165,350 research outputs found
[Report to Chief J. E. Curry, by an unknown author #1]
No full textReport to Chief J. E. Curry, by an unknown author. The report contains a list of officers who gave depositions to the United States Attorney
[Report to Chief J. E. Curry, by an unknown author #2]
No full textReport to Chief J. E. Curry, by an unknown author. The report contains a list of officers who gave depositions to the United States Attorney
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
Predicting corporate bankruptcy using the framework of Leland-Toft: Evidence from US
No full textIn this paper, we evaluate an alternative approach for bankruptcy prediction that measures the financial healthiness of firms that have coupon-paying debts. The approach is based on the framework of Leland, H. and Toft, K.B. [Optimal capital structure, endogenous bankruptcy and the term structure of credit spreads. J. Financ., 1996, 51, 987–1019], which is an extension of a widely-used model; the Black–Scholes–Merton model. Using U.S. public firms between 1995 and 2014, we show that the Leland-Toft approach is more powerful than Black–Scholes–Merton in a variety of tests. Moreover, extending popular but also contemporary corporate bankruptcy models with the probability of bankruptcy derived from the Leland-Toft model, such as Altman, E. [Financial ratios, discriminant analysis and the prediction of corporate bankruptcy. J. Financ., 1968, 23, 589–609], Ohlson, J.A. [Financial ratios and the probabilistic prediction of bankruptcy. J. Account. Res., 1980, 18, 109–131] and Campbell, J. Y., Hilscher, J. and Szilagyi, J. [In search of distress risk. J. Financ., 2008, 63, 2899–2939], yields models with improved performance. One of our tests, for example, shows that banks using these extended models, achieve superior economic performance relative to other banks. Our results are consistent under a comprehensive out-of-sample framework
Another step towards proving a conjecture by Plummer and Toft
No full textAbstractA cyclic colouring of a graph G embedded in a surface is a vertex colouring of G in which any two distinct vertices sharing a face receive distinct colours. The cyclic chromatic number χc(G) of G is the smallest number of colours in a cyclic colouring of G. Plummer and Toft in 1987 [M.D. Plummer, B. Toft, Cyclic coloration of 3-polytopes, J. Graph Theory 11 (1987) 507–515] conjectured that χc(G)≤Δ∗+2 for any 3-connected plane graph G with maximum face degree Δ∗. It is known that the conjecture holds true for Δ∗≤4 and Δ∗≥24. The validity of the conjecture is proved in the paper for Δ∗≥18
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