This question is related to this post (accepted answer):  .  After compiling the code below I obtain this outcome:   I have tried several alternatives such as adding backslashes or "&amp;" symbols but I am still unable to obtain the desired results.    Thanks in advance.   \documentclass[a4paper,12pt]{scrreprt}     \usepackage{booktabs}      \begin{document}     \begin{table}     \centering     \begin{tabular}{@{} lcccc @{}} % suppress vertical whitespace at start and end     \toprule     Company&amp; \multicolumn{3}{c}{Exceedances} &amp; No.\ of Obs.\    \cmidrule(lr){2-4}     &amp; \multicolumn{2}{c}{Empirical} &amp; Expected\    \cmidrule(lr){2-3} \cmidrule(lr){4-4}     &amp;standard &amp; standardized\\    % make columns 2 and 3 narrower     &amp;normal   &amp; Student's-$t$\    \midrule     Company 1&amp;1&amp;5&amp;9&amp;13\    Company 2&amp;2&amp;6&amp;10&amp;14\    Company 3&amp;3&amp;11&amp;15\    Company 4&amp;4&amp;8&amp;12&amp;16\    \midrule[\heavyrulewidth] % use "thick" \midrule instead of \bottomrule     \multicolumn{4}{@{}l}{\footnotesize An additional hint about a detail}     \end{tabular}     \caption{Here is the caption.}     \label{labelhere}     \end{table}      \end{document}
I use the following table:  \documentclass[a4paper,              12pt,                                        bibliography=totoc,              index=totoc,             abstracton,              headsepline,             ]{scrreprt}  \usepackage{booktabs}    \begin{document}   \begin{table}[H]\hspace*{-1cm} \centering \begin{tabular}{lcclll} \toprule  Company&amp; \multicolumn{2}{c}{exceedances (empirical)}&amp;exeedances (expected)&amp;no. of obs.\\ \cmidrule(r){2-3}\\ &amp;standard normal&amp;standardized Student's-t&amp;&amp;\\ \midrule Company1&amp;1&amp;5&amp;9&amp;13\\ Company2&amp;2&amp;6&amp;10&amp;14\\ Company3&amp;3&amp;11&amp;15\\ Company4&amp;4&amp;8&amp;12&amp;16\\ \bottomrule \multicolumn{4}{l}{\begin{footnotesize}an additional hint about a detail\end{footnotesize}} \end{tabular} \caption{Here is the caption.} \label{labelhere} \end{table}   \end{document}     Which gives    I have two problems:   The space after the \cmidrule(r){2-3} is too big, how can I change this? The table looks not that good, how can I improve it in general?
Increase iPhone call history can't find using System.Web.UI.HtmlControls namespace Should I mention about my governmental-funded PhD scholarship which I don't want to use Proof that $\frac {1} {2\pi i} \oint \frac {{\rm d}z} {P(z)} $ over a closed curve is zero. Prove that $$\frac {1} {2\pi i} \oint \frac {{\rm d}z} {P(z)} $$ over a closed  smooth simple curve that contains all of the roots of the polynomial $P(z)$ is either zero if $n \geq 2$ or equals $\frac{1} {a_0} $ if it's degree is $1$.   Proof: $n\geq 2$ $$\frac {1} {P(z)=(z-z_0)(z-z_1)\dots(z-z_n)}$$ So after partial decomposition of the fraction I'll have something like $$\frac {A} {z-z_0} +\frac{B} {z-z_1}+\cdots$$ where $A,B \in \mathbb{C}$ (Is this fact true that $A,B$ wont be polynomials and just coefficients I can see it why in an intuitive way but cannot write a full proof of it for the decomposition trying to get a linear system or something) then use Cauchy's theorem and integrate all of these on  different circles with their center at each root  and argue that  the integral is the same as the sum of those circle integrals. Now since $\frac {1}{z-z_n}$ will be analytic inside the circle when I'm integrating on circles that do not contain $z_n$  some  of those integrals  will be zero. and now since my curves are of the form $\gamma(t)=z_n+e^{it}$ , $t \in [0,2\pi]$ the rest of the integrals  will look like $$\int_0^{2\pi}  \frac{Aie^{ti}} {e^{it}}\,{\rm d}t $$  and all of them will be $A_i$.   Is my proof correct? Only part I cannot show is that I won't have any problem with decomposing the fraction. And I'm also using the assumption that after the decomposition I'll have as numerators simple complex numbers not not functions of any kind. If $|z_1|=1,|z_2|=1$, how can one prove $|1+z_1|+|1+z_2|+|1+z_1z_2|\ge2$ Is StringBuilder really faster than Aggreggate? Antecedent Precedence? What is an observer in quantum mechanics? My question is not about (pseudo) philosophical debate; it concerns mathematical operations and experimental facts.  