# All Questions

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### Single element extensions of subspace arrangement over finite field

Matroids have single element extensions found by Crapo[2] to create ground set size $n+1$ matroids from ground set size $n$ matroids. Do subspace arrangements over a finite field $\mathbb{F}_q$ have ...
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### notable inductive proofs relating to fractals

what are notable/ prominent inductive proofs relating to fractals? the motivation for this question is: fractals are very difficult mathematical objects to work with, and many ...
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### Can eta invariant be written in terms of topological data?

The eta invariant was introduced by Atiyah, Patodi, and Singer. It roughly measures the asymmetry of the spectrum of a self-adjoint elliptic operator with respect to the origin. In ...
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### norm is invariant under scaling for subspace of wiener space

Consider the subspace H_1 of $C_0(0,\infty)$, where $\phi=\int_0^t\dot{\phi}(s)ds$ and $\int_0^{\infty}{\dot{\phi}}^2ds<\infty$. The transformation is $(T\phi)(t)=t\phi(\frac{1}{t})$. How to show ...
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### Eigenvalue of (0-1) matrix [on hold]

Assume I have 2 matrices, each of size nxn with only 1 and 0 as entries in both. (n>10) The first matrix (call it A) has each row summing up to 2 (ie: on each row, it has two "1" and n-2 "0"). It is ...
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### On the geometry of roots of a sum of complex linear fractions

I was wondering if there is anything known about the geometry (position) of the roots of a rational map of the form $$R(z):= \sum_{j=1}^{n} \frac{a_j}{z-p_j},$$ where the $a_j$'s are nonzero complex ...
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### Gradient Estimation Using Bicubic Interpolation and Finite Differences [closed]

Suppose we know the values f(x,y) takes on in a 4x4 grid defined by all pairwise combinations of x={0,1,2,3} and y={0,1,2,3}. Bicubic interpolation using centered differences provides a way of ...
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### complexe integration around a branch point [closed]

I have this complex integral to which I don't know if it's possible to assign a value: The integral is on a small circle around the origin. The function is 1/((z-1)*sqrt(z)). The fact is that z=0 is ...
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### Section of the homology functor on spectra

Consider the (reduced) homology functor $H_*$ from the category of spectra to the category of graded Abelian groups. I wanted to know whether there is a "section" of this functor, i.e., a functor $F$ ...
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### What is “tilting” in the context of large deviations?

I have seen references to the "tilting method" in the theory of large deviations. Is there a simple explanation of what this is, exactly?
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### Bounds for the fat tail after trimming the mean?

I am interested in the quantity $$f(X,t) = \int_t^\infty\negthinspace x\ p(x)\ dx,$$ where $p$ is a probability distribution for a positive variable $X$. 1) Does this quantity $f(X,t)$ have a name? ...
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### Suppose I know $\int h(t) dt = H(t)$, is there a way to find $\int h(t)^N dt$?

I am trying to find the -1 moments of sum of N geometric random variable, i.e. $E[\frac{1}{\sum_{i=1}^N X_i}]$ Suppose the probability mass function is $f_X(x) = (1 - p)^{x - 1} p$ The moment ...
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### Follow up: Is continuity preserved when taking comma object?

Here, I asked wether taking lax pullback preserves continuity, but got no precise answer. However, I have found this recent article by Riehl and Verity which proves something very similar, but I ...
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### Is an even-dimensional real projective space (RP^2 or RP^4) a spin(or spin^C) manifold or not? [closed]

I have a dumb question. Let us consider an even-dimensional real projective space (for instance, RP^2 or RP^4). I wonder if those spaces allow spin structure. In other words, is the real projective ...
Let $\mathcal{A}, \mathcal{B}, \mathcal{C}$ be bicategories. We say a 'pseudofunctors of 2-variables' consists of two families of pseufunctors Fix $A\in obj\mathcal{A}$, we have a pseudofunctor ...
I'm looking at a M/M/1 queue system and trying to show that $\{M_t\}_{t\geq}0$, the number of clients in the system, is a birth-death process. In the simplest of cases this is true if \$\lambda_i = ...