Passing request parameters as UTF-8 encoded strings
How to pass Unicode characters as JSP/Servlet request.getParameter?
Is some of my internal memory missing? How do you get the root namespace of an assembly? Given an instance of System.Reflection.Assembly. Let $a_n$ be a sequence such that $\forall n\in \mathbb n: 0&lt;a\le a_n\le b &lt;\infty.$      Prove:          $\displaystyle\limsup_{n\to\infty}\frac 1 {a_n}=\frac 1 {\displaystyle\liminf_{n\to\infty}a_n}$   $\displaystyle\limsup_{n\to\infty}a_n\cdot \limsup_{n\to\infty}\frac 1 {a_n} \ge 1$ and there's an equality iff $a_n$ is converging.       Suppose there are two subsequences: $a_{n_l}, \ a_{n_k}$ such that $\lim a_{n_k} = k, \ \lim a_{n_l}=l$ and suppose $l\le k$, so $\lim \frac 1 {a_{n_k}}=\frac 1 k , \ \lim \frac 1 {a_{n_l}}=\frac 1 l$ so clearly: $\frac 1 k\le \frac 1 l\le l\le k$ so it's easy to see once the largest limit (supermum) is 'inverted' it has to become the smallest limit (infimum).   I realize this doesn't show equality, I don't know how to do the other way and I'm not even sure if what I did is good. If $a_n$ converges, suppose to $L$ as its limit then we have: $L\cdot \frac 1 L=1$.  If it does not converge then $a_n$ may tend to infinity or won't have a limit. From 1 we can change it to $\displaystyle\limsup_{n\to\infty}a_n\cdot \frac 1 {\displaystyle\liminf_{n\to\infty}a_n} \ge 1$ and from BW, every sequence has a converging subsequence, and since for converging subsequences: $\liminf a_n\le \limsup a_n$ we have $\frac {\limsup a_n} {\liminf a_n}=\limsup a_n\cdot \limsup\frac 1 {a_n} \ge 1$.   This should probably be in absolute value since one of those subsequnce limits can be negative, but it isn't in absolute value in the question. I am trying to find all the Sylow 2 subgroups of S4 using Sylow’s theorems. Now, I know that a Sylow 2 subgroup of S4 has size 8, and that there are either 1 or 3 of them (as the number of of Sylow 2-subgroups has form 1+2k and divides 3, the index).  Now my lecturer states “stabilisers of the 3 different bisections of {1,2,3,4} yield 3 distinct Sylow 2 subgroups”  Now my questions are:  1) What does it mean by stabilisers of 3 different bijections of {1,2,3,4}? Is that to say the elements of S4 which send {1,2} and {3,4} to {1,2},{3,4} i.e. by (12)(34)?  2) How does he know that there are 8 elements of this set? Perhaps this will become clearer after the 1st question is answered.  Many thanks, group theory is hard. How to create a GUID / UUID I'm trying to create globally-unique identifiers in JavaScript.  I'm not sure what routines are available on all browsers, how &quot;random&quot; and seeded the built-in random number generator is, etc. The GUID / UUID should be at least 32 characters and should stay in the ASCII range to avoid trouble when passing them around. Does deleting iCloud photos affect them on devices? How would gravity change on a planet rotating around itself very fast? Let's take a planet identical to Earth, but with rotation speed multiplied by ten thousand. What would happen with the gravity if it was spinning madly around itself? Would the centrifugal force make objects seem lighter than on normal Earth? Would the people on that planet be able to jump higher? Do I need quote marks when I quote myself? Hello language lovers,   English isn't my first language and I would like to know if I need to use quotation marks when I quote something I said in the past. Performance impact of updating target columns with same values ON CONFLICT This is a question about the inner-workings of Postgres (v10) and performance.  Given a table, github_repos, with a multi-column unique index on org_id and github_id columns, is there any performance difference (or other issues to be aware of) between the two bulk upsert operations below? The difference is that in the first query, the org_id and github_id columns are included in the UPDATE, whereas in the second query they are not. Since the UPDATE runs ON CONFLICT, the updated values of org_id and github_id will be the same as the old values, but those columns are included in the UPDATE because the underlying library I am using is designed that way. I'm wondering if its safe to use as-is or whether I should be explicitly excluding those columns in the UPDATE.  Query #1:  INSERT INTO "github_repos" ("org_id","github_id","name") VALUES (1,1,'foo') ON CONFLICT (org_id, github_id) DO UPDATE SET "org_id"=EXCLUDED."org_id","github_id"=EXCLUDED."github_id","name"=EXCLUDED."name" RETURNING "id"   Query #2:  INSERT INTO "github_repos" ("org_id","github_id","name") VALUES (1,1,'foo') ON CONFLICT (org_id, github_id) DO UPDATE SET "name"=EXCLUDED."name" RETURNING "id"   github_repos table:        Column       |       Type        | Collation | Nullable  -------------------+-------------------+-----------+----------+  id                | bigint            |           | not null |  org_id            | bigint            |           | not null |  github_id         | bigint            |           | not null |  name              | character varying |           | not null |  Indexes:     "github_repos_pkey" PRIMARY KEY, btree (id)     "unique_repos" UNIQUE, btree (org_id, github_id) Exactly half of the elements of $\mathcal{P}(A)$ are odd-sized Let $A$ be a non-empty set and $n$ be the number of elements in $A$, i.e. $n:=|A|$.  