In the context of electrical engineering and physics, the terms "power," "root power," and "field quantities" have specific meanings. Here’s an overview of each: ### Power Power is defined as the rate at which energy is transferred, converted, or used. It is measured in watts (W) in the International System of Units (SI).
A "toy model" is a simplified representation of a complex system or phenomenon used to gain insights, test hypotheses, or illustrate concepts. These models are typically characterized by their abstraction and reduction of real-world complexities, allowing researchers and scientists to focus on specific features or behaviors without the distractions of extraneous details. Toy models are commonly used in various fields such as physics, economics, biology, and computer science.
Univariate refers to involving or consisting of a single variable. It is a term commonly used in statistics, data analysis, and machine learning to describe data, analysis, or models that focus on just one variable at a time.
"Without loss of generality" (often abbreviated as WLOG) is a phrase commonly used in mathematical proofs and reasoning. It indicates that a certain assumption can be made without affecting the generality of the argument or conclusion being presented. In other words, focusing on a specific case or example is permissible because the logic or outcome will hold true for other similar cases.
The Comparison Theorem is a fundamental result in real analysis, particularly in the study of improper integrals and series. It is often used to determine the convergence or divergence of a given integral or series by comparing it to another integral or series whose convergence is known. There are two main contexts in which the Comparison Theorem is applied: for integrals and for series.
The Laplace transform is a powerful integral transform used in various fields, especially in engineering and differential equations. It transforms a function of time (usually denoted as \( f(t) \)) into a function of a complex variable \( s \). Here is a list of some common Laplace transforms: 1. **Unit Step Function**: \[ \mathcal{L}\{u(t)\} = \frac{1}{s} \] 2.
The classification of complex surfaces is a rich area in algebraic geometry. A complex surface is a two-dimensional complex manifold, which can be studied both from the perspective of complex geometry and algebraic geometry. ### Types of Complex Surfaces Complex surfaces can be classified based on their geometric and algebraic properties. Here’s a list of important types of complex surfaces along with some examples: 1. **Algebraic Surfaces**: These surfaces can be defined by polynomial equations in projective space.
A list of tessellations refers to various patterns or arrangements that fill a plane without any gaps or overlaps. In mathematics and art, tessellations are studied for their geometric properties and aesthetic appeal. Here are some common types of tessellations: 1. **Regular Tessellations**: These are formed using a single type of regular polygon.
Nonlinear ordinary differential equations (ODEs) are differential equations that are not linear in the unknown function and its derivatives. The list of nonlinear ODEs can encompass a wide variety of forms and classifications. Here are some common types and examples of nonlinear ODEs: ### 1.
The study of partial differential equations (PDEs) encompasses a wide array of topics, which can be organized into several categories. Below is a list of topics often encountered in the study of PDEs: ### 1. **Basic Concepts** - Definition of PDEs - Linear vs. Nonlinear PDEs - Order of PDEs - Classification of PDEs (elliptic, parabolic, hyperbolic) ### 2.
A list of polygons typically refers to a classification or enumeration of different types of polygons based on their number of sides and other characteristics.
Set theory is a branch of mathematical logic that deals with sets, which are collections of objects. Below is a list of topics commonly studied in set theory: 1. **Basic Definitions** - Sets, Elements, and Notation - Empty Set (Null Set) - Universal Set - Subsets - Proper Subsets 2.
TransferWise by Ciro Santilli 37 Updated 2025-07-16
This is a good company, first they truly helped reduce international transfer fees. They they continued to morph into a decent challenger bank.
Their Wise Interest account was amazing as of late 2023: wise.com/gb/interest/
Instant access with representative national interests and 0.29% fees.
Brick and mortar banks were way way behind in that regard!
E.g. October 2023, Wise was doing 4.87% interest after fees, while Barclay's best option was 1.16% above 5k pounds on the Rainy Day Saver (5% below). Ridiculous!
Personal finance by Ciro Santilli 37 Updated 2025-07-16
  • the American stock market gives 10% / year, which is about 2x over 10 years. It has been the sure-fire best investment on a 10 year horizon for many decades, and should serve as your benchmark.
  • risky diversified investments (e.g. ETFs that track a market index) are basically the best investment if you can keep your money in them in the long term (10 years)
  • risky investments can gown down for a while, and you cannot take your money out then. This effectively means risk is a form of illiquidity
  • investment funds have taxes, which eat into your profit. The best investments are dumb index tracking investments (like an ETF that tracks the stock market) that are simply brainless to manage, and therefore have lowest taxes. No fund has managed to beat the market long term essentially.
  • when you are young, ideally you should invest everything into riskier higher yielding assets like stock. And as you get older, you should move part of it to less risky (and therefore more liquid, but lower yielding) assets like bonds
    The desire to buy a house however complicates this for many people.

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