Vector Fields, Flows and Lie Groups of Diffeomorphisms

The freedom in choosing finite renormalizations in quantum field theories (QFT) is characterized by a set of parameters $\{c_i \}, i = 1 ..., n >...$, which specify the renormalization prescriptions used for the calculation of physical quantities. For the sake of simplicity, the case of a single $c$ is selected and chosen mass-independent if masslessness is not realized, this with the aim of expressing the effect of an infinitesimal change in $c$ on the computed observables. This change is found to be expressible in terms of an equation involving a vector field $V$ on the action's space $M$ (coordinates x). This equation is often referred to as ``evolution equation'' in physics. This vector field generates a one-parameter (here $c$) group of diffeomorphisms on $M$. Its flow $\sigma_c (x)$ can indeed be shown to satisfy the functional equation $$\sigma_{c+t} (x) = \sigma_c (\sigma_t (x)) \equiv \sigma_c \circ \sigma_t$$ $$\sigma_0 (x) = x,$$ so that the very appearance of $V$ in the evolution equation implies at once the Gell-Mann-Low functional equation. The latter appears therefore as a trivial consequence of the existence of a vector field on the action's space of renormalized QFT.Comment: (8 pages, latex

The so-called renormalization group method applied to the specific prime number logarithmic decrease

A so-called Renormalization Group (RG) analysis is performed in order to shed some light on why the density of prime numbers in $\Bbb N^*$ decreases like the single power of the inverse neperian logarithm.Comment: 6 pages, late

Effects of Movement, Growth Mindset and Math Talks on Math Anxiety

Mathematical anxiety is prevalent in our schools. This research provides insight into how mathematical anxiety develops and how it affects students throughout their lives. This study focuses on the mathematical anxiety and mathematical self-concept of five second grade classes at an economically disadvantaged school in rural North Texas. The study looked to see if adding the interventions of movement, mathematical growth mindset and math talks to a classroom would improve the mathematical self-concept of the children in the classrooms which participated. The study contained three classrooms of students who participated in the interventions and two classrooms which were used as a control group. All five second grade classrooms completed a pre and post-intervention survey of mathematical self-concepts. The three main categories measured by the survey were math self-concept, comfort using different mathematical strategies and comfort level with discussing and using math concepts in front of peers. The children received mathematical movement lessons on Mondays, growth mindset journaling and discussions on Tuesdays and mental math number talks on Wednesdays. After the four-week study, the results showed an overall gain in positive responses for the three categories, which were measured for this study in the intervention group. The control group did not show as much of a positive gain as the intervention group did, and in some cases actually went down in positive responses

A review of empirical evidence on gender differences in nonland agricultural inputs, technology, and services in developing countries

This paper reviews existing microeconomic empirical literature on gender differences in use, access, and adoption of nonland agricultural inputs in developing countries. This review focuses on four key areas: (1) technological resources, (2) natural resources, (3) human resources, and (4) social and political capital. In general, there has been more empirical research on inorganic fertilizer, seed varieties, extension services, and group membership than on tools and mechanization, life-cycle effects, and political participation. Across input areas, generally men have higher input measures than women; however, this finding is often sensitive to the use of models that control for other background factors, as well as the type of gender indicator implemented in the analysis. We find few studies that meet our inclusion criteria outside Sub-Saharan Africa. Finally, future directions, opportunities, and recommendations for microeconomic gender analysis of nonland agricultural inputs are discussed.access to farm inputs, Agricultural inputs, Agriculture, assets, Developing countries, Gender, life-cycle effects, mechanization, Women,

Examining contributions to core consumer inflation measures

The purpose of this paper is to examine the composition of inflation over time. The authors calculate the contributions to inflation for individual series of the consumer price index (CPI) and personal consumption expenditures price index (PCEPI) and then aggregate those contributions into major consumer expenditure categories. This technique provides a wealth of information concerning aggregate inflation behavior in a concise way, enabling the authors to describe the composition of inflation at any point in time. A particularly important benefit of this method is that it allows them to distinguish broad-based changes in inflation from changes due to relative price movements of a few components. The authors examine long-term trends in contributions to PCEPI core inflation and make inferences about the direction of inflation in the near term. In addition, they examine the decline in CPI core inflation over the 2002–03 period and find that the decline was largely driven by relative price changes of two components.

Local Solutions to Global Problems: Policy Choice and Regulatory Jurisdiction

This paper considers the efficiency of various types of environmental regulations when they are applied locally to pollutants whose damages extend outside the jurisdiction of the local regulator. We draw on examples from state- and city-level efforts to address climate change by enacting policies to reduce greenhouse gases. While previous work has noted the possibility for leakage, whereby the polluting sources move outside the jurisdiction of the regulation in order to escape it, we note an additional problem when policies are targeted downstream at consumers of goods whose production creates pollution. Specifically, we show how consumer-based policies can be circumvented by a simple reshuffling of who is buying from whom. We argue that the leakage and reshuffling problems are most pronounced with more flexible or market-based regulations. We conclude that localities may have the most effect on global pollutants when they enact efficiency standards or targeted subsidies.

Decomposing inflation

As U.S. core inflation measures have declined in recent years, analysts have renewed their efforts to understand inflation dynamics. A common approach to this issue is to make inferences about how price changes of major components affect the aggregate inflation rate. This article takes a more rigorous approach, calculating and plotting the precise contributions of major consumer expenditure categories to core inflation measures over time. ; This technique has distinct advantages. It highlights the underlying trends in inflation, enabling analysts to make more informed inferences about the near-term direction of inflation. It also allows analysts to distinguish broad-based changes in inflation from changes due to relative price movements of a few components. ; The analysis focuses on the core components of the consumer price index (CPI) and the personal consumption expenditures price index (PCEPI). Over the long term, the authors note, the composition of core services inflation has remained relatively stable while the composition of core goods inflation has changed dramatically. Over the 2002–03 period, movements in core inflation measures resulted mainly from significant relative price changes of two components that were persistent enough to alter the path of core inflation for a sustained period, the authors conclude. ; The results of this study highlight the importance of gauging the impact of relative changes in a low-inflation environment and suggest that recent concern about overall price deflation was perhaps overstated.Inflation (Finance)

The Seventy-Fifth Anniversary History of Philadelphia College of Osteopathic Medicine: A Condensed Record of the Courage, Convictions, and the Transcending Determination of the Early Osteopathic Pioneers, and those who have since Carried on their Concept of Better Healing and Health Care

This book explains the early history of Philadelphia College of Osteopathic Medicine from 1899 to 1974.https://digitalcommons.pcom.edu/history/1003/thumbnail.jp