1. ### I Did von Neumann coin the eth or dyet for the inexact differential?

Today the inexact differential is usually denoted with δ, but in a text by a Russian author I found a dyet (D-with stroke, crossed-D) instead: In response to my question to the author about this deviation from normal usage, he stated that this was a suggestion from von Neumann. (Which of course...
2. ### I Standard crystallographic notation confusion

I'm revising for my condensed matter exam, and I've never understood the point group notation, in particular of the 32 crystallographic point groups, so let me try and explain what I understand of it and point out where my confusion lies. Please point out any other misunderstandings I have. We...
3. ### I Confusion about index notation and operations of GR

Hello, I am an undergrad currently trying to understand General Relativity. I am reading Sean Carroll's Spacetime and Geometry and I understand the physics (to a certain degree) but I am having trouble understanding the notation used as well as the ideas for tensors, dual vectors and the...
4. ### B Binomial coefficient problem

I am learning binomial theorem now on my long journey to calculus. I noticed that in older textbooks, the binomial coefficient looks like C(n on top,k on bottom) I don’t think that I can display it here and in newer ones,they look like ##\binom{n}{k}## is the old notation outdated?or this is...
5. ### How to write this in Set Theory notation?

Hello Everyone, I am trying to write the intersection of a physical problem in the most compact way. I am not really familiar with Set Theory notation, but I think it has the answer. It is about the intersection of two circular areas: - Area 1: A - Area 2: B If I want to write this in Set...
6. ### I What purpose does the delta notation serve in this context?

In a book on atmospheric physics I'm reading, the author begins a derivation by examining a fluid element of volume V = δxδyδz. In this context, what purpose is delta δ serving? Is it just a placeholder for an unspecified volume in the x, y, and z directions, or is it referring to an...
7. ### B When do we use which notation for Delta and Differentiation?

I was taking notes recently for delta y/ delta x and noticed there's more than one way to skin a cat... or is there? I saw the leibniz dy/dx, the triangle of change i was taught to use for "difference" Δy/Δx, and the mirror six ∂f/∂x which is some sort of partial differential or something...
8. ### Conversion of Piezoelectric coefficients

Hello everyone, I am interested on simulating the converse Piezoelectric effect of materials and I have given the mechanical (Youngs modulus and Poissoin's ratio) and electric material properties (Electric Permittivity, Piezoelectric coupling matrix etc). However from the literature I got...
9. ### I What does the vertical line in this equation mean?

Hey, What does the vertical line with the "I_b" on the bottom right mean? Link here: https://imgur.com/a/nII9g Thanks, -Yael
10. ### I Induction axiom

So , what I was wondering about was a slight difference in notation, for which I am not certain if correct (mine, in particular.). The induction axiom says: If M is a subset of ℕ, and if holds that: a)1∈M b)(∨n∈ℕ)(n∈M→s(n)∈M) then M=ℕ. Now my question is: why do we write (∨n∈ℕ)(n∈M→s(n)∈M)...
11. ### I Double sided arrow notation in Dirac Field Lagrangian

In a thesis, I found double sided arrow notation in the lagrangian of a Dirac field (lepton, quark etc) as follows. \begin{equation} L=\frac{1}{2}i\overline{\psi}\gamma^{\mu}\overset{\leftrightarrow}{D_{\mu}}\psi \end{equation} In the thesis, Double sided arrow is defined as follows...
12. ### I Difference Between d3x and triple Integral

So My Question Is Simple, But It confuse me too much! What Is Difference between the notation ∫d3x and ∫∫∫dxdydz ?
13. ### I Bracket VS wavefunction notation in QM

In some sources QM is explained using bracket notation. I quite understand algebra of bracket notation, but I do not understand how is this notation related with physically meaningful things? How is bracket notation related to wavefunction notation? Could you tell me whether following is true...
14. ### A Frankel: Geometry of Physics

Good Day Early on, in Frankel's text "The Geometry of Physics" (in the introductory note on differential forms, in fact, on page 3) he writes: "We prefer the last expression with the components to the right of the basis vectors." Well, I do sort of like this notation and after reading a bit...
15. ### I A directional, partial derivative of a scalar product?

