This book contains the notes of the lectures delivered at an Advanced Course on Combinatorial Matrix Theory held at Centre de Recerca Matemàtica (CRM) in Barcelona. These notes correspond to five series of lectures. The first series is dedicated to the study of several matrix classes defined combinatorially, and was delivered by Richard A. Brualdi. The second one, given by Pauline van den Driessche, is concerned with the study of spectral properties of matrices with a given sign pattern. Dragan Stevanović delivered the third one, devoted to describing the spectral radius of a graph as a tool to provide bounds of parameters related with properties of a graph. The fourth lecture was delivered by Stephen Kirkland and is dedicated to the applications of the Group Inverse of the Laplacian matrix. The last one, given by Ángeles Carmona, focuses on boundary value problems on finite networks with special in-depth on the M-matrix inverse problem.
Group inverses for singular M-matrices are useful tools not only in matrix analysis, but also in the analysis of stochastic processes, graph theory, electrical networks, and demographic models. Group Inverses of M-Matrices and Their Applications highlights the importance and utility of the group inverses of M-matrices in several application areas. After introducing sample problems associated with Leslie matrices and stochastic matrices, the authors develop the basic algebraic and spectral properties of the group inverse of a general matrix. They then derive formulas for derivatives of matrix functions and apply the formulas to matrices arising in a demographic setting, including the class of Leslie matrices. With a focus on Markov chains, the text shows how the group inverse of an appropriate M-matrix is used in the perturbation analysis of the stationary distribution vector as well as in the derivation of a bound for the asymptotic convergence rate of the underlying Markov chain. It also illustrates how to use the group inverse to compute and analyze the mean first passage matrix for a Markov chain. The final chapters focus on the Laplacian matrix for an undirected graph and compare approaches for computing the group inverse. Collecting diverse results into a single volume, this self-contained book emphasizes the connections between problems arising in Markov chains, Perron eigenvalue analysis, and spectral graph theory. It shows how group inverses offer valuable insight into each of these areas.
I May Be Big But I Didn't Cause That Solar Eclipse is award-winning Canadian humorist Gordon Kirkland's fifth book. Three of his previous books received Canada's prestigious literary award, The Stephen Leacock Award of Merit For Humour. His syndicated newspaper column. Gordon Kirkland At Large, is enjoyed by readers in the United States and Canada every week. He is also a frequent guest on radio and television shows in both countries. In addition, he is in great demand as a speaker at conferences, conventions, and festivals throughout North America. An April 2006 profile of Kirkland in the Canadian edition of Reader's Digest said, "Kirkland's specialty is making others laugh at him, at themselves, and at life in general." In this book, Kirkland once again takes on subjects ranging from marriage to dealing with a canine companion. He looks at the odd events of daily life, and even finds humor in the experiences of moving and having a serious illness.
Enter once more the world of Roland Deschain—and the world of the Dark Tower...now presented in a stunning graphic novel omnibus form that will unlock the doorways to terrifying secrets and bold storytelling as part of the dark fantasy masterwork and magnum opus from #1 New York Times bestselling author Stephen King. “The man in black fled across the desert, and the gunslinger followed.” With these unforgettable words, millions were introduced to Stephen King’s iconic character Roland Deschain of Gilead. Roland is the last of his kind, a “gunslinger” charged with protecting whatever goodness and light remains in his world—a world that “moved on,” as they say. In this desolate reality—a dangerous land filled with ancient technology and deadly magic, and yet one that mirrors our own in frightening ways—Roland is on a spellbinding and soul-shattering quest to locate and somehow save the mystical nexus of all worlds, all universes: the Dark Tower. Now, in the graphic novel series adaptation Stephen King’s The Dark Tower: The Gunslinger, originally published by Marvel Comics in single-issue form and creatively overseen by Stephen King himself, the full story of Roland’s troubled past and lifelong odyssey is revealed. Sumptuously drawn by Sean Phillips, Luke Ross, Michael Lark, Laurence Campbell, Alex Maleev, and Richard Isanove, adapted by Stephen King expert Robin Furth, and scripted by New York Times bestselling author Peter David, The Gunslinger is an extraordinary and terrifying journey—ultimately serving as the perfect introduction for new readers to Stephen King’s modern literary classic The Dark Tower, while giving longtime fans thrilling adventures transformed from his blockbuster novels. This single-volume omnibus edition includes the complete graphic novel series: The Gunslinger: The Journey Begins; The Little Sisters of Eluria; The Battle of Tull; The Way Station; The Man in Black; Last Shots.
Enter once more the world of Roland Deschain—and the world of the Dark Tower...now presented in a stunning graphic novel omnibus form that will unlock the doorways to terrifying secrets and bold storytelling as part of the dark fantasy masterwork and magnum opus from #1 New York Times bestselling author Stephen King. “The man in black fled across the desert, and the gunslinger followed.” With these unforgettable words, millions were introduced to Stephen King’s iconic character Roland Deschain of Gilead. Roland is the last of his kind, a “gunslinger” charged with protecting whatever goodness and light remains in his world—a world that “moved on,” as they say. In this desolate reality—a dangerous land filled with ancient technology and deadly magic, and yet one that mirrors our own in frightening ways—Roland is on a spellbinding and soul-shattering quest to locate and somehow save the mystical nexus of all worlds, all universes: the Dark Tower. Now, in the graphic novel series adaptation Stephen King’s The Dark Tower: The Drawing of the Three, originally published by Marvel Comics in single-issue form and creatively overseen by Stephen King himself, the full story of Roland’s troubled past and lifelong odyssey is revealed. Sumptuously drawn by Piotr Kowalski and Jonathan Marks, adapted by Stephen King expert Robin Furth, and scripted by New York Times bestselling author Peter David, The Drawing of the Three is an extraordinary and terrifying journey—ultimately serving as the perfect introduction for a new audience to Stephen King’s modern literary classic The Dark Tower, while giving longtime fans thrilling adventures transformed from his blockbuster novels. This single-volume omnibus edition includes the complete graphic novel series The Drawing of the Three: The Prisoner; House of Cards; The Lady of Shadows; Bitter Medicine.
This title features facts, figures, stats and trivia on legions of record-breakers, record losers, actors, singers, sportsmen, historical figures, the famous and infamous, felons, inventors, rulers, heartthrobs, politicians and scientists called Stephen.
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