Studies in free module and it\u27s basis

The purpose of this project was to study some basic properties of free modules over a ring. A module with a basis is called a free module and a free module over a division ring (or field) is called a vector space. We show every vector has a basis and any two bases of a vector space have same cardinality. However, a free module over an arbitrary ring (with identity) does not have this property

Status and Multiple Growth Regimes

In order to explain multiple growth regimes, one of the working hypotheses is based on initial conditions. Using a standard optimal growth with the status effect represented by wealth a la Friedman (1953), this paper obtains multiple growth regimes based on initial conditions without reliance on other assumptions such as nonlinearities of production or consumption functions and heterogeneous agents/savings behavior. With the status effect, the resulting equilibrium distribution is characterized by a group with a lower level of income and another group with a higher level of income. Globally, a sufficiently strong monetary policy may be an instrument in order for an economy in poverty traps to take off and become wealthy in the long run. Locally, our model sheds light on the relationship between money/inflation and capital in the long run that, given general cash-in-advance constraints on investment relative to consumption, is determined by the curvature of the utilities of wealth and consumption.one-sector growth model, wealth effect, CIA constraint, takeoff

Inflation and Growth: Impatience and a Qualitative Equivalence

This paper studies the role of an endogenous time preference on the relationship between inflation and growth in the long run in both the money-in-utility-function (MIUF) and transaction costs (TC) models. We establish a qualitative equivalence between the two models in a setup without a labor-leisure tradeoff. When the time preference is decreasing (or increasing) in consumption and real balances, both the MIUF and TC models are qualitatively equivalent in terms of predicting a negative (or positive) relationship between inflation and growth in a steady state. Both a decreasing and an increasing time preference in consumption are consistent with the arguments in the literature. While a decreasing time preference in real balances corroborates with empirical evidence, there is no evidence in support of an increasing time preference in real balances.endogenous time preferences, superneutrality, qualitative equivalence

Assessing the Effects of Acupuncture by Comparing Needling the Hegu Acupoint and Needling Nearby Nonacupoints by Spectral Analysis of Microcirculatory Laser Doppler Signals

We aimed to assess the effects of acupuncture by analyzing the frequency content of skin blood-flow signals simultaneously recorded at the Hegu acupoint and two nearby nonacupoints following acupuncture stimulation (AS). Laser Doppler flowmetry (LDF) signals were measured in male healthy volunteers in two groups of experiments: needling the Hegu acupoint (n = 13) and needling a nearby nonacupoint (control experiment; n = 10). Each experiment involved recording a 20 min baseline-data sequence and two sets of effects data recorded 0–20 and 50–70 min after stopping AS. Wavelet transform with Morlet mother wavelet was applied to the measured LDF signals. Needling the Hegu acupoint significantly increased the blood flow, significantly decreased the relative energy contribution at 0.02–0.06 Hz and significantly increased the relative energy contribution at 0.4–1.6 Hz at Hegu, but induced no significant changes at the nonacupoints. Also, needling a nearby nonacupoint had no effect in any band at any site. This is the first time that spectral analysis has been used to investigate the microcirculatory blood-flow responses induced by AS, and has revealed possible differences in sympathetic nerve activities between needling the Hegu acupoint and its nearby nonacupoint. One possible weakness of the present design is that different De-Qi feelings following AS could lead to nonblind experimental setup, which may bias the comparison between needling Hegu and its nearby nonacupoint. Our results suggest that the described noninvasive method can be used to evaluate sympathetic control of peripheral vascular activity, which might be useful for studying the therapeutic effects of AS