Using the Taylor Center to Teach ODEs

This article introduces a powerful ODE solver called the Taylor Center for PCs (http://taylorcenter.org/Gofen/) as a tool for teaching and performing numeric experiments with ODEs. The Taylor Center is an All-in-One GUI-style application for integrating ODEs by applying the modern Taylor Method (Automatic Differentiation). The Taylor Center also offers dynamic graphics (including 3D stereo vision). After a brief review of the features of the Taylor Center, we consider instructive examples of ODEs in various applications and also several particular examples illustrating intricacies of numeric integration. The article therefore continues the thesis of Borrelli and Coleman (CODEE Journal, http://www.codee.org/ref/CJ09-0157) that awareness and caution are needed while interpreting the results of numeric integration. We offer practical ideas and advice on how to use the Taylor Center for teaching ODEs, and to increase the motivation and interest of students. Note: This article was revised on Sep 1, 2020 to reflect an address change of http://www.ski.org/gofen/ to http://taylorcenter.org/Gofen

one = zero

In this paper, I use Mathematics in addition to the three most pure sciences --- Physics, Chemistry, and Rap --- to prove that 1=0. The argument uses The Ideal Gas Law, Ohm\u27s Law, the Definitions of Power and Velocity in addition to indefinite integrals, simple mathematical operations, and the 99 Problems Law. The intuition-crushing result can be applied to all branches of mathematics and sciences and will likely go down as one of the greatest discoveries of all time

The polity of implementation: Organizational and institutional arrangements in policy implementation

Policy implementation is a formative stage of the policy process. It determines policy's form and effect while also lying at the intersection of politics, policy, and the public. Policy implementation takes place within a given institutional setting and requires specific structure and organization to conduct it both of which allocate decision power and mint specific roles in the implementation process. Nevertheless, current implementation literature tends to overlook implementation arrangements as structures influencing, and influenced by, power. This special issue draws on various aspects of implementation arrangements to demonstrate the significant, yet underexplored, polity of implementation. To do so, this introduction begins by reviewing the conceptual frameworks available in the current implementation scholarship. This is followed by a discussion of the special issue's seven contributions. Finally, the conclusion proposes recommendations for conducting future research on the polity of implementation

Frontline organizations as experimental settings for policy change: why public management matters even more

Denominado aquí como Innovación de políticas a nivel de calle, este estudio dirige la atención al papel de los administradores públicos en los procesos de cambio de políticas durante los cuales las adaptaciones de implementación a nivel de calle se adoptan formalmente como un nuevo instrumento de política. El estudio desarrolla un marco analítico a partir del caso del programa Banquetas Libres en México. En resumen, surgen tres procesos, como el rediseño de los arreglos de implementación, la acumulación de evidencia y la adopción del instrumento experimentado como un cambio de política formal. El artículo contribuye a comprender el papel de las organizaciones de primera línea como escenarios donde los gerentes exploran, experimentan y experimentan con nuevos instrumentos de política.ITESO, A.C

Compliance with COVID-19 measures: A comparative study of street-level managers in Switzerland, Italy, Germany and Israel

Responsible for the direct-delivery of public services, street-level organizations (SLOs) serve as the operational arm of the state in general, and as the frontline of governmental efforts during times of crisis. Street-level managers (SLMs), who occupy the sole, top managerial tier in SLOs are under-studied not only during crises but also in routine, although exerting immediate significant influence on the daily life of local publics. To better understand on-the-ground policy efforts during the pandemic, this study focuses on SLMs’ compliance in Switzerland, Germany, Italy, and Israel. Data comprises 399 “compliance stories” gathered from interviews with SLMs in nurseries, schools, health and welfare offices, police stations as well as care homes. Standardized coding of the stories identified different levels of (non)compliance as well as the prominent explanatory variables that shape (non)compliance. Three influences emerged as the main compliance barriers, that is, lack of resources, relationship with the local public, and perception of the measure's effectiveness. Emphasizing that SLMs often act as local policy entrepreneurs who use their discretion to solve problems and serve their local public, findings further demonstrate the key role of SLMs in shaping the face of government for the public

Performance management from the bottom up

Current interest in middle-managers’ compliance with performance management (PM) reforms focuses on their downward roles. To explore their understudied upward roles, this analysis draws on police chiefs’ voice directed to senior management regarding the Israeli PM system as documented since its first introduction in 1999, and as reported both by chiefs and senior managers (N = 54). Unfolding four patterns of inconsistencies between PM systems’ design and the operational, daily, course-of-work, close-to-the-field managers’ upward roles allows us to move beyond criticism to constructive efforts, and provides new insights for reconciling the well-documented gap between policy intentions and outcomes in PM reforms.The politics and administration of institutional chang

Status of the differential transformation method

Further to a recent controversy on whether the differential transformation method (DTM) for solving a differential equation is purely and solely the traditional Taylor series method, it is emphasized that the DTM is currently used, often only, as a technique for (analytically) calculating the power series of the solution (in terms of the initial value parameters). Sometimes, a piecewise analytic continuation process is implemented either in a numerical routine (e.g., within a shooting method) or in a semi-analytical procedure (e.g., to solve a boundary value problem). Emphasized also is the fact that, at the time of its invention, the currently-used basic ingredients of the DTM (that transform a differential equation into a difference equation of same order that is iteratively solvable) were already known for a long time by the "traditional"-Taylor-method users (notably in the elaboration of software packages --numerical routines-- for automatically solving ordinary differential equations). At now, the defenders of the DTM still ignore the, though much better developed, studies of the "traditional"-Taylor-method users who, in turn, seem to ignore similarly the existence of the DTM. The DTM has been given an apparent strong formalization (set on the same footing as the Fourier, Laplace or Mellin transformations). Though often used trivially, it is easily attainable and easily adaptable to different kinds of differentiation procedures. That has made it very attractive. Hence applications to various problems of the Taylor method, and more generally of the power series method (including noninteger powers) has been sketched. It seems that its potential has not been exploited as it could be. After a discussion on the reasons of the "misunderstandings" which have caused the controversy, the preceding topics are concretely illustrated.Comment: To appear in Applied Mathematics and Computation, 29 pages, references and further considerations adde