泰勒公式在证明不等式中的应用

通过几个例子说明泰勒公式在证明不等式中的应用．     

高等代数中的间接证法

用反证法、反例证明代数命题     

The role of data analysis in inclusion processes and practices

This article outlines BPRS funded investigations into my own school's and other establishments' practices and processes within data analysis, needs identification and tracking of children's academic progress. It describes the evaluation of my school's then current practices and policies and the use of questionnaires and semi-structured interviews with my own staff, and assessment coordinators and senior leaders within exemplar schools. As well as outlining the main findings of my research this article assesses the introduction of new models of assessment for my own staff and pupils. This article also highlights how my research developed and the way my research process changed as it continued.     

The role of attention processes in near transfer of cognitive skills

We tested hypotheses about the respective roles of working memory, perceptual speed, knowledge, and attention disengagement processes in skill transfer errors that resemble einstellung effects or strong-but-wrong slips. Correlational evidence was consistent with the hypothesis that these errors are primarily due to the inability of learners to disengage attention from expected or familiar operations. The data also supported the notion that error proneness during near transfer generalizes across different skills. Contrary to expectations, working memory capacity had little or no relationship to either transfer errors or attention disengagement ability. Results are discussed with respect to skill training and individual differences in skill performance ability.     

随机变量的特征函数在恒等式证明中的探讨

本文重点阐述了随机变量的特征函数在恒等式证明中的应用方法,说明它比用分 布函数证明恒等式更方便,并用实例加以说明.     

微积分在不等式证明中的应用

不等式是数学中的重要内容之一,也是解决许多问题的一种十分重要的思想方法。证明不等式的方法很多,本文给出了应用微积分知识证明不等式的几种常见方法,并采用举例的方式进行了归纳和总结。     

Decision-oriented educational research in school districts: The role of dissemination processes

This article addresses the broad issue of how research information can be integrated into the policy and decision processes of educational systems. Our specific foci here is on one type of educational system -- school districts; on research designed to answer specific questions for that district; and, on one major element of the research process -- dissemination. This paper draws heavily upon our experiences in a large, urban American school district, where we work on the problem of how to improve the system's evaluation research capability. This work began in 1978 and continues today. This article has four major section. Background is provided on the nature of the collaboration with the school district. Then, basic strategies for conducting decision-oriented educational research that have emerged from the work are described briefly. This is followed by a discussion of the broad issue of research use. The final section is a detailed review of what we have learned about the relationship between dissemination and utilization.     

导数在不等式证明中的应用

基于代数不等式证明的重要性,本文给出利用导数证明几种代数不等式的方法.     

Creativity: The role of unconscious processes in idea generation and idea selection

Today's world of continuous change thrives on creative individuals. Anecdotal reports suggest that creative performance benefits from unconscious processes. Empirical research on the role of the unconscious in creativity, though, is inconsistent and thus far has focused mainly on one aspect of the creative process - idea generation. This is the first study to assess the role of the unconscious mind for both idea generation and idea selection. Participants generated creative ideas immediately, after conscious thought, or after a period of distraction during which unconscious thought was hypothesized to take place. After having listed their ideas, participants selected their most creative idea. Performance in idea generation was similar between conscious and unconscious thought; however, individuals who had unconsciously thought about ideas were better in selecting their most creative idea. These findings shed more light on the role of unconscious processes in creativity, and provide a means to enhance creative performance.     

Relational learning in pigeons: The role of perceptual processes in between-key recognition of complex stimuli

In Experiment 1, we used six procedures in a series of unsuccessful attempts to obtain relational learning using trial-unique pictorial stimuli in pigeons. The Experiment began by testing conventional (three-key) matching-to-sample (MTS) and nonmatching-to-sample (NMTS); in subsequent stages of the experiment we progressively incorporated features of techniques that do obtain relational learning in a single-key apparatus. In Experiment 2, we found that acquisition of NMTS using pictorial stimuli proceeded no more rapidly than acquisition of a conditional discrimination. Experiment 3 showed that acquisition of NMTS was more rapid than acquisition of MTS when plain colored stimuli were used, but not when pictorial stimuli were used. These three experiments suggest that pigeons do not recognize pictorial stimuli shown on different keys. In Experiment 4, between-key recognition was obtained with familiar but not with novel pictorial stimuli. It is argued that perceptual learning facilitates the detection of the between-key identity of complex stimuli, and that perceptual processes may underlie the difficulty in demonstrating relational learning in pigeons.     

Independent effects of stimulus and cycle duration in conditioning: The role of timing processes

Rats received delay conditioning procedures with a white-noise conditioned stimulus (CS), a food unconditioned stimulus (US), and head entries into the food cup as the conditioned response. The stimulus duration (S) and the interval between food deliveries (C) were varied between groups:S=15, 30, 60, and 120 sec;C=90, 180, and 360 sec. The stimulus/cycle duration ratio was negatively related to the asymptotic level of conditioning but had no effect on the rate of acquisition. Conditioning and timing of responses emerged together in training. Timing occurred during the CS-US interval (ISI) and the US-US interval (ITI), as evidenced by increasing response rate gradients that were steeper for shorter intervals. The effects of the stimulus/cycle ratio on conditioning were attributed to independent timing of theS andC durations. Serial-, parallel-, and single-process accounts of conditioning and timing are compared.     

