On optimal growth models when the discount factor is near 1 or equal to 1

The aim of this paper is to fill the gap between intertemporal growth models when the discount factor beta is close to one and when it equals one.We show that the value function and the policy function are continuous with respect both to the discount factor and the initial stock of capitalx0. We prove that the optimal policy g(x0) is differentiable and that Dg(x0) is continuous with respect to (beta, x0). As a by-product, a globalturnpike result is proved.Optimal growth, discount factor, value function, policy function,differentiability, turnpike.

Monotone concave operators: An application to the existence and uniqueness of solutions to the Bellman equation

We propose a new approach to the issue of existence and uniqueness of solutions to the Bellman equation, exploiting an emerging class of methods, called monotone map methods, pioneered in the work of Krasnosel’skii (1964) and Krasnosel’skii-Zabreiko (1984). The approach is technically simple and intuitive. It is derived from geometric ideas related to the study of fixed points for monotone concave operators defined on partially order spaces.Dynamic Programming; Bellman Equation; Unbounded Returns

Monotone Concave Operators: An application to the existence and uniqueness of solutions to the Bellman equation

We propose a new approach to the issue of existence and uniqueness of solutions to the Bellman equation, exploiting an emerging class of methods, called monotone map methods, pioneered in the work of Krasnosel'skii-Zabreiko (1984). The approach is technically simple and intuitive. It is derived from geometric ideas related to the study of fixed points for monotone concave operators defined on partially order spaces.Dynamic programming; Bellman equation; Unbounded returns

Joachim Koester

Overview of the film and video work by the artist Joachim Koeste

Developing Resources to Build Statewide Capacity and Cohesion for Mathematics and Science Standards Implementation

Two resource development programs received funding as part of an initiative to help build capacity for mathematics and science standards implementation across California: The Fostering NGSS Implementation Program and the Fostering Math Standards Implementation Program.The programs drew on a diverse body of expertise and cross-regional and organizational leadership to encourage the creation of math and science resources that could both address common standards implementation challenges found statewide and promote equitable math and science opportunities for all students.This resulted in education leaders (e.g., county office of education, content specialists, coordinators, and non-profit representatives) working together in three teams for science resources, and one team for math.This brief focuses on these four teams' experiences with planning, developing, and piloting resources aimed at reducing the variability in and building capacity for mathematics and science standards implementation across California.It first examines aspirations and expectations for the resources, and perspectives on progress made toward aims. It then examines key processes and activities concerning leadership structures, planning and development, and piloting that teams engaged in to develop their products and attain their goals.The brief concludes with key challenges and lessons learned, then provides a list of recommendations for funding or implementing further resource development efforts requiring statewide collaboration and scale

Decision-Making Experiences and Patterns in Residential Care Homes for Older Residents, Family Members and Care Providers

Aim: To explore the decision-making experiences and processes taking place in residential care homes from older residents, their families and staff members, particularly how residents’ needs were met and their degree of involvement in making decisions

Reinforced sol–gel thermal barrier coatings and their cyclic oxidation life

Cyclic oxidation life enhancement of sol–gel thermal barrier coatings is obtained via the reinforcement of the controlled micro-crack network that forms during the initial sintering of the deposit. Two different sol–gel methods are used to fill in the process-induced cracks, namely dipcoating and spray-coating. Filling parameters, for instance the number of passes or the viscosity of the sol are adjusted, using various techniques such as profilometry and microstructural analysis, to optimise crack filling. Cyclic oxidation tests are implemented at both 1100C and 1150C to investigate the efficiency of the various reinforcement procedures developed and address the influence of the specific microstructure on the oxidation behaviour

Core to College Evaluation: Sustaining Core Strength, How Core to College States Continue Alignment Efforts Between K-12 and Higher Education

The evaluation team collected general data on states' Common Core efforts by reviewing recent news articles, journals, online documents, and systems-change literature. Using this knowledge base, the team drafted driving research questions for this final report that focused on exploring how states' higher education systems are involved in standards efforts today, including aligning course sequences, updating placement policies, and supporting faculty awareness of college readiness standards. These research questions informed an interview protocol through which the team engaged several Core to College states in semi-structured conversations.The WestEd team spoke by phone with key Core to College contacts from seven of the Core to College states: Colorado, Hawai'i, Kentucky, Louisiana, Massachusetts, Oregon, and Washington. These individuals (many held the title of Alignment Director under the grant) had been part of the Core to College work and, for the most part, are still involved in work that has evolved from the initiative. The other four states involved in the initiative did not have applicable staff for the team to speak with.This report uses a case-study approach to describe how three of the Core to College states -- Washington, Hawai'i, and Louisiana -- continue their Core to College–initiated efforts of aligning K–12 and postsecondary education systems to better prepare students for college. The case studies include details about key components of each state's respective Core to College work, including the state's history with systemschange efforts in education; key staff and organizations that "championed" the Core to College efforts and promoted cross?system collaboration; specific strategies used to align the state's K–12 and higher education systems; the state's approach to standardized assessments and course-placement policies; and key outcomes of the Core to Collegerelated efforts