On the mean value of the Smarandache LCM function

For any positive integer n, the F.Smarandache LCM function SL(n) is defined as the smallest positive integer k

Burnout and the Retirement Decision

We introduce the process of psychological burnout and recovery as an explanation for the phenomenon known as unretirement. We illustrate theoretically how predictable time variation in burnout could generate retirement and subsequent re-entry in a standard retirement model. We apply this model to the longitudinal Health and Retirement Study, presenting a novel measure of burnout, the Burnout EX3 Index. The index is correlated with different types of work stressors, and its time profile discriminates among different types of retirees. For example, prior to retirement, burnout rises steeply for future unretirees then falls rapidly after retirement; whereas burnout among future partial retirees is low and changes little over time. Using a series of econometric models derived from our theoretical model, we show that as burnout rises, retirement becomes more probable, and as burnout recedes following retirement, re-entry becomes more probable. While access to public and private pension benefits increases the likelihood of retirement for all retirees, pension accruals are least important for those who will later unretire, suggesting that unretirees are more willing to trade future gains in pension wealth for leisure than other retirees. Indeed, for this group, the effect of burnout dominates that of the net return to work.

Does the Rise in the Full Retirement Age Encourage Disability Benefits Applications? Evidence from the Health and Retirement Study

As the Social Security full retirement age rises, the relative generosity of Social Security retirement benefits compared to disability benefits is declining, raising the incentive for insured people to apply for disability benefits. After controlling for other differences in observable characteristics, such as life-time earnings, we find that an average four month increase in the FRA slightly increases the two-year DI application rate by 0.04-0.30 percentage points. The effect is greater among those with a work limiting health problem (0.22-0.89 percentage points).

Discouraged Workers? Job Search Outcomes of Older Workers

Many have suggested we adopt policies that explicitly encourage the elderly to work. Behind this suggestion is the assumption that if an older person desires a job, one will be found; however, little is known about the extent to which this is true, and in the Health and Retirement Study, many more respondents say they expect to work after retirement than actually undertake work. This raises an important question: To what extent can the elderly readily find suitable jobs? In the context of a theoretical job search model, we examine the decision to search for a job and the probability of transitioning to employment using a large sample of non-workers from the Health and Retirement Study. The effects of both supply-side factors (individual characteristics) and demand-side factors (local labor market conditions) are estimated. We find employment transition rates are relatively low for older searchers: only half of older searchers successfully attain jobs. We examine various explanations for this result, including variation in search intensity, reservation wages, and the possibility of intervening health shocks. We conclude that about 13% of older job searchers becomes a discouraged worker in the sense of being willing to work at the prevailing wage, but unable to find a job.

Metallothionein overexpression prolongs grafts survival in the early phase of pancreatic islet transplantation.

Pancreatic islet transplantation is a very promising treatment for type I diabetes. Many clinical trials have failed due to early islet loss and immune rejection. Reactive oxygen species (ROS) have been demonstrated to be involved in graft damage during transplantation. Metallothionein (MT) is an inducible antioxidant protein. Prior studies in our laboratory have shown that overexpression of MT in beta-cells reduces DNA damage and diabetes induced by streptozotocin (STZ), which damages beta cells by generating ROS. Therefore in this study we examined whether overexpression of MT in beta cells is beneficial to pancreatic islet transplantation. Isolated MT transgenic and normal FVB islets were transplanted under the kidney capsule of Balb/c mice that were treated with STZ to induce severe diabetes. We found that diabetic mice transplanted with MT islets maintained near normal glucose levels for 16.2 [plus or minus] 2.52 days while those animals transplanted with control islets maintained normal glucose values for only 8.36 [plus or minus] 1.67 days (p \u3c 0.01). To determine whether the early benefit of MT was due to protection from early islet loss or from immune rejection, islets were transplanted into same strain mice, thereby free of immune rejection

Lie symmetry to nonlinear oscillator systems and applications

In this paper, we apply the theory of Lie symmetry to study a generalized second-order nonlinear differential equation, which includes several physical nonlinear oscillators such as force-free Helmholtz oscillator, force-free Duffing and Duffing-van der Pol oscillators, modified Emden-type equation and its hierarchy etc, and investigate the dynamical properties of this rather general equation. We identify and classify several new integrable cases for arbitrary values of exponents, which determine the tangent vector as well as the infinitesimal generator. Using the Lie point symmetry, we find the useful infinitesimal generators and canonical coordinates, and obtain the first integrals of the second-order nonlinear systems under certain parametric conditions. It shows that many classical integrable nonlinear oscillators can be derived as subcases of the obtained results and significantly enlarge the list of integrable equations that exists in the contemporary literature. Applications to wave equations of Korteweg-de Vries- Burgers-type equations are also presented