Activity for MathPhysicsâ€
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Comment | Post #278553 |
According to the ergodic hypothesis in statistical physics, the time average of a process is the same as the average over the statistical ensemble. So, in the definition of the degree of the degree of first-order coherence we have $\langle E(t_1) E(t_2) \rangle = \frac{1}{T} \int_{T} E(t_1)E(t_2) dt_... (more) |
— | over 3 years ago |
| Comment | Post #278553 |
In the definition of coherence in optics we always time average fields. The definitions of higher order coherences is a different subject; they are not correlation of some variables. They are defined in some way analogous to the first order one. (more) |
— | over 3 years ago |
| Comment | Post #278553 |
The latter is the general definition of **correlation**. However, since in optics we deal with fields having zero time average, because they are sinusoidal in time, we have $\langle X \rangle = \langle Y \rangle =0$, so we get the former definition. (more) |
— | over 3 years ago |
| Edit | Post #278435 |
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— | over 3 years ago |
| Edit | Post #278435 |
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— | over 3 years ago |
| Edit | Post #278435 | Initial revision | — | over 3 years ago |
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MathJax overbrace and commutative diagrams on Math Codidact are not rendered perfectly There are some MathJax codes having imperfect appearances after/when being rendered. I mention two of them with some examples (I do not have enough time to check others). Since I cannot upload any image on Codidact networks, as I reported the related bug on Meta earlier, I use some sharing website... (more) |
— | over 3 years ago |
| Edit | Post #278431 |
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| Edit | Post #278431 |
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| Edit | Post #278431 |
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| Edit | Post #278431 |
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| Edit | Post #278431 |
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| Edit | Post #278431 |
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| Edit | Post #278431 |
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| Edit | Post #278431 | Initial revision | — | over 3 years ago |
| Answer | — |
A: Existence of a set of all sets Let $V$ be a set of all sets. According to the Axiom Schema of Comprehension, we can have the following set: $$U= \\{ x\in V \mid x \not \in x \\}.$$ Now, there are two cases: - $U \in U$, which, according to the definition of the set $U$, implies that $U \not \in U$, which is a contradictio... (more) |
— | over 3 years ago |
| Edit | Post #278430 | Initial revision | — | over 3 years ago |
| Question | — |
Existence of a set of all sets Suppose that we have an axiomatic set theory having the following axiom: The Axiom Schema of Comprehension: Let $\mathbf{P}(x)$ be a property of $x$. For any set $A$, there is a set $B$ such that $x\in B$ if and only if $x\in A$ and $\mathbf{P}(x)$. Can a set of all sets exist within such an ax... (more) |
— | over 3 years ago |
| Edit | Post #278398 | Initial revision | — | over 3 years ago |
| Question | — |
Some codes are not rendered after saving a post while they are rendered in the preview. When I was writing this post, I noticed that the color style html codes rendered well in the preview, but after posting, I saw that they were not rendered. I know that all html codes may not be supported on Codidact; however, I expect that those of them rendered in the preview also can be rendered... (more) |
— | over 3 years ago |
| Edit | Post #278382 | Initial revision | — | over 3 years ago |
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What topics can I ask about here? Mathematics Codidact (MCD) is for people studying mathematics at any level and professionals in related fields. The following is an outline of subjects covered in MCD. It is not necessarily a complete set of independent related fields; it only wants to help users to know the scope of MCD. If yo... (more) |
— | over 3 years ago |
| Comment | Post #278337 |
I cannot upload any image on Codidact platform. I sent you an image in Codidact Community Server on Discord. (more) |
— | over 3 years ago |
| Edit | Post #278338 |
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— | over 3 years ago |
| Edit | Post #278338 | Initial revision | — | over 3 years ago |
| Answer | — |
A: Similar triangles with the same area One can easily prove the following fact: If two triangles are similar, then the ratio of their areas is the square of the ratio of their sides. Now, if two similar triangles have the same area, it follows that the ratio of the corresponding sides must be the square root of $1$, which is $1$. So... (more) |
— | over 3 years ago |