A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different concepts and experiences. All communication (and data processing) is achieved through the use of symbols. Symbols take the form of words, sounds, gestures, ideas, or visual images and are used to convey other ideas and beliefs. For example, a red octagon is a common symbol for "STOP"; on maps, blue lines often represent rivers; and a red rose often symbolizes love and compassion. Numerals are symbols for numbers; letters of an alphabet may be symbols for certain phonemes; and personal names are symbols representing individuals. The variable 'x', in a mathematical equation, may symbolize the position of a particle in space.
The academic study of symbols is semiotics. In cartography, an organized collection of symbols forms a legend for a map.
https://tug.ctan.org/info/symbols/comprehensive/symbols-a4.pdf
The symbol I've described isn't in this list. I've searched "crescent" and "moon", but to no avail. Will I have to go through the trouble of creating one myself using TikZ, or something?
Also, I need a horizontal border to insert...
Hi Pfs,
I can get a taurus from a square: I identify the oppsite sides. It has the symbol $R^2/ Z^2 $
Suppose now that i replace this square by a rectangle with the length L ans 2L. I identify the opposite sides in the same manner. The new taurus is also a quotient of $R^2$ but how to write it?
Hi, just wondering what this thing means.
$$
E^2_k|_{k=k_{res}}
$$
Just the k=k(res) after the vertical line. There is no definition in the textbook but in math does that mean from K=K(res) to something that can be dependent on a function or a situation?
Like definite integrals answer...
Consider ## (999|823) ##.
Then ## 999\equiv 176\pmod {823} ##.
This implies ## (999|823)=(176|823)=(16|823)(11|823)=(4^{2}|823)(11|823) ##.
Since ## (a^{2}|p)=1 ##, it follows that ## (4^{2}|823)=1 ##.
Thus ## (999|823)=(11|823) ##.
Applying the Quadratic reciprocity law, we have that
##...
I'm reading Tipler's 1976 paper, "Causality Violation in Asymptotically Flat Spacetimes" and he keeps using a symbol which seems to resemble the symbol for Future Null Infinity in a strange font, but it's usage doesn't make sense with what I would expect if that's what the symbol meant. He...
I've solved further Term Symbol problems. The task is: derive the term symbols of the ground states of the following atoms: a) H, b) F, c) Cu, d) F- , e) P, f) Na, g) Sc
Why is the d-orbital considered here in g)? Why isn't the s orbital taken into account here? The 4s orbital is energetically...
My references are:
https://en.wikipedia.org/wiki/Friedmann_equations#Detailed_derivation
https://en.m.wikipedia.org/wiki/Cosmological_constant
Ω_Λ is a term in the Friedmann equation along with terms for radiation, mass, and curvature.
Λ is the coefficient of the term g_μν in the Einstein field...
Hello there, for the above question I have no issue finding the term symbols but I am a little unsure about employing Hund's rules to the electron configuration, particularly those referring to the energies based on the total angular momentum J. These state:
- In a less than ##\frac12##-filled...
I'm probably inadequately equipped to understand this paper by Bucholtz, Longo and Rehren on "Causal Lie products of free fields and the emergence of quantum field theory", but I decided to give it a try. Alas, I got stuck in the 1st para of sect 2 where it says:
Although I've seen the term...
I was not given a formal teaching on christoffel symbols and how to find them so I just need some help.
I'm trying to find the cristoffel symbol:
\begin{equation}
\Gamma^{i}_{00}
\end{equation}
I set my equation up as:
\begin{equation}
\Gamma^i_{00} = \frac{1}{2} g^{ij} (\partial_0 g_{0j} +...
Personal Question:
Internet says the standardized math symbol for integers is ## \mathbb {Z}##. However, my Alberta MathPower 10 (Western Edition) textbook from 1998 says the symbol is I. I'm guessing that textbook is wrong? Or are both answers correct?
both "mew"(sorry i couldn't get the symbol on on my keyboard so I'm writing it😊) and n are used for depicting refractive index i want to know which is more relevant and is there any reason for it or which symbol should be used in what cases.
in video "Einstein Field Equation - for Beginner!" by "DrPhysicsA" on youtube, in 01:10:56, the christoffel symbol equation is written, then i see in "Physics Videos by Eugene Khutoryansky" video with title "Einstein's Field Equations of General Relativity Explained" in minute 05:02 on how the...
It's a detail, but annoying to me: ##{\partial u\over \partial x} = {\partial \phi \over \partial x} \;+ ...##
$${\partial u\over \partial x} = {\partial \phi \over \partial x} \;+ ...$$
How do I move up ##\partial u## a little bit so it aligns with ##\partial \phi## ?
I am trying to understand the following:
$$
\epsilon^{mni} \epsilon^{pqj} (S^{mq}\delta^{np} - S^{nq}\delta^{mp} + S^{np}\delta^{mq} - S^{mp}\delta^{nq}) = -\epsilon^{mni} \epsilon^{pqj}S^{nq}\delta^{mp}
$$
Where S^{ij} are Lorentz algebra elements in the Clifford algebra/gamma matrices...
You see this symbol on power switches, but what does it really mean?
From https://en.wikipedia.org/wiki/Power_symbol,
But the switches that I've seen the symbol on doesn't cause a "sleep mode" but powers the device on and off.
... Grrr
Hi All,
I am just trying to understand a circuit but cannot figure out the meaning of the following symbol. Did not get very far from googling electrical symbols.
The symbol is given below. I know it is a switch but what does "x" mean on one of the wires and what do the half sine and square...
I was reading chapter 3 of Carroll's book up to page 100, where he mentions that the coefficients of Christoffel symbol in flat spacetime vanish in cartesian coordinates but not in curvilinear coordinate systems.
