Persistence of invariant manifolds for nonlinear PDEs

We prove that under certain stability and smoothing properties of the semi-groups generated by the partial differential equations that we consider, manifolds left invariant by these flows persist under $C^1$ perturbation. In particular, we extend well known finite-dimensional results to the setting of an infinite-dimensional Hilbert manifold with a semi-group that leaves a submanifold invariant. We then study the persistence of global unstable manifolds of hyperbolic fixed-points, and as an application consider the two-dimensional Navier-Stokes equation under a fully discrete approximation. Finally, we apply our theory to the persistence of inertial manifolds for those PDEs which possess them. teComment: LaTeX2E, 32 pages, to appear in Studies in Applied Mathematic

Avifaunal Community Composition in a Tropical Forest Corridor: A Case Study from the Atherton Tableland, North Queensland

Bird communities in tropical forest ecosystems are highly threatened by habitat loss and fragmentation. Replanted corridors connecting isolated forest remnants are a popular method of ameliorating certain negative impacts of habitat fragmentation. Such linkages can theoretically facilitate greater dispersal, increase gene flow, and reduce the risk of local extinctions in forest birds. However, relatively few studies have examined the utilization of reforested corridors by birds, and little hard data exists to support claims that this type of resource and time intensive project is the best use of often scarce funding for conservation. This study examined the avifaunal community present in the Lakes Corridor, located on the Atherton Tableland in northeast Queensland, Australia. Point counts were conducted at multiple sites during April 2016 to determine the range and abundance of species utilizing this 18 year old corridor. Reference sites in the two large forest fragments which it connects were also surveyed in order to provide a comparison between community composition in regrowth and remnants. Results were compared with data from two past studies of a similar nature at the same location, thereby showing change over time associated with the maturation of corridor vegetation. The Lakes Corridor was found to support similar species richness and a greater abundance of individuals than remnant forest. However, community composition varied between the two habitats, driven primarily by differences in the abundance of certain foraging guilds and the absence of many endemic species in the corridor. Although the corridor shows promise for increasing connectivity for many rainforest birds, questions remain about its effectiveness for certain species of particular conservation concern

Address at Wreath-laying in the George Eliot Memorial Garden, Nuneaton 17 June 2007

As I reflected on \u27famous sons and daughters of Nuneaton\u27, I came up with a short list. George EliotlMary Anne Evans, Larry Grayson, Ken Loach. George Eliot must have cut quite an unconventional figure in her day. Larry Grayson, that rather gentle comedian, was also quite an unconventional character. Then Ken Loach, perhaps not so controversial in his personal life, none the less often espousing unconventional causes through his films. Is it something about Nuneaton that those it throws up into the arms of fame should have something of the unconventional about them? - or at least an eye for the unconventional, a sympathy for the unconventional? I must thank you for the privilege of being invited here today as vicar of St Nicolas, Nuneaton, vicar of the \u27Milby Church\u27 in George Eliot\u27s novels. And I must thank John Burton for furnishing me with my copy of Scenes o/Clerical Life - 150th anniversary edition. It has been interesting and instructive to read about life in Nuneaton 150 years ago: of the events and people associated with our church and town in such a different age. What struck me was the sympathy and insight of Mary Anne Evans. Perhaps her own struggles with society and its expectations explain something of her acute awareness that things aren\u27t always what they seem at first glance. When you first glimpse the rather sad and burnt-out figure of old Mr. Gilfil- how easy it is to dismiss him and not give a second glance. Yet for George Eliot there is a story here. He was once a vigorous young man in love - and so the story unfolds. She sees behind the public face - the shop front of people\u27s lives - to the complex human stories that make us all at the same time both ordinary and extraordinary: perhaps both conventional and unconventional. That\u27s what I\u27ve discovered about Nuneaton over the last eleven years as vicar of Nuneaton. When I first came here people said it was a very ordinary town. \u27It\u27s a good place to get away from.\u27 As if its proximity to the motorway network was its major asset! When, a few years after I arrived, the famous water feature was erected at the roundabout by Halfords, it was even hailed as the major tourist attraction for the town! \u27See the dandelion and you\u27ve seen the sights of Nuneaton!\u2

