Least-squares Solutions of Linear Differential Equations

This study shows how to obtain least-squares solutions to initial and boundary value problems to nonhomogeneous linear differential equations with nonconstant coefficients of any order. However, without loss of generality, the approach has been applied to second order differential equations. The proposed method has two steps. The first step consists of writing a constrained expression, introduced in Ref. \cite{Mortari}, that has embedded the differential equation constraints. These expressions are given in term of a new unknown function, $g (t)$, and they satisfy the constraints, no matter what $g (t)$ is. The second step consists of expressing $g (t)$ as a linear combination of $m$ independent known basis functions, $g (t) = \mathbf{\xi}^T \mathbf{h} (t)$. Specifically, Chebyshev orthogonal polynomials of the first kind are adopted for the basis functions. This choice requires rewriting the differential equation and the constraints in term of a new independent variable, $x\in[-1, +1]$. The procedure leads to a set of linear equations in terms of the unknown coefficients vector, $\mathbf{\xi},$ that is then computed by least-squares. Numerical examples are provided to quantify the solutions accuracy for initial and boundary values problems as well as for a control-type problem, where the state is defined in one point and the costate in another point.Comment: Study partially presented as: Mortari, D. "Least-squares Solutions of Linear Differential Equations,? AAS 17-256, 2017 AAS/AIAA Space Flight Mechanics Meeting Conference, San Antonio, TX, February 5-9, 201

Non-dimensional Star-Identification

This study introduces a new "Non-Dimensional" star identification algorithm to reliably identify the stars observed by a wide field-of-view star tracker when the focal length and optical axis offset values are known with poor accuracy. This algorithm is particularly suited to complement nominal lost-in-space algorithms, which may identify stars incorrectly when the focal length and/or optical axis offset deviate from their nominal operational ranges. These deviations may be caused, for example, by launch vibrations or thermal variations in orbit. The algorithm performance is compared in terms of accuracy, speed, and robustness to the Pyramid algorithm. These comparisons highlight the clear advantages that a combined approach of these methodologies provides.Comment: 17 pages, 10 figures, 4 table

Educating to Think in Environmental Education

Each epoch has a burning question it needs to address. Certainly, our age has to consider the ecological question. From a pedagogic standpoint, the ecological crisis is not only a question of lack of scientific knowledge, but also of thoughtlessness. Given this assumption, it can be supposed that the priority question in environmental education is that of educating to think, and specifically educating to think by oneself. Consequently, analysis of the following issues is necessary: (a) What does educating to think in an ecological way mean? (b) How do we educate to think, that is, through what kind of learning contexts

Spiritual Care:The Spiritual Side of a Culture of Care

Looking more carefully at the very notion of spirituality, Italian philosopher Luigina Mortari interrogates the nature of spirituality regarding an ethic of care in “Spiritual Care: The Spiritual Side Of A Culture Of Care.” This sweeping analysis takes us on a journey that includes Ancient Greek philosophy, Continental Philosophy, ontology, epistemology, empirical research, and poet-philosopher Maria Zambrano’s work, among others. Mortari argues that there is an ontological call to care as an essential technique for living. Accordingly, Mortari finds the examined life a necessity: “To con- ceive the technique of living means having the knowledge and wis- dom of care; in other words, knowing what good care is, and how to put it into practice.” Mortari leverages a Platonic notion of the soul to frame a spiritual pursuit of care as a quest for the good and not just an ethical determination of what is right. She states, “the practice of care teaches me that it is not only necessary to search for a concrete, immanent idea of good embodied in the daily life (about this, it is possible to speak of a materialistic spirituality as the generative matrix of care ethics), but also to cultivate a manner of thinking that is congruent with both the human limits of thinking and the essence of care.” Seldom do care theorists present care ethics in the broad- brush strokes that Mortari’s epic narrative offers. This chapter may not be a typical philosophical analysis of care, but it suggests several provocative insights into the relationship between care and spirituality

An Overview of Different Perspectives

The article grounds on the assumption that researchers, in order to be not mere technicians but competent practitioners of research, should be able to reflect in a deep way. That means they should reflect not only on the practical acts of research but also on the mental experience which constructs the meaning about practice. Reflection is a very important mental activity, both in private and professional life. Learning the practice of reflection is fundamental because it allows people to engage into a thoughtful relationship with the world-life and thus gain an awake stance about one's lived experience. Reflection is a crucial cognitive practice in the research field. Reflexivity is largely practiced in qualitative research, where it is used to legitimate and validate research procedures. This study introduces different perspectives of analysis by focusing the discourse on the main philosophical approaches to reflection: pragmatistic, critical, hermeneutic, and finally phenomenological. The thesis of this study is that the phenomenological theory makes possible to analyze in depth the reflective activity and just by that to support an adequate process of training of the researcher

Characterization Of Immunoregulatory Cells And Factors Derived From Normal Human Bone Marrow

The bone marrow is a primary lymphoid organ whose main function is to provide a continuous source of hematopoietic cells to the peripheral immune system. This study was undertaken to elucidate the roles of bone marrow cells and their mediators in immunoregulation.;Fractionation of bone marrow cells resolved two distinct immunoregulatory activities. A population of bone marrow cells of the phenotype HNK-1{dollar}\sp{lcub}+{rcub}{dollar} (human natural killer cell antigen, CD57), SSEA-1{dollar}\sp{lcub}+{rcub}{dollar} (stage specific embryonic antigen) and OKM1{dollar}\sp{lcub}+{rcub}{dollar} (human monocyte antigen, CD11B) was found to be highly suppressive for primary antibody responses. Conversely, a lymphocyte enriched bone marrow cells fraction could enhance the same antibody response. Neither population expressed surface markers for mature T nor B cells. Noteworthy was the finding that bone marrow depleted of natural suppressor cells was capable of mounting a primary antibody response. In addition, the two bone marrow cell populations acted antagonistically in the regulation of IgM antibody responses.;Both activities are mediated by soluble factors. Bone marrow Derived Suppressor Factor (BDSF) is a phospholipid that is synthesized de novo by HNK-1{dollar}\sp{lcub}+{rcub}{dollar} bone marrow cells during a 24 hour culture. BDSF appears to mediate its suppressive effects by inhibiting interleukin-1 synthesis. On the other hand, Bone marrow Derived Enhancing Factor (BDEF) is a glycoprotein of MW 60,000 daltons and has the additional property of being directly mitogenic for both bone marrow cells and thymocytes. Both molecules act during the inductive phase of the generation of antibody responses and their action is not restricted by major histocompatibility antigens.;The fact that both activities are constitutively present within the bone marrow, in conjunction with their antagonistic action, make them ideally situated mediators to regulate bone marrow immunoglobulin levels. Furthermore, their potential effects on bone marrow stem cells suggest that the two activities contribute to the maintenance of bone marrow homeostasis