I was thinking on why this happens. My logic tells me that these coefficients...
Suppose the emf of cell ##X## exceeds that of ##Y##, such that conventional current is driven in in an anti-clockwise direction.
There is a little ambiguity in my mind about the circuit symbol for ##Y##. In the above setup, the larger bar of ##Y## is at higher potential and the smaller bar at...
Hello, dear friends of mathhelpboards;
I stumbled with a striking claim in https://www.cut-the-knot.org/do_you_know/GoldenRatioInYinYang.shtml
Sorry, I couldn't paste the pic. The question is if there is an algebraical or trig proof for this claim, as the angle seems to be just 45º. Then, is...
A ground state configuration table for carbon is shown below. I am wondering why although configuration 4 and 5 share the same ML and MS ,they belong to different energy levels 1D2 and 3P2. It is just randomly chosen or they do have some rules? What cause the difference of energy levels of No.3...
In a certain derivation, the author begins with
$${g(-t)=}\frac 1 {2\pi}\int_{-\infty}^\infty {G(\omega)}e^{-i\omega t}d\omega$$
and then says he will replace ##t## with ##\omega## and ##\omega## with ##t##. He then writes
$${g(-\omega)=}\frac 1 {2\pi}\int_{-\infty}^\infty {G(t)}e^{-it\omega...
I don't understand what the last paragraph of the attached page means. Why does the Kronecker delta being an invariant symbol mean that the product of a representation R and its complex conjugate representation has the singlet representation with all matrices being zero?
Doesn't the number...
I hope you can understand my notation. The Christoffel symbol can be defined through the relation$$
\frac{\partial \pmb{Z}_i} {\partial Z^k} = \Gamma_{ik}^j \pmb{Z}_j
$$ I can solve for the Christoffel symbol this way: $$
\frac{\partial \pmb{Z}_i} {\partial Z^k} \cdot \pmb{Z}^m = \Gamma_{ik}^j...
Homework Statement
I know that by definition Γijkei=∂ej/∂xk implies that Γmjk=em ⋅ ∂ej/∂xk (e are basis vectors, xk is component of basis vector). Can I write it in the following form? Γjjk=ej ⋅ ∂ej/∂xk Why or why not?
Homework EquationsThe Attempt at a Solution
When dealing with any tensor quantity, when making a coordinate transformation, we should put a bar (or whatever symbol) over the functions or over the indices? For exemple, should the metric coefficients ##g_{\mu \nu}## be written in another coord sys as ##\bar g_{\mu \nu}## or as ##g_{\bar \mu...
Here is the formula in the screenshot figuring piston assembly inertia.
piston assembly inertia = Reciprocating Mass * CRANK RADIUS * W^2*(COS(Wt)+(crank radius/rod length)*COS(2*Wt))
W=angular frequency (crank rotations in 1 second times 6.28)
Wt=unknown
CRANK RADIUS=piston stroke/2
Please...
I need to know what the w is in this formula.
Also I am not 100% sure which angle it is using.
This is for figuring the inertia of the piston assembly in a 2 stroke engine.
thanks
Homework Statement
Considering the molecule of ##C_2^+## in an excited state with valence configuration ##2\sigma_g^2## ##2\sigma_u^2## ##1\pi_u^2## ##3\sigma_g^1##. Finding all the possible term symbol.
Homework Equations
Term symbol ##^{2S+1}\Lambda##
##L=0 \rightarrow \Sigma##
##L=1...
This problem is fairly objective (though quite stupid)
What does î(o) represent?
Does it refer to a vector making angle 0 degrees with the x axis?
I searched but couldn't find the answer anywhere. Please help.
Moderator note: post edited and moved from hoemwork
considering the symbol of an element, under the cambridge curriculum , is the nucleon number written on top or at the bottom on the left side of the element?
(I should say that I have never done proper coursework in introductory proofs like a mathematics major would.)
I figure there must be a way to denote a situation in which, from sloppy intuition, etc., a certain proposition might (erroneously) imply a result, but that that result could happen...
Hi, I was looking for a symbol in math that is commonly applied when a limit to a function does not exist. Is there such a symbol? I could not find any.
It is an X like in a cross product but with a vertical line connecting upper-left and lower-left endpoints. I will write it as |X . Example context:
R^4 |X SL(2,C)
where the R and C are real numbers and complex numbers.
In expressing a limit as below ...\text{lim}_{ x \rightarrow 0+ } \frac{ F( c + h ) - F(c) }{h} = f(c) How does one get the x \rightarrow 0+ to appear under the text "lim" as in the following:Help will be appreciated ...
Peter
Hello everyone,
my question concerns the following: Though widely used, there does not seem to be any standard reference where the common symmetrization and anti-symmetrization identities are rigorously proven in the general setting of ##n##-dimensional pseudo-Euclidean spaces. At least I have...
Consider a force-free particle moving on a geodesic with four-velocity v^\nu.
The formula for the four-acceleration in any coordinate system is
\frac{dx^\mu}{d\tau} = - \Gamma^\mu_{\nu\lambda} v^\nu v^\lambda
Since the four-acceleration on the left side is orthogonal to the four-velocity, this...
Homework Statement
definition of εijk
εijk=+1 if ijk = (123, 231, 312)
εijk = −1if ijk = (213, 321, 132) , (1.1.1)
εijk= 0,otherwise .
That is,εijk is nonzero only when all three indices are different.
From the definition in Eq. (1.1.1), show that...
Homework Statement
i am showing the invariance of the Levi-Civita symbol in 4 dimensions
The Attempt at a Solution
$$\varepsilon_{ijkl}'=R_{im}R_{jn}R_{kp}R_{lt}\varepsilon_{mnpt}$$...