In the context of differential geometry and complex analysis, a **complex geodesic** typically refers to a generalization of the concept of a geodesic in the realm of complex manifolds or complex spaces. The classical notion of a geodesic is a curve that is locally a distance minimizer between points in a given space. In Riemannian geometry, geodesics are trajectories that exhibit extremal properties (typically, minimizing lengths) in a curved space.
Causality conditions refer to the criteria or principles that must be met in order to establish a causal relationship between two or more variables. In various fields such as statistics, philosophy, and science, causality is a foundational concept that helps in understanding how one event (the cause) can influence another event (the effect). Here are some key aspects typically associated with causality conditions: 1. **Temporal Precedence**: The cause must precede the effect in time.
The McVittie metric is a solution to the Einstein field equations in the context of general relativity that describes a specific type of spacetime geometry. It is named after the physicist William P. McVittie, who introduced it in the context of cosmology and gravitational theory. The McVittie metric represents a static, spherically symmetric gravitational field that can be considered as a black hole surrounded by a cosmological constant, which accounts for the effects of the expanding universe.
A Penrose diagram, also known as a conformal diagram, is a two-dimensional depiction of the causal structure of spacetime in the context of general relativity. It is named after the physicist Roger Penrose, who developed this diagrammatic representation to help visualize complex features of spacetime, especially in the vicinity of black holes and cosmological models.
Zoltan Torey is a psychologist, researcher, and writer known for his work in the fields of neuroscience and psychology. He is particularly recognized for his contributions to understanding consciousness, cognition, and the development of the self. His work often explores the intersection of psychology, philosophy, and neuroscience, and he has written extensively on topics related to human consciousness and the nature of thought.
Static spacetime is a concept in general relativity that refers to a type of spacetime geometry that is both time-independent (static) and has a specific symmetry. More formally, a static spacetime is one where the gravitational field does not change over time and exhibits certain symmetries, particularly time translation symmetry and spatial symmetry. Key characteristics of static spacetimes include: 1. **Time Independence**: The metric tensor, which describes the geometry of spacetime, does not vary with time.
In the context of general relativity, a tensor is a mathematical object that generalizes scalars, vectors, and matrices, serving as a fundamental building block in the formulation of the theory. Tensors are defined in such a way that they can be manipulated independently of the specific coordinate system used, making them essential for expressing physical laws in a way that is invariant under coordinate transformations.
Canonical quantum gravity is a theoretical framework that seeks to quantize the gravitational field using the canonical approach, which is derived from Hamiltonian mechanics. This approach is distinctive because it aims to reconcile general relativity, the classical theory of gravitation, with quantum mechanics, providing insights into how gravity behaves at the quantum scale. The key features of canonical quantum gravity include: 1. **Hamiltonian Formulation**: It begins by expressing general relativity in a Hamiltonian framework.
Linearized gravity is an approximation of general relativity that simplifies the complex equations describing the gravitational field. It is based on the idea that the gravitational field can be treated as a small perturbation around a flat spacetime, typically Minkowski spacetime, which describes a region of spacetime without significant gravitational effects. In the framework of general relativity, the gravitational field is represented by the geometry of spacetime, which is described by the Einstein field equations.
The geodesic equations describe the paths taken by particles moving under the influence of gravity in a curved spacetime, such as that described by Einstein's theory of general relativity. A geodesic represents the shortest path between two points in a curved space, analogous to a straight line in flat (Euclidean) space. In mathematical terms, the geodesic equations can be derived from the principle of least action or variational principles and are expressed in the form of a second-order differential equation.
Alojz Kodre is not widely recognized in popular culture, historical records, or significant contemporary events up to my last knowledge update in October 2023. It is possible that Alojz Kodre is a less well-known individual, such as a local figure, artist, or someone specific to a certain field.
As of my last knowledge update in October 2021, there isn't a widely known figure named Andrew Neitzke who is prominent in public discourse, media, or scholarship. It's possible that he could be a private individual or a relatively unknown person in a specific field. If Andrew Neitzke has since gained prominence or relevance in any particular context after this date, I wouldn't have that information.
Anne Schilling could refer to a number of individuals, and without more context, it's difficult to provide a specific answer. If you're referring to a person, it could be beneficial to include additional details, such as their profession, achievements, or any specific context in which you've heard the name. For instance, Anne Schilling might refer to a researcher, artist, or another professional in a particular field.
Antonio Giorgilli is a figure known in the context of mathematics and mathematical physics. He has made contributions to the field of dynamical systems and has played a notable role in various academic publications.
Bruno Nachtergaele is an accomplished mathematician known for his work in the fields of mathematical physics, particularly in the areas of quantum mechanics and statistical mechanics. He has made significant contributions to the mathematical foundations of these fields and is recognized for his research in operator algebras and quantum information theory. His research often involves the use of concepts from functional analysis, and he has published various papers and articles that explore the mathematical structures underlying physical theories.
NP-hardness is a classification used in computational complexity theory to describe certain types of problems. Specifically, a problem is said to be NP-hard if: 1. **It is at least as hard as the hardest problems in NP (nondeterministic polynomial time)**: This means that any problem in NP can be reduced to it in polynomial time. In more technical terms, if you can solve an NP-hard problem efficiently (in polynomial time), you can also solve any NP problem efficiently.
As of my last update in October 2023, Dario Graffi is not a widely recognized public figure or concept in mainstream media, literature, or academia. It’s possible that this name could refer to a person in a specific context (such as a local figure, artist, or professional) or might have emerged more recently.
Eric Zaslow is a name that doesn't point to a widely recognized public figure or concept as of my last knowledge update in October 2023. If he is a person relevant in a specific context, such as a professional field or a recent news story, please provide more details, and I'll do my best to assist you. Otherwise, it's possible that he might not be a prominent figure within the commonly available sources.
Feza Gürsey (1921-1992) was a prominent Turkish physicist known for his contributions to theoretical physics, particularly in the fields of general relativity and quantum mechanics. He made significant contributions to the understanding of various physical phenomena and was involved in the development of theoretical frameworks that linked ideas in particle physics and cosmology. Gürsey was also dedicated to science education and played an important role in promoting scientific research in Turkey.
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.Figure 3. Visual Studio Code extension installation.Figure 5. . You can also edit articles on the Web editor without installing anything locally. Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension. - Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact