From Baking a Cake to Solving the Schrodinger Equation

The primary emphasis of this study has been to explain how modifying a cake recipe by changing either the dimensions of the cake or the amount of cake batter alters the baking time. Restricting our consideration to the genoise, one of the basic cakes of classic French cuisine, we have obtained a semi-empirical formula for its baking time as a function of oven temperature, initial temperature of the cake batter, and dimensions of the unbaked cake. The formula, which is based on the Diffusion equation, has three adjustable parameters whose values are estimated from data obtained by baking genoises in cylindrical pans of various diameters. The resulting formula for the baking time exhibits the scaling behavior typical of diffusion processes, i.e. the baking time is proportional to the (characteristic length scale)^2 of the cake. It also takes account of evaporation of moisture at the top surface of the cake, which appears to be a dominant factor affecting the baking time of a cake. In solving this problem we have obtained solutions of the Diffusion equation which are interpreted naturally and straightforwardly in the context of heat transfer; however, when interpreted in the context of the Schrodinger equation, they are somewhat peculiar. The solutions describe a system whose mass assumes different values in two different regions of space. Furthermore, the solutions exhibit characteristics similar to the evanescent modes associated with light waves propagating in a wave guide. When we consider the Schrodinger equation as a non-relativistic limit of the Klein-Gordon equation so that it includes a mass term, these are no longer solutions.Comment: 23 pages, 10 Postscript figure

An all-year pasture system for Missouri

Caption title.Digitized 2006 AES MU

Report of crop and pasture experiments at Lathrop in northwestern Missouri, 1940-1944

Cover title."Cooperatively written by the Field Crops Department, Missouri Agricultural Experiment Station, The Division of Forage Crops and Diseases, Bureau of Plant Industry, Soils and Agricultural Engineering, Agricultural Research Administration, United States Department of Agriculture; and C.L. Van Buren, Lathrop, Missouri"--Cover.Includes bibliographical references

Prostate Cancer Metastatic to Bone has Higher Expression of the Calcium-Sensing Receptor (CaSR) than Primary Prostate Cancer

The calcium-sensing receptor (CaSR) is the principal regulator of the secretion of parathyroid hormone and plays key roles in extracellular calcium (Ca2+o) homeostasis. It is also thought to participate in the development of cancer, especially bony metastases of breast and prostate cancer. However, the expression of CaSR has not been systematically analyzed in prostate cancer from patients with or without bony metastases. By comparing human prostate cancer tissue sections in microarrays, we found that the CaSR was expressed in both normal prostate and primary prostate cancer as assessed by immunohistochemistry (IHC). We used two methods to analyze the expression level of CaSR. One was the pathological score read by a pathologist, the other was the positivity% obtained from the Aperio positive pixel count algorithm. Both of the methods gave consistent results. Metastatic prostate cancer tissue obtained from bone had higher CaSR expression than primary prostate cancer (P0.05). The expression of CaSR in cancer tissue was not associated with the stage or status of differentiation of the cancer. These results suggest that CaSR may have a role in promoting bony metastasis of prostate cancer, hence raising the possibility of reducing the risk of such metastases with CaSR-based therapeutics

Winter barley : a new factor in Missouri agriculture

Cover title.Includes bibliographical references

An all-year pasture system for Missouri

Caption title.Digitized 2006 AES MoU

An all-year pasture system for Missouri

Caption title.Digitized 2006 AES MoU

Family and school social capital, school burnout and academic achievement : a multilevel longitudinal analysis among Finnish pupils

Research on the associations between family and school social capital, school burnout and academic achievement in adolescence is scarce and the results are inconclusive. We examined if family and school social capital at the age of 13 predicts lower school burnout and better academic achievement when graduating at the age of 16. Using data from 4467 Finnish adolescents from 117 schools and 444 classes a three-level multilevel analysis was executed. School social capital, the positive and supportive relationships between students and teachers, predicted lower school burnout and better academic achievement among students. Classmates' family social capital had also significance for students' academic achievement. Our results suggest that building school social capital is an important aspect of school health and education policies and practices.Peer reviewe

Breakup of 17^{17}F on 208^{208}Pb near the Coulomb barrier

Angular distributions of oxygen produced in the breakup of $^{17}$F incident on a $^{208}$Pb target have been measured around the grazing angle at beam energies of 98 and 120 MeV. The data are dominated by the proton stripping mechanism and are well reproduced by dynamical calculations. The measured breakup cross section is approximately a factor of 3 less than that of fusion at 98 MeV. The influence of breakup on fusion is discussed.Comment: 7 pages, 8 figure

Climate and southern Africa's water-energy-food nexus

In southern Africa, the connections between climate and the water-energy-food nexus are strong. Physical and socioeconomic exposure to climate is high in many areas and in crucial economic sectors. Spatial interdependence is also high, driven for example, by the regional extent of many climate anomalies and river basins and aquifers that span national boundaries. There is now strong evidence of the effects of individual climate anomalies, but associations between national rainfall and Gross Domestic Product and crop production remain relatively weak. The majority of climate models project decreases in annual precipitation for southern Africa, typically by as much as 20% by the 2080s. Impact models suggest these changes would propagate into reduced water availability and crop yields. Recognition of spatial and sectoral interdependencies should inform policies, institutions and investments for enhancing water, energy and food security. Three key political and economic instruments could be strengthened for this purpose; the Southern African Development Community, the Southern African Power Pool, and trade of agricultural products amounting to significant transfers of embedded water