22,253 research outputs found
Negaton and Positon solutions of the soliton equation with self-consistent sources
The KdV equation with self-consistent sources (KdVES) is used as a model to
illustrate the method. A generalized binary Darboux transformation (GBDT) with
an arbitrary time-dependent function for the KdVES as well as the formula for
-times repeated GBDT are presented. This GBDT provides non-auto-B\"{a}cklund
transformation between two KdV equations with different degrees of sources and
enable us to construct more general solutions with arbitrary -dependent
functions. By taking the special -function, we obtain multisoliton,
multipositon, multinegaton, multisoliton-positon, multinegaton-positon and
multisoliton-negaton solutions of KdVES. Some properties of these solutions are
discussed.Comment: 13 pages, Latex, no figues, to be published in J. Phys. A: Math. Ge
Adverse Selection and the Challenges to Stand-Alone Prescription Drug Insurance
This paper investigates a possible predictor of adverse selection problems in unsubsidized stand-alone' prescription drug insurance: the persistence of an individual's high spending over multiple years. Using MEDSTAT claims data and data from the Medicare Survey of Current Beneficiaries, we find that persistence is much higher for outpatient drug expenses than for other categories of medical expenses. We then use these estimates to develop a simple and intuitive model of adverse selection in competitive insurance markets and show that this high relative persistence makes it unlikely that unsubsidized drug insurance can be offered for sale, even with premiums partially risk adjusted, without a probable adverse selection death spiral. We show that this outcome can be avoided if drug coverage is bundled with other coverage, and briefly discuss the need either for comprehensive coverage or generous subsidies if adverse selection is to be avoided in private and Medicare insurance markets.
Generalized Darboux transformations for the KP equation with self-consistent sources
The KP equation with self-consistent sources (KPESCS) is treated in the
framework of the constrained KP equation. This offers a natural way to obtain
the Lax representation for the KPESCS. Based on the conjugate Lax pairs, we
construct the generalized binary Darboux transformation with arbitrary
functions in time for the KPESCS which, in contrast with the binary Darboux
transformation of the KP equation, provides a non-auto-B\"{a}cklund
transformation between two KPESCSs with different degrees. The formula for
N-times repeated generalized binary Darboux transformation is proposed and
enables us to find the N-soliton solution and lump solution as well as some
other solutions of the KPESCS.Comment: 20 pages, no figure
The Solutions of the NLS Equations with Self-Consistent Sources
We construct the generalized Darboux transformation with arbitrary functions
in time for the AKNS equation with self-consistent sources (AKNSESCS)
which, in contrast with the Darboux transformation for the AKNS equation,
provides a non-auto-B\"{a}cklund transformation between two AKNSESCSs with
different degrees of sources. The formula for N-times repeated generalized
Darboux transformation is proposed. By reduction the generalized Darboux
transformation with arbitrary functions in time for the Nonlinear
Schr\"{o}dinger equation with self-consistent sources (NLSESCS) is obtained and
enables us to find the dark soliton, bright soliton and positon solutions for
NLSESCS and NLSESCS. The properties of these solution are analyzed.Comment: 24 pages, 3 figures, to appear in Journal of Physics A: Mathematical
and Genera
Death Spiral or Euthanasia? The Demise of Generous Group Health Insurance Coverage
Employers must determine which sorts of healthcare insurance plans to offer employees and also set employee premiums for each plan provided. Depending on how they structure the premiums that employees pay across different healthcare insurance plans, plan sponsors alter the incentives to choose one plan over another. If employees know they differ by risk level but premiums do not fully reflect these risk differences, this can give rise to a so-called "death spiral" due to adverse selection. In this paper use longitudinal information from a natural experiment in the management of health benefits for a large employer to explore the impact of moving from a fixed dollar contribution policy to a risk-adjusted employer contribution policy. Our results suggest that implementing a significant risk adjustment had no discernable effect on adverse selection against the most generous indemnity insurance policy. This stands in stark contrast to previous studies, which have tended to find large impacts. Further analysis suggests that previous studies which appeared to detect plans in the throes of a death spiral, may instead have been experiencing an inexorable movement away from a non-preferred product, one that would have been inefficient for almost all workers even in the absence of adverse selection.
Integrable dispersionless KdV hierarchy with sources
An integrable dispersionless KdV hierarchy with sources (dKdVHWS) is derived.
Lax pair equations and bi-Hamiltonian formulation for dKdVHWS are formulated.
Hodograph solution for the dispersionless KdV equation with sources (dKdVWS) is
obtained via hodograph transformation. Furthermore, the dispersionless
Gelfand-Dickey hierarchy with sources (dGDHWS) is presented.Comment: 15 pages, to be published in J. Phys. A: Math. Ge
The Advantage of Playing Home in NBA: Microscopic, Team-Specific and Evolving Features
The idea that the success rate of a team increases when playing home is
broadly accepted and documented for a wide variety of sports. Investigations on
the so-called home advantage phenomenon date back to the 70's and every since
has attracted the attention of scholars and sport enthusiasts. These studies
have been mainly focused on identifying the phenomenon and trying to correlate
it with external factors such as crowd noise and referee bias. Much less is
known about the effects of home advantage in the microscopic dynamics of the
game (within the game) or possible team-specific and evolving features of this
phenomenon. Here we present a detailed study of these previous features in the
National Basketball Association (NBA). By analyzing play-by-play events of more
than sixteen thousand games that span thirteen NBA seasons, we have found that
home advantage affects the microscopic dynamics of the game by increasing the
scoring rates and decreasing the time intervals between scores of teams playing
home. We verified that these two features are different among the NBA teams,
for instance, the scoring rate of the Cleveland Cavaliers team is increased
0.16 points per minute (on average the seasons 2004-05 to 2013-14) when playing
home, whereas for the New Jersey Nets (now the Brooklyn Nets) this rate
increases in only 0.04 points per minute. We further observed that these
microscopic features have evolved over time in a non-trivial manner when
analyzing the results team-by-team. However, after averaging over all teams
some regularities emerge; in particular, we noticed that the average
differences in the scoring rates and in the characteristic times (related to
the time intervals between scores) have slightly decreased over time,
suggesting a weakening of the phenomenon.Comment: Accepted for publication in PLoS ON
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