De Branges's theorem, often referred to in the context of de Branges spaces, is a significant result in the theory of entire functions, specifically related to the representation of certain types of entire functions through Hilbert spaces. The theorem addresses the existence of entire functions that can be represented in terms of their zeros and certain properties related to their growth and behavior. More formally, it provides conditions under which a function defined by its Taylor series can be expressed in terms of its zeros or certain integral representations.
The Virasoro conformal block is a fundamental concept in conformal field theory (CFT), particularly in two-dimensional CFTs. It plays an important role in the study of correlation functions of primary fields in such theories. ### Key Points: 1. **Virasoro Algebra**: The Virasoro algebra is an extension of the Lie algebra of the conformal group, which arises in the context of 2D conformal field theories.
The Ibragimov–Iosifescu conjecture pertains to the behavior of certain types of stochastic processes, particularly concerning the convergence of $\phi$-mixing sequences. A sequence of random variables \((X_n)_{n \in \mathbb{N}}\) is said to be $\phi$-mixing if it satisfies a certain criterion that measures the dependence between random variables that are separated by a certain distance.
The Arnold conjecture, proposed by the mathematician Vladimir Arnold in the 1960s, is a statement in the field of symplectic geometry and dynamical systems. It relates to the fixed points of Hamiltonian systems, which arise in the study of physics and mechanics.
The Chronology Protection Conjecture is a theoretical idea in physics that was proposed by physicist Stephen Hawking. It suggests that the laws of physics may prevent time travel to the past in order to avoid potential paradoxes and violations of causality.
Ehrhart's volume conjecture is a conjecture in the field of combinatorial geometry and involves the study of convex polytopes and their integer lattice points. More specifically, it relates the number of integer points in dilates of a polytope to the volume of the polytope.
The Duffin–Schaeffer theorem is a result in the field of number theory, specifically in the study of Diophantine approximation. It addresses the question of how well real numbers can be approximated by rational numbers under certain conditions.
Lafforgue's theorem is a result in the field of mathematics, specifically in the area of number theory and the theory of automorphic forms. It is associated with Laurent Lafforgue and pertains to the Langlands program, which aims to connect number theory and representation theory.
Automation refers to the use of technology to perform tasks with minimal human intervention. It typically involves the use of control systems such as computers or robots to handle processes and machinery in various applications, including manufacturing, service delivery, and information technology. Key aspects of automation include: 1. **Process Efficiency**: Automation aims to increase efficiency by speeding up processes and reducing the likelihood of errors, thus optimizing performance.
The Pacman conjecture, proposed by mathematicians in the context of topology and geometric analysis, deals primarily with the area of geometric shapes and their properties, particularly in relation to convex shapes. It essentially posits a relationship between the area of a certain shape, referred to as the "Pacman" shape, and various mathematical properties surrounding convex polygons. The conjecture gets its name from the resemblance of the shape to the well-known video game character Pac-Man.
The Virtual Cybernetic Building Testbed (VCBT) is a research and development platform that focuses on the integration and simulation of cyber-physical systems in building environments. It typically aims to enhance the design, operation, and adaptability of buildings by integrating advanced technologies such as Internet of Things (IoT), artificial intelligence (AI), machine learning, and real-time data analytics.
Abraham H. Haddad is not widely known in public domains as of my last knowledge update in October 2023. There may be individuals with that name, but specific information about a notable person or topic named Abraham H. Haddad might not be available in the general reference resources I have access to.
Antonella Ferrara is not a widely recognized public figure as of my last update in October 2023. Without additional context, it's difficult to provide specific information, as there could be individuals with that name in various fields such as academia, art, or business.
Arthur Pollen was a notable British architect and designer, known for his contributions to the field during the late 19th and early 20th centuries. He was particularly recognized for his work in the Arts and Crafts movement, which emphasized traditional craftsmanship and the use of natural materials. Pollen's designs often reflected this philosophy, blending aesthetics with functionality.
Dimitri Bertsekas is a prominent American researcher and professor known for his contributions to the fields of optimization, dynamic programming, and computational methods in areas such as control theory, artificial intelligence, and operations research. He has authored several influential books and papers and has taught at institutions including the Massachusetts Institute of Technology (MIT). Bertsekas is particularly well-known for his work on algorithms for optimization problems and for his contributions to reinforcement learning and approximate dynamic programming.
Domitilla Del Vecchio is not widely recognized in mainstream contexts, and there may be limited information available about her. It’s possible that she could be a private individual, an emerging figure in a specific field, or a fictional character.
Jacquelien Scherpen is a prominent figure in the field of engineering and control systems. She is known for her work in systems and control theory, often focusing on topics related to robust control, decision-making, and the application of these principles in various technological contexts. Scherpen is also recognized for her academic contributions, including her role in teaching and conducting research at the university level, as well as her involvement in various professional organizations related to engineering and control.
Harold Chestnut was an influential figure in the field of control systems and engineering. He is best known for his work in the theoretical foundations of control theory and for his contributions to the development of various control system design techniques. Especially notable are his contributions to what is sometimes referred to as the "Chestnut Stability Criterion," which pertains to the stability analysis of control systems.
Henrik I. Christensen is a prominent figure in the field of robotics and artificial intelligence. He is known for his contributions to computer vision, robotic perception, and autonomous systems. As of my last knowledge update in October 2023, Christensen has held academic and research positions, including being a professor at various institutions and serving as a director of robotics initiatives. He has been involved in numerous research projects and collaborations, often focusing on how robots can interact with their environment in a meaningful way.
Howard Harry Rosenbrock is a name associated with various contexts, but you may be referring to the British mathematician and computer scientist known for his work in the field of optimization and computational mathematics. He has made significant contributions, particularly in the areas of numerical analysis and the development of optimization algorithms.

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!
We have two killer features:
  1. 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-calculus
    Articles 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/derivative
  2. 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.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    Figure 3.
    Visual Studio Code extension installation
    .
    Figure 4.
    Visual Studio Code extension tree navigation
    .
    Figure 5.
    Web editor
    . 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.
    Video 4.
    OurBigBook Visual Studio Code extension editing and navigation demo
    . Source.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
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