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Mastering Development

Performance when dealing with large matrices in React

I have a Minesweeper game written in React-Redux with somewhat basic visuals. The game has to support very large boards in the form of matrices (up to 400×400). In order to avoid mutability, I have to re-render the entire matrix everytime the player presses a tile. With larger boards (70×70+) it takes a while, and […]

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Bound the value of function by integration of derivatives

Given $f(x,y) \in C^2([0,1]^2)$ (by which I mean $C^2$ in some open neighborhood), with $f_x, f_y, f_{xy} \in L^1([0,1]^2, dxdy)$ (which is sure case since they are continuous), does the following hold? $$ \sup |f| \le \iint |f|+|f_x|+|f_y|+|f_{xy}|\, dxdy $$ I think it is safe to discretise this function under the assumptions, divide $f$ into […]

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Tightness of Hilbert-space-valued arrays

I posted this on Stackexchange already here. Since I got no answer, I wanted to give it a try here (I hope this question is advanced enough). Let $\mathcal{H}$ be a separable Hilbert space. Assume we have some triangular array $W_{n,j}, j=1, \ldots ,n $ of $\mathcal{H}$-valued random elements with $\mathbb{E} \Vert W_{n,j} \Vert_{\mathcal{H}}^2 < […]

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Determine if two annuli intersect by just looking at the generating triangles

Draw a random triangle on the plane and label its vertices $A$, $B$ and $C$: Now draw a circle with $A$ as its center and $\overline{AB}$ as its radius, and one with $\overline{AC}$ as its radius: These two circles ($OA_B$ and $OA_C$) form an annulus. Do the same with $B$ as the center: We have […]

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Tightness of Hilbert-space-valued arrays

Let $\mathcal{H}$ be a separable Hilbert space. Assume we have some triangular array $W_{n,j}, j=1, \ldots ,n $ of $\mathcal{H}$-valued random elements with $\mathbb{E} \Vert W_{n,j} \Vert_{\mathcal{H}}^2 < \infty$ that is strictly stationary (which means that $W_{n,1},\ldots , W_{n,n}$ is strictly stationary for every $ n$). After Remark 3.3 in “Central Limit and Functional Central […]

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What does it mean for an equation to contain another equation within it?

I’m reading a paper, specifically “Forecasting correlated time series with exponential smoothing models” by Corberan-Vallet et al, and I came across this little beauty: A lower triangular $n\times n$ Matrix $L$ whose entries below the main diagonal are given by $$ L_{ij}=\alpha+\alpha\beta(i-j)+\gamma(i=j\text{ mod } s) $$ such that $j < i$ I don’t understand the […]

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Mastering Development

Storing paragraphs (strings) into an array which will be used to iterate – word vba

I’ve been modifying a macro I found on youtube to separate pages (mailing) into new pdf files. I added some code to add into the file name the name of the company. However when I run the code it says “It is not a valid file name.” The issue is when I store the pharagraphs […]

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Evaluating $\int\prod_{i=1}^{n}(x-a_i)^{b_i}\mathrm dx$ using generalised Newton’s binomial theorem

This post is in reference to this question which asks about the general antiderivative of the following function with the arbitrary constants $a_i,b_i\in \mathbb{R}\forall i\in[1,n]\cap\mathbb{Z^{+}}$. $$\int\prod_{i=1}^{n}(x-a_i)^{b_1}\mathrm dx$$ It seems easy at first to generalise because this is practically a polynomial, but the source of ambiguity are the real exponents, because they seem to make applying […]

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R dplyr::nth returns NA when correct value exists

I’m using dplyr::nth to summarize the nth value given a time period and identification number. Should be a simple task, right? Notice that on TP 7, there is an NA for the max value of AWND1. This doesn’t make sense as R returns a a 2nd and 3rd largest AWND value for that id and […]

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Tightness of Hilbert-space-valued arrays

Let $\mathcal{H}$ be a separable Hilbert space. Assume some triangular array $W_{n,j}, j=1, \ldots ,n $ of $\mathcal{H}$-valued random elements with $\mathbb{E} \Vert W_{n,j} \Vert_{\mathcal{H}}^2 < \infty$ that is strictly stationary (which means that $W_{n,1},\ldots , W_{n,n}$ is strictly stationary for every $ n$). After Remark 3.3 in “Central Limit and Functional Central Limit Theorems […]