Solution of differential equations by application of transformation groups

Report applies transformation groups to the solution of systems of ordinary differential equations and partial differential equations. Lies theorem finds an integrating factor for appropriate invariance group or groups can be found and can be extended to partial differential equations

Application of group and transformation theory to the solution of ordinary and partial differential equations Final report, 17 Jan. 1967 - 16 Jan. 1968

Application of transformation groups to solution of partial differential equation

Application of group and transformation theory to the solution of ordinary and partial differential equations Final report

Lie transformation group for solution of partial differential equation

Prospective Teachers\u27 Use of Representations in Solving Statistical Tasks with Dynamic Statistical Software

This study examined a random stratified sample (n=62) of prospective teachers\u27 work across eight institutions on three tasks that utilized dynamic statistical software. Our work was guided by considering how teachers may utilize their statistical knowledge and technological statistical knowledge to engage in cycles of investigation. Although teachers did not tend to take full advantage of dynamic linking capabilities, they utilized a large variety of graphical representations and often added statistical measures or other augmentations to graphs as part of their analysis

Integration of Arrival-Time Datasets for Consistent Quality Control: A Case Study of Amphibious Experiments along the Middle America Trench

We have integrated waveform and arrival-onset data collected in Costa Rica as part of the National Science Foundation (NSF)-sponsored Costa Rica Seismogenic Zone Experiment (CRSEIZE) and along central Costa Rica and Nicaragua as part of the German SFB 574 program. The five arrays, composed of different sensor types (one-and three-component land and ocean bottom seismometers and hydrophones), were archived using different software packages (Antelope and SEISAN) and were automatically and manually picked using various quality criteria resulting in a disparate set of pick weights. We evaluate pick quality using automated arrival detection and picking algorithm based on the wavelet transform and Akaike information criterion picker. The consistency of the arrival information over various scales provides a basis for assigning a quality to the analyst pick. Approximately 31% of P arrival times and 26% of S times have been classified as high-quality picks (quality 0-1). An additional 21% of P times and 27% of S arrivals are good quality (quality 2-3). The revised quality picks are mapped directly into new pick weights for inversion studies. We explore the effect of new weighting and removal of poor data by relocating hypocenters through a minimum 1D velocity model and conducting double-difference local earthquake tomography (LET). Analysis of the hypocenter relocation and seismic velocity tomography results suggest that using the improved quality determinations have a greater effect on improving sharpness in the velocity images than on the magnitude of hypocentral movement

Effects of stocking rate and corn gluten feed supplementation on performance of young beef cows grazing winter-stockpiled tall fescue-red clover pasture

A winter grazing experiment was conducted to evaluate the effects of stocking rate and corn gluten feed supplementation on forage mass and composition and the BW and BCS of bred 2-yr-old cows grazing stockpiled forage during winter. Two 12.2-ha blocks containing Fawn, endophyte-free, tall fescue and red clover were each divided into 4 pastures of 2.53 or 3.54 ha. Hay was harvested from the pastures in June and August of 2003 and 2004, and N was applied at 50.5 kg/ha at the initiation of stockpiling in August. On October 22, 2003, and October 20, 2004, twenty-four 30-mo-old Angus-Simmental and Angus cows were allotted by BW and BCS to strip-graze for 147 d at 0.84 or 1.19 cow/ha. Eight similar cows were allotted to 2 dry lots and fed tall fescue-red clover hay ad libitum. Corn gluten feed was fed to cows in 2 pastures to maintain a mean BCS of 5 (9-point scale) at each stocking rate and in the dry lots (high supplementation level) or when weather prevented grazing (low supplementation level) in the remaining 2 pastures at each stocking rate. Mean concentrations of CP in yr 1 and 2 and IVDMD in yr 2 were greater (P \u3c 0.10) in hay than stockpiled forage over the winter. At the end of grazing, cows fed hay in dry lots had greater (P \u3c 0.05) BCS in yr 1 and greater (P \u3c 0.10) BW in yr 2 than grazing cows. Grazing cows in the high supplementation treatment had greater (P \u3c 0.10) BW than cows grazing at the low supplementation level in yr 1. Cows in the dry lots were fed 2,565 and 2,158 kg of hay DM/cow. Amounts of corn gluten feed supplemented to cows in yr 1 and 2 were 46 and 60 kg/ cow and did not differ (P = 0.33, yr 1; P = 0.50, yr 2) between cows fed hay or grazing stockpiled forage in either year. Estimated production costs were greater for cows in the dry lots because of hay feeding

Clonal Growth of Dermal Papilla Cells in Hydrogels Reveals Intrinsic Differences between Sox2-Positive and -Negative Cells In Vitro and In Vivo

