The existence of steady solutions of the Kuramoto-Sivashinsky equation

AbstractWe investigate the existence of steady solutions of the Kuramoto-Sivashinsky equation. For wave speed c = 1 we show that there are two periodic solutions and two heteroclinic orbits for the resultant third order ordinary differential equation. A discussion is given concerning the possibility of using these solutions to obtain the existence of more complicated patterns

The asymptotic behavior of solutions of a system of reaction-diffusion equations which models the Belousov-Zhabotinskii chemical reaction

AbstractWe investigate the boundary value problem ∂u∂t = ∂2u∂x2 + u(1 − u − rv), ∂v∂t = ∂2v∂x2 − buv, u(−∞, t) = v(∞, t) = 0, u(∞, t) = 1, and v(−∞, t) = γ ∀t > 0 where r > 0, b > 0, γ > 0 and x ϵ R. This system has been proposed by Murray as a model for the propagation of wave fronts of chemical activity in the Belousov-Zhabotinskii chemical reaction. Here u and v are proportional to the concentrations of bromous acid and bromide ion, respectively. We determine the global stability of the constant solution (u, v) ≡ (1,0). Furthermore we introduce a moving coordinate and for each fixed x ϵ R we investigate the asymptotic behavior of u(x + ct, t) and v(x + ct, t) as t → ∞ for both large and small values of the wave speed c ⩾ 0

Radially Symmetric Solutions of

We investigate solutions of and focus on the regime and . Our advance is to develop a technique to efficiently classify the behavior of solutions on , their maximal positive interval of existence. Our approach is to transform the nonautonomous equation into an autonomous ODE. This reduces the problem to analyzing the phase plane of the autonomous equation. We prove the existence of new families of solutions of the equation and describe their asymptotic behavior. In the subcritical case there is a well-known closed-form singular solution, , such that as and as . Our advance is to prove the existence of a family of solutions of the subcritical case which satisfies for infinitely many values . At the critical value there is a continuum of positive singular solutions, and a continuum of sign changing singular solutions. In the supercritical regime we prove the existence of a family of “super singular” sign changing singular solutions

Performance of Historically Underrepresented Firms in the Public-Private Sector

This study examines the performance of historically underrepresented firms, which includes women-owned businesses and socially disadvantaged businesses. We examine performance in the context of securing public contracts and compare the performance of these historically underrepresented firms to those of non-minority small and large businesses. Utilizing a sample of all contracts awarded by the Johnson Space Center, a NASA directorate located in Houston, Texas, which identified 5,676 contracts totaling approximately $157 billion, we found that small businesses received around 63% of all contracts. The results indicate that more diverse firms received higher awards than specialists and that disadvantaged firms received higher dollar awards than general small businesses. In addition, women-owned businesses neither outperformed nor performed more poorly than general small business in the dollar amounts of contracts received, and they are neither more or less specialized than general small and large businesses. A discussion, practical implications, and future research ideas are also presented

Spacelab Data Processing Facility (SLDPF) quality assurance expert systems development

Spacelab Data Processing Facility (SLDPF) expert system prototypes were developed to assist in the quality assurance of Spacelab and/or Attached Shuttle Payload (ASP) processed telemetry data. The SLDPF functions include the capturing, quality monitoring, processing, accounting, and forwarding of mission data to various user facilities. Prototypes for the two SLDPF functional elements, the Spacelab Output Processing System and the Spacelab Input Processing Element, are described. The prototypes have produced beneficial results including an increase in analyst productivity, a decrease in the burden of tedious analyses, the consistent evaluation of data, and the providing of concise historical records

Collaborative Preference: The Role of Homophily, Multiplexity, and Advantageous Network Position across Small and Medium-sized Organizations

The purpose of this paper is to examine collaboration between individuals across organizations. While both for profit and not-for-profit organizations utilize collaborative efforts, the factors that are important for bringing individuals and businesses together for collaboration still remain somewhat unresolved. In this paper, colleague similarity, the quality of pre-existing relationships, and the relative power of the other colleague are all examined for their correlation with the desirability of collaboration with that individual. In a study of pastors of small and medium sized churches in a southwestern protestant conference, we examined these areas through the lenses of homophily theory, multiplicity theories, and network positioning theories and found support for each of our hypotheses. Implications for management as well as future research directions are also presented

Implementation of a health management mentoring program: year-1 evaluation of its impact on health system strengthening in Zambézia Province, Mozambique

Background: Avante Zambézia is an initiative of a Non-Governmental Organization (NGO), Friends in Global Health, LLC (FGH) and the Vanderbilt Institute for Global Health (VIGH) to provide technical assistance to the Mozambican Ministry of Health (MoH) in rural Zambézia Province. Avante Zambézia developed a district level Health Management Mentorship (HMM) program to strengthen health systems in ten of Zambézia’s 17 districts. Our objective was to preliminarily analyze changes in four domains of health system capacity after the HMM’s first year: accounting, Human Resources (HRs), Monitoring and Evaluation (M&E), and transportation management. Methods: Quantitative metrics were developed in each domain. During district visits for weeklong, on-site mentoring, the health management mentoring teams documented each indicator as a success ratio percentage. We analyzed data using linear regressions of each indicator’s mean success ratio across all districts submitting a report over time. Results: Of the four domains, district performance in the accounting domain was the strongest and most sustained. Linear regressions of mean monthly compliance for HR objectives indicated improvement in three of six mean success ratios. The M&E capacity domain showed the least overall improvement. The one indicator analyzed for transportation management suggested progress. Conclusion: Our outcome evaluation demonstrates improvement in health system performance during a HMM initiative. Evaluating which elements of our mentoring program are succeeding in strengthening district level health systems is vital in preparing to transition fiscal and managerial responsibility to local authorities