I tried for a while to classifiy the singularities of $\frac{1}{z}-\frac{1}{\sin z}$ at the origin, but I am stucked. Is there someone who is able to help me at this point?
I tried for a while to classifiy the singularities of $\frac{1}{z}-\frac{1}{\sin z}$ at the origin, but I am stucked. Is there someone who is able to help me at this point?
Find splitting field of $x^5-4x+2$ over $\mathbb{Q}$ I know how to get the splitting field from the roots but I just can't come up with any factorisation that gives me roots. Any suggestions? How are app sales/acquisitions taxed in the US? In Volo's Guide to Monsters, there is a race in the bestiary called Grungs. Were these created for 5e specifically?  I'm pretty sure they were created for 5e, as they have no deities listed which is always a bit suspicious, but I'm just making sure. Find the sum of two elements in a matrix Given $[a_{ij}]_{10\times10}=\left[ \begin{array}{ccc}   1&amp;2&amp;4&amp;7&amp;...&amp;...&amp;...\\   3&amp;5&amp;8&amp;...&amp;...&amp;...&amp;...\\   6&amp;9&amp;...&amp;...&amp;...&amp;...&amp;...\\   10&amp;...&amp;...&amp;...&amp;...&amp;...&amp;...&amp;\\   ...&amp;...&amp;...&amp;...&amp;...&amp;...&amp;...\\   ...&amp;...&amp;...&amp;...&amp;...&amp;...&amp;98\\   ...&amp;...&amp;...&amp;...&amp;...&amp;99&amp;100\\ \end{array} \right]$, what's $a_{7,3}+a_{7,7}$?  Is there a better way than write down all the elements? It's not easy to find the formula of $a_{i,j}$ Prove that if 51 positive integers between 1 and 100 are chosen, then one of them must divide another. Given $51$ integers $a_1, a_2, \ldots, a_{51}$ satisfying $1 \leq a_i \leq 100$. Prove that there exist $i$ and $j$ such that $a_i \mid a_j$.   I'm a little unsure how to approach this problem. Thanks for any help. Completely synchronise multiple Macs How to Start Web Mapping? Evaluate the following integral:  $$\int \frac{\sqrt{\sin ^4x+\cos ^4x}}{\sin ^3x \cos x }dx$$ where $x \in \big(0,\frac{\pi}{2} \big)$  Could some give me hint as how to approach this question?  I tried to use the fact that $\sin ^4x+\cos ^4x=1-\frac{sin^22x}{2}$ but it didn't help. How should I proceed? I've got a weird question. Assume that you have a small sample where the dependent variable that you're going to analyze with a simple linear model is highly left skewed. Thus you assume that $u$ is not normally distributed, because this would result in normally distributed $y$. But when you compute the QQ-Normal plot there is evidence, that the residuals are normally distributed. Thus anyone can assume that the error term is normally distributed, although $y$ is not. So what does it mean, when the error term seems to be normally distributed, but $y$ does not? Impossibility of constructing a continuum-size linearly independent set in $\Bbb R$ This is a response to the following exchange at    [Bill constructs a $\aleph_0$ linearly independent set in $\Bbb R$]  Can you extend the idea of this proof to get the right dimension? Currently, you only have a countably infinite independent set, but the dimension is size continuum. –   I believe the answer to this question is no, for the following reason. Suppose we have a spanning set for $\Bbb R$ over $\Bbb Q$, of cardinality $\frak n$. Then by definition we have the cardinality equation ${\frak c}\le^*[{\frak n}]^{&lt;\omega}\cdot \aleph_0$ (where $[{\frak n}]^{&lt;\omega}$ is the cardinality of finite subsets, and $\frak m\le^*n$ means there is a surjection from $\frak n$ to $\frak m$). If $\frak n$ is finite, then we get ${\frak c}\le^*\aleph_0$ which is false, so $\frak n$ is infinite (but not necessarily Dedekind-infinite). If we assume the axiom of choice, then the equation reduces to $\frak c\le n$, hence every Hamel basis is size continuum. But without AC I don't know any way to simplify the original equation to get anything stronger than &quot;$\frak n$ is infinite&quot;. This is at best heuristic evidence for the original question, since it is considering a different problem (spanning sets instead of linearly independent sets). How could one show that there are no ZF-constructible $\Bbb Q$-linearly independent subsets of $\Bbb R$ of cardinality continuum? Which statistical test to analyse? I am trying to find out how inflammatory markers change in response to a mechanical device change. I have daily readings for the 5 days before the event and for the 5 days after the event. I am expecting a rise in inflammatory markers in the pre readings followed by a fall after the device change. I also need to find out how the change differs in two subgroups (sample sizes of the subgroups are n=21 and n=88). The aim is to find out if the change is significant, to consider these markers as predictors of the device failing and hence needing to be changed.    I would like to know what test would be appropriate to analyse this. I need to keep things simple as I and the people reading the results are non-statisticians. How do I design a user friendly survey with more than 150 questions? I am designing UI/UX for a survey webapp which has more than 150 questions. Right now they are using 5 radio buttons for each question. Similar to the image below:      So the question is, how to make it super user friendly, easy and fun to do?   Further I am looking for a solution from responsive web design perspective too.  I hate designing it like the following image below but what are some other options. I would like to get a USB token to secure my keys. My use case is protection of 3 GnuPG keys that I will be using 10 times per day at least. I plan to create a new key ring from scratch. Because ECC seems more future-oriented than RSA, this is what I chose to use. I'm wondering which USB token to choose as well as which curve.  On  it is said that many people think curves recommended by the NIST or defined by Brainpool have a doubtful origin; therefore, they recommend the non-standardized Bernstein’s Curve 25519. On  one poster says that    He is not aware of any profound criticism of Brainpool curves, and Bernstein’s Curve 25519 is hard to protect against side-channel attacks when implemented in embedded devices.   As a result, I'm a bit lost as to which key/curve to choose. Are there any programs that will let me dictate (speech-to-text) to any program? Or at least to a text editor and text fields in Firefox.  I’m not interested in anything that uses an online service, it has to be on-device. It may be a commercial product. What is a good introductory book on quantum mechanics? I'm really interested in quantum theory and would like to learn all that I can about it. I've followed a few tutorials and read a few books but none satisfied me completely. I'm looking for introductions for beginners which do not depend heavily on linear algebra or calculus, or which provide a soft introduction for the requisite mathematics as they go along.  What are good introductory guides to QM along these lines? Would fewer Jedi be more powerful? Can Muggles publicly establish the existence of a magical community? Putting a table next to a figure I am having problems with the su command. I know my password and I am typing it correctly but su indicates authentication failure.  So I checked on the internet and then went into recovery mode and changed my username's password to what I was entering before.  Even now entering the same password on su gives me authentication failure.  Please suggest what am I doing wrong?? bash regex with quotes?