Progress in Highdimensional Percolation And Random Graphs

This text presents an engaging exposition of the active field of high-dimensional percolation that will likely provide an impetus for future work. With over 90 exercises designed to enhance the reader’s understanding of the material, as well as many open problems, the book is aimed at graduate students and researchers who wish to enter the world of this rich topic. The text may also be useful in advanced courses and seminars, as well as for reference and individual study.

This volume contains five review articles, two in the Algebra part and three in the Geometry part, surveying the fields of cate­ gories and class field theory, in the Algebra part, and of Finsler spaces, structures on differentiable manifolds, and packing, cover­ ing, etc., in the Geometry part. The literature covered is primar­ Hy that published in 1964-1967. Contents ALGEBRA CATEGORIES …………… . 3 M. S. Tsalenko and E. G. Shul'geifer § 1. Introduction……….. 3 § 2. Foundations of the Theory of Categories . . . . . 4 § 3. Fundamentals of the Theory of Categories . . . . . 6 § 4. Embeddings of Categories … . . . . . . . . . . . . 14 § 5. Representations of Categories . . . . . . . . . . . . . 16 § 6. Axiomatic Characteristics of Algebraic Categories . . . . . . . . . . . . . . . . . . . . . . . . . . 18 § 7. Reflective Subcategories; Varieties. . . 20 § 8. Radicals in Categories . . . . . . . 24 § 9. Categories with Involution. . . . . . 29 § 10. Universal Algebras in Categories . 30 § 11. Categories with Multiplication . . . 34 § 12. Duality of Functors. .. ……. 37 § 13. Homotopy Theory . . . . .. ……….. 39 § 14. Homological Algebra in Categories. . . . . . 41 § 15. Concrete Categories . . . . .. ……… 44 § 16. Generalizations.. . . . . . . 45 Literature Cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 CLASS FIELD THEORY. FIELD EXTENSIONS. . . . . . . . 59 S. P. Demushkin 66 Literature Cited vii CONTENTS viii GEOMETRY 75 FINSLER SPACES AND THEIR GENERALIZATIONS ..

This book provides an overview of the progress in landslide research and technology and is part of a book series of the International Consortium on Landslides (ICL). The book provides a common platform for the publication of recent progress in landslide research and technology for practical applications and the benefit for the society contributing to the Kyoto Landslide Commitment 2020, which is expected to continue up to 2030 and even beyond to globally promote the understanding and reduction of landslide disaster risk, as well as to address the 2030 Agenda Sustainable Development Goals.

This book provides an overview of the progress in landslide research and technology and is part of a book series of the International Consortium on Landslides (ICL). The book provides a common platform for the publication of recent progress in landslide research and technology for practical applications and the benefit for the society contributing to the Kyoto Landslide Commitment 2020, which is expected to continue up to 2030 and even beyond to globally promote the understanding and reduction of landslide disaster risk, as well as to address the 2030 Agenda Sustainable Development Goals.

This book provides the most current advancements in the medical care of glioma patients, accompanied by clinical cases. Clinical implementations of the new multilayered integrated diagnosis of gliomas according to WHO CNS5 are also demonstrated here. New adjuvant therapies, such as chemotherapy/targeted therapy, immunotherapy, and physiotherapy, are discussed in the book. The book also covers the applications of genomics and epigenomics of gliomas in clinical practice. In essence, this book shows the management of gliomas with new treatment modalities, which can prolong the overall survival time of patients fighting glioma.