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Matroid representation theory studies the question of when a matroid is representable by the columns of a matrix over some field. The matroids representable over GF 2 and GF 3 were characterized by their excluded minors in the s and the s respectively.
Rota then conjectured that the matroids representable over any finite field GF q could be characterized in terms of a finite list of excluded minors. For more than twenty five years, progress on Rota's conjecture stalled.
The proofs for GF 2 and GF 3 relied on the uniqueness properties of representations over these fields, properties that do not hold for other fields.
Thus the result of Geelen, Gerards and Kapoor came as a big surprise.
- Volume 52, Issue March-AprilChemical characterization of okra stalk (Abelmoschus esculentus) as potential raw material for biorefinery utilization. An ion (/ ˈ aɪ ɒ n, -ə n /) is an atom or molecule that has a non-zero net electrical charge (its total number of electrons is not equal to its total number of protons).A cation is a positively-charged ion, while an anion is negatively charged. Therefore, a cation molecule has a hydrogen proton without its electron, and an anion has an extra electron. Because of their opposite electric. Effect of welding speed on microstructures, hardness distribution and tensile properties of the welded joints were investigated. By varying the process parameters, defect free .
The paper of Geelen, Gerards and Kapoor gives an excluded minor characterization for matroids represented over GF 4 by working around the non-uniqueness of the representation.
It has reawakened interest in the area of matroid representation and brought renewed hope of progress towards the solution of Rota's conjecture. Bertrand Guenin, "A characterization of weakly bipartite graphs", Journal of Combinatorial Theory B 83 A long-standing area of interest in the field of discrete optimization is finding conditions under which a given polyhedron has integer vertices, so that integer optimization problems can be solved as linear programs.
In the case of a particular set covering formulation for the maximum cut problem, a graph is called weakly bipartite if the polyhedron has integer vertices for that graph.
Guenin's result gives a precise characterization of the graphs that are weakly bipartite in terms of an excluded minor.
This solves the graphical case of a famous conjecture about ideal binary clutters made by Seymour in his Fulkerson Prize-winning paper.
Guenin's proof makes an ingenious use of a deep theorem of Lehman, also itself a Fulkerson Prize winner.
Guenin's work has motivated several remarkable subsequent papers. Satoru Iwata, Lisa Fleischer, and Satoru Fujishige, "A combinatorial, strongly polynomial-time algorithm for minimizing submodular functions", Journal of the ACM 48, and Alexander Schrijver, "A combinatorial algorithm minimizing submodular functions in strongly polynomial time", Journal of Combinatorial Theory B 80 Submodular functions provide a discrete analog of convex functions, and submodular function minimization arises in such diverse areas as dynamic and submodular flows, facility location problems, multiterminal source coding, and graph connectivity problems.
Inthe papers of Iwata, Fleischer, and Fujishige, and of Schrijver independently gave combinatorial, strongly polynomial-time algorithms for this fundamental problem. These results are a significant step in the history of combinatorial, strongly polynomial-time algorithms for discrete optimization problems, and can be compared with the Edmonds-Karp algorithm for the maximum flow problem and Tardos's algorithm for the minimum-cost flow problem.The dissociation rates of unlabeled drugs have been well studied by kinetic binding analyses.
Since kinetic assays are laborious, we developed a simple method to determine the kinetic binding parameters of unlabeled competitors by a preincubation endpoint assay. The probe binding after preincubation of a competitor can be described by a single equation as a function of time.
Characterization of bubbly flow systems, A review this technique is suited for studying the time-averaged flow properties only, Optimization of an experimental setup for void fraction determination by the X–ray attenuation technique.
In Measuring techniques in gas–liquid two–phase flows, Springer. p– Reservoir Characterization Advance your understanding to optimize reservoir performance The better you understand your reservoir, the better positioned you are to optimize its lifetime performance.
A good test setup with many methods of monitoring different fuel cell and fuel properties allows you to control and analyze how the fuel cell can be improved. Some of the parameters that can be monitored are the fuel temperatures, pressures, and flow rates. Flow chart of the optimization algorithm to determine the mechanical properties from the load–displacement curves.
In the ABAQUS input file, Characterization of elastoplastic properties based on inverse analysis and finite element modeling of two separate indenters.
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