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Results tagged with gm.general-mathematics
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Questions about mathematics which don't fall into the other arXiv categories. If you have a general question about mathematics but it is not research level, it's off-topic but it might be welcomed on Mathematics Stack Exchange.
4
votes
Accepted
What are some (popular) references on variants of the classical gambler's ruin problem that ...
Multi-dimensional generalizations (one player against $d$ other players) are explored by P. Lorek in Generalized Gambler's Ruin Problem: explicit formulas via Siegmund duality.
For the analogue on a r …
- 188k
4
votes
Zentralblatt MATH volume numbering
The numbering is sequential in the order in which a review is entered, so not strictly tied to a particular year of publication. For example, volume 1430 has mainly papers published in 2019 and 2020, …
- 188k
8
votes
When are the chirp signals orthogonal?
just for the record, the distance function has a complicated expression in terms of the imaginary error function erfi:
$$d(x,y)=2T+\operatorname{Re}\,\left\{(\alpha+\alpha')^{-1/2}(-1)^{3/4} \left[\t …
- 188k
27
votes
History of right hand rule
John Ambrose Fleming is credited with the invention of the right-hand-rule in the context of electromagnetism.
The figure below, illustrating $X=Y\times Z$ in a right-handed coordinate system, is from …
- 188k
6
votes
How do I solve the following definite integral (preferably by an asymptotic method)?
Here is a log-log plot of
$$\delta I=I_{\text{appr}}-\int_{1}^{\infty} \frac{\sin^2 (\mu \sqrt{x^2 -1})}{(x+1)^{\frac{9}{2}} (x-1)^{\frac{3}{2}}} \,dx,$$
as a function of $\mu$, with
$$I_{\text{appr}} …
- 188k
7
votes
Limit of recursion relation
Mathematica can actually solve the recursion relation in closed form,
$$F_n(n)=-\tfrac{1}{2}(n^2-1)^{-1}\left(\frac{n-1}{n}\right)^n\left[n \left(\frac{n}{n-1}\right)^n \Phi \left(\frac{n}{n-1},1,n+1\ …
- 188k
6
votes
Accepted
Why are discreteness and smoothness in physics inversed with respect to geometry?
The "manifold picture" can be applied to physics in the context of the Brillouin zone, see for example On Brillouin Zones. The reason that discreteness and smoothness appear inverted, is that the Bril …
- 188k
5
votes
Question on pure mathematics helping climate change research
Chris Budd is one mathematician who has made a career in numerical weather prediction. He describes some of the challenges in The Mathematics of Climate Change. He explains the need for ‘simple’ mathe …
- 188k
1
vote
What is the most "informative" Yes/No math question you know?
A general strategy:
Since you state that the yes/no answer will come with a proof, I presume the proof will be understandable by humans, so it will need to contain much background material. I would ar …
7
votes
Surprising applications of the theory of games?
For applications of game theory to elections, this is a classic reference:
A game-theoretic model of party affiliation of candidates and office holders
We develop a formal model of ambition theory, e …
- 188k
0
votes
The sum of triangular functions
Solving for definite $n\in\mathbb{Z}$ I find something a bit more complicated than what is written in the OP:
$$\frac{1}{2}+\sum _{q=1}^{N-1} \frac{\cos (\pi (n-1) q/N)+\cos (\pi n q/N)}{\cos (\pi q …
- 188k
37
votes
What are possible applications of deep learning to research mathematics?
In the context of algebraic geometry, neural networks have become useful tools in the study of Calabi-Yau manifolds. The computation of their topological invariants, metrics and volumes is of particul …
1
vote
Accepted
What is the ideal form of an h-curve?
A stochastic model for the publishing and citation process is discussed in Detecting h-index manipulation through self-citation analysis, from the fraud-detection point of view of the OP. The function …
- 188k
2
votes
Are gyrogroups useful for anything else other than the Einstein velocity addition rule?
Gyrogroups have been used in the theory of signal processing:
M. Ferreira, Spherical continuous wavelet transforms arising from sections of the Lorentz
group. [publishers version]
- 188k
25
votes
How to deal with an advisor that offers you nearly no advising at all?
In the German tradition a PhD advisor is called a "Doktorvater/Doktormutter" --- a thesis parent. It might help to think about your relationship with your advisor along those lines. Many parents like …