Strange products of projections

Let H be an infinite-dimensional Hilbert space. We show that there exist three orthogonal projections X ₁,X ₂,X ₃ onto closed subspaces of H such that for every 0 ≠ z ₀ ∈ H there exist k ₁, k ₂, · · · ∈ {1, 2, 3} so that the sequence of iterates defined by z _n = X _kn z _n ?1 does not converge in norm.     

Nonadiabatic dynamics of two strongly coupled nanomechanical resonator modes

The Landau-Zener transition is a fundamental concept for dynamical quantum systems and has been studied in numerous fields of physics. Here, we present a classical mechanical model system exhibiting analogous behavior using two inversely tunable, strongly coupled modes of the same nanomechanical beam resonator. In the adiabatic limit, the anticrossing between the two modes is observed and the coupling strength extracted. Sweeping an initialized mode across the coupling region allows mapping of the progression from diabatic to adiabatic transitions as a function of the sweep rate.     

Automatic generation of linear programming problems for computer aided instruction

The paper presents a method for generating random linear programming problems with a previously selected type of solution. The user can choose a problem whose solution is unbounded, bounded for minima, maxima or both, unique or multiple, with given structure, at wish. Initially, the feasible solution of the LPP is generated as the sum of a linear space, a cone, and a polytope, depending on the desired properties of the solution. With the aim of obtaining a simple set of constraints, the generators of these three structures are selected as random vectors with integer simple components, the range of which can be given. Next, an objective function that satisfies the required conditions, i.e. leads to a solution of the desired type, is obtained. The generating algorithms have been implemented in Mathematica and some illustrative examples are given to clarify the generation process. With this tool, a LPP can be generated, according to the instructor requirements, where this is a human or an expert system. They can control student progress and generate a sequence of problems covering all possible cases, in steps of increasing difficulty. Combining this tool with another (also produced by the same authors) that solves the problems and explains the whole process, step by step, a computer aided module for learning LPP, which is completely autonomous, can be easily obtained.     

Equivariant Classification of <Emphasis Type="Italic">b</Emphasis><Superscript><Emphasis Type="Italic">m</Emphasis></Superscript>-symplectic Surfaces

Inspired by Arnold’s classification of local Poisson structures [1] in the plane using the hierarchy of singularities of smooth functions, we consider the problem of global classification of Poisson structures on surfaces. Among the wide class of Poisson structures, we consider the class of b^m-Poisson structures which can be also visualized using differential forms with singularities as b^m-symplectic structures. In this paper we extend the classification scheme in [24] for b^m-symplectic surfaces to the equivariant setting. When the compact group is the group of deck-transformations of an orientable covering, this yields the classification of these objects for nonorientable surfaces. The paper also includes recipes to construct b^m-symplectic structures on surfaces. The feasibility of such constructions depends on orientability and on the colorability of an associated graph. The desingularization technique in [10] is revisited for surfaces and the compatibility with this classification scheme is analyzed in detail.     

The Planar Slope Number of Planar Partial 3-Trees of Bounded Degree

It is known that every planar graph has a planar embedding where edges are represented by non-crossing straight-line segments. We study the planar slope number, i.e., the minimum number of distinct edge-slopes in such a drawing of a planar graph with maximum degree Δ. We show that the planar slope number of every planar partial 3-tree and also every plane partial 3-tree is at most O(Δ ⁵). In particular, we answer the question of Dujmovi? et al. (Comput Geom 38(3):194–212, 2007) whether there is a function f such that plane maximal outerplanar graphs can be drawn using at most f(Δ) slopes.     

Decision support system for mass dispensing of medications for infectious disease outbreaks and bioterrorist attacks

