Rate of Decay of Stable Periodic Solutions of Duffing Equations

In this paper, we consider the second-order equations of Duffing type. Bounds for the derivative of the restoring force are given that ensure the existence and uniqueness of a periodic solution. Furthermore, the stability of the unique periodic solution is analyzed; the sharp rate of exponential decay is determined for a solution that is near to the unique periodic solution.Comment: Key words: Periodic solution; Stability; Rate of deca

Stability and exact multiplicity of periodic solutions of Duffing equations with cubic nonlinearities

We study the stability and exact multiplicity of periodic solutions of the Duffing equation with cubic nonlinearities. We obtain sharp bounds for h such that the equation has exactly three ordered T-periodic solutions. Moreover, when h is within these bounds, one of the three solutions is negative, while the other two are positive. The middle solution is asymptotically stable, and the remaining two are unstable.Comment: Keywords: Duffing equation; Periodic solution; Stabilit

Existence, uniqueness, and stability of periodic solutions of an equation of Duffing type

We consider a second-order equation of Duffing type. Bounds for the derivative of the restoring force are given which ensure the existence and uniqueness of a periodic solution. Furthermore, the unique periodic solution is asymptotically stable with sharp rate of exponential decay. In particular, for a restoring term independent of the variable $t$, a necessary and sufficient condition is obtained which guarantees the existence and uniqueness of a periodic solution that is stable.Comment: Key words and phrases: Periodic solution, topological degree, stabilit

Mother's Education and Child Health: Is There a Nurturing Effect?

In this paper, we examine the effect of maternal education on the health of young children by using a large sample of adopted children from China. As adopted children are genetically unrelated to the nurturing parents, the educational effect on them is most likely to be the nurturing effect. We find that the mother's education is an important determinant of the health of adopted children even after we control for income, the number of siblings, health environments, and other socioeconomic variables. Moreover, the effect of the mother's education on the adoptee sample is similar to that on the own birth sample, which suggests that the main effect of the mother's education on child health is in post-natal nurturing. Our work provides new evidence to the general literature that examines the determinants of health and that examines the intergenerational immobility of socioeconomic status.

Observational Learning: Evidence from a Randomized Natural Field Experiment

We present results about the effects of observing others' choices, called observational learning, on individuals' behavior and subjective well-being in the context of restaurant dining from a randomized natural field experiment. Our experimental design aims to distinguish observational learning effect from saliency effect (because observing others' choices also makes these choices more salient). We find that, depending on specifications, the demand for the top 5 dishes was increased by an average of about 13 to 18 percent when these popularity rankings were revealed to the customers; in contrast, being merely mentioned as some sample dishes did not significantly boost their demand. Moreover, we find that, consistent with theoretical predictions, some modest evidence that observational learning effect was stronger among infrequent customers. We also find that customers' subjective dining experiences were improved when presented with the information about the top choices by other consumers, but not when presented with the names of some sample dishes.

Competitive bidding strategy in the construction industry : a game theoretic approach

A game theoretic approach is applied to analyze competitive bidding in the construction industry because previous models do not consider the conflict of interest that exists among competitors. The game theoretic model improves corporate performance when compared to previous Bayesian analyses. The game theoretic model is discussed in conjunction with construction contracting practice. Competitive bidding is formulated as a game theoretic model in which a contractor optimizes his bid price to maximize his utility or corporate performance. Using available historical data, order statistics are employed to access the distribution of estimated costs among bidders for a project. The winner\u27s curse problem related to biased estimated cost is also solved by means of order statistics. An empirical approach is proposed to define the degree of the winner\u27s curse in a local market. A basic model is derived using complex mathematics. This is followed by a simplified solution that enhances the understanding and application of game theory in the construction industry. The simplified model is in a linear form that makes it practical for use in a business environment. The historical bidding data of two contractors engaged in the construction industry are used to evaluate the proposed simplified model. The results show that, even in its linear form, the model improves the contractors\u27 performance significantly when compared to previous Bayesian analyses. Future research directions in game theoretic modelling for competitive bidding are suggested

A Numerical Approach to Virasoro Blocks and the Information Paradox

We chart the breakdown of semiclassical gravity by analyzing the Virasoro conformal blocks to high numerical precision, focusing on the heavy-light limit corresponding to a light probe propagating in a BTZ black hole background. In the Lorentzian regime, we find empirically that the initial exponential time-dependence of the blocks transitions to a universal $t^{-\frac{3}{2}}$ power-law decay. For the vacuum block the transition occurs at $t \approx \frac{\pi c}{6 h_L}$, confirming analytic predictions. In the Euclidean regime, due to Stokes phenomena the naive semiclassical approximation fails completely in a finite region enclosing the `forbidden singularities'. We emphasize that limitations on the reconstruction of a local bulk should ultimately stem from distinctions between semiclassical and exact correlators.Comment: 45 pages, 23 figure