The Föppl–von Kármán equations are a set of nonlinear partial differential equations that describe the large deflections of thin plates and shells in mechanical engineering and structural analysis. These equations extend the classical linear plate theory by accounting for nonlinear effects due to large deformations, making them especially useful for analyzing structures under significant loads.
The Infinite Element Method (IEM) is a numerical analysis technique used to solve problems involving unbounded domains, particularly in engineering and physics. It extends the finite element method (FEM) by allowing for an effective treatment of problems where fields (such as electromagnetic, acoustic, or structural fields) can extend infinitely far from the region of interest. This approach is particularly useful for problems with infinite or semi-infinite domains, such as wave propagation, soil formation, and fluid dynamics.
In the context of physics and engineering, particularly in structural mechanics, **limit load** refers to the maximum load that a structure or component can carry without experiencing failure. This load is associated with the onset of plastic deformation, where the material will no longer return to its original shape upon unloading. The limit load is an important concept in the design and analysis of structures, as it helps engineers determine the safety and reliability of various materials and configurations under expected loads.
Covariance Intersection (CI) is a technique used in the field of Bayesian estimation and data fusion, particularly when it comes to combining estimates and uncertainties from different sources with potentially inconsistent or non-coherent covariance matrices. The basic idea is to merge these estimates in a way that preserves the integrity of the uncertainty information. In traditional Kalman filtering, a common approach is to simply take the average of multiple estimations.
Deadbeat control is a control strategy used in discrete-time control systems that aims to drive the system output to its desired value (setpoint) in the minimum possible time, effectively reaching the target in a finite number of sampling periods without any overshoot. The term "deadbeat" comes from the concept that the response of the system "dies" after the target is achieved, meaning that the control action rapidly stabilizes the system at the desired state without oscillations or lingering transient behavior.
Constructive realism is a philosophical approach that combines elements of constructive mathematics and realism. It emphasizes the idea that mathematical objects and theories are constructed by mathematicians rather than simply discovered as pre-existing entities. In constructive mathematics, a statement is considered true only if there is a constructive proof that demonstrates the existence of a mathematical object. This contrasts with classical mathematics, where existence can be asserted without necessarily providing a specific example.
Industrial process control refers to the methods and technologies used to manage and regulate industrial processes to ensure that they operate efficiently, safely, and consistently. This field encompasses a wide range of activities, including monitoring, automation, and feedback systems, with the goal of maintaining specific conditions within production environments. ### Key Components of Industrial Process Control: 1. **Control Systems**: These are the frameworks that manage and direct the operation of industrial processes.
Recursive economics is a concept that generally refers to economic models or analyses that utilize recursive methods to understand and evaluate economic behaviors and systems over time. The term "recursive" itself indicates that the process involves referencing or repeating a certain operation or set of operations. In the context of economics, recursive methods can often be found in: 1. **Dynamic Programming**: This approach is used to solve optimization problems where decisions are made at various time periods, and the outcomes depend on previous decisions.
Iterative Learning Control (ILC) is a control strategy designed to improve the performance of systems that operate in a repetitive manner, by learning from previous iterations or cycles of operation. This approach is particularly useful in applications where the same or similar tasks are performed repeatedly, such as robotic manipulation, manufacturing processes, and various kinds of automated systems. ### Key Features of ILC 1.
Minor loop feedback is a concept commonly used in control systems, particularly in the context of feedback control in electrical circuits and systems. It refers to a type of feedback loop that operates on a subset of the overall control system, specifically within a single control path or sub-system. In the context of major and minor loop feedback: 1. **Major Loop**: This typically refers to the primary feedback loop that encompasses the overall control dynamics of a system.
Standard Telephones and Cables (STC) is a company that was historically involved in the manufacturing of telecommunications equipment and related technologies. Founded in the early 20th century, STC became known for its production of telecommunication systems, cables, and devices, contributing to the development of telephone networks and infrastructure. The company played a significant role in the telecom sector, particularly in the UK, supplying equipment for both domestic and international markets.
Scenario optimization is a mathematical and computational approach used to make decisions under uncertainty by evaluating multiple possible future scenarios. This method is particularly relevant in fields such as finance, supply chain management, operations research, and energy systems, where outcomes can significantly vary based on uncertain factors. Here are the key elements of scenario optimization: 1. **Scenarios**: These are distinct representations of future states based on different assumptions regarding uncertain parameters.
A time-variant system is a type of system in which the system characteristics change over time. This means that the output response of the system to a given input can vary depending on when the input is applied. In contrast, a time-invariant system has consistent properties, and the response to an input is always the same, regardless of when the input is applied.
Ivan Cherednik is known for his contributions to the field of mathematics, particularly in areas related to representation theory and special functions. He is most recognized for his work on Cherednik algebras, which are an important topic in the intersection of algebra, geometry, and mathematical physics. Cherednik's research often involves the study of quantum groups, harmonic analysis, and combinatorial aspects of representation theory.
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 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. - 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