What is an observer? What are the conditions required to be qualified of observer, both mathematically and experimentally? How can I make my ad hoc iPhone application's icon show up in iTunes? I've got an iPhone app with icon file Icon.png.  This icon shows up properly when the app is on the phone itself, but it doesn't show up in the applications pane in iTunes.  What do I need to do to get it to show up properly? Find a bijection to prove a fact about integer partitions Prove that for fixed positive integers $k$ and $n$, the number of partitions of $n$ is equal to the number of partitions of $2n + k$ into $n + k$ parts.  I tried this with different values of n but can't seem to get a bijection between the two partitions. I'm trying to re-learn my undergrad math, and I'm using Stephen Abbot's Understanding Analysis. In section 2.7, he has the following exercise:  Exercise 2.7.5 (a) Show that if $\sum{a_n}$ converges absolutely, then $\sum{a_n^2}$ also converges absolutely. Does this proposition hold without absolute convergence?  I'm posting about this here because my answer to that last question about whether the proposition holds without absolute convergence is "Yes", but my suspicions are raised by him merely asking the question. Usually questions like this are asked to point out that certain conditions are necessary in the statement of propositions, theorems, etc. I just want to see if I'm missing something here.  Anyway, here's how I prove the absolute convergence of $\sum{a_n^2}$, and note that I never use the fact that $\sum{a_n}$ is absolutely convergent:  Proof: Let $s_n = \sum_{i=1}^n{a_n^2}$. I want to show that $(s_n)$ is a Cauchy sequence. So, let $\epsilon &gt; 0$ and $n &gt; m$, and consider, \begin{equation}   \begin{aligned}     |s_n - s_m| &amp;= |(a_1^2 + a_2^2 + \cdots a_n^2) - (a_1^2 + a_2^2 + \cdots a_m^2)|\\                 &amp;= |(a_{m+1})^2 + (a_{m+2})^2 + \cdots + a_n^2|\\                 &amp;= |a_{m+1}|^2 + |a_{m+2}|^2 + \cdots + |a_n|^2\\   \end{aligned} \end{equation} Now, since $\sum{a_m}$ converges, the sequence $(a_m)$ has limit 0. Therefore I can choose an $N$ such that $|a_m| &lt; \sqrt{\epsilon/n}$ for all $m &gt; N$. So for all $n &gt; m&gt; N$,  we have, \begin{equation}   \begin{aligned}     |s_n - s_m| &amp;= |a_{m+1}|^2 + |a_{m+2}|^2 + \cdots + |a_n|^2\\                 &amp;&lt; \left(\sqrt{\frac{\epsilon}{n}}\right)^2 + \left(\sqrt{\frac{\epsilon}{n}}\right)^2 + \cdots + \left(\sqrt{\frac{\epsilon}{n}}\right)^2\\                 &amp;&lt; \left(\sqrt{\frac{\epsilon}{n-m}}\right)^2 + \left(\sqrt{\frac{\epsilon}{n-m}}\right)^2 + \cdots + \left(\sqrt{\frac{\epsilon}{n-m}}\right)^2\\                 &amp;= \epsilon   \end{aligned} \end{equation} Therefore $(s_n)$ is Cauchy and $\sum{a_n^2}$ converges. And since $\sum{a_n^2} = \sum{|a_n^2|}$, the series $\sum{a_n^2}$ is absolutely convergent. &#x220E;  Am I doing something wrong here? Am I right in thinking that $\sum{a_n}$ need not be absolutely convergent for $\sum{a_n^2}$ to be absolutely convergent? One of my coworkers has provided me with a Bash syntax that I am unfamiliar with.  My Google foo has failed me on figuring out what it does and why/when I should use it.    The command that he sent me was of this form:  someVariable=something command   Initially, I thought that this was equivalent to the following:   someVariable=something ; command   Or  someVariable=something  command   But this doesn't appear to the be case.  Examples:   [Jan-03 11:26][~]$ # Look at the environment variable BAZ. It is currently empty [Jan-03 11:26][~]$ echo $BAZ  [Jan-03 11:27][~]$ # Try running a command of the same format     [Jan-03 11:27][~]$ BAZ=jake echo $BAZ  [Jan-03 11:27][~]$     [Jan-03 11:27][~]$ # Now, echo BAZ again. It is still empty:     [Jan-03 11:27][~]$ echo $BAZ  [Jan-03 11:27][~]$     [Jan-03 11:28][~]$     [Jan-03 11:28][~]$ # If we add a semi-colon to the command, we get dramatically different results: [Jan-03 11:28][~]$ BAZ=jake ; echo $BAZ jake [Jan-03 11:28][~]$ [Jan-03 11:28][~]$ # And we can see that the variable is actually set: [Jan-03 11:29][~]$ echo $BAZ jake [Jan-03 11:29][~]$   What does this syntax do?  