I know that the number of elements of the power set of $A$ is $2^n$, i.e.  $|\mathcal{P}(A)|=2^n$.  I came across the fact that exactly half of the elements of $\mathcal{P}(A)$ contain an odd number of elements, and half of them an even number of elements.  Can someone prove this? Or hint at a proof? Finding $\tan t$ if $t=\sum\tan^{-1}(1/2t^2)$ I am solving this problem. If $$\sum\limits_{i=1}^{\infty} \tan^{-1}\biggl(\frac{1}{2i^{2}}\biggr)= t$$ then find the value of $\tan{t}$.   My solution is like the following: I can rewrite: \begin{align*} \tan^{-1}\biggl(\frac{1}{2i^{2}}\biggr) &amp; = \tan^{-1}\biggl[\frac{(2i+1) - (2i-1)}{1+(2i+1)\cdot (2i-1)}\biggr] \\\ &amp;= \tan^{-1}(2i+1) - \tan^{-1}(2i-1) \end{align*}  and when I take the summation the only term which remains is $-\tan^{-1}(1)$, from which I get the value of $\tan{t}$ as $-1$. But the answer appears to be $1$. Can anyone help me on this. How to add keyboard shortcuts? I want Ctrl+Alt+B bring up a browser.  Ctrl+Alt+Delete is handy.  Can I set up Ctrl+Alt+B to bring up a browser (either default or specific)? Question of an isomorphism of $\epsilon_ 0$ and a subset of the rationals. I don't know if this question is appropriated for this site. Anyway, I'm searching for an isomorphism of order $f:K \longrightarrow \epsilon_o $, such that $(K, \leq)$ is a subset(proper or not) of $(\mathbb{Q}, \leq)$ and $\epsilon_o = \sup\{\omega, \omega^{\omega}, \omega^{\omega^{\omega}}, ... \}$. Actually,  I'm not finding neither an isomorphism between $K$ and $\omega^{\omega}$.  Thanks in advanced. Names of some months don't make sense I'm not a native English speaker but I'm always trying to do my best. Unfortunately I have a real problem with dates for some odd reason, I couldn't learn when was my birthday until I was 12 years old.  Anyway, as I was learning names of the months on English, and since I know some Latin from high school I noticed that English months don't match up with their Latin numeral counterparts. For example:  September - 9. month October - 10. month November - 11. month December - 12. month  While on latin septem, octo, novem and decem are words for 7, 8, 9 and 10.  So, does anyone know why is that. At first I thought it had something to do with switch from Julian to Gregorian calendar but I figured it's too small of a difference.  Anyone? :) I would like to solve the beginner's standard exercise which claims that a point of $\mathrm{Spec} \ R$ is closed iff it is a maximal ideal.  The reverse implication is easy. The direct one seems much subtler. If $P = V(I)$ then, since there exist a maximal ideal $M$ containing $P$, it would follow that $\{P, M\} \subseteq V(I) = P$, whence $P=M$. In order to show the existence of $M$ I applied Zorn's lemma to the set of ideals containing $P$.  The question is the following: is there any other proof of the above implication that does not (indirectly) use the axiom of choice? My concern is that I may be using a cannon to shoot a fly. Also, it would be the first time that I see closedness of points to require the axiom of choice. If the axiom is indeed needed in general, are there "nice" classes of rings for which we could get away without it? Set a global policy for floats positioning I have a document with many floats (figures, specifically).  I want to be able to change the global floats positioning policy from htbp to just h (or even H with the floats package).  For my-own reasons, I don't want to do this by appending the [h] argument to each float env.  One option that I can think of is using a macro:  \newcommand{\mypos}{h} % or htbp \begin{figure}[\mypos]...   I also prefer not to do that - It is cumbersome.  Is there a way to set the global float positioning argument globally? Choosing C++ debugger on linux how to represent geography or zip code in machine learning model or recommender system? I am building a model and I think that geographic location is likely to be very good at predicting my target variable.  I have the zip code of each of my users. I am not entirely sure about the best way to include zip code as a predictor feature in my model though.  Although zip code is a number, it doesn't mean anything if the number goes up or down.   I could binarize all 30,000 zip codes and then include them as features or new columns (e.g., {user_1: {61822: 1, 62118: 0, 62444: 0, etc.}}.  However, this seems like it would add a ton of features to my model.   Any thoughts on the best way to handle this situation? if $a,b$ are nilpotent elements of a commutative ring $R$, show that $a+b$ is also nilpotent How to Identify Overfitting in Convolutional Neural network? I understand that dropout is used to reduce over fitting in the network. This is a generalization technique. In convolutional neural network how can I identify overfitting? One situation that I can think of is when I get training accuracy too high compared to testing or validation accuracy. In that case the model tries to overfit to the training samples and performs poorly to the testing samples. Is this the only way that indicates whether to apply dropout or should dropout be blindly added to the model hoping that it increases testing or validation accuracy