In neonatal mouse skin, two types of dermal papilla (DP) are distinguished by Sox2 expression: CD133+Sox2+ DP are associated with guard/awl/auchene hairs, whereas CD133+Sox2− DP are associated with zigzag (ZZ) hairs. We describe a three-dimensional hydrogel culture system that supports clonal growth of CD133+Sox2+, CD133+Sox2−, and CD133−Sox2− (non-DP) neonatal dermal cells. All three cell populations formed spheres that expressed the DP markers alkaline phosphatase, α8 integrin, and CD133. Nevertheless, spheres formed by CD133− cells did not efficiently support hair follicle formation in skin reconstitution assays. In the presence of freshly isolated P2 dermal cells, CD133+Sox2+ and CD133+Sox2− spheres contributed to the DP of both AA and ZZ hairs. Hair type did not correlate with sphere size. Sox2 expression was maintained in culture, but not induced significantly in Sox2− cells in vitro or in vivo, suggesting that Sox2+ cells are a distinct cellular lineage. Although Sox2+ cells were least efficient at forming spheres, they had the greatest ability to contribute to DP and non-DP dermis in reconstituted skin. As the culture system supports clonal growth of DP cells and maintenance of distinct DP cell types, it will be useful for further analysis of intrinsic and extrinsic signals controlling DP function

The Quality of Mathematics Education Technology Literature

Background: The present study evaluated the quality of 1,165 scholarly literature papers about mathematics education technology literature.Purpose: The purpose of the present study was to determine the extent to which mathematics education technology literature reports the information needed to support the scientific basis of a study.Setting: N/AIntervention: N/AResearch Design: A systematic review was used to organize the data collection and analysis processes Data Collection and Analysis: A literature search was conducted to identify scholarly papers that addressed the use of technology in mathematics education. A coding process was developed to record descriptive information about each paper. The Quality Framework developed for this process provided a structure to identify key information across research types based on types of analyses conducted, assigning a certain number of possible points based on the type of research conducted.Findings: Dissertations accounted for a surprisingly high portion of the literature and research: 39.7% of the available literature and 57.0% of the research studies. The overall quality of the mathematics education technology literature was lower than we expected, averaging only 48.9% of the points possible. We noted that the quality of research papers, with respect to possible point values averaged 54.6% over four decades. For mathematics education technology researchers, manuscript reviewers, and editors, these results suggest that more attention is needed on the information being included and excluded from scholarly papers, especially with regard to connections to theoretical frameworks and research designs

Research in Mathematics Educational Technology: Current Trends and Future Demands

This systematic review of mathematics educational technology literature identified 1356 manuscripts addressing the integration of educational technology into mathematics instruction. The manuscripts were analyzed using three frameworks (Research Design, Teacher Knowledge, and TPACK) and three supplementary lenses (Data Sources, Outcomes, and NCTM Principles) to produce a database to support future research syntheses and meta-analyses. Preliminary analyses of student and teacher outcomes (e.g., knowledge, cognition, affect, and performance) suggest that the effects of incorporating graphing calculator and dynamic geometry technologies have been abundantly studied; however, the usefulness of the results was often limited by missing information regarding measures of validity, reliability, and/or trustworthiness

Inhibition of β-catenin signalling in dermal fibroblasts enhances hair follicle regeneration during wound healing.

New hair follicles (HFs) do not form in adult mammalian skin unless epidermal Wnt signalling is activated genetically or within large wounds. To understand the postnatal loss of hair forming ability we monitored HF formation at small circular (2 mm) wound sites. At P2, new HFs formed in back skin, but HF formation was markedly decreased by P21. Neonatal tail also formed wound-associated HFs, albeit in smaller numbers. Postnatal loss of HF neogenesis did not correlate with wound closure rate but with a reduction in Lrig1-positive papillary fibroblasts in wounds. Comparative gene expression profiling of back and tail dermis at P1 and dorsal fibroblasts at P2 and P50 showed a correlation between loss of HF formation and decreased expression of genes associated with proliferation and Wnt/β-catenin activity. Between P2 and P50, fibroblast density declined throughout the dermis and clones of fibroblasts became more dispersed. This correlated with a decline in fibroblasts expressing a TOPGFP reporter of Wnt activation. Surprisingly, between P2 and P50 there was no difference in fibroblast proliferation at the wound site but Wnt signalling was highly upregulated in healing dermis of P21 compared with P2 mice. Postnatal β-catenin ablation in fibroblasts promoted HF regeneration in neonatal and adult mouse wounds, whereas β-catenin activation reduced HF regeneration in neonatal wounds. Our data support a model whereby postnatal loss of hair forming ability in wounds reflects elevated dermal Wnt/β-catenin activation in the wound bed, increasing the abundance of fibroblasts that are unable to induce HF formation