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...
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...
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...
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is the old notation outdated?or this is...
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...
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...
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...
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...
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)...
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...
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...
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...
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...
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 \ \...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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
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)?
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...
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...