Elliptic Functions and Modular Forms

We researched elliptic functions and modular forms in order to prove a relationship between the sum of the divisors of a number raised to the 7th powers and the sum of the divisors of the same number raised to the 3rd power. We used complex functions and number theory to work through our book written by Tom Apostol

Comparison of the Association Between Disease Burden and Inappropriate Medication Use Across Three Cohorts of Older Adults

Background: Use of potentially inappropriate medications is common in nursing facilities (NFs), in which frail older adults are particularly vulnerable to adverse drug effects. The community-dwelling elderly are generally healthier and have lower overall rates of medication use, but their prescribed medications are not subjected to the same degree of regulatory scrutiny as those of residents in NFs. Frail elderly (FE) adults who are nursing home eligible but are receiving home- and community-based services (HCBS) constitute a distinct group sharing a high disease burden and high levels of medication use with the NF population. Objective: The goal of this study was to examine the relationship between disease burden and inappropriate medication use in these 3 cohorts, with adjustment for demographic and clinical differences. Methods: We performed retrospective analyses of Medicaid claims data from May 2000 through April 2001 to identify 3 cohorts of Kansas Medicaid beneficiaries: community-dwelling older adults (the ambulatory cohort); persons receiving HCBS through the Kansas Frail Elderly Program (the FE cohort); and elderly NF residents (the NF cohort). Demographic, clinical, and medication data were extracted from the Medicaid claims data. Unconditionally inappropriate medications were identified using the 1997 Beers criteria. The Cumulative Illness Rating Scale for Geriatrics was used to calculate the disease burden sum, classified as 0 or 1, 2 or 3, 4 or 5, or ≥6 disease categories. Odds ratios for inappropriate medication use at each level of disease burden in each cohort were derived using multivariable models adjusted for demographic and clinical factors, including overall level of medication use. Results: The final sample included 3185 persons in the 3 cohorts (1163 ambulatory, 858 FE, 1164 NF). Inappropriate medication use was determined to have occurred in 21%, 48%, and 38% of the respective cohorts and was highest in FE cohort members with the greatest disease burden (61%). For the ambulatory and FE cohorts, inappropriate medication use rose as the disease burden increased. The same was not observed in the NF cohort, in whom rates of inappropriate medication use showed little variation regardless of disease burden. Conclusions: The relationship between disease burden and inappropriate medication use varied by setting. Those members of the FE cohort with the highest disease burden had the greatest risk for inappropriate medication use

Patterns of Potentially Inappropriate Medication Use Across Three Cohorts of Older Medicaid Recipients

BACKGROUND Potentially inappropriate medication use is a serious quality concern, especially when it occurs in more vulnerable older adults or for extended durations. OBJECTIVE To characterize patterns of inappropriate medication use and duration among 3 cohorts with differing health status. METHODS We identified unconditionally inappropriate drug use, using Beers 1997 criteria, among 3185 older Kansas Medicaid beneficiaries. Claims from May 2000 to April 2001 provided data for 3 cohorts: nursing facility (NF) residents, recipients of home- and community-based services through the Frail Elderly (FE) program, and persons with neither NF/FE care (Ambulatory). Duration, categorized as short-term (≤1 month\u27s supply), extended (\u3e1–9 mo), or chronic (\u3e9–12 mo), was determined for each drug and cohort. Drug–disease associations were explored. RESULTS Any inappropriate medication use occurred in 21%, 48%, and 38% of Ambulatory, FE, and NF cohorts, respectively. Inappropriate analgesics, antihistamines, antidepressants, muscle relaxants, and oxybutynin were most common, but prevalence and duration varied by cohort. Short-term analgesic and antihistamine use was common. FE cohort members had the highest use rates for all drugs. The NF cohort had less antidepressant and muscle relaxant use. Drug–disease associations were noted for amitriptyline use in diabetes mellitus, propoxyphene use in musculoskeletal and upper gastrointestinal conditions, and muscle relaxant use in musculoskeletal conditions. CONCLUSIONS Cross-sectional, one-year prevalence figures are comprised of both short- and long-term use that varies by drug and cohort. NF residence is associated with reduced use of drugs scrutinized during mandated medication review. Relevant diseases are associated with specific inappropriate prescribing. Future efforts should target extended and chronic duration of use and persons at highest risk for adverse effects, including recipients of home- and community-based care