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Differential equations --- Eigenvalues. --- Numerical solutions.
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Microwave amplifiers --- Poisson's equation --- Design and construction. --- Numerical solutions.
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Helmholtz equation --- Waves --- Numerical solutions. --- Diffraction --- Mathematical models.
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Sampling (Statistics) --- Poisson distribution. --- Poisson's equation --- Numerical solutions.
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This book offers a systematic exposition of conformal methods and how they can be used to study the global properties of solutions to the equations of Einstein's theory of gravity. It shows that combining these ideas with differential geometry can elucidate the existence and stability of the basic solutions of the theory. Introducing the differential geometric, spinorial and PDE background required to gain a deep understanding of conformal methods, this text provides an accessible account of key results in mathematical relativity over the last thirty years, including the stability of de Sitter and Minkowski spacetimes. For graduate students and researchers, this self-contained account includes useful visual models to help the reader grasp abstract concepts and a list of further reading, making this an ideal reference companion on the topic. This title, first published in 2016, has been reissued as an Open Access publication on Cambridge Core.
Conformal geometry. --- Conformal mapping. --- Conformal representation of surfaces --- Mapping, Conformal --- Transformation, Conformal --- Geometric function theory --- Mappings (Mathematics) --- Surfaces, Representation of --- Transformations (Mathematics) --- Circular geometry --- Geometry of inverse radii --- Inverse radii, Geometry of --- Inversion geometry --- Möbius geometry --- Geometry --- General relativity (Physics) --- Geometry, Differential. --- Einstein field equations --- Space and time. --- Mathematics. --- Numerical solutions.
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Ischemia and Loss of Vascular Autoregulation in Ocular and Cerebral Diseases: A New Perspective presents evidence that ischemia and loss of autoregulation of blood flow are associated with the onset of the major ocular and cerebral diseases including macular degeneration, diabetic retinopathy, low and normal tension open angle glaucoma, stroke and Alzheimer’s disease. Recognition of these vascular changes underline the critical need for clinicians to monitor blood flow and autoregulation to improve early diagnosis and to optimize therapies of ocular and cerebral vascular diseases. The text brings to clinicians in Ophthalmology, Neurology, Medicine, Optometry and Geriatrics decisive guidance on the practical aspects for early diagnosis and treatment of ocular and cerebral diseases. The author brings together in a concise form the progress made over the span of his career and provides new perspectives and understanding of the fluid circulations of the eye and the brain. In addition, he explains the new analytical technologies that made the new concepts possible. The physiological and functional importance of blood flow autoregulation in the eye and in the brain in minimizing the progression of pathology, including the ischemia resulting from stenosis of the internal carotid artery and stroke, are also presented . ABOUT THE AUTHOR: Dr. Langham was born in London, England. In 1947, he joined the Ophthalmological Research Unit, newly formed by the Medical Research Council of the United Kingdom under the direction of Sir Stewart Duke-Elder. In 1956, the author enjoyed a research fellowship at Harvard University. After returning to England for a time, he accepted a position of Associate Professor of Ophthalmology and Director of Research at the Wilmer Ophthalmological Institute of the Johns Hopkins Hospital and Medical school in 1959. There he initiated a program in which all residents spent time engaged in research. This productive interaction between the disciplines led to many important clinical diagnostic and therapeutic advances.
Bifurcation theory. --- Differential equations, Partial --Numerical solutions. --- Representations of groups. --- Differential equations, Partial --- Bifurcation theory --- Representations of groups --- Ischemia --- Homeostasis --- Eye --- Regional Blood Flow --- Peripheral Vascular Diseases --- Intraocular Pressure --- Face --- Blood Circulation --- Pathologic Processes --- Vascular Diseases --- Sense Organs --- Physiological Processes --- Ocular Physiological Phenomena --- Phenomena and Processes --- Cardiovascular Diseases --- Anatomy --- Head --- Physiological Phenomena --- Pathological Conditions, Signs and Symptoms --- Cardiovascular Physiological Processes --- Cardiovascular Physiological Phenomena --- Body Regions --- Diseases --- Circulatory and Respiratory Physiological Phenomena --- Calculus --- Ophthalmology & Optometry --- Mathematical Theory --- Pathology --- Medicine --- Mathematics --- Physical Sciences & Mathematics --- Health & Biological Sciences --- Numerical solutions --- Ischemia. --- Peripheral vascular diseases --- Cerebral ischemia. --- Blood-vessels --- Diseases. --- Diagnosis. --- Ischaemia --- Brain ischemia --- Chevalley groups. --- Medicine. --- Angiology. --- Neurology. --- Ophthalmology. --- Medicine & Public Health. --- Biomedicine general. --- Group theory --- Differential geometry. Global analysis --- Cerebrovascular disease --- Blood circulation disorders --- Numerical solutions. --- Finite groups. --- Angiography. --- Diagnosis, Radioscopic --- Radiography, Medical --- Clinical sciences --- Medical profession --- Human biology --- Life sciences --- Medical sciences --- Physicians --- Nervous system --- Neuropsychiatry --- Radiography --- Neurology . --- Biomedicine, general. --- Health Workforce --- Groupes algébriques linéaires --- Groupes algébriques linéaires --- Représentations de groupes --- Equations aux derivees partielles --- Bifurcations --- Colloque
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