A simulation and decision support system, RealOpt^©, for planning large-scale emergency dispensing clinics to respond to biological threats and infectious disease outbreaks is described. The system allows public health administrators to investigate clinic design and staffing scenarios quickly. RealOpt^© incorporates efficient optimization technology seamlessly interfaced with a simulation module. The system's correctness and computational advantage are validated via comparisons against simulation runs of the same model developed on a commercial system. Simulation studies to explore facility layout and staffing scenarios for smallpox vaccination and for an actual anthrax-treatment dispensing exercise and post event analysis are presented. The system produces results consistent with the model built on the commercial system, but requires only a fraction of the computational time. Each smallpox scenario runs within 1 CPU minute on RealOpt^©, versus run times of over 5–10 h on the commercial system. The system's fast computational time enables its use in large-scale studies, in particular an anthrax response planning exercise involving a county with 864,000 households. The computational effort required for this exercise was roughly 30 min for all scenarios considered, demonstrating that RealOpt^© offers a very promising avenue for pursuing a comprehensive investigation involving a more diverse set of scenarios, and justifying work towards development of a robust system that can be widely deployed for use by state, local, and tribal health practitioners. Using our staff allocation and assignments for the Anthrax field exercise, DeKalb county achieved the highest throughput among all counties that simultaneously conducted the same scale of Anthrax exercise at various locations, with labor usage at or below the other counties. Indeed, DeKalb exceeded the targeted number of households, and it processed 50% more individuals compared to the second place county. None of the other counties achieved the targeted number of households. The external evaluators commented that DeKalb produced the most efficient floor plan (with no path crossing), the most cost-effective dispensing (lowest labor/throughput value), and the smoothest operations (shortest average wait time, average queue length, equalized utilization rate). The study proves that even without historical data, using our system one can plan ahead and be able to wisely estimate the required labor resources. The exercise also revealed many areas that need attention during the operations planning and design of dispensing centers. The type of disaster being confronted (e.g., biological attack, infectious disease outbreak, or a natural disaster) also dictates different design considerations with respect to the dispensing clinic, facility locations, dispensing and backup strategies, and level of security protection. Depending on the situation, backup plans will be different, and the level of security and military personnel, as well as the number of healthcare workers required, will vary. In summary, the study shows that a real-time decision support system is viable through careful design of a stand-alone simulator coupled with powerful tailor-designed optimization solvers. The flexibility of performing empirical tests quickly means the system is amenable for use in training and preparation, and for strategic planning before and during an emergency situation. The system facilitates analysis of “what-if'' scenarios, and serves as an invaluable tool for operational planning and dynamic on-the-fly reconfigurations of large-scale emergency dispensing clinics. It also allows for “virtual field exercises” to be performed on the decision support system, offering insight into operations flow and bottlenecks when mass dispensing is required for a region with a large population. The system, designed in modular form with a flexible implementation, enables future expansion and modification regarding emergency center design with respect to treatment for different biological threats or disease outbreaks. Working with emergency response departments, further fine-tuning and development of the system will be made to address different biological attacks and infectious disease outbreaks, and to ensure its practicality and usability.     

Pseudochelin A,a siderophore of Pseudoalteromonas piscicida S2040

A new siderophore containing a 4,5-dihydroimidazole moiety was isolated from Pseudoalteromonas piscicida S2040 together with myxochelins A and B, alteramide A and its cycloaddition product, and bromo- and dibromoalterochromides. The structure of pseudochelin A was established by spectroscopic techniques including 2D NMR and MS/MS fragmentation data. In bioassays selected fractions of the crude extract of S2040 inhibited the opportunistic pathogen Pseudomonas aeruginosa. Pseudochelin A displayed siderophore activity in the chrome azurol S assay at concentrations higher than 50 μM, and showed weak activity against the fungus Aspergillus fumigatus, but did not display antibacterial, anti-inflammatory or anticonvulsant activity.     

The PV-Researcher's Siren: Hybrid metal halide perovskites

Metal-halide perovskite semiconductors are certainly one of the hottest topic in solar energy conversion. Optimization of both the absorber material and device architecture has led to an astoundingly rapid increase in the reported device efficiencies. Initially developed in the context of dye-sensitized solar cell research, metal-halide perovskite devices now reach efficiency values and hence need to be compared to more conventional photovoltaic technologies such as silicon, copper indium gallium diselenide and cadmium telluride. Strong direct band gap absorption, long charge carrier diffusion length, ease and flexibility in processing at low temperatures and facile tunability makes these materials ideal for solar energy conversion applications. This review will both reflect on favorable properties of these hybrid and ionic semiconductors as well as reflecting on lead toxicity, material and device stability as the most critical issues that need to be solved in order for these materials to become technologically viable.     

Bis(merocyanine) Hetero-Folda-Dimers: Evaluation of Exciton Coupling between Different Types of π-Stacked Chromphores

Exciton coupling between different types of chromophores has been rarely investigated. Herein, a systematic study on the exciton coupling between merocyanine chromophores of different conjugation length with varying excited state energies is presented. In this work well-defined hetero-dimer stacks were obtained upon folding of bis(merocyanine) dyes in nonpolar solvents. They show distinctly different absorption properties in comparison with the spectra of the single chromophores, revealing a significant coupling between the different chromophores. The simulated absorption spectra obtained from time-dependent density functional theory (TD-DFT) calculations are in good agreement with the experimental spectra. Our theoretical analysis based on an extension of Kasha's exciton theory discloses strong coupling between the dyes’ transition dipole moments despite of an excited-state energy difference of 0.60 eV between the chromophores.