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Squeeze Theorem for functional limits

I am writing a proof for the squeezing principle supposing $f,g,h$ are functions on $X$ and $a\in$ cl$X$ with $g(x)\leq f(x) \leq h(x)$ and lim$_{x\rightarrow a}g(x)=L$ and lim$_{x\rightarrow a}h(x)=L$. Want to show: lim$_{x\rightarrow a}f(x)=L$. I’m fine with the general proof if $a$ is a limit point of $X$. However, the problem says $a$ is in […]

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how to summarise multiple logistic regression models in a table?

I have a dataset with age as continuous and as a factor, sex as a factor and 4 groups. logistic_s <- data.frame( ID = c(1:6), Age = c(9, 12, 16, 57, 29, 24), Age1 = factor(c(1, 2, 2, 6, 3, 3)), Sex = factor(c(“F”, “M”, “F”, “M”, “F”, “F”)), N = c(rep(1, 6)), G = […]

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How to match strings in two files and replace strings?

I have a file like this: (has 308545 lines) head output11.frq CHR SNP A1 A2 MAF NCHROBS 1 1:775852:T:C T C 0.1707 3444 1 1:1120590:A:C C A 0.08753 3496 1 1:1145994:T:C C T 0.1765 3496 1 1:1148494:A:G A G 0.1059 3464 1 1:1201155:C:T T C 0.07923 3496 … And another file (marker-info) which has the […]

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How can I change the angle of a line in MATLAB?

I’m trying to compute two lines, with both having the same value for the first Y(1) , but with different lengths. How can I change the angle of the green line, without changing the first Y(1) value, in order to have the same inclination as the red one? Code: xx4=[-4.07, -43.9450]; yy4=[1.25, 0.46]; xxlais=[37.1225 -35.93]; […]

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How to replace a string from one file with a match in another one?

I have a file like this: (has 308545 lines) head output11.bim 1 1:775852:T:C 0 775852 T C 1 1:1120590:A:C 0 1120590 C A 1 1:1145994:T:C 0 1145994 C T 1 1:1148494:A:G 0 1148494 A G 1 1:1201155:C:T 0 1201155 T C 1 1:1468016:T:C 0 1468016 C T … And another file (marker-info) which has the […]

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Rational Peano curves

An rr function (i.e. rational rational function) is a quotient $$\frac fg\,:\, \Bbb Q\ \to\ \Bbb Q\cup\{\infty\}$$ such that $\ f,g\,\in\,\Bbb Z[X],\$ where $\ g\ne 0.$ QUESTION Do there exist rr functions $\ \phi\ \psi\$ such that set $$\{(\phi(x)\ \ \psi(x))\,:\, x\in\Bbb Q\}\ \subseteq \ (\Bbb Q\cup\{\infty\})^2$$ is dense […]

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Setting markers colour in plotly 3D scatter plot according to R, G, B stored in data frame columns

I have the following pandas dataframe: >>> print(df.head()) X Y Z R G B 0 -846.160 -1983.148 243.229 22 24 19 1 -846.161 -1983.148 243.229 31 37 28 2 -846.157 -1983.148 243.231 20 21 18 3 -846.160 -1983.148 243.230 21 25 18 4 -846.159 -1983.147 243.233 38 48 34 And I plot data from it […]

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Inconsistent pool.map behavior

I’m testing a really simple worker pool using python using this code: from multiprocessing import Pool from itertools import cycle def do_stuff(work): core = work[0] inp = work[1] print(‘Running: “{}” “{}”‘.format(core, inp)) def main(): num_cores = 4 jobs = [‘a’, ‘b’, ‘c’, ‘d’, ‘e’, ‘f’, ‘g’, ‘h’] with Pool(num_cores) as pool: work = list(zip(cycle(range(0, num_cores)), […]

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Relaxation method on a system of two second-order, coupled, non-linear ODEs (boundary value problem)

This is my first question on Stack Exchange – I welcome any suggestions if my approach to asking it does not match the usual conventions around here. So: I need to solve a system of two second-order, non-linear, coupled differential equations for the functions f and g which depend only on one free variable, i.e. […]

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Find Non-Matching Values Between Multiple Ranges

I am looking to see if there is a formula only (no VBA) way to find the values in a list of constants that are not in a range; and can be dynamically adjusted for different lengths of lists and with different column counts. Such as: Table 1 is a 3×2, Table 2 is 4×9, […]