Deep copy of array of objects
Deep cloning objects
$E$ is a measurable set of finite measure and $1 \le p_{1} &lt; p_{2} &lt; \infty$. Consider the linear space $L^{p_{2}}(E)$ normed by $||.||_{p_{1}}$. Is this space Banach? Show that $\mathbb{Z}[i]/(2+3i)$ is a finite field.    By applying some isomorphisms and realizing $\mathbb{Z}[i]$ as the quotient ring of $\mathbb{Z}[x]/(x^{2}+1)$, I found that:  $\mathbb{Z}[i]/(2+3i) \cong \mathbb{Z}[x]/(x^2+1,2+3x)$  However, I run into trouble as I can't divide $x^{2}+1$ by $2+3x$ in $\mathbb{Z}[x]$. What would be another way to approach the problem?  Thanks for the help. Is an Anti-Symmetric Relation also Reflexive? According to the definition of an Anti-Symmetric Relation if xRy and yRx then x = y  Which means, effectively, x is in relation with itself. Does this mean that anti-symmetry implies reflexive property as well? traveller's cheques; customer's requirements: use of the singular Saxon genitive (and the plural attributive) for association May I ask if the following sentence is grammatical?      Our remit is to conduct research on customer's requirements.   In my understanding, as 'customer' is a countable noun, so the plural form 'customers''' should be used instead for this general reference (without specification of certain customers).   However, I know that we can say 'traveller's cheques' - e.g.,      Traveller's cheques are available at the bank.    In this sense, actually can we say 'customer's requirements' in the first case? Allow cross-site queries in data explorer Did I correctly derive this recurrence equation formula In the PGF/TikZ manual, sometimes I see the option right of=somenode instead of right=of somenode. They look very similar, but the effects are different.  The distance between nodes positioned with the latter option is boundary-to-boundary, as stated in the manual. However, with the first option, it seems that the distance is shorter. I couldn't find any explanation of the first option in the manual.  My question is: what is the difference between the two options? Is there any explanation in the manual that I missed? image of polynomial map is not an algebraic set I am doing an exercise about algebraic geometry, where the exercise  tell us to provide example of the image of polynomial map $f:\mathbb{C}^{m}\rightarrow \mathbb{C}^{n}$ that is not an algebraic set. But I am thinking that the image of every polynomial is $\mathbb{C}$ thus every polynomial map is surjective. What have I misunderstand? Use of a semicolon before and comma after "however" Several years ago, a previous boss told me to use a semicolon and comma with the word "however".  I've always questioned this and would like to know if the following random sentences are using the correct method.        Our plane was delayed overnight; however, the airlines reimbursed us for lodging.   It looks as though he's upset; however, she told me he always has that look on his face.   I want to find him a nice gift; however, I am a broke until payday.      Normally I would use a less "wordy" sentence in casual writing, but hopefully the example will suffice.  For example, on number 3 I would usually type:      I want to get him a nice gift, but I'm broke until payday. If $G$ has no proper subgroup, then $G$ is cyclic of prime order This is something I'm supposed to be able to prove for an upcoming test, but I can't find anything to help me prove this in my notes or the chapter, which is on cosets and Lagrange's theorem. If all I start with is the group having no proper subsets, then that means any subset is the whole group. By Lagrange's theorem, that means the index is $1$, but that doesn't get me anywhere. Where do I start? How to make a process invisible to other users? How could you launch a process and make it invisible to the top command? The process is started by a normal user (not root), and should not be visible to other normal users. Let $d=GCD(n^2+5,n^3-5n^2+6n)$ show that $d|630$ How to call shell commands from Ruby How do I call shell commands from inside of a Ruby program? How do I then get output from these commands back into Ruby? Should 'Hi', 'thanks', taglines, and salutations be removed from posts? What are the options for player characters to create traps? Number of isosceles triangle. Feature selection with Random Forests I am curious about the practical implementation of a binary split in a decision tree - as it relates to levels of a categorical predictor $X{j}$.  Specifically, I often will utilize some sort of sampling scheme (e.g. bagging, oversampling etc) when building a predictive model using a decision tree - in order to improve its predictive accuracy and stability. During these sampling routines, it is possible for a categorical variable to be presented to a tree fitting algorithm with less than the complete level set.  Say a variable X takes on levels {A,B,C,D,E}. In a sample, maybe only levels {A,B,C,D} are present. Then, when the resulting tree is used for prediction, the full set may be present.  Continuing from this example, say a tree splits on X and sends {A,B} to the left and {C,D} to the right. I would expect the logic of the binary split to then say, when faced with new data: "If X has value A or B, send to the left, otherwise, send this case to the right". What seems to happen in some implementations is "if X has value A or B, send to the left, if X has value C or D send to the right". When this case takes on value E, the algorithm breaks down.   What is the "right" way for a binary split to be handled? It seems the much more robust way is implemented often, but not always (see Rpart below).  Here are a couple examples:  Rpart fails, the others are ok.  #test trees and missing values  summary(solder) table(solder$PadType)  # create train and validation set.seed(12345) t_rows&lt;-sample(1:nrow(solder),size=360, replace=FALSE) train_solder&lt;-solder[t_rows,] val_solder&lt;-solder[-t_rows,]  #look at PadType table(train_solder$PadType) table(val_solder$PadType) #set a bunch to missing levels(train_solder$PadType)[train_solder$PadType %in% c('L8','L9','W4','W9')] &lt;- 'MISSING'   #Fit several trees, may have to play with the parameters to get them to split on the variable  ####RPART mod_rpart&lt;-rpart(Solder~PadType,data=train_solder) predict(mod_rpart,val_solder) #Error in model.frame.default(Terms, newdata, na.action = na.action, xlev = attr(object,  :  #factor 'PadType' has new level(s) D6, L6, L7, L8, L9, W4  ####TREE mod_tree&lt;-tree(Solder~PadType,data=train_solder,split="gini") predict(mod_tree,val_solder) #works fine  ####ctree mod_ctree&lt;-ctree(Solder~PadType,data=train_solder,control = ctree_control(mincriterion = 0.05)) predict(mod_ctree,val_solder) #works fine How to reduce the number of authors above >3 to 'First Author et al., (year)'? Why square the difference instead of taking the absolute value in standard deviation? In the definition of standard deviation, why do we have to square the difference from the mean to get the mean (E) and take the square root back at the end? Can't we just simply take the absolute value of the difference instead and get the expected value (mean) of those, and wouldn't that also show the variation of the data? The number is going to be different from square method (the absolute-value method will be smaller), but it should still show the spread of data. Anybody know why we take this square approach as a standard?  The definition of standard deviation:  $\sigma = \sqrt{E\left[\left(X - \mu\right)^2\right]}.$   Can't we just take the absolute value instead and still be a good measurement?  $\sigma = E\left[|X - \mu|\right]$