ASSESSING THE INTERESTS OF WHOLESALE-PRODUCEBUYERS IN THE LOWER MISSISSIPPI DELTA REGION

The need to expand the market share of Alabama fruits and vegetable producers necessitates an understanding of the attributes that would attract potential wholesale-produce buyers in the Lower Mississippi Delta Region (LMDR). A survey was developed and administered to over three thousand produce wholesale buyers in the LMDR; 317 returned surveys were analyzed for this study. Results indicate that non-Alabama wholesale-produce buyers would buy Alabama produce if the produce meet expected quality if adequate volume existed, if it were convenient, and if they were aware that the produce existed in Alabama. Produce such as peaches, sweet corn, beans, potatoes, and watermelons have greater market potential if volume is adequate and price competitive.Agribusiness,

The Relationship Between Instructional Delivery and Academic Motivation of Included Elementary Students With Special Needs

ABSTRACT Historically, it has always been important for educators to meet the needs of their children. In practice however, children with special needs were often neglected in the educational processes of schools. With the advent of NCLB and high stakes testing, the pressure on schools to demonstrate improved student achievement for all students has accelerated. As these children have been increasingly included within the regular classroom, educators have been challenged to develop methods to effectively meet their needs. This concurrent nested mixed method study explored the effect of interdisciplinary thematic instruction using constructivist principles on the motivation and performance of included 5th-grade elementary students with special needs. The study found that that experimental group students who received interdisciplinary thematic instruction as an intervention in math classes demonstrated higher motivation levels and academic performance than participants receiving traditional instruction. These results pose significant implications for schools attempting to meet the needs of included special needs children

Effects of Direct Instruction and Corrective Feedback on Second Language Acquisition

ABSTRACT This study compared the effectiveness of differing instructional approaches used within two units of study in Spanish classes at a suburban middle school. The purpose of this quantitative, pre-experimental study was to determine if direct instruction in grammar and vocabulary combined with a variety of corrective feedback types would facilitate higher levels of second language acquisition than an instructional approach that concentrated on student activity and task performance. The theoretical base of the present study focused on associative-cognitive second language theories and hypotheses that explained how second language learning occurs. The purposive convenience sample was comprised of 86 students aged 12 to 14 years enrolled in beginning-level Spanish classes. The assessment scores of the students after being exposed to the direct instructional approach were compared with the assessment scores of the students after being exposed to the student-centered instructional approach. Dependent-samples t tests were used to assess differences from pretest to posttest data collections, and to assess differences between the two posttest data collections. The analysis revealed a statistically significant result in favor of the direct instructional approach (t(85), p = .000, r = .01). The findings led to a recommendation for further study with participants of more advanced language proficiencies. The results advise instructional practices that increase students’ opportunities to develop higher levels of second language acquisition

Effects of Direct Instruction and Corrective Feedback on Second Language Acquisition

ABSTRACT This study compared the effectiveness of differing instructional approaches used within two units of study in Spanish classes at a suburban middle school. The purpose of this quantitative, pre-experimental study was to determine if direct instruction in grammar and vocabulary combined with a variety of corrective feedback types would facilitate higher levels of second language acquisition than an instructional approach that concentrated on student activity and task performance. The theoretical base of the present study focused on associative-cognitive second language theories and hypotheses that explained how second language learning occurs. The purposive convenience sample was comprised of 86 students aged 12 to 14 years enrolled in beginning-level Spanish classes. The assessment scores of the students after being exposed to the direct instructional approach were compared with the assessment scores of the students after being exposed to the student-centered instructional approach. Dependent-samples t tests were used to assess differences from pretest to posttest data collections, and to assess differences between the two posttest data collections. The analysis revealed a statistically significant result in favor of the direct instructional approach (t(85), p = .000, r = .01). The findings led to a recommendation for further study with participants of more advanced language proficiencies. The results advise instructional practices that increase students’ opportunities to develop higher levels of second language acquisition

