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This book, dedicated to Roger Penrose, is a second, mathematically oriented course in general relativity. It contains extensive references and occasional excursions in the history and philosophy of gravity, including a relatively lengthy historical introduction. The book is intended for all students of general relativity of any age and orientation who have a background including at least first courses in special and general relativity, differential geometry, and topology. The material is developed in such a way that through the last two chapters the reader may acquire a taste of the modern mathematical study of black holes initiated by Penrose, Hawking, and others, as further influenced by the initial-value or PDE approach to general relativity. Successful readers might be able to begin reading research papers on black holes, especially in mathematical physics and in the philosophy of physics. The chapters are: Historical introduction, General differential geometry, Metric differential geometry, Curvature, Geodesics and causal structure, The singularity theorems of Hawking and Penrose, The Einstein equations, The 3+1 split of space-time, Black holes I: Exact solutions, and Black holes II: General theory. These are followed by two appendices containing background on Lie groups, Lie algebras, & constant curvature, and on Formal PDE theory.

General relativity (Physics)

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Power resources. --- Force and energy. --- Low-energy nuclear reactions. --- Energy conversion. --- Nuclear physics. --- Quantum electrodynamics. --- Vacuum. --- General relativity (Physics) --- Technology. --- Engineering.

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Designed as a sequel to the authors' Introduction to Gauge Field Theory, Supersymmetric Gauge Field Theory and String Theory introduces first-year graduate students to supersymmetric theories, including supergravity and superstring theories. Starting with the necessary background in quantum field theory, the book covers the three key topics of high-energy physics. The emphasis is on practical calculations rather than abstract generalities or phenomenological results. Where possible, the authors show how to calculate, connecting the theoretical with the phenomenological. While the field continues to advance and grow, this book addresses the basic theory at the core and will likely remain relevant even if more advanced ideas change.

Supersymmetry --- Supergravity --- Superstring theories --- 530.19 --- Unified theories --- Particles (Nuclear physics) --- Symmetry (Physics) --- Superstrings (Nuclear physics) --- Theories, Superstring --- String models --- Superunified theories --- General relativity (Physics) --- Quantum theory --- Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc. --- Supergravity. --- Superstring theories. --- Supersymmetry. --- 530.19 Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc. --- Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc --- Nuclear physics

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Diagnosis and Management of Polycystic Ovary Syndrome (PCOS) is a clinical reference work for primary care physicians, internists, general endocrinologists, obstetricians, gynecologists and students. PCOS is a common but often misdiagnosed disease. Many symptoms can be alleviated by early intervention and effective management.Prominent endocrinologists have contributed recent data current research on the pathogenesis, manifestations, diagnosis and treatment of PCOS. The variety of medical issues presenting in PCOS patients result in late referrals or inappropriate advice. This title will be a tool in understanding the metabolic and genetic basis of PCOS, while providing management strategies.

Pade ́ approximant --Congresses. --- Polycystic ovary syndrome --- Hyperandrogenism --- Ovarian Cysts --- Analytical, Diagnostic and Therapeutic Techniques and Equipment --- Ovarian Diseases --- Cysts --- Gonadal Disorders --- Neoplasms --- Adnexal Diseases --- Endocrine System Diseases --- Diseases --- Genital Diseases, Female --- Female Urogenital Diseases --- Female Urogenital Diseases and Pregnancy Complications --- Polycystic Ovary Syndrome --- Diagnosis --- Medicine --- Health & Biological Sciences --- Gynecology & Obstetrics --- Clinical Endocrinology --- Polycystic ovary syndrome. --- Gynecology. --- Gynaecology --- PCOD (Gynecology) --- PCOS (Gynecology) --- Polycystic ovarian disease --- Polyfollicular ovarian disease --- Sclerocystic ovarian degeneration --- Sclerocystic ovaries --- Sclerocystic ovary syndrome --- Stein-Leventhal syndrome --- Approximation: chebyshev elementary function least squares linear approximation minimax approximation and algorithms nonlinear and rational approximation spline and piecewise polynomial approximation (Numerical analysis) --- Padé approximant --- 681.3*G12 Approximation: chebyshev elementary function least squares linear approximation minimax approximation and algorithms nonlinear and rational approximation spline and piecewise polynomial approximation (Numerical analysis) --- 530.12 <063> --- Relativity principle--Congressen --- -Relativity principle--Congressen --- 530.12 <063> Relativity principle--Congressen --- Anniversaries, etc. --- Medicine. --- General practice (Medicine). --- Endocrinology. --- Medicine & Public Health. --- General Practice / Family Medicine. --- 517.518.8 --- 517.52 --- 519.6 --- 681.3*G12 --- 681.3*G12 Approximation: chebyshev; elementary function; least squares; linear approximation; minimax approximation and algorithms; nonlinear and rational approximation; spline and piecewise polynomial approximation (Numerical analysis) --- Approximation: chebyshev; elementary function; least squares; linear approximation; minimax approximation and algorithms; nonlinear and rational approximation; spline and piecewise polynomial approximation (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- 517.52 Series and sequences --- Series and sequences --- 517.518.8 Approximation of functions by polynomials and their generalizations --- Approximation of functions by polynomials and their generalizations --- Physics --- Congresses --- Einstein, Albert, --- Numerical approximation theory --- Generative organs, Female --- Einstein, Albert --- Ovaries --- Syndromes --- Congresses. --- Physique --- Congrès --- Family medicine. --- Internal medicine --- Hormones --- Family practice (Medicine) --- General practice (Medicine) --- Physicians (General practice) --- Analyse numérique. --- Numerical analysis --- Aiyinsitan, Abote, --- Aĭnshtaĭn, Albert, --- Ainshutain, A, --- Ain̲sṭain̲, Ālparṭ, --- Ainsṭāina, Albarṭa, --- Ajnštajn, Albert, --- Āynishtayn, --- Aynshtayn, Albert, --- Eĭnshteĭn, Alʹbert, --- אינשטין, אלברט, --- איינשטיין --- איינשטיין, אלבערט, --- איינשטיין, אלברט --- איינשטיין, אלברט, --- Aynştayn, Elbêrt, --- Īnshtīn, --- Aynîştayn, --- Aiyinsitan, --- 愛因斯坦, --- 爱因斯坦, --- General relativity (Physics) --- Analyse numérique --- Numerical analysis. --- Approximation et developpements --- Approximation de pade