Run .sh file in one line command
How to execute several commands after each other with one request to the terminal (without using a file)?
Proof of $f^{-1}(B_{1}\setminus B_{2}) = f^{-1}(B_{1})\setminus f^{-1}(B_{2})$ I want to prove the following equation:  $$ f^{-1}(B_{1}\setminus B_{2}) = f^{-1}(B_{1})\setminus f^{-1}(B_{2}) $$  Is this a valid proof? I am not sure, because at one point I am looking at $f(x) \in B_1$, but then $x \in f^{-1}(B_1)$ could be actually some different points.  $$\begin{align*} x \in f^{-1}(B_{1}\setminus B_{2}) &amp;\iff f(x) \in B_{1}\setminus B_{2} \\ &amp;\iff f(x) \in B_{1} \land f(x) \notin B_{2} \\ &amp;\iff x \in f^{-1}(B_{1}) \land x \notin f^{-1}(B_{2}) \\ &amp;\iff x \in f^{-1}(B_{1})\setminus f^{-1}(B_{2}) \end{align*}$$ How do I read the manifest file for a webapp running in apache tomcat? Add lines to cron from script Is there a way to add lines to a user's cron via script?  I usually do it using crontab -e, but I would like to automate this task with a shell script. I am using k-means clustering algorithm to cluster a given dataset into two. I took two different initial points and run k-means clustering algorithm for each initial points. With the first initial points I got “within cluster sum of squared distances” (error) =23874.341. With the second initial points I got “within cluster sum of squared distances” (error) = 42913.684. 23874.341 is less than 42913.684. So, can we say the first one is the better clustering quality? If yes, is it always hold true? Or can we say less within cluster sum of squared distances is always the better clustering quality? Why couldn't they omit the Batgirl narratives and scene in The Killing Joke movie? I loved the comic book. I've read it multiple times. And given that the purpose of the book and consequently, the movie, was       for the Joker to prove that anyone can be driven mad simply because of "one bad day", all he needed was the Commissioner right?    Why would they need to have us, as viewers, bond with Batgirl emotionally for around 25-30 minutes, have her frolic around with Batman and try to prove herself to him, etc.?     Sure, you feel deep sorrow for Barbara when she gets shot and molested by Joker. And this obviously is what affects Commissioner Gordon (in part),   But it isn't essential to the crux and the essence of the movie in my opinion (and going by the book, so to speak). Did Sam Liu or Brian Bolland offer any explanation to this end? Can you get a Windows (AD) username in PHP? I have a PHP web application on an intranet that can extract the IP and host name of the current user on that page, but I was wondering if there is a way to get/extract their Active Directory/Windows username as well. Is this possible? I would like to use Zapf's Palatino font for the text in my document, which also includes a lot of maths. And I would like a good font for the maths. This is a snapshot of what I am doing.  \documentclass[10pt,letterpaper]{memoir} \usepackage{amsmath} \usepackage{amssymb} \usepackage{mathpple} \usepackage{upgreek} \usepackage{mathpazo} \usepackage{lipsum}  \begin{document}  \chapter{Demo}  Some regular text. \lipsum[1]  Now for some maths.  \begin{displaymath} P_{N-1 + m} = \frac{C}{N-{1} + m} \binom{N_{2} - N_{1}}{m}         \alpha^{m}\beta^{(N_{2} - N_{1}) -m} \end{displaymath}  The number 27 is the sum of the first 5 odd prime numbers: $27 = 1+3+5+7+11$  \end{document}   To me the text and math fonts seem a good fit but the text does not look like Palatino. In our campaign we have several characters who never remove their armor. They wear it while adventuring, sleeping, swimming, bathing, etc.  Are there any penalties for:   Wearing armor while sleeping? Wearing armor while swimming?   If there are penalties, do they change based on the category of armor (light, medium, heavy)?  I am primarily looking for RAW penalties specified for armor, but I'm also open to applications of other rules (eg - higher DC for swimming in heavy armor, disadvantage during some situations). How to choose the right bean scope? I've read many years ago in books, that the brain has no nerves on it, and if someone was touching your brain, you couldn't feel a thing.  Just two days before now, I had a very bad migraine, due to a cold. It's become better now, but when I had it I felt my head was going to literally split in half, as the pain was literally coming from my brain.  So it lead me to the question: How come people can get headaches if the brain has no nerves? I have a list with 15 numbers in, and I need to write some code that produces all 32,768 combinations of those numbers.   