Why org.apache.catalina.LifecycleException: Failed to start component
SEVERE: A child container failed during start java.util.concurrent.ExecutionException: org.apache.catalina.LifecycleException:
I want to split a long equation in many lines I have a long line in equation. I want to split it properly in two or three lines. I've been using \begin{split} and \end{split}, but still it is not in good position. The equation's code is below.  \begin{equation} \begin{split} \frac{r(r-1)c_{0}}{z} + \\ &amp;  \sum_{0}^{\infty}[[(j+r)(j+r+1)c_{j+1} - [(j+r)(j+r-1) - l(l+1)]c_{j}] \\ &amp;= 0, \end{split} \end{equation} I'm studying molecular biology and I'm trying to understand an experiment which shows the importance of promoters in the relative transcription level (RT). The image below comes from Rolf Knippers' book "Molekulare Genetik" (8th edition).    The legend says (among other things):     Die erste Zeile gibt die normale "Wildtyp"-Sequenz der 5'-flankierenden Region wieder.   Which, in english, means something like:     The first line repeats the normal wild-type sequence of the 5' flanking region.   The column on the right gives the relative transcription (RT) level, 1.0 being the highest possible level of transcription. As we can see, the lines where some parts of the "5' region" have been deleted give quite low RT levels, since some regions of the promoter are missing.  My questions are the following:  1) According to  and , I understand that RNA polymerase reads and uses both coding and non-coding strands in order to synthesize RNA. Therefore, how did they manage to use the sequences strands regions had been deleted to make a polymerase "read them" and perform transcription?  2) If the polymerase reads the template strand in the 3' -> 5' sense, shouldn't we talk of "ATAT box" or "TAAC box" instead of "TATA" or "CAAT" boxes? Does it mean that the "promoter" regions they are using on the graphic above are actually on the coding strand?  Thanks a lot for your help. If I want to add more RAM to my computer, how can I buy something compatible? What kinds are there? How do I determine which kind my computer will accept and how much I can add? How do I debug Node.js applications? Establishing a Basis for $F[x]/(f(x))$ Hypothesis:   $f(x) = a_0 + a_1 x + \ldots + a_n x^n \in F[x]$ s.t. $f(x)$ irreducible over field $F$. $deg(f(x)) = n \ge 1$. Let $V = (f(x)) \subset F[x]$.   Goal: Show that $\mathcal{B} = \{1 + V, x + V, x^2 + V, \ldots , x^{n-1} + V\}$ forms a basis for $E = F[x]/V$  Attempt:   Linear Independence: If this set weren't linearly independent, then a non-trivial $b_i \in F$ would satisfy  $$ b_0 + b_1x + \ldots + b_{n-1} x^{n-1} + V = 0 + V $$   But this would then imply that $b_0 + b_1x + \ldots + b_{n-1} x^{n-1}  \in 0 + V$. But this would contradict $V = (f(x))$ since it is impossible that $f(x)\,\,|\,\,b_0 + b_1x + \ldots + b_{n-1} x^{n-1}$ of strictly lower degree.  Now how would I show that this set spans $F[x]/V$? Installing from source - do I need to keep the extracted tarball directory If I'm installing from source, do I need to keep the extracted tarball directory?  So if I download the git tarball. I then do:  tar -xvzf git.tar.gz   This will create a git.x.x. directory, into which I cd, then run ./configure etc. Once I'm done with this process, and git, or whatever is installed, do I need to keep the original git.x.x extracted directory, or is that just used for compiling the program?  I'm somewhat confused by all the directories, and folders used for programs. ToList()-- does it create a new list? It's my understanding that a z-score can only be calculated and accurately used for data sets that are normally distributed.  Since "perfect" normal distribution almost never occurs in real-world data (where "perfect" normal distribution is defined as 1. The mean, median, and mode all equal the same number, 2. the distribution is perfectly symmetrical between all standard deviations on both sides of the mean, and 3. the distribution is asymptotic), how "close" can the distribution be to perfectly normal for the z-score to still be a valid statistical measure?  If the answer is it has to be a perfectly normal distribution, then my question is why is the z-score so important since it would seldom be a valid measure on real-world data? Can a mathematically sound prediction interval have a negative lower bound? I have used R to form a 95% prediction interval for the number of endemic species on an island. My lower bound is negative – is that mathematically sound?  In the linear model used in the prediction interval, the data used are:  Area Surface area of island, hectares DiscSC Distance from Santa Cruz, kilometres Elevation Elevation of higher point in metres and it is coded as such:   selected.model &lt;- lm(ES ~ Area + Elevation + DistSC + I(Elevation^2)                      + (Elevation:DistSC) + (A‌​rea:Elevation))    and stepwise regression was performed to find this "best" model   I'm not exactly sure how a prediction interval works. I just want to make sure it is OK. Obviously a negative number of species is incorrect, but I know it takes into account the uncertainty of the mean as well as data scatter. How can I compare time in SQL Server? How do I install Adobe Air using "Ubuntu Software Centre" I tried:   Launching Ubuntu Software Centre I typed in "air" and found "adobe air" It says "available from the 'maverick-partner' source. and has a button "use this source" I clicked "use this source", I saw a "in progress (1)" icon come up in the side bar, and disappear, but nothing happened/changed.   I'm stuck.  I have actually already added the maverick-partner source to apt so I could install sun-java6-jdk. Break a previous commit into multiple commits How to Solve this Arithmetic Progression Question? Please help-  Four different integers form an increasing AP.One of these numbers is equal to the sum of the squares of the other three numbers.Then- find all the four numbers.  I assumed the numbers to be $a,a+d,a+2d,a+3d$ and wlog let $a+3d$ this number and according to question-  $a^2+(a+d)^2+(a+2d)^2=a+3d$  but I could not solve the above equation. Word for "reading carefully" Sometimes we read books rather quickly and don't give them much (or any) thought, so the action 'reading' does not necessarily imply that we have given enough thoughts to any book we read.   Is there a word that describes reading a book with great care; usually but necessarily slowly over a long period of time. \texttt overfull hbox problem I asked a question earlier about \verb and overfull hbox :   And regarding the solution there, changed many of my \verbs to \texttt{}s.  I have come up with a new problem now.  An example:  \documentclass {article} \begin{document} \section {Introduction}      The entry point is in \texttt{TRCS.Main()} (\texttt{TRCS\char`\\TRCS.cs}).    The stateless (see \S 3.4.3) forms are started immediately, then another controller   is invoked, namely  \texttt{Workflow}. \end{document}   Compiling this example will show my problem.  \texttt{Workflow} causes an overflow, and a rather significant one.  What should I do to alleviate the problem?  Thanks in advance for your help! EntityFieldQuery display pager How do I display pager using EntityFieldQuery for fetch results? I can't find complete example.  I am doing simmilar to:   But I miss part to output simple pagination links (1,2,3... for every next page). When is a biased estimator preferable to unbiased one? Prove Or Disprove: tr(AB)=tr(A)*tr(B) $\mathrm{tr}(AB)=\sum\limits_{i=1}^n \sum\limits_{j=1}^n a_{ij}*b_{ji}$  $\mathrm{tr}(A)*\mathrm{tr}(B)=\sum\limits_{i=1}^n a_{ii}*\sum\limits_{i=1}^n b_{ii}$  Therefore $\mathrm{tr}(AB) \neq \mathrm{tr}(A)*\mathrm{tr}(B)$  Is the proof valid? What is another word for 'all round' capabilities? I am looking for a positive, passionate word to describe the all-round capabilities of a person.   Are there any words better than 'all-rounder'? Why is the copy-constructor argument const?