# All Questions

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### Linear systems of equations with singular coefficient matrix

Consider a consistent system of linear equations $Ax=b$. Let's assume for simplicity that $A$ is square $n \times n$. We are looking for an effectively computable approximate solution $\hat{x}$ in the ...
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### Categorification of covering morphisms

Given a category $\mathsf{A}$, let $\mathsf{Fam}(\mathsf{A})$ be its free coproduct cocompletion (which is always extensive). This means every object has a unique up to iso presentation as a coproduct ...
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### Techniques to solve a non linear differential equation related to curvature

Many years ago, I considered the following non linear differential equation: $y=y''.(1+y'^{2})^{-3/2}$ This equation expresses the equality between the value of a given function $y\in C^{2}(R)$ and ...
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### Can the extragradient method be computed only based on proximal steps?

As we know, for solving saddle point problems, the forward-backward algorithm is generally not guaranteed to converge. But the extragradient method converges Structured Prediction via the ...
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### System of diophantine equations with restricted set of solutions [on hold]

I'm engineer, not mathematician, so excuse me for wrong terminology, but I hope you'll understand the problem. Example situation: I have N electronic components. Each of them has reactance and ...
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### busby invariant of extensions of $C^*$-algebras

I have a question of an explicit example of a busby invariant of a extension, which can be found in Blackadars book "K-theory for Operator Algebras". Let $0\to B\to E\to A\to 0$ be a short exact ...
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### What is the best currently proven bounds on prime gaps?

I did some digging around on the internet but I found tons of different equations on both lower and upper bounds for the largest possible prime gap g(n). I was wondering what are currently the best ...
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### Newton's second law [on hold]

enter image description here Which is the speed for x=4m? Given a mass equal to 3kg.
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### Regularization by mean curvature flow

I have a $C^{1,\alpha}$ surface defined as the graph of some function $\varphi : B \to \Bbb{R}_+$ ($B$ is a ball). This surface has positive and bounded mean curvature in the weak sense (since the ...
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### Operators on Hilbert $C^*$-module and families of Fredholm operators

If $A$ is a $C^*$-algebra, there is a notion of Hilbert $A$-module (which is something like Hilbert space but the inner product takes values in $A$). The standard example is ...
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### Sine, Cosine and Tangent functions [on hold]

Is the input of a Sine, Cosine and Tangent function always an angle?
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### Algorithm for checking linear independence of algebraic numbers

Is there any if and only if condition for checking $Q$-linear independence of given a set of numbers say $\alpha_i$ ? More precisely how to check linear independence of given $n$ algebraic numbers ...
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### finding eigenvector [on hold]

I have where λ1 = λ2 = 6 and λ2 = λ3 = 0. I wish to find the eigenvectors for these eigenvalues above. I've tried to turn it into equations and trying to solve them (this is for λ1 & λ2): ...
Given any symmetric real valued matrix $A \in \mathbb{R}^{n\times n}$, I can decompose $A$ as the product of two complex matrices $$A = E'E$$ Practically this can be done easily using SVD ...