I've found  (by Googling) that apparently does what I'm looking for, but I found the code fairly opaque and am wary of using it. Plus I have a feeling there must be a more elegant solution.  The only thing that occurs to me would be to just loop through the decimal integers 1–32768 and convert those to binary, and use the binary representation as a filter to pick out the appropriate numbers.   Does anyone know of a better way? Using map(), maybe? What is the strict aliasing rule? Hi can you help me solve this exercise? Thanks. Let $f: [0;+\infty) \to \mathbb{R}$ be nonnegative and continuous function. Suppose $\forall a &gt; 0$  $\sum_{n=1}^{\infty} f(na)$ is convergent. Prove that $\int_{0}^{\infty}f(x) dx$ is convergent. I tried to solve it by using the Riemann sum, but for fixed a it doesn't work. I have no other ideas. As part of the definition of a cone spell in the handbook:     A cone's point of origin is not included in the cone's area of effect, unless you decide otherwise.   As an example, what would either case be for a casting of Burning Hands?   Could the caster include themselves? or does this mean that they can exclude the first square of the cone? How can I download an entire website? How can I download all pages from a website?  Any platform is fine. Is there an easy way to show which spheres can be Lie groups? Example of non-isomorphic structures which are elementarily equivalent I just started learning model theory on my own, and I was wondering if there are any interesting examples of two structures of a language L which are not isomorphic, but are elementarily equivalent (this means that any L-sentence satisfied by one of them is satisfied by the second).  I am using the notaion of David Marker's book "Model theory: an introduction". Chance of selecting the last k pages in correct order from a set of n pages A does the same B as does C I am working on binary classification problem, I try to evaluate the performance of some classification algorithms (LR,Decission Tree , Random forest ...). I am using  a cross validation technique (to avoid over-fitting) with AUC ROC as scoring function to compare the performance of the algorithms, but I am getting a weird results with Random forest and AdbBoost, I have a perfect AUC_ROC score (i.e. =1) despite the fact that the recall(TPR) and FPR of this algorithms are different from 1 and 0 respectively .  def FPR(y_true, y_pred):     tn, fp, fn, tp = confusion_matrix(y_true, y_pred).ravel()     result = fp / (fp+tn)     return result def FNR(y_true, y_pred):     tn, fp, fn, tp = confusion_matrix(y_true, y_pred).ravel()     result = fn / (tp+fn)     return result FPR_scorer = make_scorer(FPR) FNR_scorer = make_scorer(FNR)     def get_CrossValResults2(model,cv_rst,bestIndx):     best=pd.DataFrame.from_dict(cv_rst).iloc[bestIndx]     roc=&quot;{:.12f}&quot;.format(best['mean_test_roc_auc'])     acc =&quot;{:.0%}&quot;.format(best['mean_test_accuracy'])     prec =&quot;{:.0%}&quot;.format(best['mean_test_precision'])     rec =&quot;{:.0%}&quot;.format( best['mean_test_recall'])     f1 =&quot;{:.0%}&quot;.format(best['mean_test_f1'])     r2=&quot;{:.2f}&quot;.format(best['mean_test_r2'])     g_mean=&quot;{:.2f}&quot;.format(best['mean_test_gmean'])     pr_auc=&quot;{:.8f}&quot;.format(best['mean_test_pr'])     fnr=&quot;{:.0%}&quot;.format(best['mean_test_fnr'])     fpr=&quot;{:.0%}&quot;.format(best['mean_test_fpr'])     rst = pd.DataFrame([[ model, acc,prec,rec,fpr,fnr,f1,roc,pr_auc,g_mean,r2]],columns = ['Model', 'Accuracy', 'Precision', 'Recall','FPR','FNR', 'F1-Score','ROC_auc','PR_auc','gmean','r2'])     return rst        cross_val_rst = pd.DataFrame(columns = ['Model', 'Accuracy', 'Precision', 'Recall','FPR','FNR', 'F1-Score','ROC_auc','PR_auc','gmean','r2'])              scoring = {'accuracy':'accuracy','recall':'recall','precision':'precision','fpr':FPR_scorer,'fnr':FNR_scorer,'f1':'f1' ,'roc_auc':'roc_auc','pr':'average_precision','gmean':Gmean_scorer,'r2':'r2'}     param_grid = {'n_estimators': [200],               'max_depth': [80,90],               'min_samples_leaf': [2,3, 4],             'min_samples_split': [2,5,12],             'criterion': [ 'gini'],              'class_weight' : [class_weights], 'n_jobs' : [-1]}  clf = GridSearchCV(RandomForestClassifier(class_weight=class_weights), param_grid, cv=kfold,scoring=scoring,refit=refit)#Fit the model bestmodel = clf.fit(X,Y)       cross_val_rst = cross_val_rst.append(get_CrossValResults2(model='Random Forrest',bestIndx=bestmodel.best_index_,cv_rst=bestmodel.cv_results_),ignore_index=True)