relation between Schrodinger equation and wave equation
How is the Schroedinger equation a wave equation?
Bash auto_completion with Xubuntu and xrdp from windows I'm using Xubuntu and connecting over RemoteDesktop with Windows 7.  Everything works fine, but the auto_completion in my bash doesn't work. I checked the .bashrc file in my home directory and also the /etc/bash.bashrc.  I uncommend the lines below in my local bashrc configuration and also in bash.bashrc, but nothing changes.  if ! shopt -oq posix; then   if [ -f /usr/share/bash-completion/bash_completion ]; then     . /usr/share/bash-completion/bash_completion   elif [ -f /etc/bash_completion ]; then     . /etc/bash_completion   fi fi Detect whether Excel workbook is already open Example where schema are better than multiple databases In several database systems (e.g., PostgreSQL and MS SQL Server) there is a concept of schema. There are many questions out there asking what schema are and how they are used; here is a . Usually the answer boils down to "namespace" and "permissions". However, what remains unclear to me is why a schema has any advantage over just adding a new database. A different database allows one to have both separate namespaces and permission assignments.  Can someone provide an example in PostgreSQL where multiple schema in a single database provide an advantage over multiple databases without schema? From a purely organizational perspective they appear equivalent. Two numbers are chosen randomly and independently from the unit interval $(0,1)$.  What is the probability that they differ by more than $\frac{1}{2}$? Hint: Think of the $2$ numbers chosen as coordinates in the Cartesian plane. Draw a square with vertices at $(0,0)$,$(1,0)$,$(1,1)$, and $(0,1)$. Allowable choices for the $2$ points lie below the line $y=x-\frac{1}{2}$ or the above $y=x+\frac{1}{2}$. Find the combined area of these regions.  I need help on this. I know what $y=x-\frac{1}{2}$ and $y=x+\frac{1}{2}$ looks like but I am not understanding the problem as a whole Conditionals in English are usually formed by using if with normal word order; but for the three past (subjunctive) forms were, should, and had, it is also possible to express the conditional through subject–auxiliary inversion alone, with no if in the conditional clause.  Does forming conditionals in this manner differ semantically from if-conditionals? Is some aspect of the conditional statement or the conditionality emphasised more in one version than in the other? Or are there differences in how and when they are used? Or are they simply completely interchangeable?  For example:     If I were you, I would try it again   Were I you, I would try it again      If I had seen it, I would have told you   Had I seen it, I would have told you      If you should drink, don’t get behind the wheel   Should you drink, don’t get behind the wheel The following methods can be used to add CSS for specific versions of IE:   Paste the code into html.tpl.php:  &lt;!--[if lt IE 9]&gt;&lt;link type="text/css" rel="stylesheet" src="/sites/all/themes/mytheme/less/ie.css"&gt;&lt;![endif]--&gt; Make use of the plugin  Use drupal_add_css() function   I have always used option #1 above, and adding yet another plugin for something so simple seemed crazy. BUT working with LESS and calling in statically means the file does not get processed by the LESS pre-processor, so the question:  How do you include a stylesheet using drupal_add_css() for specific versions of IE? In January, some additional whitespace  below h1, h2 and h3 headings,  more whitespace below the headers than above them.  Could we have the whitespace above the headings be more than the whitespace below them?  I find some posts a bit hard to read, like the current rendering on the left:   &nbsp; &nbsp; &nbsp; The $ l^{\infty} $-norm is equal to the limit of the $ l^{p} $-norms. Prove a differentiable function between banach spaces is continuous I really don't know where to start with this problem. It intuitively makes sense from basic calculus knowledge but I have absolutely no clue how to show it. , A question was asked in one of my friend's interview. The question was to determine the right form from the below sentences.     Q. Correct form of English:          Samuel was with Susan and I   Samuel was with Susan and me   Samuel was with I and Susan   Samuel was with me and Susan   None of these      Now I vaguely remember a rule of thumb from my school days. That is "2-3-1" i.e. where all the persons are acting in a sentence, second person comes first, then third person and it is followed by first person.  So according to this theory, 1 seems to be correct to me. Is this theory correct? Confused AUC ROC score 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) What is approximate error of Pythagorean Theorem vs. Haversine Formula in measuring distances on sphere at various scales? Many people when first trying to calculate distances between two longitude / latitude pairs  ask if Pythagorean theorem works as an appropriate distance function.  Most often people answer "no, the Pythagorean theorem only works on a 2D Euclidean plane." Rarely, however, do people mention the effect of scale and location on the sphere on how inaccurate the Pythagorean theorem is.  The basic idea being at very small scales, the surface of a sphere looks very much like a plane. At very large scales, it distances along the surface are more curved and therefore the difference between the incorrect Pythagorean Theorem and the correct Haversine Formula is greater.  Does anyone know a formula or rule of thumb that tells you the difference between the two distance measures based on the scale of the distance you are trying to measure?   I think having this explicitly would help in:   explaining why the Pythagorean Theorem isn't perfect; and in letting people who are looking for more "rough" distances know when Pythagoras actually will serve their purposes. How to determine whether a unique factorization domain is a principal ideal domain? Could someone please provide an example of a unique factorization domain that is not a principal ideal domain?  Furthermore, is there some way to determine whether a UFD is a PID? What are the various physical mechanisms for energy transfer to the photon during blackbody emission? Adding a script to the page dynamically with jQuery never uses the cached file I need to process a large file, around 400K lines and 200 M. But sometimes I have to process from bottom up. How can I use iterator (yield return) here? Basically I don't like to load everything in memory. I know it is more efficient to use iterator in .NET. I'm trying to watch for any new output of a log file. Another script (not under my control) is deleting the file then creating a new one with the same name. Using tail -f doesn't work because the file is being deleted. How to let `dpkg -i` install dependencies for me? Say, I have foo-1.2.3.deb which depends on perl and python, however, running command:  dpkg -i ./foo-1.2.3.deb   won't install these dependencies. So I must apt-get install perl python by hand.  How to make dpkg -i install these dependencies for me automatically? I just installed Call of Duty 4 and when I try to run the single player mode nothing happens. I just see a quick flicker on the desktop but the game doesn't launch. When I try to run it again, it gives me this message:      It appears that cod4 did not quit properly the last time it ran. Do you want to run the game in safe mode?    Multiplayer seems to work fine and when I try to switch to single player from the multiplayer menu the same thing happens, it just goes back to my desktop and that message shows up again For $u:\mathbb{R}\times [0,1]$ with boundary conditions $u(0,x)=\cos (2\pi x)$ and $u(t,0)=u(t,1)$.   Solve $u_t=u_{xx}+u_x$.  I had this on an exam and tried to write $u$ as a product of two single variate functions and convert to an ode using the usual methods but things got messy and I couldn't finish. I also tried to write $u$ as a Fourier series in $x$ with coefficients $a_k(t)$ depending on $t$, but this also didn't seem to yield anything.  Is there a more clever way to approach this, possibly with Fourier series? I heard from a friend there may be a Fourier transform method since the equation was "homogeneous in momentum space."   Thanks!