190,421 research outputs found
Pseudo-differential operators with isotropic symbols, Wick and anti-Wick operators, and hypoellipticity
No full textWe study the link between ilidos and Wick operators via the Bargmann transform. We deduce a formula for the symbol of the Wick operator in terms of the short-time Fourier transform of the Weyl symbol. This gives characterizations of Wick symbols of ilidos of Shubin type and of infinite order, and results on composition. We prove a series expansion of Wick operators in terms of anti-Wick operators which leads to a sharp Garding inequality and transition of hypoellipticity between Wick and Shubin symbols. Finally we show continuity results for anti-Wick operators, and estimates for the Wick symbols of anti-Wick operators.(c) 2022 The Author(s). Published by Elsevier Masson SAS. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)
Unsolved graph colouring problems
No full textOur book Graph Coloring Problems [85] appeared in 1995. It contains descriptions of unsolved problems, organized into sixteen chapters. A large number of publications on graph colouring have appeared since then, and in particular around thirty of the 211 problems in that book have been solved. In this chapter we review some of our favourite problems that remain unsolved. Introduction A main reason for the continued interest in the area of graph colouring is its wealth of interesting unsolved problems. Many of these are easy to state, but seemingly difficult to solve. However they are not impossible, as the literature in the field will testify. The seven most striking results of the past twenty years are: • the 5-list-colourability of planar graphs (dating back to V. G. Vizing in 1975 and to P. Erdős, A. L. Rubin and H. Taylor in 1979) by Thomassen [159] • the confirmation by Robertson, Sanders, Seymour and Thomas [137] of the truth of the four-colour theorem (F. Guthrie and A. De Morgan (1852)) • the asymptotic solution by Reed [134] of the problem as to whether for k ≥ 9 there are k-chromatic graphs without complete k-graphs and of maximum degree k (V. G. Vizing (1968) and O. V. Borodin and A. V. Kostochka (1977)) • the proof by Chudnovsky, Robertson, Seymour and Thomas [39] of the strong perfect graph conjecture of C. Berge around 1960 • the proof by Thomassen [161] of the weak 3-flow conjecture of W. T. Tutte (1954) and F. Jaeger (1988) • the solution by Kostochka and Yancey [111] to the problem of critical graphs with few edges (due to T. Gallai (1963) and O. Ore (1967)) • the description found by Borodin, Dvořák, Kostochka, Lidický and Yancey [24] of all 4-critical planar graphs with exactly four triangles (B. Grünbaum (1963), V. A. Aksenov (1974) and P. Erdős (1990)). In addition to these major achievements there are many other important results – in fact, thirty-one of the original 211 problems from the lists in Jensen and Toft [85] were solved by 2013.</p
Author-wise bibliometric analysis based on entropy.
No full textAuthor-wise bibliometric analysis based on entropy.</p
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe 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
Appropriate Similarity Measures for Author Cocitation Analysis
No full textWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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