# All Questions

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### Probability that an integer contains no $1\bmod 4$ prime factor

What is the probability that and integer contains at most $r$ prime factors of form $1\bmod 4$? What is the probability that and integer contains at most $r_t$ prime factors of form $(2t+1)\bmod 2^k$ ...
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### floating point representation via the perspective of TTE/computable analysis

Floating point numbers are not compatible with the usual theory of type 2 theory of effectivity (TTE), and not even the real-RAM model; there are functions that are computable in one model but not ...
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### Are polls good approximations

Let $X$ be a finite set and $A\subseteq X$ and $m$ be a natural number satisfying $m\le |X|$ and $\epsilon$ be a small positive number. I'm interested to know if one selects a random $Y\subseteq X$ ...
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### Obtaining z-transform of a multivariate nonlinear difference equation

My research area is not Mathematics, but I am facing a conceptual mathematical issue, the answer to which I could not find in regular textbooks and other material that the internet fetched me and ...
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### segment intersecting a tetrahedron coordinates [on hold]

I am trying to write C++ code to find the intersection points of a segment intersecting a tetrahedron. I reduced the problem like this: For each face of the tetrahedron (a triangle), find the ...
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### Solution manual of real mathematical analysis PUGH [on hold]

Is there anybody know that where I can find the solution manual of real mathematical analysis PUGH ? Thanks a lot.
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### A road to inter-universal Teichmuller theory

What would be a study path for someone in the level of Hartshorne's Algebraic Geometry to understand and study inter-universal Teichmuller (IUT) theory? I know that it heavily relies on anabelian ...
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### Has unconditional convergence ever been proved other than by deducing it from absolute convergence?

Nobody's answering this question so I'll try it here. This is really a reference request: Has a certain kind of proof ever been used? A series $\displaystyle\sum_n a_n$ converges absolutely if ...
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### Sums of reciprocals involving divisor sums

This question was asked at MSE but never received an answer. Let $A\subset\mathbb{N}$ be a subset of the natural numbers, and let $\sigma(n)$ denote the sum of divisors of $n$. Recall that we have ...
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### Why do there is a unique continuous homomorphism? [migrated]

Is this a right place to ask help for an exercise? Let $n\geq 2$ be an integer and $D=\mathbb Z[1/n]$. Let $A$ be a complete commutative ring with unit for the $I$-adic topology, where $I$ is an ...
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### On an unpublished result of Magidor

In 1970th, Magidor proved the following important results: (1) Assuming the existence of a supercompact cardinal, it is consistent that $\aleph_\omega$ is strong limit and ...
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### Curves on $SU(4)$ whose adjoint action on $\mathfrak{su}(4)$ integrates to $0$

Given $\xi \in \mathfrak{su}(4)$ and positive $T \in \mathbb{R}$, is it possible to find all smooth curves $U_s \in SU(4)$ with $U_0 = I$ such that $$\int_0^T U_s \xi U_s^{\dagger} ds =0\; ?$$
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### Counting number of $2\times 2$ unimodular matrices of particular type

From set of numbers from $\Bbb S=\{0,1,\dots,m\}$, how many distinct $3\times 3$ unimodular matrices parametrized by $(a,b,c,d,e,f)\in\Bbb S^6$ of following type can one form? \begin{bmatrix} a^2 ...
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### Strong solution to an SDE with a discontinuous diffusion term

I am having an SDE for which I would be in trouble if there were no strong solution. The SDE is - $dX = \mu(x) dt + \sigma_1 (x) db_{1t} + \sigma_2(x) db_{2t}$ where $b_1$ and $b_2$ are two ...
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### Encyclopedia of Mathematics?(non-Alphabetical) [on hold]

Do you know any Encyclopedia of Mathematics which is in non-alphabetical order, like it starts from basic mathematics and then goes up to very advanced level. And what's the difference between say, ...
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### Statements generalizing representability of integers by binary quadratic forms to $n$-variable higher homogeneous forms?

Representing integers through the theory of binary quadratic forms is a well studied topic. We know that given $a,b,c\in\Bbb N$, based on discrimant $b^2-4ac$, we can study the representability of ...
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### What is the fewest number of points you must delete from $\mathbb{R}^3$ to make it not simply connected?

This question concerns a set-theoretic aspect that I found interesting in the recent question asked by user Nick R., namely, Is $\mathbb{R}^3\setminus\mathbb{Q}^3$ simply connected? He had asked ...
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### Repeats of all binary strings of length k

The question seems like it should be known, but I was not able to find it anywhere. How many binary strings of length $n$ are required so that for every $k$ positions in these strings, all $2^k$ ...
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Let $\Phi$ be the root system of a split group $G$ over a field $k$. The differentials $d\alpha$ of the roots define a polynomial called the discriminant $$\prod_{\alpha\in\Phi}d\alpha$$ on $\mathfrak ... 0answers 54 views ### What are some useful invariants for distinguishing between random graph models? Quite a few probabilistic algorithms for generating random graphs exist in the literature, such as: The Erdos-Renyi model The Stochastic Block model The Watts-Strogatz model The Barabasi-Alber model ... 0answers 61 views ### Closed form answer to a naive integral [on hold] Let a and b be positive real numbers. How to find a closed form answer to the integral $$\int_0^t \left(-a t + \big(1+ \dfrac{2bt}{3}\big)^{-3/2}\right)^{5/3} dt$$ If it is not possible to find a ... 0answers 36 views ### Linear Independence for functions defined by integration [on hold] Given that the set of functions $$f_i(x,y), \quad i=1,\dots,n$$ are linearly independent for$(x,y) \in [0,1]^2$. Is the set of functions,$g_1,\ldots,g_n$, defined by$\$ g_i(x) = \int_{y\in [0,1] } ...

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