Taylor's Theorem for Functionals on BMO with Application to BMO Local Minimizers

In this note two results are established for energy functionals that are given by the integral of $W(\mathbf x,\nabla \mathbf u(\mathbf x))$ over $\Omega \subset\mathbb{R}^n$ with $\nabla \mathbf u \in BMO(\Omega;{\mathbb R}^{N\times n})$, the space of functions of Bounded Mean Oscillation of John & Nirenberg. A version of Taylor's theorem is first shown to be valid provided the integrand $W$ has polynomial growth. This result is then used to demonstrate that, for the Dirichlet, Neumann, and mixed problems, every Lipschitz-continuous solution of the corresponding Euler-Lagrange equations at which the second variation of the energy is uniformly positive is a strict local minimizer of the energy in $W^{1,BMO}(\Omega;\mathbb{R}^N)$, the subspace of the Sobolev space $W^{1,1}(\Omega;\mathbb{R}^N)$ for which the weak derivative $\nabla\mathbf u \in BMO(\Omega;{\mathbb R}^{N\times n})$.Comment: 8 page

Applications of Partial Supersymmetry

I examine quantum mechanical Hamiltonians with partial supersymmetry, and explore two main applications. First, I analyze a theory with a logarithmic spectrum, and show how to use partial supersymmetry to reveal the underlying structure of this theory. This method reveals an intriguing equivalence between two formulations of this theory, one of which is one-dimensional, and the other of which is infinite-dimensional. Second, I demonstrate the use of partial supersymmetry as a tool to obtain the asymptotic energy levels in non-relativistic quantum mechanics in an exceptionally easy way. In the end, I discuss possible extensions of this work, including the possible connections between partial supersymmetry and renormalization group arguments.Comment: 11 pages, harvmac, no figures; typo corrected in identifying info on title pag

System dynamics advances strategic economic transition planning in a developing nation

The increasingly complex environment of today's world, characterized by technological innovation and global communication, generates myriads of possible and actual interactions while limited physical and intellectual resources severely impinge on decision makers, be it in the public or private domains. At the core of the decision-making process is the need for quality information that allows the decision maker to better assess the impact of decisions in terms of outcomes, nonlinear feedback processes and time delays on the performance of the complex system invoked. This volume is a timely review on the principles underlying complex decision making, the handling of uncertainties in dynamic envrionments and of the various modeling approaches used. The book consists of five parts, each composed of several chapters: I: Complex Decision Making: Concepts, Theories and Empirical Evidence II: Tools and Techniques for Decision Making in Complex Environments and Systems III: System Dynamics and Agent-Based Modeling IV: Methodological Issues V: Future Direction

An Overview of Progress and Problems in Educational Technology

Educational technologists have promised that great advances and improvements in learning and instruction would occur on account of new and emerging technologies. Some of these promises have been partially fulfilled, but many have not. The last decade of the previous century witnessed the consolidation of new approaches to learning and instruction under the banner of constructivism. This so−called new learning paradigm was really not all that new, but renewed emphasis on learners and learning effectiveness can clearly be counted as gains resulting from this constructivist consolidation within educational research. At the same time, technology was not standing still. Network technologies were increasing bandwidth, software engineering was embracing object orientation, and wireless technologies were extending accessibility. It is clear that we can now do things to improve education that were not possible twenty years ago. However, the potential gains in learning and instruction have yet to be realized on a significant global scale. Why not? Critical challenges confront instructional designers and critical problems remain with regard to learning in and about complex domains. Moreover, organizational issues required to translate advances in learning theory and educational technology into meaningful practice have yet to be addressed. The current situation in the field of educational technology is one of technification. New educational technologies are usable only by a scarce cadre of technocrats. Constructivist approaches to learning have been oversimplified to such a degree that learning effectiveness has lost meaning. As a consequence, education is generally managed in an ad hoc manner that marginalizes the potential gains offered by new learning technologies. This paper presents an overview of progress and problems in educational technology and argues that educational program management must be integrally linked with technology and theory in order for significant progress in learning and instruction to occur on a global scale.Educational technologists have promised that great advances and improvements in learning and instruction would occur on account of new and emerging technologies. Some of these promises have been partially fulfilled, but many have not. The last decade of the previous century witnessed the consolidation of new approaches to learning and instruction under the banner of constructivism. This so−called new learning paradigm was really not all that new, but renewed emphasis on learners and learning effectiveness can clearly be counted as gains resulting from this constructivist consolidation within educational research. At the same time, technology was not standing still. Network technologies were increasing bandwidth, software engineering was embracing object orientation, and wireless technologies were extending accessibility. It is clear that we can now do things to improve education that were not possible twenty years ago. However, the potential gains in learning and instruction have yet to be realized on a significant global scale. Why not? Critical challenges confront instructional designers and critical problems remain with regard to learning in and about complex domains. Moreover, organizational issues required to translate advances in learning theory and educational technology into meaningful practice have yet to be addressed. The current situation in the field of educational technology is one of technification. New educational technologies are usable only by a scarce cadre of technocrats. Constructivist approaches to learning have been oversimplified to such a degree that learning effectiveness has lost meaning. As a consequence, education is generally managed in an ad hoc manner that marginalizes the potential gains offered by new learning technologies. This paper presents an overview of progress and problems in educational technology and argues that educational program management must be integrally linked with technology and theory in order for significant progress in learning and instruction to occur on a global scale

