A geometric approach to the theory of optimal control

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Iterative Processes Related to Riordan Arrays: The Reciprocation and the Inversion of Power Series

We point out how Banach Fixed Point Theorem, and the Picard successive approximation methods induced by it, allows us to treat some mathematical methods in Combinatorics. In particular we get, by this way, a proof and an iterative algorithm for the Lagrange Inversion Formula.Comment: 17 pages. We extend the results in the previuous version proving finally the Lagrange Inversion Formula via Banach Fixed Point Theore

Dimensionality reduction in translational noninvariant wave guides

A scheme to reduce translational noninvariant quasi-one-dimensional wave guides into singly or multiply connected one-dimensional (1D) lines is proposed. It is meant to simplify the analysis of wave guides, with the low-energy properties of the guides preserved. Guides comprising uniform-cross-sectional sections and discontinuities such as bends and branching junctions are considered. The uniform sections are treated as 1D lines, and the discontinuities are described by equations sets connecting the wave functions on the lines. The procedures to derive the equations and to solve reduced systems are illustrated by examples, and the scheme is found to apply when the discontinuities are distant and the energy is low. When the scheme applies, it may substantially simplify the analysis of a wave guide, and hence the scheme may find uses in the study of related problems, such as quantum wire networks.Comment: 17 pages, 5 figure

Teaching what Society Needs:“Hacking” an Introductory Marketing Course with Sustainability and Macromarketing

Marketing classes are often focused on the micro level, failing to account for wider societal issues. In this article, we argue for the inclusion of a wider macro-sustainability focus, one that "hacks" marketing education. With that objective in mind, we developed and delivered an introductory marketing course that integrated both the micro and the macro, thus infusing the course with macro-sustainability. This was done through an "expanded voice" perspective that included alternate complementary micro and macro class sessions while using a traditional managerial marketing textbook supplemented by macro-sustainability materials. We also integrated a controversies approach to support discussion and learning. We taught this course to 150 undergraduate students and conducted both quantitative and qualitative assessments of the course, including comparing results with an "unhacked" marketing course. Findings indicated increased awareness of macro-sustainability topics and movement on appreciation of sustainability and the role marketing can have in achieving this awareness. Finally, we offer a model of how marketing classes at all levels can be "hacked" with a macro-sustainability approach

Macromarketing Pedagogy:Empowering Students to Achieve a Sustainable World

The United Nation's Sustainable Development Goals (SDGs) are challenging the world to work towards a more sustainable future. Its 17 goals are ambitious, requiring concerted and system-based efforts driven by critical and socially aware thinking. However, marketing education is largely falling short of teaching students to think that way. Given macromarketing's unique perspective on the interactions among markets, marketing, and society, macromarketers are poised to contribute to marketing pedagogy and to commit students to realizing the SDGs. This article first looks back at the previous 40 years of macromarketing pedagogy, before offering contemporary approaches to teaching macromarketing through four illustrative case studies found in an online repository called Pedagogy Place. It then looks forward, setting an aspiring vision for macro-oriented classrooms in the coming years

Processing and Transmission of Information

Contains research objectives and summary of research on three research projects and reports on two research projects.National Aeronautics and Space Administration (Grant NGL 22-009-013)National Science Foundation (Grant GK-41464)National Science Foundation (Grant GK-41098)Joint Services Electronics Program (Contract DAAB07-74-C-0630)National Science Foundation (Grant GK-37582

Modeling practical thinking

Intellectualists about knowledge how argue that knowing how to do something is knowing the content of a proposition (i.e, a fact). An important component of this view is the idea that propositional knowledge is translated into behavior when it is presented to the mind in a peculiarly practical way. Until recently, however, intellectualists have not said much about what it means for propositional knowledge to be entertained under thought's practical guise. Carlotta Pavese fills this gap in the intellectualist view by modeling practical modes of thought after Fregean senses. In this paper, I take up her model and the presuppositions it is built upon, arguing that her view of practical thought is not positioned to account for much of what human agents are able to do

Optical Propagation and Communication

Contains research objectives and summary of research on three research projects, and reports on three research projects.National Aeronautics and Space Administration (Grant NGL 22-009-013)National Science Foundation (Grant ENG74-00131-A01)National Science Foundation (Grant ENG74-03996-A01

Actions on permutations and unimodality of descent polynomials

We study a group action on permutations due to Foata and Strehl and use it to prove that the descent generating polynomial of certain sets of permutations has a nonnegative expansion in the basis $\{t^i(1+t)^{n-1-2i}\}_{i=0}^m$, $m=\lfloor (n-1)/2 \rfloor$. This property implies symmetry and unimodality. We prove that the action is invariant under stack-sorting which strengthens recent unimodality results of B\'ona. We prove that the generalized permutation patterns $(13-2)$ and $(2-31)$ are invariant under the action and use this to prove unimodality properties for a $q$-analog of the Eulerian numbers recently studied by Corteel, Postnikov, Steingr\'{\i}msson and Williams. We also extend the action to linear extensions of sign-graded posets to give a new proof of the unimodality of the $(P,\omega)$-Eulerian polynomials of sign-graded posets and a combinatorial interpretations (in terms of Stembridge's peak polynomials) of the corresponding coefficients when expanded in the above basis. Finally, we prove that the statistic defined as the number of vertices of even height in the unordered decreasing tree of a permutation has the same distribution as the number of descents on any set of permutations invariant under the action. When restricted to the set of stack-sortable permutations we recover a result of Kreweras.Comment: 19 pages, revised version to appear in Europ. J. Combi