I some time ago saw some sentences, "Punch him good", "You punch really good". I assume, that good works as adverb and means well. Upon assuming, I got a question: How has the word good become to mean well? Why do people occasionally use good instead of well?  Thanks.
Most of the time, I use good and well interchangeably. However, on many occasions I would find well or good a misfit. Please suggest the proper usage.
extending convergence radius using one boundary point Show that if $f(z)=\sum\limits_{n\geq0}a_nz^n$ is analytic in $\{z\in\mathbb{C}:|z|&lt;1\}\cup\{1\}$ and $\forall n\geq0:a_n\geq0$ then the radius of convergence of the power series is strictly larger than $1$.  My approach:   Let $D=\{z\in\mathbb{C}:|z|\leq1\}$.  We have that $f(1)$ converges, so $\sum\limits_{n\geq 0} a_n&lt;\infty$. Moreover since the $a_n$'s are all positive we have that $|a_n|=a_n$, therefore $\sum\limits_{n\geq 0} |a_n|=\sum\limits_{n\geq 0} a_n&lt;\infty$.  Let $f_n(z)=a_nz^n$, then $\forall z\in D, n\geq 0$ we have:  $$|f_n(z)|=|a_nz^n|=|a_n|\cdot|z^n|=a_n\cdot |z|^n\leq a_n\cdot 1^n\leq a_n$$  Then, applying Weierstrass M-test we get that the power series is convergent in $D$.  Now, I need to "find" an open ball $B$ such that $D\subset B$ and the power series is convergent in it.  Edit  $f$ is analytic in $1$, so there is an open set $U$ that contains $1$ such that   $$f(z)=\sum\limits_{n\geq 0} b_n(z-1)^n$$  Does it mean that the series is convergent in $U$?   I can see that we have that the two series coincide in $D\cap U$. What is the meaning of the beta-coefficient for an interaction term in a crossover study? I have asked a similar question here:  I am puzzled by the interpretation for an interaction term. In my data my Y is an interval variable with the health outcome of an experiment. I have used an interaction term in which I have interacted the condition with the predisposition of the subject considering health status at base level. They are both categorical variables (factor variables in R).  Now it gets complicated because the Condition was two treatments: in treatment A subjects got the placebo first and then the real medicine whereas in treatment B they go the real medicine first and the placebo second. All it changes is the order.   Health outcome = a + Condition * Health.Base   I have the worst state of health at the base level as my reference category I find that interaction with the Condition is statistically significant but I am not sure how to interpret this.  I use the lm() function of R (although my design looks more like an ANOVA) and in the output I get the b coefficient in an output that looks like this:  ConditionB:Health.Base.So.and.So         (Beta and p-value) ConditionB:Health.Base.Excellent         (Beta and p-value)   A statistically significant interaction term for those in Excellent health at baseline would mean that they are affected by the Condition B more than Condition A compared to the reference category people (Poor health at baseline). Is this right? What does the beta-coefficient represent?   If I would like to examine for each Health category at the base line separately without comparing to a reference category I would have to code each category as a dummy variable. However, in this case I would compare whether membership to a specific health status at the base line significantly changes between conditions compared to those who belong to the other health statuses at the base line. Is this right? Again, what does the beta-coefficient represent?  Would it be right to assume that the choice of the interaction between the Condition and the dummy variables is easier to interpret?  --- EDIT --- R output:  Call: lm(formula = HealthOutcome ~ Condition * HealthStatus,      data = datA)  Residuals:     Min      1Q  Median      3Q     Max  -1.5957 -0.5942 -0.2640  0.4423  2.4423   Coefficients:                                        Estimate Std. Error t value     Pr(&gt;|t|)     (Intercept)                            2.595652   0.053044  48.934  &lt; 2e-16 *** ConditionCondB                        -0.001449   0.077071  -0.019    0.985     HealthStatusSo.and.So                 -0.331693   0.078094  -4.247  2.35e-05 *** HealthStatusExcellent                 -0.836724   0.092692  -9.027  &lt; 2e-16 *** ConditionCondB:HealthStatusSo.and.So   0.137490   0.110612   1.243    0.214     ConditionCondB:HealthStatusExcellent  -0.199787   0.133943  -1.492    0.136     --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  Residual standard error: 0.8045 on 1059 degrees of freedom   (68 observations deleted due to missingness) Multiple R-squared:   0.16, Adjusted R-squared:  0.156  F-statistic: 40.33 on 5 and 1059 DF,  p-value: &lt; 2.2e-16 Code formatting - tag/block rather than indentation - code block more obvious I am creating a model of a glass and I would like to put a drawing on it (a png picture).  I know how to do it using Blender Render, but not with Cycles Render. Help :) 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 exactly happened with Dr. Crusher's husband and Captain Picard? Where can I start to learn ArcPy? Why can't we see the selected reasons when there are pending close votes for a question? When users vote to close a question, the original poster can't see the selected reason why until after the question is already closed.  If they could see this information, they might be able to edit the question to make it more acceptable and averting the need to close it.  For example, the owner of this  cannot see the reason why his question is being voted to close: Rearranging display order of attribute table fields using QGIS? "Parsing filters unsupported" error during extraction of RAR file I have received an .rar which I wish to unpack as it contains something rather important to me that I need to really have now. However even though I can view the contents of the .rar archive in the Archive Manager, I am unable to extract it due to this error:    The archive should contain two folders within it, each though contain at least 10 audio files as well as a PDF file each (I don't know what the contents exactly should be except for there should be audio files in there, and the content I have described is what I can see from the Archive Manager's view). So the only thing I am left with except the error is one of the folders and one of the audio files, but it says it has 0 bytes in it.  