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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 bm-Poisson structures which can be also visualized using differential forms with singularities as bm-symplectic structures. In this paper we extend the classification scheme in [24] for bm-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 bm-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. 相似文献
24.
Vít Jelínek Eva Jelínková Jan Kratochvíl Bernard Lidický Marek Tesař Tomáš Vyskočil 《Graphs and Combinatorics》2013,29(4):981-1005
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. 相似文献
25.
Eva K. Lee Siddhartha Maheshwary Jacquelyn Mason William Glisson 《Annals of Operations Research》2006,148(1):25-53
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. 相似文献
26.
Enrique Castillo Rosa Eva Pruneda MÓnica Esquivel IV 《International Journal of Mathematical Education in Science & Technology》2013,44(2):209-232
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. 相似文献
27.
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. 相似文献
28.
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. 相似文献
29.
Pipíška Martin Florková Eva Nemeček Peter Remenárová Lucia Horník Miroslav 《Journal of Radioanalytical and Nuclear Chemistry》2019,319(3):855-867
Journal of Radioanalytical and Nuclear Chemistry - Zeolitic material prepared by hydrothermal treatment of brown coal fly ash was used for sorption separation of Co2+ and Zn2+ ions from single and... 相似文献
30.
Lenz C Kühn-Hölsken E Urlaub H 《Journal of the American Society for Mass Spectrometry》2007,18(5):869-881
Protein-RNA interactions within ribonucleoprotein particles (RNPs) can be investigated by UV-induced crosslinking of proteins to their cognate RNAs and subsequent isolation and mass-spectrometric analysis of crosslinked peptide-RNA oligonucleotides. Because of the low crosslinking yield, a major challenge in protein-RNA UV crosslinking is the detection of the crosslinked species over the excess of non-crosslinked material, especially when complex systems (native RNPs) are investigated. Here, we applied a novel approach that uses on-line nanoLC-ESI-MS/MS to detect and subsequently sequence peptide-RNA oligonucleotide crosslinks from crude mixtures. To detect the crosslinks we made use of features shared by crosslinks and phosphopeptides, that is, the phosphate groups that both carry. A precursor ion scan for m/z 79 (negative-ion mode, -ve) is applied to selectively detect analytes bearing the phosphate-containing species (i.e., residual non-crosslinked RNA and peptide-RNA crosslinks) from crude mixtures and to determine their exact m/z values. On this basis, a multiple reaction monitoring (MRM) experiment monitors the expected decomposition from the different precursor charge states of the putative crosslinks to one of the four possible RNA nucleobases [m/z 112, 113, 136, 152 (positive-ion mode, +ve)]. On detection, a high-quality MS/MS is triggered to establish the structure of the crosslink. In a feasibility study, we detected and subsequently sequenced peptide-RNA crosslinks obtained by UV-irradiation of (1) native U1 snRNPs and (2) [15.5K-61K-U4atac] snRNPs prepared by reconstitution in vitro. MRM-triggered collision-induced dissociation (CID) MS/MS enabled us to obtain sequence information about the crosslinked peptide and RNA moiety. 相似文献