Let's say I have two vector fields a(x,y,z) and b(x,y,z). Let's say I have a scalar field f equal to a•b. I want to find a clean-looking, simple way to express the directional derivative of this dot product along a, considering only changes in b. Ideally, I would like to be able to express...
16. ### Partial derivative of inner product in Einstein Notation

Homework Statement Can someone please check my working, as I am new to Einstein notation: Calculate $$\partial^\mu x^2.$$ Homework Equations 3. The Attempt at a Solution [/B] \begin{align*} \partial^\mu x^2 &= \partial^\mu(x_\nu x^\nu) \\ &= x^a\partial^\mu x_a + x_b\partial^\mu x^b \ \...
17. ### I Subscript help

I am almost ashamed to put this question, as it verges on the silly, but it is a real question, and Physics Forums has come to my rescue so often.... I am translating a physics article from Russian, and at one place the author puts quantities (such as σ for standard deviation, etc.) with a...
18. ### I 4 vector upper and lower indices

I'm working through some intro QFT using Peskin accompanied by David Tong's notes, and have a question over notation. From Peskin I have: x^\mu=x^0+x^1+x^2+x^3=(t,\mathbf{x}) and x_\mu=g^{\mu\nu}x^\nu=x^0-x^1-x^2-x^3=(t,-\mathbf{x}) so p_\mu p^\mu=g^{\mu\nu}p^\mu p^\nu=E^2-|\mathbf{p}|^2...
19. ### Contravariant Four-gradient ESN in Wikipedia appears wrong

Homework Statement I am self studying relativity. In Wikipedia under the four-gradient section, the contravariant four-vector looks wrong from an Einstein summation notation point of view. https://en.wikipedia.org/wiki/Four-vector Homework Equations It states: E0∂0-E1∂1-E2∂2-E3∂3 = Eα∂α...
20. ### A Notation/Site for Representations of an Algebra

I'm currently reading the paper "Higher Spin extension of cosmological spacetimes in 3d: asymptotically flat behaviour with chemical potentials in thermodynamics" I'm looking at equation (3) on page 4. I know that symmetrization brackets work like this A_(a b) = (A_ab + A_ba)/2. However I have...
21. ### A 3dim Poincare Algebra - isl(2,R)

The Poincare algebra is given by isl(2, R) ~ sl(2,R) + R^3. What exactly does the i stand for? Thanks a lot in advance!
22. ### I Notation question

Hello everyone. I have read a proof but I have a question concerning the notation. To give some context, I will write down this proof as written in the book. Theorem: There is a unique binary operation ##+: \mathbb{N} \times \mathbb{N} \rightarrow \mathbb{N}## that satisfies the following two...
23. ### I Need help with derivative notation

If I have a scalar function of a variable ##x## I can write the derivative as: ##f'(x)=\frac{df}{dx}##. Now suppose ##x## is no longer a single variable but a vector: ## x=(x^1, x^2, ..., x^n)##. Then of course we have for the derivative ##(\frac{\partial f}{\partial x^1}, ..., \frac{\partial...
24. ### I Basic question about set theory

Hi, Is the following notation correct? X = {xt> max(xt-k,...,xt-1,xt+1,...,xt+k)|(t-k,...,t+k) ∈ T2k+1∧ k ∈ ℕ\{0}} where T = [1,n]∩ℕ denotes the time periods over which x runs. I basically want to say that X is the set of points that are local maxima in a neighbourhood of k points to the right...
25. ### Confusion about circuit schematic notations

I'm confused about the terminals in the picture above simply because I've seen the exact same thing mean 2 different things in schematics, namely: (1) it is an open circuit with voltage Vi(t) (2) The terminals are connected to some other circuit and thus have a voltage/current source, and the...
26. ### I Question regarding the derivative terminalogy and wording

When doing calculus, we typically say that we "take the derivative of a function ##f(x)##." However, rigorously, ##f(x)## is not a function but rather the value of the function ##f## evaluated at ##x##. Thus, in order for this wording to be correct shouldn't we have to write something like...
27. ### I Notation (index notation)

I am having trouble converting [D]=[A][ B]T[C] to index notation. I initially thought it would be Dij=AijBkjCkl but I have doubts that this is correct. Would anyone be able to elaborate on this? Regards
28. ### I Linear Transformation notation

I'm confused about the notation T:R^n \implies R^m specifically about m. From my understanding if n=2 then (x1, x2). Are we transforming n=2 to another value m for example (x1, x2, x3)?
29. ### Notation Question

Homework Statement I have these two equations from this paper: https://www.scribd.com/doc/299960566/Spiral [Broken] Homework Equations What are the vertical bars next to the drawn red starts supposed to indicate in this context? I'm trying to implement these equations into a program but...
30. ### Intro to abstract math—basic notation

Homework Statement Simplify the following statement as much as you can: (b). ##(3<4) \wedge (3<6)## Homework Equations ##\wedge= and## The Attempt at a Solution I figured that I could just write this as ##3<4<6##, but then I considered what if I didn't know that ##4<6## If it was just...