Some extremal properties of the solutions of ordinary differential equations systems

Based on variables doubling procedure the extremals flow immersion into the trajectories bunch has been considered. The conditions for existence of extremals have been obtained. The Lyapunov function for a doubled linearized system has been constructed

Illustrations of irreducibility and tops of umbrellas in the PostScript methodology

Sierpi´nski carpets and similar objects, irreducible and indecomposable continua are visually realized based on the PostScript language. Algorithmic problems associated with rendering effects and the presence of tops of umbrellas and irreducible points have been solved within the PostScript language methodology

Education for Sustainability and Pre-service Teacher Education

Aspects of environment are common topics in Australian primary schools. However Education for Sustainability (EfS), where students actively investigate the underlying causes of unsustainable practices and actively plan for and instigate change, is less well understood and less commonly practised. It cannot be assumed that pre-service teachers have the knowledge, skills and desire to incorporate EfS, as advocated in Australian policies, into their repertoires of practice, or, that they will acquire those skills as they gain teaching experience. Therefore for EfS to become an integral component of the primary school experience, carefully planned rather than ad hoc preparation for EfS is necessary in pre-service teacher education. This essentially qualitative study describes how a one semester final year pre-service primary teacher unit in EfS was shaped, and reports on how a cohort of pre-service teachers responded, particularly in terms of how well prepared they felt to engage with EfS in future teaching. Although motivation and confidence to engage with EfS varied across the cohort, pre-service teacher education appeared to make a positive contribution to both. In a longitudinal design, five teachers who had participated in the EfS unit became the focus of individual case studies early in their teaching careers. Each case study investigated ways in which the beginning teacher engaged with EfS, linking teaching decisions to pre-service teacher education. The constructivist approach adopted by the tutors was particularly valued by the early career teachers. They appreciated various modes of experiential learning including engagement with the kinds of teaching strategies advocated in EfS and a strong orientation to the curriculum requirements of primary school. However the extent to which each early career teacher implemented EfS was tempered not only by personal skill and motivation, but also by work situations which did not necessarily support EfS endeavours. Whilst pre-service teacher education has a vital role in the promulgation of EfS in schools, and this study shows that it can be effective in advancing the desires of beginning teachers to do something for the environment, there are broad implications for the institutions that so heavily impact on the capacity of school systems and university systems to act in EfS

A Developmental Perspective on Community Service in Adolescence

A substantial number of U.S. adolescents currently participate in community service and there is increased national interest in service programs. This article assesses the assumption of developmental benefits to service participants by critically reviewing 44 empirical studies. It offers a theoretical framework for understanding the findings by connecting them to identity development and delineating three pertinent concepts: agency, social relatedness, and moral-political awareness. These concepts are applied to studies that investigate: ( 1) the characteristics and motivations of participants, ( 2) the effects of service, and ( 3) the process of service. The findings support the conclusion that service activities which provide opportunities for intense experiences and social interactions are often associated with prosocial development. The findings also point to the need for more studies focused on particular service programs and on relationships between service providers and those served

New Directions in the Development of Population Estimates in the United States?

The advent of a continuously updated Master Area File (MAF) following the 2000 census represents an information resource that can be tapped for purposes of developing timely, cost-effective, and precise population estimates for even the smallest of geographical units (e.g., census blocks). We argue that the MAF can be enhanced (EMAF) for these purposes. In support of our argument we describe a set of activities needed to develop EMAF, each of which is well within the current capabilities of the U.S. Census Bureau and discuss various costs and benefits of each. We also describe how EMAF would provide population estimates containing a wide range of demographic (e.g., age, race, and sex) and socio-economic characteristics (e.g., educational attainment, income, and employment). As such, it could largely negate and eliminate the need for many of the traditional demographic methods of population estimation and possibly reduce the number of sample surveys. We identify important challenges that must be surmounted in order to realize EMAF and make suggestions for doing so. We conclude by noting that the idea of the EMAF could be of interest to other countries with MAF files and strong administrative records systems that, like the United States, are facing the challenge of producing good population information in the face of increasing census costs

Illustrations of irreducibility and tops of umbrellas in the PostScript methodology

Sierpi´nski carpets and similar objects, irreducible and indecomposable continua are visually realized based on the PostScript language. Algorithmic problems associated with rendering effects and the presence of tops of umbrellas and irreducible points have been solved within the PostScript language methodology

Invariant Wada Basins for One Periodic Second Order Differential Equation

A dissipative periodic second order differential equation with quadratic damping, cubic restoring force and with periodic coefficient at the even degree summand has been considered. Namely due to the periodic coefficient presence the invariant Wada basins with respect to the Poincar´e map has been obtained. The common boundary Wada basins and ”ocean” is the Birkhoff curve. The rotation numbers and timbre have been defined as an internal invariant with respect to the flow

Fractional Densities for the Wada Basins

Fractional density for basis zero Schnirelmann density has been defined. Definition of the fractional density is similar to the Hausdorff-Besicovitch dimension. The existence of the basis zero Schnirelmann density for every Wada basin (Wada ocean) earlier has been proved. This means every Wada basin/ocean are quite topologically characterized to be fractional density. Therefore all fractional densities are invariant with respect to a plane homeomorphism