Hadamard's dynamical system, often referred to in the context of the Hadamard transformation or as a particular example of a chaotic dynamical system, is tied to the study of chaotic maps and dynamical systems in mathematics. More precisely, it can refer to the use of a mathematical operator known as the Hadamard operator or transformation.
The Ikeda map is a mathematical model that describes a type of chaotic system. It is particularly known for its applications in the field of dynamical systems and chaos theory. The model was introduced by K. Ikeda in the context of nonlinear optics and is often used to study the behavior of light in certain kinds of optical systems.
The Kaplan–Yorke map is a mathematical model that belongs to the category of dynamical systems, specifically studied in the context of chaos and bifurcation theory. It is defined on the interval \([0, 1]\) and is often used to illustrate concepts of chaotic behavior, period doubling, and sensitivity to initial conditions.
The Kuramoto–Sivashinsky (KS) equation is a mathematical model used to describe the dynamics of nonlinear partial differential equations, particularly in the context of spatially extended systems that exhibit chaotic behavior. It is often used in physics and applied mathematics to study pattern formation and instability in systems such as flame fronts, fluid dynamics, and interface dynamics.
Mixmaster Universe is a digital platform and community focused on music creation, collaboration, and sharing. It often incorporates elements of social networking, providing users the ability to create, remix, and publish music tracks, as well as connect with other musicians and fans. The platform may offer tools for music production, a space for artists to showcase their work, and opportunities for collaboration. The specific features, interface, and objectives of Mixmaster Universe can vary, as it may undergo updates or changes over time.
The Tent map is a mathematical function that is often used in the study of chaotic systems in dynamical systems theory. It is a simple yet powerful example of how complicated behavior can arise from a deterministic system. The Tent map is typically defined over the interval \([0, 1]\) and is given by the following piecewise function: \[ T(x) = \begin{cases} 2x & \text{if } 0 \leq x < 0.
The Tinkerbell map often refers to a satirical concept or visual representation that humorously illustrates the idea of belief, imagination, and the power of faith, particularly in the context of children’s stories like Peter Pan. In some interpretations, it symbolizes the notion that something exists only if someone believes in it, much like the character Tinkerbell, who needs applause to survive in the narrative.
Meera Chandrasekhar is an accomplished scientist known for her work in the field of theoretical and experimental physics, particularly in the area of atomic, molecular, and optical physics. She has contributed significantly to research on various topics, including quantum mechanics, Bose-Einstein condensates, and ultracold atoms.
Aurophilicity refers to the phenomenon in which gold (Au) atoms or clusters exhibit a preference for interacting with other gold atoms. This term is particularly relevant in the fields of chemistry and materials science, where gold is known for its unique properties, including its ability to form aggregates or clusters due to these interactions.
Bioconjugation refers to the process of chemically linking two biological molecules, such as proteins, peptides, nucleic acids, or small molecules, to create a stable conjugate that retains the functional properties of the individual components. This technique is widely used in various fields, including biochemistry, molecular biology, drug development, and diagnostics.
Bond cleavage refers to the breaking of chemical bonds between atoms in a molecule. This process is crucial in many chemical reactions, including those involved in organic synthesis, biochemistry, and various industrial processes. Bond cleavage can occur in several ways, primarily categorized as either homolytic or heterolytic cleavage: 1. **Homolytic Cleavage**: In this type of cleavage, the bond breaks symmetrically, resulting in the formation of two radical species.
The Bond Valence Method (BVM) is a semi-empirical approach used in solid-state chemistry and crystallography to analyze and predict the bonding characteristics of atoms in a crystal or molecular structure. It is particularly useful for understanding the distribution and strengths of bonds in complex materials, such as minerals and coordination compounds.
Inverted ligand field theory (ILFT) is a theoretical framework used to understand the electronic structure and behavior of transition metal complexes, particularly in the context of their crystal field environments. It is a modification of traditional ligand field theory (LFT), which focuses on the effects of the surrounding ligands on the energy levels of metal d-orbitals.
A carbon-carbon (C-C) bond is a chemical bond between two carbon atoms. These bonds can be found in various types of organic molecules and are fundamental to the structure of many compounds. There are three main types of carbon-carbon bonds: 1. **Single bonds (C-C)**: This is formed when two carbon atoms share one pair of electrons. This is the most common bond in organic compounds, such as in alkanes.
Thérèse Delpech was a prominent French intellectual and expert in international relations, particularly known for her work on nuclear policy and disarmament. Born in 1948 and passing away in 2012, she had a significant influence on discussions around French and global security issues. Delpech served as a director at the French Institute of International Relations (IFRI) and contributed to various scholarly publications on topics related to strategic studies and geopolitics.
The carbon-fluorine (C-F) bond is a chemical bond between carbon and fluorine atoms. It is characterized by several important features: 1. **Polarity**: The C-F bond is highly polar due to the significant difference in electronegativity between carbon (2.5) and fluorine (3.98). This polarity means that the bond has a partial negative charge on the fluorine atom and a partial positive charge on the carbon atom.
A chemical bond is a lasting attraction between atoms, ions, or molecules that enables the formation of chemical compounds. Chemical bonds are fundamental to the structure and properties of substances and are involved in chemical reactions. There are several main types of chemical bonds: 1. **Ionic Bonds**: Formed when one atom donates one or more electrons to another atom, leading to the formation of charged ions.
"Compliance constants" is not a standard term widely recognized in regulatory contexts, but it could refer to a set of factors, values, or principles that guide organizations in maintaining compliance with relevant laws, regulations, and policies. In various industries, compliance refers to adhering to legal and regulatory requirements, as well as internal policies and standards.
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