What happens to the variable that has been set?  Why does this work? Atiyah-Macdonald, Exercise 5.4 I was having some trouble with the following exercise from Atiyah-Macdonald.     Let $A$ be a subring of $B$ such that $B$ is integral over $A$. Let $\mathfrak{n}$ be a maximal ideal of $B$ and let $\mathfrak{m}=\mathfrak{n} \cap A$ be the corresponding maximal ideal of $A$. Is $B_{\mathfrak{n}}$ integral over $A_{\mathfrak{m}}$?   The book gives a hint which serves as a counter-example. Consider the subring $k[x^{2}-1]$ of $k[x]$ where $k$ is a field, and let $\mathfrak{n}=(x-1)$. I am trying to show that $1/(x+1)$ could not be integral over $k[x^{2}-1]_{\mathfrak{n}^{c}}$.  I have understood why this situation serves as a counterexample. But I am essentially stuck at trying to draw a contradiction. A hint or any help would be great. Linear regression best polynomial (or better approach to use)? Any ideas on other polynomials I could successfully use for applying regression? My goal is a solution that has fit error strictly based on the noise. Is this possible since it is a bell-like curve? The tails can be long, short or non-existent. Am I looking for the impossible? Please note it has been a while since I have plunged this far into linear regression.   Anyway, my data points do not fit the $ax+bx^2+c$ polynomial well enough. I would like a replacement for this polynomial to apply regression (or different approach). In the following example, each point misses the fit curve by $20\%$ of the $Y$ range on average (of the data points). I looked at splines, but I do not know how to apply the regression since they look piece-wise.   Example $Y$ values (evenly spaced in $X$). It looks kind of like a bell curve. I would be applying 5 to 50 data points to determine the polynomial coefficients. Ultimately, I am interested in the best $X$ location for the peak based on the data points.     X      Y -40    -21142.1111111111 -30    -21330.1111111111 -20    -12036.1111111111 -10      7255.3888888889   0     32474.8888888889  10     32474.8888888889  20      9060.8888888889  30    -11628.1111111111  40    -15129.6111111111 Concentric circles with CSS Android reject incoming call From this  on Bayesian Least Mean Square estimation:  $$\mathbf E\left[(\Theta -\hat\theta)^2\right] = \rm{var}(\Theta -\hat\theta) + \left(\mathbf E[\Theta -\hat\theta]\right)^2 = \rm{var}(\Theta) + \left(\mathbf E[\Theta -\hat\theta]\right)^2$$  which is to say that $\rm{var}(\Theta -\hat\theta) = \rm{var}(\Theta)$.  I would like to ask how that comes about?  Thanks.  $\Theta$ is the random variable being estimated, and $\hat\theta$ is a constant estimate. Why doesn't the frequency of light change during refraction? View history of commands run in terminal Is there a way to save all my typed terminal commands and view it like history in a log book? Equipartition of energy Let $u$ solve the initial-value problem or the wave equation in one dimension: $$\begin{cases}u_{tt}-u_{xx}=0 &amp; \text{in } \mathbb{R} \times (0,\infty) \\ u = g, u_t = h &amp; \text{on } \mathbb{R} \times \{t=0\}. \end{cases}$$ Suppose $g,h$ have compact support. The kinetic energy is $k(t) := \frac 12 \int_{-\infty}^\infty u_t^2(x,t) \, dx$ and the potential energy is $p(t) := \frac 12 \int_{-\infty}^\infty u_x^2(x,t) \, dx$. Prove (a) $k(t)+p(t)$ is constant in $t$, (b) $k(t)=p(t)$ for all large enough times $t$.  This is Chapter 2, Exercise 24 of PDE Evans, 2nd edition. I am only doing part (a) right now; my work is shown below: Define $$e(t):=k(t)+p(t)=\int_{-\infty}^\infty u_t^2+u_x^2 \, dx.$$ Then $$e'(t)=\frac 12 \int_{-\infty}^\infty 2u_tu_{tt}+2u_{x}u_{xt} \, dx= \int_{-\infty}^\infty u_tu_{tt}+u_{x}u_{xt} \, dx.$$ Now, I want to get $e'(t)=0$ so that $e(t)$ is constant. How can I go about doing this? I do know that I can use $u_{tt}-u_{xx}=0$, if $t &gt; 0$. With $t&gt;0$ into mind, do I have to consider the $t=0$ case separately? Or can I treat both cases together as $t \ge 0$, since $g$ and $h$ have compact support?