、阶级与国家等历史过程的实现形式。分工导致了对偶制家庭向专偶制家庭的过渡,随着分工的发展,私有制、阶级与国...     

Inbreds and non‐inbreds among Russian academics: Short‐term similarity and long‐term differences in productivity

This paper studies the publication productivity of inbreds and non‐inbreds among Russian academics. Existing literature provides ambiguous results on the relationship between inbred status and productivity. This may be explained by the use of different indicators for measuring publication productivity. We use data, which include indicators of both current publication productivity (at a certain point of time) and cumulative productivity (throughout the career) to identify whether inbreds and non‐inbreds differ in their productivity. We did not find any difference in current publication productivity of inbreds and non‐inbreds. We found, however, a difference in their cumulative publication productivity: non‐inbreds are being more productive on an individual level throughout their careers. Although the conclusions are based on the Russian data, the analysis provides an explanation for existing contradictory results on the relationship between academic inbreeding and productivity in general.     

生产社会化的二重发展与企业规模的变化

生产集中化和社会分工的发展实际上是生产社会化的二重表现和形式 ,通过集中化 ,提高劳动的社会生产力和规模效益 ;通过社会分工 ,实现专业化 ,提高劳动的个别生产力和专业生产水平。生产社会化的二重性及其相互转化 ,是影响生产规模和企业规模最深刻的基础 ,也是资本主义生产方式至今没有退出历史舞台的最深刻的原因之一     

A genetically sensitive investigation of the effects of the school environment and socio‐economic status on academic achievement in seven‐year‐olds

Although it is well established that school characteristics (SCH) and socio‐economic status (SES) are associated with academic achievement (ACH), these correlations are not necessarily causal. Because academic achievement shows substantial genetic influence, it is useful to embed such investigations in genetically sensitive designs in order to examine environmental influences more precisely by controlling genetic influence on ACH. In the first study of this kind for academic achievement, data were collected for 1,063 same‐sex pairs of seven‐year‐old MZ and DZ twins for teacher‐assessed ACH, UK statistics on SCH, and parent‐reported SES. Exclusive of genetic influence on school achievement, shared environment (environmental influences that make siblings similar) accounts for 12% of the variance in academic achievement. SCH accounts for 17% and SES accounts for 83% of this shared environmental variance. Exclusive of genetic and shared environmental influence including SCH and SES, nonshared environment (environmental influences that do not make siblings similar) accounts for 19% of the variance in academic achievement. The importance of nonshared environmental influences on academic achievement leads to the question of what these child‐specific experiences might be that are not shared by children in the same family, school, and classroom.     

劳动生产率与商品价值量关系的思考

无论从单个商品来看,还是从商品价值总量来看,商品价值量都是随着劳动生产率的提高而反向变动,即成反比。考察劳动生产率与劳动复杂程度同时提高发现,商品价值量与劳动生产率仍然成反比,而与劳动复杂程度成正比。商品价值总量的增加只能用社会分工的发展来解释,这正是被众多文献所忽视的。     

例谈留数与方程的解

复函数在孤立奇点处的留数的计算往往较复杂,不过对于极点处,可以通过方程的解而求得留数.特别针对于一阶零点,更是有较为初等的留数计算公式,也有较为初等的计算积分的公式.同时,又可以通过计算留数而得出某些常微分方程的解,也有较为初等的解的表达公式.     

基于SPSS安顺市耕地生产效益分析

文章采用安顺市近8年统计年鉴中有关数据资料及其计算指标,选取5种影响耕地生产效益因素指标进行分析研究。运用SPSS统计软件,将影响因素作为自变量,耕地生产率为因变量,采用多元回归分析方法进行分析。结果表明：据回归模型,安顺市耕地生产率与农机总动力、地膜使用面积及有效灌溉面积比率呈正相关,而与化肥使用量及农药使用量呈负相关关系。通过分析,根据安顺市耕地利用特点,提出提高耕地生产效益的对策。     

Plastic limit load analysis for pressure pipe with incomplete welding defects based on the extended Net Section Collapse Criteria

With von Mises yield criterion, the loading range of Net Section Collapse （NSC） Criteria is extended from combined tension and bending loadings to combined bending, torsion and internal pressure loadings. A new theoretical analyzing method of plastic limit load for pressure pipe with incomplete welding defects based on the extended NSC Criteria is presented and the correlative formulas are deduced, the influences of pipe curvature, circumferential length and depth of incomplete welding defects on the plastic limit load of pressure pipe are considered as well in this method. Meanwhile, according to the orthogonal experimental design method, the plastic limit loads are calculated by the finite element method and compared with the theoretical values. The results show that the expressions of plastic limit load of pressure pipe with incomplete welding defects under bending, torsion and internal pressure based on extended NSC criteria are reliable. The study provides an important theoretical basis for the establishment of safety assessment measure towards pressure pipe with incomplete welding defects.     

Predicting elementary science learning using national assessment data

This study made use of data collected during 1981—1982 from a random sample of 1960 nine-year-old students from 124 elementary schools involved in a national assessment of educational progress in science sponsored by the National Science Foundation. This data base was used in secondary analyses which probed the validity of a model of educational productivity involving a set of nine aptitudinal, instructional, and environmental variables which require optimization to increase student learning. When controlled for other factors, ability, motivation, class environment, home environment, amount of television viewing (negative direction), gender, and race were all found to be significantly related to achievement. For an attitude outcome, the factors linked with attitudinal attainment were ability, motivation, class environment, and race. Overall the findings supported the model of educational productivity and suggested that elementary science students' achievement and attitude are influenced jointly by a number of factors rather than one or two dominant ones. Also the study attests to the potential value of science education researchers performing secondary analyses on the high-quality random data bases generated as part of this national assessment.     

基于改进BP神经网络的供热负荷预测模型

为在自然环境条件下对供热负荷进行较为准确的预测,分析了对供热负荷产生影响的自然因素,利用回归分析法建立负荷预测模型。在误差较大情况下提出利用神经网络法建模,采用差分进化算法对神经网络的阈值和权值进行优化。使用经过优化的神经网络进行负荷预测,在MATLAB环境下进行仿真。仿真结果表明,采用该方法可得到更为准确的供热负荷预测模型,对供热站节能运行有一定意义。     

曲线箱梁桥均匀温度变化效应分析

温度荷载的作用是造成曲线箱梁桥工程问题的主要原因之一。文章运用曲线梁桥的微分方程,详细分析了混凝土曲线箱梁在均匀温度荷载作用下的效应,推导出了单跨曲线箱梁在径向受到约束时受均匀温度荷载作用产生的支反力及内力计算公式,并利用公式及有限元软件进行实例计算,验证了公式的准确性,得出了曲线箱梁桥在均匀温度荷载作用下,径向反力的大小与桥梁半径的二次方呈反比例关系,与桥梁的刚度、轴线圆心角呈正比例关系,即桥梁的半径越小,桥梁越宽,圆心角越大,桥梁的径向反力越大的结论,为解决曲线箱梁在均匀温度荷载作用下的工程问题提供理论支持。