A characterization of duality through section/projection correspondence in the finite dimensional setting

In this paper, we show that the well-known duality operation in the context of convex bodies in Rn is completely characterized by its property of interchanging sections with projections. Our results are compared to results by Böröczky-Schneider and Artstein-Milman, who showed that in many cases, the property of order reversing is sufficient to determine a duality operation, up to obvious linear modifications. In fact, we provide another result that recovers a known characterization of duality by the property of order reversing, and up to a mild condition, also a characterization of duality by interchanging sections by projections.     

A Generalized Two-Agent Location Problem: Asymmetric Dynamics and Coordination

We generalize a static two-agent location problem into dynamic, asymmetric settings. The dynamics is due to the ability of the agents to move at limited speeds. Since each agent has its own objective (demand) function and these functions are interdependent, decisions made by each agent may affect the performance of the other agent and thus affect the overall performance of the system. We show that, under a broad range of system’s parameters, centralized (system-wide optimal) and non-cooperative (Nash) behavior of the agents are characterized by a similar structure. The timing of these trajectories and the intermediate speeds are however different. Moreover, non-cooperative agents travel more and may never rest and thus the system performance deteriorates under decentralized decision-making. We show that a static linear reward approach, recently developed in Golany and Rothblum (Nav. Res. Logist. 53(1):1–15, 2006), can be generalized to provide coordination of the moving agents and suggest its dynamic modification. When the reward scheme is applied, the agents are induced to choose the system-wide optimal solution, even though they operate in a decentralized decision-making mode.     

Stereochemistry of the sn2′ displacement of chiral 1, 3-disubstituted bromoallenes to form chiral acetylenes

Optically active 1,3-disubstituted bromoallenes react with a variety of cuprate reagents preferentially in an S_N2′ fashion with very high $\text{anti}$ selectivity.     

Edge flames stabilized in a non-premixed microcombustor

The dynamics of an edge flame confined in a non-premixed microcombustor model is studied numerically within the context of a diffusive-thermal model. Fuel and oxidizer, separated upstream by a thin plate, flow through a channel with a prescribed velocity. At the tip of the plate, the fuel and oxidizer mix and, when ignited, an edge flame is sustained at some distance from the plate. The objective in this work is to consider the effects of confinement, differential diffusion, and heat loss on the dynamics of an edge flame in a narrow channel. We consider a wide range of channel widths and allow for changing Lewis numbers, and both adiabatic conditions and heat losses along the channel walls. The results illustrate how the flame shape and standoff distance are affected by the channel width, by mixture composition through variations in Lewis numbers and by heat losses. Conditions for flame stabilization, flame oscillations and flame extinction or blowoff are predicted.     

The physics of categorization

In the context of cognition, categorization is the process through which several elements (i.e., words) are grouped into a single set which by naming becomes an abstraction of its elements. For example, tiger, kitty, and max can be categorized as Cats. In this article, we aim to show how the physical, biological and cognitive dimensions are related in the process of categorization or abstraction through the physics of computation. Drawing on Landauer's principle, we show that the price paid in terms of entropy is higher when grouping elements of low ranking (high probability) than when grouping elements of high ranking (low probability). Therefore, the logic of the cognitive process of abstraction is explained through constraints imposed by memory on the computation of categories. © 2015 Wiley Periodicals, Inc. Complexity 21: 269–274, 2016     

Small heterocyclics as hydrogen bond acceptors and donors: the case of the C2H3XS···NH3 complexes (X = H, F and CH3)

B3LYP/6-311++G(d,p) calculations were employed in order to examine the molecular parameters of the C₂H₃XS···NH₃ heterocyclic hydrogen-bonded complexes with X = H, F and CH₃. Intermolecular criteria were taken into account when studying the formation of these hydrogen-bonded complexes, such as geometry analysis, charge density quantification and interpretation of the harmonic vibrational spectrum, in which case the appearance of red-shift and blue-shift effects was discussed. It was assumed from the outset that many hydrogen bond types may exist in these systems, and these were investigated using the results of topological integrations from the quantum theory of atoms in molecules (QTAIM) and intermolecular charge transfer calculations using the ChelpG scheme. The proton donor/acceptor behavior of C₂H₃XS was interpreted in terms of hydrogen bond energies, whose values were corrected using the basis sets superposition error (BSSE) and zero point energy (ZPE). Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.