Generating and using examples in the proving process

We report on our analysis of data from a dataset of 26 videotapes of university students working in groups of 2 and 3 on different proving problems. Our aim is to understand the role of example generation in the proving process, focusing on deliberate changes in representation and symbol manipulation. We suggest and illustrate four aspects of situations in which example generation seems to play a positive role in proving. These aspects integrate qualities of students and of problems: experience of utility of examples in proving, personal example spaces and technical tools, formulation of the problem, and relational necessity. Our analysis led to integrating two theoretical ideas: the alignment of conceptual insight and technical handle when trying to prove; and manipulating, getting-a-sense-of, and articulating as phases of work associated with example construction.     

Family abduction in a national sample of US children

This study examined the prevalence and characteristics of family abduction episodes occurring in a nationally representative sample of US children ages 0–17. It drew on the experiences of 13,052 children and youth from the aggregation of three cross-sectional waves (2008, 2011, and 2014) of the National Surveys of Children Exposed to Violence. The overall prevalence rate was 4.1% for a lifetime and 1.2% for a past year episode. Rates were higher for younger than older children. Parents constituted 90% of the abductors with females outnumbering males 60% to 40%, although men outnumbered women as perpetrators for certain types of abductions. A bit less than half of the episodes (43%) were reported to police. The experience of a lifetime family abduction had an independent association with traumatic stress symptoms independent of exposure to other kinds of victimization including child maltreatment and witnessing family violence.     

Exploring processes of collaborative creativity—The role of emotions in children''s joint creative writing

This paper reports a study on children's classroom-based collaborative creative writing. Based on socio-cultural theory, the central aim of the research was to contribute to current understanding of young children's creativity, and describe ways in which peer collaboration can resource, stimulate and enhance classroom-based creative writing. The study drew on longitudinal observations of ongoing classroom activities in year 3 and year 4 classrooms, working with 24 children (12 pairs) aged 7–9 in England. The pairs’ collaborative creative writing sessions were observed and recorded using video and audio equipment in the literacy classroom and in the ICT suite with 2–4 recordings per pair. A functional model was developed to analyse cognitive processes associated with creative text composition (engagement and reflection) via the in-depth study of collaborative discourse. Based on the analysis of paired talk, the study has identified discourse patterns and collaborative strategies which facilitate sharedness and thus support joint creative writing activities. A key finding was the centrality of emotions in the observed creative writing sessions. This paper discusses the role of emotion-driven thinking in phases of shared engagement. The study has implications for creativity research and pedagogy, revealing the special features of shared creative thinking. It also contributes to the current methodological debate about how best to analyse collaborative discourse, highlighting the need to explore the generalisability and domain specificity of existing characterisations of productive groupwork.     

积分不等式在证明不等式中的应用

不等式的证明方法繁多,讨论几类重要不等式相互关系的基础上重点阐述了积分不等式在证明其它不等式中的应用.     

The role of motor processes in three-dimensional mental rotation: Shaping cognitive processing via sensorimotor experience

An extensive body of literature has explored the involvement of motor processes in mental rotation, yet underlying individual differences are less documented and remain to be fully understood. We propose that sensorimotor experience shapes spatial abilities such as assessed in mental rotation tasks. Elite wrestlers' and non-athletes' mental rotation accuracy and response times were measured in three different conditions: mental rotation (a), mental rotation with visual (b) and movement (c) interference. Results showed that both groups were equally affected by the visual interference task, as hypothesized from previous literature. However, the movement interference task impacted tremendously more wrestlers' mental rotation performance. These findings suggest that experts in motor activities rely heavily on motor processes in three-dimensional mental rotation problems solving, thus performing more poorly when simultaneously holding movements. The implications of this work in providing further evidence for the close tie between perceptive, motor and cognitive processes are discussed.     

中值命题证明中构造辅助函数的方法

运用微分中值定理证明有关中值命题的关键是构造辅助函数。而构造合适的辅助函数往往是比较困难的。为此，我们将探讨有关构造辅助函数的方法。     

Mathematical development: the role of broad cognitive processes

This study investigated the role of broad cognitive processes in the development of mathematics skills among children and adolescents. Four hundred and forty-seven students (age mean [M] = 10.23 years, 73% boys and 27% girls) from an elementary school district in the US southwest participated. Structural equation modelling tests indicated that calculation complexity was predicted by long-term retrieval and working memory; calculation fluency was predicted by perceptual processing speed, phonetic coding, and visual processing; problem solving was predicted by fluid reasoning, crystallised knowledge, working memory, and perceptual processing speed. Younger students’ problem solving skills were more strongly associated with fluid reasoning skills, relative to older students. Conversely, older students’ problem solving skills were more strongly associated with crystallised knowledge skills, relative to younger students. Findings are consistent with the theoretical suggestion that broad cognitive processes play specific roles in the development of mathematical skills among children and adolescents. Implications for educational psychologists are discussed.     

The VET system and industrial SMEs: the role of employees with VET qualifications in innovation processes

Reforms of the vocational education and training (VET) system in Spain are committed to a closer relationship between the VET system and companies’ needs. One of these needs is for a greater contribution of the VET system to innovation in companies, especially SMEs, which have limited resources to innovate. This contribution could materialise through a closer relationship between VET centres and SMEs, and also through a greater participation of employees with VET qualifications in innovation in SMEs. This article examines the role of these employees in SME innovation processes. We present the results of a survey of industrial SMEs in two Spanish industrial regions with high levels of experimental cooperation between VET centres and SMEs. The results point to the existence of obstacles to this participation. However, other factors that enable greater participation of this employee profile in SME innovation were also observed.