An Overview of Progress and Problems in Educational Technology

Educational technologists have promised that great advances and improvements in learning and instruction would occur on account of new and emerging technologies. Some of these promises have been partially fulfilled, but many have not. The last decade of the previous century witnessed the consolidation of new approaches to learning and instruction under the banner of constructivism. This so−called new learning paradigm was really not all that new, but renewed emphasis on learners and learning effectiveness can clearly be counted as gains resulting from this constructivist consolidation within educational research. At the same time, technology was not standing still. Network technologies were increasing bandwidth, software engineering was embracing object orientation, and wireless technologies were extending accessibility. It is clear that we can now do things to improve education that were not possible twenty years ago. However, the potential gains in learning and instruction have yet to be realized on a significant global scale. Why not? Critical challenges confront instructional designers and critical problems remain with regard to learning in and about complex domains. Moreover, organizational issues required to translate advances in learning theory and educational technology into meaningful practice have yet to be addressed. The current situation in the field of educational technology is one of technification. New educational technologies are usable only by a scarce cadre of technocrats. Constructivist approaches to learning have been oversimplified to such a degree that learning effectiveness has lost meaning. As a consequence, education is generally managed in an ad hoc manner that marginalizes the potential gains offered by new learning technologies. This paper presents an overview of progress and problems in educational technology and argues that educational program management must be integrally linked with technology and theory in order for significant progress in learning and instruction to occur on a global scale.Educational technologists have promised that great advances and improvements in learning and instruction would occur on account of new and emerging technologies. Some of these promises have been partially fulfilled, but many have not. The last decade of the previous century witnessed the consolidation of new approaches to learning and instruction under the banner of constructivism. This so−called new learning paradigm was really not all that new, but renewed emphasis on learners and learning effectiveness can clearly be counted as gains resulting from this constructivist consolidation within educational research. At the same time, technology was not standing still. Network technologies were increasing bandwidth, software engineering was embracing object orientation, and wireless technologies were extending accessibility. It is clear that we can now do things to improve education that were not possible twenty years ago. However, the potential gains in learning and instruction have yet to be realized on a significant global scale. Why not? Critical challenges confront instructional designers and critical problems remain with regard to learning in and about complex domains. Moreover, organizational issues required to translate advances in learning theory and educational technology into meaningful practice have yet to be addressed. The current situation in the field of educational technology is one of technification. New educational technologies are usable only by a scarce cadre of technocrats. Constructivist approaches to learning have been oversimplified to such a degree that learning effectiveness has lost meaning. As a consequence, education is generally managed in an ad hoc manner that marginalizes the potential gains offered by new learning technologies. This paper presents an overview of progress and problems in educational technology and argues that educational program management must be integrally linked with technology and theory in order for significant progress in learning and instruction to occur on a global scale