Local and nonlocal solvable structures in ODEs reduction

Solvable structures, likewise solvable algebras of local symmetries, can be used to integrate scalar ODEs by quadratures. Solvable structures, however, are particularly suitable for the integration of ODEs with a lack of local symmetries. In fact, under regularity assumptions, any given ODE always admits solvable structures even though finding them in general could be a very difficult task. In practice a noteworthy simplification may come by computing solvable structures which are adapted to some admitted symmetry algebra. In this paper we consider solvable structures adapted to local and nonlocal symmetry algebras of any order (i.e., classical and higher). In particular we introduce the notion of nonlocal solvable structure

Blurring the boundaries between synthesis and evaluation. A customized realist evaluative synthesis into adolescent risk behavior prevention

Realist methodologies have been increasingly advocated for the investigation of complex social issues. Public health programs, such as those designed to prevent adolescent risk behavior, are typically considered complex. In conducting a realist review of the empirical literature relating to such programs, we encountered several challenges, including (a) an overabundance of empirical evidence, (b) a problematic level of heterogeneity within and between methodological approaches, (c) discrepancies between theoretical underpinnings and program operationalization, (d) homogeneity of program outcomes, with very little variation in program effectiveness, and (d) a paucity of description relating to content and process. To overcome these challenges, we developed a customized approach to realist evidence synthesis, drawing on the VICTORE (Volition, Implementation, Contexts, Time, Outcomes, Rivalry, and Emergence) complexity checklist and incorporating stakeholder engagement as primary data to achieve greater depth of understanding relating to contextual and mechanistic factors, and the complex interactions between them. Here we discuss the benefits of this adapted methodology alongside an overview of the research through which the methodology was developed. A key finding from this research was that combining the complexity checklist with primary data from stakeholder engagement enabled us to systematically interrogate the data across data sources, uncovering and evidencing mechanisms which may otherwise have remained hidden, giving greater ontological depth to our research findings. This paper builds on key methodological developments in realist research, demonstrating how realist methodologies can be customized to overcome challenges in developing and refining program theory from the literature, and contributes to the broader literature of innovative approaches to realist research

Vascular endothelial growth factor expression, S-phase fraction and thymidylate synthase quantitation in node-positive colon cancer: Relationships with tumor recurrence and resistance to adjuvant chemotherapy

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