Transversal Lattices

A flat of a matroid is cyclic if it is a union of circuits; such flats form a lattice under inclusion and, up to isomorphism, all lattices can be obtained this way. A lattice is a Tr-lattice if all matroids whose lattices of cyclic flats are isomorphic to it are transversal. We investigate some sufficient conditions for a lattice to be a Tr-lattice; a corollary is that distributive lattices of dimension at most two are Tr-lattices. We give a necessary condition: each element in a Tr-lattice has at most two covers. We also give constructions that produce new Tr-lattices from known Tr-lattices.Comment: 12 pages; 5 figure

Lattice path matroids: the excluded minors

A lattice path matroid is a transversal matroid for which some collection of incomparable intervals in some linear order on the ground set is a presentation. We characterize the minor-closed class of lattice path matroids by its excluded minors.Comment: 13 pages, 2 figure

Beyond Bathsheba: Managing Ethical Climates Through Pragmatic Ethics

This paper explores the puzzling nature of leader behavior in order to understand the conditions that encourage unethical decision-making. Building on the extant literature of pragmatic ethics, I explore how leaders can increase the quality of ethical decision-making within their organizations by understanding the incentives of rational choice. I have developed a rational choice-based ethical decision-making model to understand the incentives behind ethical leader behavior and find that ethical behavior is likely to be rational as long as audience costs remain higher than the savings benefits incurred by unethical behavior. I conclude with analysis of how the ethical rational model compares to other prominent theories that explain unethical leader behavior and propose that the probable outcomes derived from my model better explain bad leader behavior than competing control-oriented models. The results of this inquiry underscore the transactional and practical characteristics of leadership as a tool to help leaders manage their ethical climates, improve business practices and management policies, understand the nature of individual incentives, and capture transactional components of leader behavior

Transition Delay in Hypervelocity Boundary Layers By Means of CO₂/Acoustic Instability Interaction

The potential for hypervelocity boundary layer stabilization was investigated using the concept of damping Mack’s second mode disturbances by vibrational relaxation of carbon dioxide (CO₂) within the boundary layer. Experiments were carried out in the Caltech T5 hypervelocity shock tunnel and the Caltech Mach 4 Ludwieg tube. The tests used 5-degree half-angle cones (at zero angle of attack) equipped near the front of the cone with an injector consisting of either discrete holes or a porous section. Gaseous CO₂, argon (Ar) and air were injected into the boundary layer and the effect on boundary layer stability was evaluated by optical visualization, heat flux measurements and numerical simulation. In T5, tests were carried out with CO₂ in the free stream as well as injection. Injection experiments in T5 were inconclusive; however, experiments with mixtures of air/CO₂ in the free stream demonstrated a clear stabilizing effect, limiting the predicted amplification N-factors to be less than 13. During the testing activities in T5, significant improvements were made in experimental technique and data analysis. Testing in the Ludwieg tube enabled optical visualization and the identification of a shear-layer like instability downstream of the injector. Experiments showed and numerical simulation confirmed that injection has a destabilizing influence beyond a critical level of injection mass flow rate. A modified injection geometry was tested in the Ludwieg tube and we demonstrated that it was possible to cancel the shock wave created by injection under carefully selected conditions. However, computations indicate and experiments demonstrate that shear-layer like flow downstream of the porous wall injector is unstable and can transition to turbulence while the injected gas is mixing with the free stream. We conclude that the idea of using vibrational relaxation to delay boundary layer transition is a sound concept but there are significant practical issues to be resolved to minimize the flow disturbance associated with introducing the vibrationally-active gas into the boundary layer

How properties hold together in Substances

This article aims to clarify how aspects of current chemical understanding relate to some important contemporary problems of philosophy. The first section points out that the long-running philosophical debates concerning how properties stay together in substances have neglected the important topic of structure-determining closure. The second part describes several chemically-important types of closure and the third part shows how such closures ground the properties of chemical substances. The fourth section introduces current discussions of structural realism (SR) and contextual emergence: the final sections reconsider the coherence of the properties of substances and concludes that recognition that structures qualify as determinants of specific outcomes—as ‘causes’ as that designation is used in Standard English—clarifies how properties stay together in chemical entities, and by analogy, how characteristics cohere in ordinary items