What is a singularity in general relativity: Robert Geroch. Mathematics Department, Birkbeck College, Queens Square, London W.C. 1, Englanddoi:10.1016/0003-4916(68)90093-6NoneELSEVIERAnnals of Physics
The general covariance of relativity theory creates serious difficulties in formulating a suitable definition of a singularity in this theory. We review and, by means of an example, add to these difficulties. We examine the arguments which lead from one's intuitive picture of a singularity as "...
What is the line drawn in Stewart's theorem? How is Pick's theorem used in real life? Describe the fundamental theorem of calculus. Give one example or application. What is spectral theorem and why is it useful? What is a singularity in complex analysis?
In technology, the singularity describes a hypothetical future where technology growth is out of control and irreversible. These intelligent and powerful technologies will radically and unpredictably transform our reality. The wordsingularityhas many different meanings in science and mathematics. It all depe...
In technology, the singularity describes a hypothetical future where technology growth is out of control and irreversible. These intelligent and powerful technologies will radically and unpredictably transform our reality. The wordsingularityhas many different meanings in science and mathematics. It all de...
What is a singularity in complex analysis? Regarding real-life applications, when would a linear inequality be more appropriate to use than a linear equation? Give examples What is the uniqueness theorem? What is a negative curvature? What would be the two inputs for this linear equation? f(...
But, what is a singularity? How can you stop singularities from spoiling your otherwise perfect robot program? It can be hard to find a clear, simple definition of robot singularities. A lot of the best information on the topic is hidden deep in the pages of textbooks or academically-written...
Singularity and determinant of random matrices. Here, I present recent progress in understanding the question of how likely a random matrix (e.g. one whose entries are all +1 or -1 with equal probability) is to be invertible, as well as the related question of how large the determinant sh...
I didn’t fully succeed; but I think the approach I outline below is in principle feasible. The manifold I will work on is a cylinder , where is a smooth compact manifold, and the metric on is just the sum of the standard metric on the first coordinate and : (I have experimented...
a pivotal role in determining the properties of subatomic particles. They also provide the conceptual underpinnings needed by the five primary variants of string theory to make the mathematics work. Yet even with 10 dimensions, the variants still fall short in the quest for a theory of every...