Dilations and the Equation of a Line

2016 ◽  
Vol 21 (7) ◽  
pp. 406-414
Author(s):  
David A. Yopp
Keyword(s):  
Proportional Reasoning ◽  
Similar Triangle ◽  
Linear Relationships ◽  
Transformational Geometry

Track students' understanding of proportional reasoning by combining transformational geometry, similar-triangle reasoning, and linear relationships.

A Unifying Theme

2003 ◽  
Vol 8 (8) ◽  
pp. 387
Keyword(s):  
Middle Grades ◽  
Proportional Reasoning ◽  
Additive Models ◽  
Classroom Teaching ◽  
Central Component ◽  
Active Engagement ◽  
Mathematics Students ◽  
Linear Relationships

Roportionality is a central component of middle-grades mathematics. Students encounter contexts and concepts involving ratios, proportions, fractions, decimals, percents, similarity, rates, linear relationships, and related situations when counting and additive models are no longer appropriate or efficient methods to apply. Experience has shown us that it takes time and active engagement to develop the thinking needed to conceptualize these areas. Such understanding lays an important foundation for later mathematics. To provide you with classroom-based ideas and examples and to stimulate your own thinking about proportional reasoning, the Editorial Panel brings you this focus issue. The authors share activities and insights for classroom teaching on a variety of proportional reasoning topics.

Development of simple models for agrichemical uptake into plant foliage

2003 ◽  
Vol 56 ◽  
pp. 61-65
Author(s):  
J.A. Zabkiewicz ◽  
W.A. Forster
Keyword(s):  
Vicia Faba ◽  
Initial Dose ◽  
Plant Leaves ◽  
Linear Relationships ◽  
Plant Foliage ◽  
Mass Uptake ◽  
Uptake Mechanisms ◽  
Simple Models

Pesticide uptake into plants is typically reported as percentage uptake of the amount applied but in studies of the mechanism of cuticular penetration this approach has not been helpful It can be shown that relating percentage uptake to initial dose of bentazone applied to Vicia faba foliage cannot provide pertinent relationships that can be used to explain cuticular uptake mechanisms However applying the principles of Ficks Law and using mass or molar quantities does provide excellent linear relationships between mass uptake and initial dose applied Universal equations can be derived that relate dose uptake to initial dose applied onto plant leaves

Application of an LC-MS/MS Method to a Urinary Excretion Study of Triflusal and its Main Metabolite 2-hydroxy-4-trifluoromethyl Benzoic Acid in Human Urine

2020 ◽  
Vol 16 (3) ◽  
pp. 328-334
Author(s):  
Jie Ge ◽  
Jin-Wen Wang ◽  
Qi-Yan Guo ◽  
Ai-Dong Wen
Keyword(s):  
Benzoic Acid ◽  
Urinary Excretion ◽  
Human Urine ◽  
Multiple Reaction Monitoring ◽  
Main Metabolite ◽  
Linear Relationships ◽  
Pharmacokinetic Properties ◽  
Liquid Chromatography Tandem Mass ◽  
Excretion Study ◽  
Acetate Aqueous Solution

Objective: A validated liquid chromatography-tandem mass spectrometry method (LCMS/ MS) was established to simultaneously determine the concentration of triflusal and its main metabolite 2-hydroxy-4-trifluoromethyl benzoic acid(HTB) in human urine. Methods: The separation was performed on a Dikma C18 column using isocratic elution with acetonitrile-4 mmol/L ammonium acetate aqueous solution containing 0.3 % formic acid water (78: 28, V/V). The method involved extraction with methanol using protein precipitation. The precursor-toproduct ion transitions with multiple reaction monitoring was m/z 247.1→161.1, 204.8→106.7and 136.9→93.0 for triflusal, HTB and salicylic acid(IS), respectively. The method showed good linear relationships over the ranges of 0.08 to 48 μg/mL and0.5 to 50 μg/mL. Results: It was the first time that a urinary excretion study of triflusal capsule as oral. The cumulative urinary recovery showed 8.5% and 2.7% for triflusal and HTB, respectively. Conclusion: This method was successfully used for evaluating the pharmacokinetic properties of triflusal and HTB in urine in Chinese healthy subjects.