Using Emergence Theory-Based Curriculum to Teach Compromise Skills to Students with Autistic Spectrum Disorders

This study addresses the compromise skills that are taught to students diagnosed with autistic spectrum disorders (ASD) and related social and communication deficits. A private school in the southeastern United States implemented an emergence theory-based curriculum to address these skills, yet no formal analysis was conducted to determine its effectiveness. Guided by cognitive development and constructivist theories, a concurrent, mixed methods, case study design was used to investigate the impact of this curriculum on teaching compromise skills to middle school students with ASD and related deficits. For the qualitative sequence, teacher observations and compromise interventions from eight participants were open coded and analyzed thematically. The frequency of each thematic occurrence was analyzed using descriptive statistics. For the quantitative sequence, an ANCOVA and descriptive statistics were used to analyze posttest scores between a treatment group that used emergence theory-based curriculum and a control group, while controlling for pretest scores. Three most frequently occurring themes emerged regarding teachers’ need (a) to understand the cognitive deficits exhibited by students, (b) for further instruction in emergence theory-based curriculum, and (c) for opportunities to plan lessons together using emergence theory. Moreover, the ANCOVA revealed a significant interaction between the pretest scores and the curriculum used. This study indicated that importance for remediating cognitive deficits related to compromise within the population of students with ASD and improving educator understanding and success in working with this student population

EFFECTS OF READING STRATEGIES AND THE WRITING PROCESS WITH WRITTEN RECASTS ON SECOND LANGUAGE ACHIEVEMENT

This study examined the effectiveness of teaching methods used with a second language reading and writing unit. This investigation addressed discrepancies between assessment scores in the four communicative language skill areas of students in beginning-level Spanish classes at a suburban middle school. Accordingly, the purpose of this study was to explore how literacy-based practices that included teaching strategies used with reading, teaching use of the writing process with a writing assignment, and teacher employment of written recasts affect second language achievement. The theoretical base of the study consisted of second language theories and hypotheses that explained how second language learning occurs. The academic achievement of the students exposed to the literacy-based teaching methods was compared with the achievement of students not exposed to literacy-based teaching methods. A purposive convenience sample consisted of 116 students between the ages of 12 and 14 years enrolled in beginning-level Spanish classes. An independent-measures and repeatedmeasures t tests were used to assess among- and between-group differences from pretest, posttest, and delayedposttest data collections. The between-groups analysis revealed a statistically-significant result in favor of the experimental group between the pretest and the posttest (t(114), p = .04, d = .36), and between the pretest and the delayed posttest (t(114), p = .03, d = .51). The findings led to a recommendation for further use and study of the methods, with additional assessment tools. The results inform instructional practices that increase students’ opportunities to be exposed to comprehensible language, thus affecting positive social change

USING EMERGENCE THEORY-BASED CURRICULUM TO TEACH COMPROMISE SKILLS TO STUDENTS WITH AUTISTIC SPECTRUM DISORDERS

This study addressed the compromise skills taught to students with autistic spectrum disorders (ASD) and related social and communication deficits. A private school in the southeastern United States implemented an emergence theory-based curriculum to address these skills, but no formal analysis was conducted to determine its effectiveness. Guided by cognitive development and constructivist theories, a concurrent, mixed-methods case study design was used to investigate the impact of this curriculum on teaching compromise skills to middle school students with ASD and related deficits. Teacher observations and compromise interventions were open coded and analyzed thematically using descriptive statistics. For the quantitative sequence, an ANCOVA and descriptive statistics were used to analyze posttest scores between the treatment group and the control group while controlling for pretest scores. The three most frequently occurring themes that emerged were in regard to teachers’ need to (a) understand the cognitive deficits exhibited by students, (b) receive instruction in emergence theory-based curriculum, and (c) plan lessons together using emergence theory. The ANCOVA revealed a significant interaction between the pretest scores and the curriculum used. This study indicated the importance of remediating the cognitive deficits of students with ASD and improving educator understanding and success in working with this student population