Lie group stability of finite difference schemes

Differential equations arising in fluid mechanics are usually derived from the intrinsic properties of mechanical systems, in the form of conservation laws, and bear symmetries, which are not generally preserved by a finite difference approximation, and leading to inaccurate numerical results. This paper proposes a method that enables us to build a scheme that preserves some of those symmetries.Comment: 10 page

Bi-module Properties of Group-Valued Local Fields and Quantum-Group Difference Equations

We give an explicit construction of the quantum-group generators ---local, semi-local, and global --- in terms of the group-valued quantum fields $\tilde g$ and $\tilde g^{-1}$ in the Wess-Zumino-Novikov-Witten (WZNW) theory. The algebras among the generators and the fields make concrete and clear the bi-module properties of the $\tilde g$ and the $\tilde g^{-1}$ fields. We show that the correlation functions of the $\tilde g$ and $\tilde g^{-1}$ fields in the vacuum state defined through the semi-local quantum-group generator satisfy a set of quantum-group difference equations. We give the explicit solution for the two point function. A similar formulation can also be done for the quantum Self-dual Yang-Mills (SDYM) theory in four dimensions.Comment: 12 pages; uses latex; minor revisions for publication in Phys. Lett.

Difference-form group contests

Contests are situations in which a set of agents compete for a valuable object, rent or award. The present paper analyzes difference-form group contests, that is, contests fought among groups and where their probability of victory depends on the difference of their effective efforts. First, we show that the non-existence of pure-strategy equilibria and the monopolization results obtained in previous analysis of difference-form contests rest critically on the assumption of a linear cost of effort. Under exponential costs, we show that pure strategy equilibria exist in a large set of cases and that more tan one group can expend positive effort in equilibrium. Second, we show that inequality of valuations of victory within groups hinders their chances of prevailing in the contest. If possible; members may find beneficial to engage in progressive redistribution within their group

Lie group analysis of a generalized Krichever-Novikov differential-difference equation

The symmetry algebra of the differential--difference equation $$\dot u_n = [P(u_n)u_{n+1}u_{n-1} + Q(u_n)(u_{n+1}+u_{n-1})+ R(u_n)]/(u_{n+1}-u_{n-1}),$$ where $P$, $Q$ and $R$ are arbitrary analytic functions is shown to have the dimension 1 \le \mbox{dim}L \le 5. When $P$, $Q$ and $R$ are specific second order polynomials in $u_n$ (depending on 6 constants) this is the integrable discretization of the Krichever--Novikov equation. We find 3 cases when the arbitrary functions are not polynomials and the symmetry algebra satisfies \mbox{dim}L=2. These cases are shown not to be integrable. The symmetry algebras are used to reduce the equations to purely difference ones. The symmetry group is also used to impose periodicity $u_{n+N}=u_n$ and thus to reduce the differential--difference equation to a system of $N$ coupled ordinary three points difference equations

The Dependent Coverage Provision Is Good for Mothers, Good for Children, and Good for Taxpayers

Importance The effect of the Affordable Care Act (ACA) dependent coverage provision on pregnancy-related health care and health outcomes is unknown. Objective To determine whether the dependent coverage provision was associated with changes in payment for birth, prenatal care, and birth outcomes. Design, Setting, and Participants Retrospective cohort study, using a differences-in-differences analysis of individual-level birth certificate data comparing live births among US women aged 24 to 25 years (exposure group) and women aged 27 to 28 years (control group) before (2009) and after (2011-2013) enactment of the dependent coverage provision. Results were stratified by marital status. Main Exposures The dependent coverage provision of the ACA, which allowed young adults to stay on their parent’s health insurance until age 26 years. Main Outcomes and Measures Primary outcomes were payment source for birth, early prenatal care (first visit in first trimester), and adequate prenatal care (a first trimester visit and 80% of expected visits). Secondary outcomes were cesarean delivery, premature birth, low birth weight, and infant neonatal intensive care unit (NICU) admission. Results The study population included 1 379 005 births among women aged 24 to 25 years (exposure group; 299 024 in 2009; 1 079 981 in 2011-2013), and 1 551 192 births among women aged 27 to 28 years (control group; 325 564 in 2009; 1 225 628 in 2011-2013). From 2011-2013, compared with 2009, private insurance payment for births increased in the exposure group (36.9% to 35.9% [difference, −1.0%]) compared with the control group (52.4% to 51.1% [difference, −1.3%]), adjusted difference-in-differences, 1.9 percentage points (95% CI, 1.6 to 2.1). Medicaid payment decreased in the exposure group (51.6% to 53.6% [difference, 2.0%]) compared with the control group (37.4% to 39.4% [difference, 1.9%]), adjusted difference-in-differences, −1.4 percentage points (95% CI, −1.7 to −1.2). Self-payment for births decreased in the exposure group (5.2% to 4.3% [difference, −0.9%]) compared with the control group (4.9% to 4.3% [difference, −0.5%]), adjusted difference-in-differences, −0.3 percentage points (95% CI, −0.4 to −0.1). Early prenatal care increased from 70% to 71.6% (difference, 1.6%) in the exposure group and from 75.7% to 76.8% (difference, 0.6%) in the control group (adjusted difference-in-differences, 0.6 percentage points [95% CI, 0.3 to 0.8]). Adequate prenatal care increased from 73.5% to 74.8% (difference, 1.3%) in the exposure group and from 77.5% to 78.8% (difference, 1.3%) in the control group (adjusted difference-in-differences, 0.4 percentage points [95% CI, 0.2 to 0.6]). Preterm birth decreased from 9.4% to 9.1% in the exposure group (difference, −0.3%) and from 9.1% to 8.9% in the control group (difference, −0.2%) (adjusted difference-in-differences, −0.2 percentage points (95% CI, −0.3 to −0.03). Overall, there were no significant changes in low birth weight, NICU admission, or cesarean delivery. In stratified analyses, changes in payment for birth, prenatal care, and preterm birth were concentrated among unmarried women. Conclusions and Relevance In this study of nearly 3 million births among women aged 24 to 25 years vs those aged 27 to 28 years, the Affordable Care Act dependent coverage provision was associated with increased private insurance payment for birth, increased use of prenatal care, and modest reduction in preterm births, but was not associated with changes in cesarean delivery rates, low birth weight, or NICU admission