Results 51 to 60 of about 20,159 (298)
Notes on Maskit's planarity theorem [PDF]
We give an account of the Planarity Theorem of Maskit. This gives a classification of finitely generated groups acting effectively properly discontinuously by orientation-preserving homeomorphisms on a planar surface.
Bowditch, B. H.
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Planarity ranks for varieties of equationally noetherian semigroups [PDF]
The problem of describing semigroup varieties with finite planarity rank is researched. In addition to the previously obtained results the author finds new countable infinite series of semigroup varieties with finite planarity rank.
Solomatin, Denis Vladimirovich
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Regularity and Planarity of Token Graphs
Let G = (V, E) be a graph of order n and let 1 ≤ k < n be an integer. The k-token graph of G is the graph whose vertices are all the k-subsets of V, two of which are adjacent whenever their symmetric difference is a pair of adjacent vertices in G.
Carballosa Walter +3 more
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Non-1-Planarity of Lexicographic Products of Graphs
In this paper, we show the non-1-planarity of the lexicographic product of a theta graph and K2. This result completes the proof of the conjecture that a graph G ◦ K2 is 1-planar if and only if G has no edge belonging to two cycles.
Matsumoto Naoki, Suzuki Yusuke
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On flips in planar matchings [PDF]
In this paper we investigate the structure of flip graphs on non-crossing perfect matchings in the plane. Specifically, consider all non-crossing straight-line perfect matchings on a set of $2n$ points that are placed equidistantly on the unit circle. A flip operation on such a matching replaces two matching edges that span an empty quadrilateral with ...
Marcel Milich +2 more
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We present robust protocols for the preparation of supported lipid bilayers (SLBs) incorporating either Salmonella smooth LPS or outer membrane vesicles (OMVs). We use a combination of quartz crystal microbalance with dissipation (QCM‐D) and fluorescence microscopy to both characterize the SLBs of various compositions and to probe their interactions ...
Hudson P. Pace +6 more
wiley +1 more source
On the planar edge-length ratio of planar graphs
The edge-length ratio of a straight-line drawing of a graph is the ratio between the lengths of the longest and of the shortest edge in the drawing. The planar edge-length ratio of a planar graph is the minimum edge-length ratio of any planar straight-line drawing of the graph. In this paper, we study the planar edge-length ratio of planar graphs.
Borrazzo, Manuel, Frati, Fabrizio
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Ordered Level Planarity, Geodesic Planarity and Bi-Monotonicity
We introduce and study the problem Ordered Level Planarity which asks for a planar drawing of a graph such that vertices are placed at prescribed positions in the plane and such that every edge is realized as a y-monotone curve.
Günter Rote +3 more
core +1 more source
α‐Synuclein aggregation landscape from phase separation to neurotoxic intermediates
Alpha‐synuclein aggregation in Parkinson's disease involves a complex landscape of transient intermediates, including oligomers, fibrils and liquid–liquid phase separation (LLPS). A view is emerging in which LLPS maturation into solid‐like condensates may contribute to the formation of neurotoxic species.
Silvia Arino +2 more
wiley +1 more source
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