Equipping Children and Pre–Teens to Read and Study Their Bibles

There is a shortage of material which teaches children and pre–teens how to read and study the Bible. It is important for educators to help them become good Bible readers and interpreters. This paper presents five crucial steps that are important to instruct children and pre–teens in the skills necessary to work out the appropriate meaning and application of the Biblical text. Because children and adolescents learn by “doing,” this article suggests core activities to help them understand and develop Bible interpretation skills

On the convergence of spectral deferred correction methods

In this work we analyze the convergence properties of the Spectral Deferred Correction (SDC) method originally proposed by Dutt et al. [BIT, 40 (2000), pp. 241--266]. The framework for this high-order ordinary differential equation (ODE) solver is typically described wherein a low-order approximation (such as forward or backward Euler) is lifted to higher order accuracy by applying the same low-order method to an error equation and then adding in the resulting defect to correct the solution. Our focus is not on solving the error equation to increase the order of accuracy, but on rewriting the solver as an iterative Picard integral equation solver. In doing so, our chief finding is that it is not the low-order solver that picks up the order of accuracy with each correction, but it is the underlying quadrature rule of the right hand side function that is solely responsible for picking up additional orders of accuracy. Our proofs point to a total of three sources of errors that SDC methods carry: the error at the current time point, the error from the previous iterate, and the numerical integration error that comes from the total number of quadrature nodes used for integration. The second of these two sources of errors is what separates SDC methods from Picard integral equation methods; our findings indicate that as long as difference between the current and previous iterate always gets multiplied by at least a constant multiple of the time step size, then high-order accuracy can be found even if the underlying "solver" is inconsistent the underlying ODE. From this vantage, we solidify the prospects of extending spectral deferred correction methods to a larger class of solvers to which we present some examples.Comment: 29 page

The Acute Effect of Water Intake on Glucose Regulation in Low Drinkers

Previous evidence suggests the hormone arginine vasopressin (AVP) may be a modifiable factor contributing to hyperglycemia. Significant differences in urine concentration and copeptin, a marker for AVP, have been observed between low and high water drinkers. Purpose: The purpose was to investigate the acute effect of adequate water intake on glucose regulation in low drinkers. Methods: 7 healthy (5 males, 2 female) low drinkers were recruited using a water frequency questionnaire (WFQ), spot and 24-h urine sample (age 43±6 y, BMI 30.9±3, WFQ volume 823±403 mL∙d-1, 24 h Uosm 961±105 mmol∙kg-1, copeptin 8.17±3.05 pmol∙L-1). During two experimental protocols, participants remained in the laboratory for 11 h and were provided either the Institute of Medicine’s (IOM) recommended amount of water excluding food (males: 3 L, females: 2 L) or an amount representing the bottom quartile of water consumption observed in the National Health and Nutrition Examination Survey (NHANES) (males: 0.5 L, females: 0.4 L). Food was provided to participants and standardized to body weight (100 kJ∙Kg-1) using a consistent ratio of macronutrients. Results: 11 h urine volume was significantly higher in the high water trial (P \u3c 0.001). 11 h UOsm was significantly higher in the low water trial (P \u3c 0.001). Plasma osmolality was acutely lower as a result of increased water intake (P = 0.007). Copeptin was suppressed as a result of high water intake (P = 0.019). Glucagon was similar between trials (P = 0.372), however, there was a main effect of water intake on cortisol (P = 0.009). No differences in plasma glucose were found due to water intake (P = 0.07). Conclusion: Acute increases in water intake do not reduce post-prandial plasma glucose responses in low drinkers, however, cortisol may be acutely reduced