The Fundamental Gap For Hyperbolic Triangles

In 1983, M. van den Berg made his Fundamental Gap Conjecture about the difference between the first two Dirichlet eigenvalues (the fundamental gap) of any convex domain in the Euclidean plane. Recently, progress has been made in the case where the domains are polygons and, in particular, triangles. We examine the conjecture for triangles in hyperbolic geometry, though we seek an for an upper bound for the fundamental gap rather than a lower bound.

Geophysical Investigation of Subsurface Three-Dimensional Architecture of Icy Debris Fans With Ground Penetrating Radar in the Wrangell Mountains, Alaska

Icy debris fans have are newly-described landforms (Kochel and Trop, 2008 and 2012) as landforms developed immediately after deglaciation on Earth and similar features have been observed on Mars. Subsurface characteristics of Icy debris fans have not been previously investigated. Ground penetrating radar (GPR) was used to non-invasively investigate the subsurface characteristics of icy debris fans near McCarthy, Alaska, USA. The three fans investigated in Alaska are the East, West, and Middle fans (Kochel and Trop, 2008 and 2012) which below the Nabesna ice cap and on top of the McCarthy Creek Glacier. Icy debris fans in general are a largely unexplored suite of paraglacial landforms and processes in alpine regions. Recent field studies focused on direct observations and depositional processes. Their results showed that the fan's composition is primarily influenced by the type and frequency of depositional processes that supply the fan. Photographic studies show that the East Fan receives far more ice and snow avalanches whereas the Middle and West Fans receive fewer mass wasting events but more clastic debris is deposited on the Middle and West fan from rock falls and icy debris flows. GPR profiles and Wide-angle reflection and refraction (WARR) surveys consisting of both, common mid-point (CMP), and common shot-point (CSP) surveys investigated the subsurface geometry of the fans and the McCarthy Creek Glacier. All GPR surveys were collected in July of 2013 with 100MHz bi-static antennas. Four axial profiles and three cross-fan profiles were done on the West and Middle fans as well as the McCarthy Creek Glacier in order to investigate the relationship between the three features. GPR profiles yielded reflectors that were continuous for 10+ m and hyperbolic reflections in the subsurface. The depth to these reflections in the subsurface requires knowledge of the velocity of the subsurface. To find the velocity of the subsurface eight WARR surveys collected on the fans and on the McCarthy Creek glacier to provide information on variability of subsurface velocities. The profiles of the Middle and West fan have more reflections in their profiles compared to profiles done on the McCarthy Creek Glacier. Based on the WARR surveys, we interpret the lower energy return in the glacier to be caused by two reasons. 1) The increased attenuation due to wet ice versus drier ice and on the fan with GPR velocities >0.15m/ns. 2) Lack of interfaces in the glacier compared to those in the fans which are inferred to be produced by the alternating layers of stratified ice and lithic-rich layers. The GPR profiles on the West and Middle Fans show the shallow subsurface being dominated by lenticular reflections interpreted to be consistent with the shape of surficial deposits. The West Fan is distinguished from the Middle Fan by the nature of its reflections patterns and thicknesses of reflection packages that clearly shows the Middle fan with a greater thickness. The changes in subsurface reflections between the Middle and West Fans as well as the McCarthy Creek Glacier are thought to reflect the type and frequency of depositional processes and surrounding bedrock and talus slopes.

The Provision and Use of Mental Health Services in Nursing Homes: Results from the National Medical Expenditure Survey

Data from the Institutional Population Component of the National Medical Expenditure Survey were used to provide national estimates of annual mental health service provision and use in nursing homes. In addition, the relationship between service provision and setting characteristics such as ownership, size, Medicaid certification, and chain status was examined. Although more than three quarters of residents with a mental disorder resided at a nursing home that provided counseling services, fewer than one fifth actually received any mental health services within the year.

Mental Health Services for Nursing Home Residents: What Will It Cost?

The Nursing Home Reform Act of 1987 requires nursing homes to provide basic mental health services for all residents and to give active mental health treatment, a set of specialized mental health services, to those residents who are admitted with a serious mental illness. This article examines the potential size of the nursing home population who will require mental health services, its demographic composition, and the facilities in which these individuals reside using the Institutional Population Component of the National Medical Expenditure Survey. Estimates of the potential costs of providing monthly psychotherapy and pharmacological management to this population in nursing homes indicate that the mandate will have significant financial effects on nursing facilities. Conclusions about how the requirements for maintaining the mental and psychosocial well-being of nursing home residents may affect the future of nursing home care and mental health care are considered.

Determinants of the Use of Specialist Mental Health Services by Nursing Home Residents

This study examines the effects of resident and facility characteristics on the probability of nursing home residents receiving treatment by mental health professionals.

How Many Elders Receive Assistance?: A Cross-National Comparison

To examine models of informal support received by elders in the United States and Sweden and to test whether differences in informal support appear to stem from demographic differences between the nations alone or whether cultural and historical differences must also be considered.

Use of Mental Health Services by Persons With A Mental Illness in Nursing Facilities: Initial Impacts of OBRA87.

To identify mental health service use patterns in nursing facilities subsequent to nursing home reforms in the Omnibus Budget Reconciliation Act of 1987.

Exploring Assistance in Sweden and the United States

Few international comparisons of health services are performed using microlevel data. Using such data, this paper compares the need for and receipt of assistance with activities of daily living (ADLs) in comparable samples in the United States and Sweden, a country with a universal system of community-based services.Design and Methods: Data from national surveys of community residents completed at approximately the same time in each nation are used to create comparable measures of need and assistance. Descriptive and logistic regression analyses compare need and assistance patterns across the nations and identify individual factors that explain receipt of assistance and unmet needs.Results:Our results indicate that a simple story of greater use of paid formal services in Sweden and more unpaid informal use in the United States masks a more complex relationship. Assistance with ADLs seems to be more targeted in Sweden; narrow differences in assistance widen considerably when the analysis is limited to those reporting need. Implications:Although these two different health systems result in similar levels of overall ADL assistance, a detailed microlevel comparison reveals key distinctions. Further microlevel comparisons of access, cost, and quality in cross-national data can further aid our understanding of the consequences of health policy.

Life on the Edge: Patterns of Formal and Informal Help to Older Adults in the United States and Sweden

Objectives Our objective in this study was to compare assistance received by individuals in the United States and Sweden with characteristics associated with low, moderate, or high 1-year placement risk in the United States. Methods We used longitudinal nationally representative data from 4,579 participants aged 75 years and older in the 1992 and 1993 waves of the Medicare Current Beneficiary Survey (MCBS) and cross-sectional data from 1,379 individuals aged 75 years and older in the Swedish Aging at Home (AH) national survey for comparative purposes. We developed a logistic regression equation using U.S. data to identify individuals with 3 levels (low, moderate, or high) of predicted 1-year institutional placement risk. Groups with the same characteristics were identified in the Swedish sample and compared on formal and informal assistance received. Results Formal service utilization was higher in Swedish sample, whereas informal service use is lower overall. Individuals with characteristics associated with high placement risk received more formal and less informal assistance in Sweden relative to the United States. Discussion Differences suggest formal services supplement informal support in the United States and that formal and informal services are complementary in Sweden.