So how exactly do I fix this problem? I am running Ubuntu GNOME 16.04.1 with GNOME 3.20.  Information Update:  In reply to a comment requesting the output from the dpkg -l unrar unrar-free command:  Desired=Unknown/Install/Remove/Purge/Hold | Status=Not/Inst/Conf-files/Unpacked/halF-conf/Half-inst/trig-aWait/Trig-pend |/ Err?=(none)/Reinst-required (Status,Err: uppercase=bad) ||/ Name           Version      Architecture Description +++-==============-============-============-================================= un  unrar          &lt;none&gt;       &lt;none&gt;       (no description available) dpkg-query: no packages found matching unrar-free Referencing subfigures in main caption (with \subfloat and \subref) I've used subfloat to include subfigures, with their relevant labels but with empty captions. what I'm going to do is to reference these figures with \subref in the main caption of the figure. But what I get is only ?? signs in the caption [main caption]. I can't figure out what's the problem. this is what I have:  \begin{figure} \centering \subfloat[][] { \includegraphics[scale=0.55]{signal} \label{signal_model} } \subfloat[][] { \includegraphics[scale=0.55]{amplitude} \label{amplitude_mod} } \caption{phase noise variability: \subref{signal model} some text \subref{amplitude_mod} some other text} \end{figure} Check if url has domain name and not an ip Smart phone Smartphone Smart-phone   I am really looking for some help regarding hyphen (-) issue in text found in research article. Is there any standard method how to use it? Where does gravity get its energy from? Number Theory: Complete set of residues modulo $n$ I have this problem assigned for homework and I'm struggling with the proof of it:  If $a_1,a_2,\dotsc,a_n$ is a complete set of residues modulo $n$ and $\gcd(a,n)=1$, prove that $aa_1,aa_2,\dotsc,aa_n$ is also a complete set of residues modulo $n$.  (Hint: It suffices to show that the numbers in question are incongruent modulo $n$.)  I'm in elementary number theory so I'm not allowed to use an high-level theorems to prove this, I pretty much have to use the basics of modulo.  Thanks! which vectors are perpendicular to each other?  $\vec a = (1, -2, 3)$, $\vec b = (5, 4, 1)$, $\vec c = (1, 0, -5)$  Do i just take the dot product of 2 of them. If the dot product they are at $90^\circ$? But how do i know if there perpendicular? Which Wifi Channel should I use? Very confused.  I'm using inSSiDer, WiFi Overview 360 and Wifi Analyzer apps to try to determine the best wifi channel to use. Assuming all channels are in use and there are about 20 different users in close proximity...  Q1: Signal Strength    If all channels are in equal use, do you select a channel where others that use it have the lowest signal strength?  I'm guessing that a higher signal strength means that it's from a router from your closest neighbour and you want to avoid that.  Is that the case?  Does lower signal strength mean the person using it is further away and therefore less likely to interfere with your signal? If 2 people are on channel 1 and have high signal strength and 2 people are on channel 11 and have low signal strength, do you choose channel 11?  Assume 6 cannot be used.    Q2: Signal Strength Weighted Against Number of People    What is the impact of signal strength compared to number of people using channel?  If 1 person is on channel 1 with very high signal strength and 2 people are on channel 11 with low signal strength, do you choose channel 11 over 1?  Assume 6 cannot be used?    Q3: Channel Overlap    If, for example, I had 11 routers sitting on top of each other, each set to a different channel, I'm guessing channel 1 and 11 would be the least interferred.  Is that right?  People go on about the fact that only channel 1, 6 or 11 should be used (in US) as they don't overlap but surely that statement is wrong.  Yes, if only 3 people were using Wifi, the best channels to use would be 1, 6 and 11 as they don't overlap but in practice, there are about 20 people using the channels in the same area.  What do you do in that scenerio.  Do you go for the shoulder channels if all channels are being used equally with equal strength?    Q4: Auto Channel Select    Do routers set to auto channel select only choose between 1, 6 and 11?  How do they make the choice?  Do they select by choosing channel with lowest other routers and do they factor in signal strengths.  My router auto chooses channel 1 but my closest neighbour is on that channel.  Is that correct.      Q5: Baby Monitors and Wireless Phones    What channels do 2.4 GHz baby monitors and wireless phones use?  No useful info on the internet for them.  Do inSSiDer, etc. pick them up?    Q6: I have access to channel 13.  All other things being equal, am I better to use this over channel 11 as it is further away from the other channels?    Those questions have puzzled me for a number of years and Google is not helping!!  Would really be grateful if someone could give sensible answers to one or all of them.  Thanks, Mike. Bookmark panel in Chrome/Chromium like in Firefox $ \int_{0}^{ \infty} \int_{0}^{ \infty} \frac { e^{-(x+y)}}{x+y} dx dy $ Question : The integral   $$ \int_{0}^{ \infty} \int_{0}^{ \infty} \frac { e^{-(x+y)}}{x+y} \mathop{dx}\mathop{dy} $$  is   (a) infinite   (b) finite but can not be evaluated in closed form   (c) 1  (d) 2 .  I tried substituting $u=x+y$ and $v=y$ that led me no where . I'm not even sure about convergence of integral .Any help would be greatly appreciated . I'm trying to setup OpenVPN using NetworkManager. The GUI seems buggy and unresponsive. Are there any other tools for setting up a VPN client?