New Strategies for Clinical Trials in Autism Spectrum Disorder

2020 ◽  
Vol 15 ◽  
Author(s):  
Rini Pauly ◽  
Catherine A. Ziats ◽  
Ludovico Abenavoli ◽  
Charles E. Schwartz ◽  
Luigi Boccuto
Keyword(s):  
Autism Spectrum Disorder ◽  
Clinical Trials ◽  
Autism Spectrum ◽  
Spectrum Disorder ◽  
Genetic Profiling ◽  
Omics Technologies ◽  
Molecular Abnormalities ◽  
Sequencing Technologies ◽  
Linear Relationships ◽  
Personalized Approach

Background: Autism spectrum disorder (ASD) is a complex neurodevelopmental condition that poses several challenges in terms of clinical diagnosis and investigation of molecular etiology. The lack of knowledge on the pathogenic mechanisms underlying ASD has hampered the clinical trials that so far have tried to target ASD behavioral symptoms. In order to improve our understanding of the molecular abnormalities associated with ASD, a deeper and more extensive genetic profiling of targeted individuals with ASD was needed. Methods: The recent availability of new and more powerful sequencing technologies (third-generation sequencing) has allowed to develop novel strategies for characterization of comprehensive genetic profiles of individuals with ASD. In particular, this review will describe integrated approaches based on the combination of various omics technologies that will lead to a better stratification of targeted cohorts for the design of clinical trials in ASD. Results: In order to analyze the big data collected by assays such as whole genome, epigenome, transcriptome, and proteome, it is critical to develop an efficient computational infrastructure. Machine learning models are instrumental to identify non-linear relationships between the omics technologies and therefore establish a functional informative network among the different data sources. Conclusion: The potential advantage provided by these new integrated omics-based strategies is to better characterize the genetic background of ASD cohorts, identify novel molecular targets for drug development, and ultimately offer a more personalized approach in the design of clinical trials for ASD.

scholarly journals Lack of an association between gallstone disease and bilirubin levels with risk of colorectal cancer: a Mendelian randomisation analysis

2021 ◽  
Author(s):  
Richard Culliford ◽  
Alex J. Cornish ◽  
Philip J. Law ◽  
Susan M. Farrington ◽  
Kimmo Palin ◽  
...  
Keyword(s):  
Colorectal Cancer ◽  
Large Scale ◽  
Causal Effect ◽  
Gallstone Disease ◽  
Epidemiological Studies ◽  
Mendelian Randomisation ◽  
Linear Relationships ◽  
Potential Risk Factors ◽  
The Relationship ◽  
Circulating Levels

Abstract Background Epidemiological studies of the relationship between gallstone disease and circulating levels of bilirubin with risk of developing colorectal cancer (CRC) have been inconsistent. To address possible confounding and reverse causation, we examine the relationship between these potential risk factors and CRC using Mendelian randomisation (MR). Methods We used two-sample MR to examine the relationship between genetic liability to gallstone disease and circulating levels of bilirubin with CRC in 26,397 patients and 41,481 controls. We calculated the odds ratio per genetically predicted SD unit increase in log bilirubin levels (ORSD) for CRC and tested for a non-zero causal effect of gallstones on CRC. Sensitivity analysis was applied to identify violations of estimator assumptions. Results No association between either gallstone disease (P value = 0.60) or circulating levels of bilirubin (ORSD = 1.00, 95% confidence interval (CI) = 0.96–1.03, P value = 0.90) with CRC was shown. Conclusions Despite the large scale of this study, we found no evidence for a causal relationship between either circulating levels of bilirubin or gallstone disease with risk of developing CRC. While the magnitude of effect suggested by some observational studies can confidently be excluded, we cannot exclude the possibility of smaller effect sizes and non-linear relationships.

scholarly journals Estimation of permeability and saturation based on imaginary component of complex resistivity spectra: A laboratory study

2020 ◽  
Vol 12 (1) ◽  
pp. 299-306
Author(s):  
Jiang Jia ◽  
Shizhen Ke ◽  
Junjian Li ◽  
Zhengming Kang ◽  
Xuerui Ma ◽  
...  
Keyword(s):  
Water Saturation ◽  
Pore Space ◽  
Evaluation Model ◽  
Low Frequency ◽  
Petroleum Exploration ◽  
Western China ◽  
Imaginary Component ◽  
Estimation Model ◽  
Complex Resistivity ◽  
Linear Relationships

AbstractLow-frequency resistivity logging plays an important role in the field of petroleum exploration, but the complex resistivity spectrum of rock also contains a large amount of information about reservoir parameters. The complex resistivity spectra of 15 natural sandstone cores from western China, with different water saturations, were measured with an impedance analyzer. The pore space of each core was saturated with NaCl solution, and measurements were collected at a frequency range of 40–15 MHz. The results showed a linear relationship between the real resistivity at 1 kHz and the maximum values of imaginary resistivity for each core with different water saturations. The slopes of the linear best-fit lines had good linear relationships with the porosity and the permeability of cores. Based on this, a permeability estimation model was proposed and tested. In addition, the maxima of imaginary resistivity had power exponential relationships with the porosity and the water saturation of the cores. A saturation evaluation model based on the maxima of imaginary resistivity was established by imitating Archie’s formula. The new models were found to be feasible for determining the permeability and saturation of sandstone based on complex resistivity spectrum measurements. These models advance the application of complex resistivity spectrum in petrophysics.

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