Should be a comma here? I read this sentence in a book, and it seems to be a little strange without a comma. Or is it only a style? And is the place of now right, considering the word order? Is this beginning of the sentence formal and appropriate for academic style? Thank you  To go further[,] we will need now to apply ...
I am no native speaker and always confused about the comma in introductory phrases, in particular in prepositional phrases. Is there any hard rule when a comma must be set? If I make a google search for certain phrases, I often find both variants. Typical examples where I am not sure whether a comma must be set are:        First[ly][,] I must phone mother   In this case[,] we must...   For simple problems[,] the algorithm...   From Lemma 1.2[,] we obtain...   For a typical user[,] the algorithm...   In our theory[,] we...   A dark line on the horizon[,] the mountain range we were headed for seemed somehow not as threatening as when we had started out on the trip.   Avidly reading her novel[,] Jane did not notice that her stop was approaching.   To be sure[,] it is not easy to see a solution.   When you get to Rome[,] give me a ring.
To find the total no. of six digit numbers that can be formed having property that every succeeding digit is greater than preceding digit. I have a question and got strucked on this.. To find the total no. of six digit numbers that can be formed having property that every succeeding digit is greater than preceding digit. Please guide me to solve this. Thanks in advance. How to install Wireshark I am new to Linux and have a need to install Wireshark 2.0.0 on VirtualBox's Xubuntu 14.04. I have already downloaded .tar.gz package and extracted it. Then I opened terminal in the wireshark folder and type /.configure with intention to follow it by make and sudo make install executions but the attempt as unsuccessful as sudo apt-get install wireshark. Could somebody help me how to install Wireshark step by step, please? Prove existence of a real root. Problem: If   $$C_0+\frac{C_1}{2}+\cdots + \frac{C_{n-1}}{n}+\frac{C_n}{n+1} =0,$$  where $C_0,...,C_n$ are real constants, prove that the equation  $$C_0+C_1x+\cdots +C_{n-1}x^{n-1}+C_nx^n=0$$  has at least one real root between $0$ and $1$.  Source: W. Rudin, Principles of Mathematical Analysis, Chapter 5, exercise 4. In definition of vector multiplication, the direction of the resulting vector is given by the right hand rule. However I don't know any mathematical requirement to pick right hand instead of left for this purpose. Is there any? How does one type Chinese in LaTeX? "the 90s were the best decade ever" or "the 90s was the best decade ever"  "the 90s" and "decade" are both referring to the same singular period of 10 years, so "was" seems to make more sense. "90s were" rolls off the tongue better though. How can I create an executable JAR with dependencies using Maven? If $(A-2I)^3(A+2I)^2=0$, then what are the possible Jordan canonical forms of $A$? Here is the exercise:     Let $A$ be a $5\times5$ complex matrix such that $(A-2)^3(A+2)^2=0$, where we define $A-\mu:=A-\mu I$ for scalar $\mu$. Assume that $\lambda=2$ is an eigenvalue of $A$ and its geometric multiplicity is at least $2$. What are the possibilities for the Jordan canonical form (JCF)?   What I know so far from the assumption is that    the minimal polynomial of $A$ is of the form $f(x)=(x-2)^i(x+2)^j$ where $1\leq i\leq 3$ and $0\leq j\leq 2$.  The number of blocks in the Jordan segment $J(2)$ is at least $2$.    One can write the possible minimal polynomial one by one, which gives the information of the size of the largest block in each Jordan segment, and use the possible geometric multiplicity of $\lambda=2$ to find JCF.   Here are my questions:   Is there an alternative approach?  Can we use the characteristic polynomial of $A$ here? Now that Unity is gone, the usual way of setting a Compose Key (via Keyboard Preferences > Layout) no longer works (because in Ubuntu 18.04, Devices > Keyboard has no Layout tab).  How do we set a Compose Key in Ubuntu 18.04 Bionic Beaver? Why is the ROC curve two-dimensional instead of three-dimensional? Acknowledgements outside of document environment How do I add an acknowledgements section (maybe not specifically \section) outside of (before) my document environment?  in my .cls, there is  \def\@acknowledge{} ... \def\acknowledge#1{\booltrue{@ack} \gdef\@acknowledge{#1}} ... \def\ackpage{ \chapter*{Acknowledgments} \@acknowledge \newpage }   but it seems that I find problems when I put newlines in the  \acknowledge{folks in here}  (see  ) Okay, maybe I'm missing something obvious but consider $h_n(x) = x^{ 1+ \frac{1}{2n-1}}$ on the set $[-1,1]$. Now consider a fixed $x \in [-1,1]$, we have:  $$\lim_{n\rightarrow \infty} h_n(x) = x \lim_{n \rightarrow \infty} x^\frac{1}{2n-1} = x$$  But my book says it's $|x|$? Why? Redefining "cited on" string (and others) in biblatex Why does no physical energy-momentum tensor exist for the gravitational field? Integral around unit sphere of inner product For arbitrary $n\times n$ matrices M, I am trying to solve the integral  $$\int_{\|v\| = 1} v^T M v.$$  Solving this integral in a few low dimensions (by passing to spherical coordinates) suggests the answer in general to be  $$\frac{A\,\mathrm{tr}(M)}{n}$$ where $A$ is the surface area of the $(n-1)$-dimensional sphere. Is there a nice, coordinate-free approach to proving this formula? String comparison in Python: is vs. == Correct use of will & would? What would be the correct use of will &amp; would in these sentences?  1) What will happen if I say to my boss that I will not come tomorrow?  2) What will happen if I would say to my boss that I will not come tomorrow?  3) What will happen if I will say to my boss that I will not come tomorrow?  4) What would happen if I would say to my boss that I will not come tomorrow?  There are four sentences which one should I use and in which situation? Why does Leia's accent change during A New Hope? I am embedding a PDF file inside my LaTeX-generated PDF file using embedfile:  \usepackage{embedfile} \embedfile{myfile.pdf}   I would like to also insert a link that the user can click on to open the attachment.  Is there any way to do that? HowTo redirect HTTP to HTTPS on the same httpd? Here is what I have got:   CentOS 5.4 (32-bit)    installed Apache httpd (Server version: Apache/2.2.11 (Unix)) mod_rewrite already presents   Question: how to redirect simple  to  not using VirtualHost defines?  PS: tried to find in later answers on SF, but doesn't find nice solution.  Thanks.