# All Questions

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### Boundary regularity of rectifiable multiplicity 1 hypercurrents

Background. I have just recently started studying this aspect of geometric measure theory (and I am also by no means well versed in the latter) and I really can not seem to get the slightest hang of ...
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### How to determine the coefficient of the main term of $S_{k}(x)$?

Let $k\geqslant 2$ be an integer, suppose that $p_1,p_2,\dotsc,p_k$ are primes not exceeding $x$. Write $$S_{k}(x) = \sum_{p_1 \leqslant x} \dotsb \sum_{p_k \leqslant x} \frac{1}{p_1+\dotsb +p_k}.$$...
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### Gaussian integral $\int_X \|x\|_X^2 \mu(dx)$ in Banach space

For a centered Gaussian measure $\mu$ on a Hilbert space $X$, it is known that $$\int_X \|x\|^2 \mu(dx) = tr(Q)$$ where $Q$ is the covariance operator. Is there a similar version for Gaussian measures ...
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### How to solve equation $e^x \log x=2$

I want to know how to solve the equation $$e^x\log x=2.$$ We can get a numerical solution but it seems difficult to get an exact solution. I know the Lambert W function but unable to use it for the ...
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### Maximizing distance between points on the positive surface of the unit hyper-sphere

Suppose we want to place $k$ ($k \geq 3$) points on the positive surface of a unit hyper-sphere in $\mathbb{R}^n$ ($n \geq 3$), where all coordinates of a point are positive, such that the minimum ...
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### Question regarding Algebra problem [closed]

"T.L. and Quina plan to add a 6-inch thick layer of gravel to their driveway. The driveway is 9 yards long and 3 yards wide. What volume of gravel in cubic yards is required?" My approach to ...
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### Some computational results and goals of stable motivic homotopy theory of schemes

I am trying to learn ($\mathbb{P}^1$-)stable motivic ($\mathbb{A}^1$-)homotopy theory of schemes from the Cisinski-Deglise book, Triangulated Categories of Mixed Motives. In order to keep myself going ...
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### Quasi-concavity of minimum of function

Consider a differentiable function $F(x,y,z)$ defined on $[0,1]\times[0,1]\times[0,1]$, which is increasing and quasi-concave in (x,y). That is, the partial derivatives of $F$ with respect to $x$, $y$ ...
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### Complex conjugation inducing a trivial map on the fundamental group

Let $V$ be a smooth projective complex variety defined over the reals such that $G=\pi_1(V)$ is a non-abelian finite simple group. Assume that $V$ has a real point. Can the map $G\to G$ induced by ...
Crossposted from StackOverflow. The generalised diagonalization of two matrices $A$ and $B$ can be done in Matlab via [V,D] = eig(A,B); where the columns of $V$ ...
Let $\mathcal{A}$ be an abelian category, $D(\mathcal{A})$ be its derived category and $X,Y$ be complexes with morphisms in $\mathcal{A}$. I am trying to understand what does it mean to say that $X$ ...