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1,689,128 questions
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Extended Geometric–Informational Multi-Agent System with Hybrid Frames and Complex Dynamics
Dear Math Stack Exchange.
I need some help figuring out if my writing makes any sense and what central equation to propose. I hope it's fair to see that I have had a bit of a fever dream going.
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Where is the exact meaning of $p,q\in S$ regarding whether this implies $p\ne q$ discussed?
I have noticed that different authors use different rules for such simple statements as: Let there be two numbers $p$ and $q$. Some (most) treat that as including the possibility that $p$ and $q$ are ...
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Past and present views on dimension in algebraic geometry
In the past, Riemann wrote a paper on non-Euclidean geometry, which is the basis of Einstein's theory of relativity, and the content was based on Gauss's achievements, and he described it by expanding ...
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Reference request: Quasi/Semilinear Elliptic PDE with Neumann Boundary condition
I am working on Quasi/semi-linear Elliptic PDEs with Neumann Boundary conditions, but I am struggling to find any book that dives into it. Most standard PDE books cover the Dirichlet Problem in detail ...
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Solving in closed form: $e^{x^3}\ln x + x^2 = 0$
My task is to solve $$e^{x^3}\ln x + x^2 = 0$$ with Lambert $W$ function.
I could not derive the form $ue^u=a$ .
$$e^{x^3}\ln x + x^2 = 0$$
$$\ln x=-\frac {x^2}{e^{x^3}}$$
$$x=e^{-\frac {x^2}{e^{x^3}}}...
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Subgroups of fundamental group of circle $S^1$ and covering space such that the image of the induced map is isomorphic to such a subgroup
I know that the fundamnetal group of the circle is isomorphic to $(\mathbb{Z},+)$, so every subgroup of $\pi_{1}(S^1)$ is of the form $n\mathbb{Z},n\in\mathbb{N}$. Now given an $H\leq\pi_{1}(S^1)$ ...
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How do you use defining contrasts in fractional factorial design?
I've been given the following question: Find the $2^{4-1}$ design for factors A, B, C and D with defining contrast C=-DA.
To solve this I initially found the order of the independent factors and got ...
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Measure Theory - MIRA Book - Understanding the proof of 5.32 Fubini's Theorem
I'm reading Sheldon Axler's MIRA book and have a question about the proof of 5.32 Fubini's Theorem.
My question is on the paragraph that starts with "Subtracting the second function".
Here ...
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Showing (with elementary methods) that a 'coin slot' is not simply connected.
I have been trying to come up with an example of a set that can be shown to be connected, yet not simply connected with elementary methods. Having struggled too much with $\mathbb{R}^2\setminus{\{\...
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Why is $\lim_{h \rightarrow 0} |f(t+h) - f(t)| = 0$ sufficient for proving uniform continuity?
The second page of https://web.ma.utexas.edu/users/gordanz/notes/oldchar.pdf proves that the characteristic function $\varphi$ of a random variable is uniformly continuous. The proof is that
$$|\...
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Minimum length of a chain of numbers
What is the minimum length of a chain of numbers such that all chains of $4$ numbers that do not start with zero are present in it as fragments of four consecutive numbers?
What I understand: let's ...
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Prove That There Exists a $\lambda$, Such That $T(x) = \lambda x$
Suppose that $X$ is an inner product space and $T : X \rightarrow X$ is a continuous linear map. If there exists a $x_0 \in X$, where $||x_0|| = 1$ and $\lVert T\rVert = \left\lvert\langle T(x_0), x_0\...
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Prove There Exists a Linear Operator $||T|| \geq r$
Suppose that $\{e_n\}_{n=1}^{\infty}$ is an orthonormal basis for Hilbert Space $H$.
Prove that for any $r > 0$, there exists a linear operator $T:H \rightarrow H$ such that
$||T(e_n)|| \leq 1$ for ...
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Is the Topological definition of Continuity a generalization of continuity that we learned in Calculus?
I used to think the topological definition of continuity was a generalization of the continuity we learned in Calculus. However, I learned that this applies for functions that map elements from one ...
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Rotate a vertical plane about two axis to achieve a set an angle in each rotation
I am running a 3D cad program. Z +up, Y +to left, X + into page.
If I want a new plane (A) that is 20 degrees from the YZ about Y, no problem. Simple rotation about Y axis and enter 20 degrees.
If I ...
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