Vincenzo Balzani is an Italian chemist known for his work in the fields of physical chemistry and nanotechnology, particularly in molecular machines and solar energy conversion. He has contributed significantly to research involving molecular systems that can perform specific functions, often inspired by biological processes. Balzani's work often emphasizes the development of new materials and methods for energy production and storage, as well as the integration of chemistry with technology for the advancement of sustainable energy solutions.
The term "Polish physical chemists" refers to scientists from Poland who specialize in the field of physical chemistry. Physical chemistry is a branch of chemistry that deals with the study of how matter behaves on a molecular and atomic level, and it combines principles of physics and chemistry. Polish physical chemists have made significant contributions to various areas of research, including thermodynamics, kinetics, quantum chemistry, and materials science.
Relativity theory, primarily associated with Albert Einstein, has contributions from various scientists of different nationalities. Here are some key figures and their nationalities: 1. **Albert Einstein** (German-Swiss-American) - The primary developer of the theory of relativity, whose work in the early 20th century revolutionized physics. 2. **Hermann Minkowski** (German) - Developed the concept of spacetime, which is central to the understanding of relativity.
Jaume Mora could refer to various things depending on the context, but it is not a widely recognized term or figure that I am aware of based on my last knowledge update in October 2023. It might refer to a person, a place, or perhaps a brand or concept that emerged after my last update.
As of my last knowledge update in October 2021, Gady Kozma is not widely recognized in mainstream media or literature, so there may not be readily available information about a prominent figure or concept by that name. It's possible that Gady Kozma refers to a person who gained recognition after that time or is notable in a specific field that wasn't widely publicized.
Henri Brocard (1845–1922) was a French mathematician known for his contributions to number theory and various aspects of mathematics. He is perhaps best known for his work on Diophantine equations and for the Brocard sequence, which is a sequence of integers that arises in number theory. Additionally, he is remembered for his contributions to mathematical education and for promoting mathematics through his writings and lectures.
Nikolai Lobachevsky (1792–1856) was a Russian mathematician known primarily for his contributions to geometry, particularly for developing the concept of non-Euclidean geometry. He is often referred to as the "father of non-Euclidean geometry." Lobachevsky challenged the long-held assumption in Euclidean geometry that through any point not on a given line, there is exactly one line parallel to the given line.
Virgil of Salzburg, also known as Saint Virgil, was an important early Christian bishop and theologian in what is now Austria. He is believed to have been born around 700 AD and is recognized for his role as the Bishop of Salzburg from approximately 745 until his death in 784. Virgil is known for his contributions to the spread of Christianity in the region and his efforts in establishing monastic and ecclesiastical structures.
Hilbert's axioms refer to a set of axiomatic foundations for geometry proposed by the mathematician David Hilbert in his influential work "Foundations of Geometry" (originally published in 1899). Hilbert aimed to provide a more rigorous and complete framework for Euclidean geometry than what was offered in Euclid's Elements. His axioms are organized into several groups that correspond to different types of geometric concepts.
"Surfaces" can refer to different concepts depending on the context. Here are a few interpretations: 1. **Mathematics and Geometry**: In mathematics, particularly in geometry, a surface is a two-dimensional shape that can exist in three-dimensional space. Examples include spheres, planes, and more complex shapes like toruses or paraboloids. Surfaces can be described mathematically using equations.
As of my last knowledge update in October 2023, there is no widely recognized product, service, or concept specifically known as "Circumgon." It may be a term, brand, or a concept that emerged after that time or could potentially be a misspelling or a lesser-known term.
Statistical shape analysis is a field of study that focuses on the statistical analysis of shapes, often in the context of biological and medical data, but also applicable in various other domains. It involves the mathematical modeling and comparison of shapes, allowing researchers to quantify and analyze the variations and features of shapes across different objects or populations. Key elements of statistical shape analysis include: 1. **Shape Representation**: Shapes can be represented in various forms, such as points, curves, or surfaces.
The term "Triple Helix" refers to a model of innovation that emphasizes the collaboration between three key sectors: academia, industry, and government. This concept is used to explain how these three entities can interact and collaborate to foster economic growth, technological advancement, and social innovation. 1. **Academia**: Represents research institutions and universities that generate knowledge, conduct research, and develop new technologies.
A parity graph is a type of graph that is primarily focused on the concept of parity, which pertains to whether the count of certain elements (like vertices or edges) is even or odd. In the context of graph theory, parity graphs can be understood in various ways depending on the specific problem or application being addressed. One common interpretation of parity graphs involves **vertex parity**.
Ptolemy's inequality is a mathematical statement that relates the lengths of the sides and diagonals of a cyclic quadrilateral. A cyclic quadrilateral is a four-sided figure (quadrilateral) where all vertices lie on the circumference of a single circle.
Proper motion is the apparent angular motion of a star or other celestial object across the sky, as observed from a specific location over time. It is measured in arcseconds per year and represents the object's movement perpendicular to the line of sight from the observer. Proper motion is a consequence of the object's actual motion through space relative to the observer, combined with the effects of the observer's position (like being on Earth) and the object's distance.
The Lucchesi–Younger theorem is a result in the field of combinatorial optimization, particularly related to the study of directed graphs and their networks. The theorem states that for any directed acyclic graph (DAG), there exists a way to assign capacities to the edges of the graph such that the maximum flow from a designated source node to a designated sink node can be achieved by the flow through a certain subset of the edges.
The New Digraph Reconstruction Conjecture is a conjecture in graph theory, specifically concerning directed graphs (digraphs). It builds upon the classical Reconstruction Conjecture concerning simple (undirected) graphs. The classical Reconstruction Conjecture posits that a graph with at least three vertices can be uniquely reconstructed (up to isomorphism) from the collection of its vertex-deleted subgraphs.
In graph theory, the graph product is a way to combine two graphs to create a new graph. There are several types of graph products, each with different properties and applications.
The tensor product of graphs, also known as the Kronecker product or categorical product, is a way to combine two graphs into a new graph.

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