# Questions tagged [transformation]

Transformation has many meanings in mathematics. If using this tag, add another tag related to the object being transformed. If there is a tag for your specific kind of transformations, use that one instead: e.g., (laplace-transform), (fourier-analysis), (z-transform), (integral-transforms), (rigid-transformations).

751 questions
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### Transformations of RV's Ensuring Absolute Continuity of Quantile Functions

Given a real random variable $X$, suppose $T:\mathbb{R}\to\mathbb{R}$ is non-decreasing. Define $Y=T\left(X\right)$. Let $Q_{X}$, $Q_{Y}$ be the corresponding right-continuous quantile functions. ...
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### Way to Tietze's Transformation Theorem

During our knot-theory lecture we have talking about the following theorem: Given two finite presentations of the same group, one can be obtained from the other by a finite sequence of Tietze ...
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### Certain symmetrized product of cosines - can it be transformed into more manageable form

I am interested in the following expression: $$F_{k_1,\ldots,k_n}(t):=\sum_{\sigma\in S_n}\cos(\sigma(1)k_1t)\cos(\sigma(2)k_2t)\cdots\cos(\sigma(n)k_nt)$$ where $k_1, \ldots, k_n$ are natural ...
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### How to use polynomial or conformal transformation

In my research, I came to a transformation problem. The simple version is an initial circle (or sphere) region is advected by some deformational flow. After some time the circle will be deformed into ...
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### Changing coordinate system with non standard definitions

The standard coordinate transformation to polar coordinates is $$\begin{cases} x=r\cos(\varphi)\\ y=r\sin(\varphi) \end{cases}$$ with $r\in[0,\infty), \ \varphi\in[0,2\pi)$ The question is whether I ...
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### Proof for a summation-procedure using the matrix of Eulerian numbers?

I've discussed a procedure for divergent summation using the matrix of Eulerian numbers occasionally in the last years (initially here, and here in MSE and MO but not in that generality and thus(?) ...
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### Does, under iteration, all strongly mixing transformations tend to spread sets out, not only in (ordinary) diameter, but also in harmonic diameter?

In [R. E. Rice, On mixing transformations, Aequationes Math. 17 (1978), 104 – 108; Theorem 2 (motivated by some physical phenomena and offer some clarifications of these phenomena)] it is shown that, ...
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### how to transform ellipse back to circle

I have a circle in a $xz$ plane with its center at Origin $O$ as shown in the diagram. The circle is being observed by a camera from point $C$ at $yz$ plane at an angle $\beta$ with the $z-$ Axis. ...
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### Alternative definition of Legendre transform as an integral

Let $f(x)$ be a convex function. Define $g(y)$ via the integral: $$\mathrm{e}^{-g(y)} = \int_{-\infty}^\infty \mathrm{d}x \, \mathrm{e}^{yx-f(x)}$$ assuming that the integral converges. The domain ...
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### Transform an exponential equation within another exponential equation

My question comes from a statistical problem I am bumping into but I think it is more a math question than a stats question, therefore I post it here. Anyway, I have a Structural Equation Model that ...
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### How to relate two polar coordinate systems with different origins

Suppose I have a polar coordinate system defined by $\theta$ and $R$. How do I relate this system to a new polar coordinate system $(\nu, r)$ whose origin lies at $\theta=\theta_0$, $R=d$? My first ...
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### Conformal mapping - known points?

I have a hopefully rather simple question: I want to experiment with different geometries of flowlines and equipotential lines in a 2-Dimensional space in order to fit experimental data. Flow lines ...