1,720,967 research outputs found
Clasp-pass Moves on Spatial Graphs (<Special Issue> The Proceedings of the Workshop of Graph Theory and Related Topics, held at GSIS, Tohoku University, November, 1999)
Full text linkapplication/pdfIn this paper our main object is the graph embedded into the 3-space, called the spatial graph. We study a clasp-pass equivalence on spatial graphs, which is an equivalence relation generated by clasp-pass moves and ambient isotopies. Our approach is an analogy of the delta equivalence classification on spatial graphs, where a delta equivalence is an equivalence relation generated by delta moves and ambient isotopies and implied by a clasp-pass equivalence. Consequently, clasp-pass classifications on spatial embeddings of several non-planar graphs and a specified planar graph are given. This is a preliminary report on our recent work and details will appear elsewhere.紀要類(bulletin)1176100 bytesdepartmental bulletin pape
A refinement of the Conway–Gordon theorems
No full textAbstractIn 1983, Conway–Gordon showed that for every spatial complete graph on 6 vertices, the sum of the linking numbers over all of the constituent 2-component links is congruent to 1 modulo 2, and for every spatial complete graph on 7 vertices, the sum of the Arf invariants over all of the Hamiltonian knots is also congruent to 1 modulo 2. In this article, we give integral lifts of the Conway–Gordon theorems above in terms of the square of the linking number and the second coefficient of the Conway polynomial. As applications, we give alternative topological proofs of theorems of Brown–Ramírez Alfonsín and Huh–Jeon for rectilinear spatial complete graphs which were proved by computational and combinatorial methods
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
On generalizations of the Conway-Gordon theorems (Intelligence of Low-dimensional Topology)
Full text linkAn unknotting theorem for delta and sharp edge-homotopy
No full textTwo spatial embeddings of a graph are said to be delta (resp. sharp) edge-homotopic if they are transformed into each other by self delta (resp. sharp) moves and ambient isotopies. We show that any two spatial embeddings of a graph are delta (resp. sharp) edge-homotopic if and only if the graph does not contain a subgraph which is homeomorphic to the theta graph or the disjoint union of two 1-spheres, or equivalently G is homeomorphic to a bouquet. © 2007 WILEY-VCH Verlag GmbH & Co. KGaA
Converses to generalized Conway--Gordon type congruences
Full text linkIt is known that for every spatial complete graph on vertices, the
summation of the second coefficients of the Conway polynomials over the
Hamiltonian knots is congruent to modulo , where if , and if . In particular the case of
is famous as the Conway--Gordon theorem. In this paper,
conversely, we show that every integer is realized as the
summation of the second coefficients of the Conway polynomials over the
Hamiltonian knots in some spatial complete graph on vertices.Comment: 11 pages, 7 figure
Delta link-homotopy on spatial graphs
No full textWe study new equivalence relations in spatial graph theory. We consider natural generalizations of delta link-homotopy on links, which is an equivalence relation generated by delta moves on the same component and ambient isotopies. They are stronger than edge-homotopy and vertex-homotopy on spatial graphs which are natural generalizations of link-homotopy on links. Relationship to existing familiar equivalence relations on spatial graphs are stated, and several invariants are defined by using the second coefficient of the Conway polynomial and the third derivative at 1 of the Jones polynomial of a knot
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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