Orbital stability of periodic waves in the class of reduced Ostrovsky equations

Periodic travelling waves are considered in the class of reduced Ostrovsky equations that describe low-frequency internal waves in the presence of rotation. The reduced Ostrovsky equations with either quadratic or cubic nonlinearities can be transformed to integrable equations of the Klein--Gordon type by means of a change of coordinates. By using the conserved momentum and energy as well as an additional conserved quantity due to integrability, we prove that small-amplitude periodic waves are orbitally stable with respect to subharmonic perturbations, with period equal to an integer multiple of the period of the wave. The proof is based on construction of a Lyapunov functional, which is convex at the periodic wave and is conserved in the time evolution. We also show numerically that convexity of the Lyapunov functional holds for periodic waves of arbitrary amplitudes.Comment: 34 page

Geology and Ground-Water Hydrology of the Valleys of the Republican and Frenchman Rivers Nebraska

The geology and ground-water resources of the upper Republican River valley west of the town of Alma, Nebr., to the Nebraska-Colorado State line and of the Frenchman River valley from its confluence with the Republican River to a point about 12 miles upstream from Wauneta, Nebr., were studied from January 1950 to April 1951. The purpose of the study was to relate the occurrence of ground water to irrigation and flood control and to aid in the evaluation of the effects of irrigation on the land in the area. The area included in this study consists of 370 square miles of flat or gently sloping terraces and bottom land that border the Republican and Frenchman Rivers on either side. The Republican River is a comparatively shallow stream, ranging in width from about 150 feet at the western end of the area to about 300 feet at the eastern end. The channel banks are low, except where the river cuts into bordering terraces. In many places, natural levees of loose sand and gravel have been formed adjacent to the river banks. The bedrock formations exposed in the area are the Niobrara formation and the Pierre shale of Cretaceous age and the Ogallala formation of Tertiary age. Deposits of sand and gravel, of early Pleistocene age, are present in the bottom of the ancestral Republican River valley and along the north side of the present valley. These coarse deposits are mantled by finer sediments of later Pleistocene and Recent age. Large quantities of ground water are available from the Pleistocene and Recent deposits throughout most of the Republican River valley. In the center of the valley as much as 40 to 60 feet of the deposits are saturated. The ground-water reservoir is recharged principally by precipitation. Ground water also enters the Republican River valley by underflow through the fill of tributary valleys. Ground water is discharged by evaporation, transpiration, and effluent streams; ground water also is drawn upon extensively for irrigation, for municipal supplies, and for domestic and stock use in rural areas

Geology and Ground-Water Hydrology of the Valleys of the Republican and Frenchman Rivers Nebraska

The geology and ground-water resources of the upper Republican River valley west of the town of Alma, Nebr., to the Nebraska-Colorado State line and of the Frenchman River valley from its confluence with the Republican River to a point about 12 miles upstream from Wauneta, Nebr., were studied from January 1950 to April 1951. The purpose of the study was to relate the occurrence of ground water to irrigation and flood control and to aid in the evaluation of the effects of irrigation on the land in the area. The area included in this study consists of 370 square miles of flat or gently sloping terraces and bottom land that border the Republican and Frenchman Rivers on either side. The Republican River is a comparatively shallow stream, ranging in width from about 150 feet at the western end of the area to about 300 feet at the eastern end. The channel banks are low, except where the river cuts into bordering terraces. In many places, natural levees of loose sand and gravel have been formed adjacent to the river banks. The bedrock formations exposed in the area are the Niobrara formation and the Pierre shale of Cretaceous age and the Ogallala formation of Tertiary age. Deposits of sand and gravel, of early Pleistocene age, are present in the bottom of the ancestral Republican River valley and along the north side of the present valley. These coarse deposits are mantled by finer sediments of later Pleistocene and Recent age. Large quantities of ground water are available from the Pleistocene and Recent deposits throughout most of the Republican River valley. In the center of the valley as much as 40 to 60 feet of the deposits are saturated. The ground-water reservoir is recharged principally by precipitation. Ground water also enters the Republican River valley by underflow through the fill of tributary valleys. Ground water is discharged by evaporation, transpiration, and effluent streams; ground water also is drawn upon extensively for irrigation, for municipal supplies, and for domestic and stock use in rural areas

Doctors at Risk: A Problem As Viewed by Decision Analysis

The authors closely analyze a case in which a Peer Review Organization cited a physician for treatment with potential for significant adverse effect. They also critique the regulatory scheme under which peer review occurs and conclude that such regulation interferes with physicians\u27 primary obligations, fails to encourage cost-effective behavior and may decrease the quality of medical care

Being Prepared and Staying Connected: Scouting’s Influence on Social Capital and Community Involvement

Objectives In recent years, scholars have become concerned about the effects that declining levels of social capital are having on community life in the United States. Data suggest that Americans are less likely to interact with neighbors and less likely to participate in community groups than they were in the past. Nevertheless, researchers have found that participation in some types of organizations has a positive impact on social capital and civic involvement. Each year, millions of American youth participate in programs designed to promote positive youth development. Here, we examine the effect that participation in one of the largest youth organizations, the Boy Scouts of America (BSA), has on adult social capital and community involvement. Methods Utilizing a national survey of adult males, we compare measures of social capital and community involvement for former Scouts and non‐Scouts. Results Our findings suggest that level of involvement in the Boy Scouts is significantly related to measures of adult social capital and community engagement. Conclusion Scouting tends to have a significant impact on the lives of its most committed members. Future research must continue to explore the long‐term effects of participation in youth organizations

The propagation and decay of a coastal vortex on a shelf

A coastal eddy is modelled as a barotropic vortex propagating along a coastal shelf. If the vortex speed matches the phase speed of any coastal trapped shelf wave modes, a shelf wave wake is generated leading to a flux of energy from the vortex into the wave field. Using a simply shelf geometry, we determine analytic expressions for the wave wake and the leading order flux of wave energy. By considering the balance of energy between the vortex and wave field, this energy flux is then used to make analytic predictions for the evolution of the vortex speed and radius under the assumption that the vortex structure remains self similar. These predictions are examined in the asymptotic limit of small rotation rate and shelf slope and tested against numerical simulations. If the vortex speed does not match the phase speed of any shelf wave, steady vortex solutions are expected to exist. We present a numerical approach for finding these nonlinear solutions and examine the parameter dependence of their structure

Structured Voluntary Youth Activities and Positive Outcomes in Adulthood: An Exploratory Study of Involvement in Scouting and Subjective Well-Being

This study explores whether youth involvement in Scouting has positive consequences later in life. We examine whether the number of years of participation in Scouting is positively associated with human and social capital and recreational lifestyles in adulthood, and whether these are linked to subjective well-being: relational, emotional, and physical health. To explore this potential relationship, we estimated a structural equation model, analyzing data from a national sample of adult males. We found that youth involvement in Scouting is positively related to subjective well-being indirectly via the positive adult outcomes