The boy comes running.  My father stands behind me smiling. (I saw the first example in a grammar book and the second in a prose)    In which cases is this particular form (S + action-verb + s/es of the verb + 'ing' form of the another action-verb) applicable?
For various such sentences in many cases I get confused, it seems different for different cases. I want to know if someone left doing something for permanantly then what should be used? Also give some examples for different cases. Suppose... "I left my bag" means "I forgot my bag". but If I want to say the same for permanentaly "I left bringing my bag". Where should we use "stop" and "quit" then?
How do rich people guarantee the safety of their money, when savings exceed the FDIC limit? I am curious how a millionaire would guarantee the safety of his money, given that the FDIC only insures up to $250K of an individual's deposits at a bank.  If someone had $3 million that they wanted to put into the bank, would they have to open up 12 different bank accounts and deposit $250K into each one, so that all of his money is insured by the FDIC?  Or is there an easier way to guarantee the safety of all his money? Lie algebra of $\left(\begin{smallmatrix}a & b\\ & a^2\end{smallmatrix}\right )$ in $GL_2(\mathbb{R})$ I'm working on the question     Let $G$ be the group of invertible real matrices of the form $\left [\begin{array}{c c}a &amp; b\\ &amp; a^2\end{array}\right ]$. Determine the Lie algebra $L$ of $G$, and compute the bracket on $L$.   I'm familiar with how to derive the Lie algebra for a linear group like $U_n$, $SU_n$, etc. but I'm not sure what to do in a more explicit case like this. Unity Tweak tool fails to start with the error "com.canonical.unity.webapps schema is missing" com.canonical.unity.webapps   In order to work properly, Unity Tweak Tool recommends you install the necessary packages I installed few environments that I wanted to try out on Ubuntu 12.04, but none of them worked at all. It could be that I installed them all at the same time, meaning the OS didn't get a chance to work everything out, but either way, they didn't work. I would now like to remove them.   The one's that I installed are Xubuntu/Xfce, Lubuntu/LXDE, Kubuntu/KDE, Fluxbox, OpenBox, cinnamon, and MATE. I installed them. Everything seemed to have been working properly until I actually tried to use the shells and nothing loaded at all. Except for Fluxbox, I think that one worked. I want to know of any way to repair or perhaps just remove the packages entirely. I might have already removed them because I did the apt-get remove command on all of them, but they were still in the list on the login screen. Let $f:[0,+\infty)\to\Bbb R$ be a function bounded on each finite interval. I want to show that if $\lim\limits_{x\to+\infty}[f(x+1)-f(x)]= L,$ then also $\lim\limits_{x\to+\infty}\dfrac{f(x)}x = L$ Area of intersection between two circles Suppose you have 2 circles that intersect each other in such a way that each circle passes through the other's center. What is the area between the circle(or common area) i.e. area between the centres of the circles? WAMP Server not working Okay so a continuation from , where you experts intro'd me to , which can basically execute PHP within a Windows XP environment.  So now I've got it installed, but the tray icon forever shows YELLOW, and when I visit any PHP page in my browser, it just shows me the PHP source!  Also, when I visit "" in IE7 it gives me a 404 Not Found, FF3 just shows a blank page.    BTW I've tried "Restart All Services" and restarting my machine, but it still won't work.  Any ideas? Any of you had this problem and solved it? Please help me here, I'm desperate to execute PHP client-side and I'm just reverting to testing on-server for now! Same mesh with different colors Allowing only one download per Apple ID What Does it Really Mean to Have Different Kinds of Infinities? Can someone explain to me how there can be different kinds of infinities?  I was reading "" by  and came across the concept of countable and uncountable infinities, but they're only words to me.  Any help would be appreciated. I want to kill all running processes of a particular user from either a shell script or native code on a Linux system.  Do I have to read the /proc directory and look for these?  Any ideas? Is there a dynamic mapping of the pids under UIDs in Linux? Isn't this in the proc?  If not, then where is this list maintained? Should I read from it? Also where is the static list of all UIDs in the system so I can validate this this user exists and then proceed to kill all processes running under it? When I include a  \usepackage{forest} all colored text title, section headings disappears with IEEE Access journal template How can I tackle this problem? Find the condition on $a$ and $b$ so that the two tangents drawn to the parabola $y^2=4ax$ from a point are normals to the parabola $x^2=4by.$  The required condition is $a^2&gt;8b^2$.I dont know how to prove it.I tried.  Let $(h,k)$ be the point from where tangents are drawn to the parabola $y^2=4ax$.Let $m_1,m_2$ be the slopes of the tangents.Equations of tangents are $y=m_1x+\frac{a}{m_1}$ and $y=m_2x+\frac{a}{m_2}$ and equations of normal to the parabola $x^2=4by$ is $y=m_1x-2bm_1-bm^3_1$ and $y=m_2x-2bm_2-bm^3_2$.  As $y=m_1x+\frac{a}{m_1}$ and $y=m_1x-2bm_1-bm^3_1$  are the same lines.Therefore,$\frac{a}{m_1}=-2bm_1-bm^3_1$  $bm^4+2bm^2+a=0$  And I am stuck.I cannot get the desired condition.Please help me. Why do we need sigma-algebras to define probability spaces? We have a random experiment with different outcomes forming the sample space $\Omega,$ on which we look with interest at certain patterns, called events $\mathscr{F}.$ Sigma-algebras (or sigma-fields) are made up of events to which a probability measure $\mathbb{P}$ can be assigned. Certain properties are fulfilled, including the inclusion of the null set $\varnothing$ and the entire sample space, and an algebra that describes unions and intersections with Venn diagrams.  Probability is defined as a function between the $\sigma$-algebra and the interval $[0,1]$.  Altogether, the triple $(\Omega, \mathscr{F}, \mathbb{P})$ forms a probability space.  Could someone explain in plain English why the probability edifice would collapse if we didn't have a $\sigma$-algebra? They are just wedged in the middle with that impossibly calligraphic "F". I trust they are necessary; I see that an event is different from an outcome, but what would go awry without a $\sigma$-algebras?     The question is: In what type of probability problems the definition of a probability space including a $\sigma$-algebra becomes a necessity?       provides a plain English accessible explanation. The idea is a spinning pointer rotating counterclockwise on a circle of unit perimeter:       We begin by constructing a spinner, which consists of a circle of unit   circumference and a pointer as shown in [the] Figure. We pick a point   on the circle and label it $0$, and then label every other point on the   circle with the distance, say $x$, from $0$ to that point, measured   counterclockwise. The  experiment  consists  of spinning the pointer and    recording the label of the point at the tip of the pointer. We let the random   variable $X$ denote the value of this outcome.  The sample space is   clearly the interval $[0,1)$.  We would like to construct a   probability model in which each outcome is equally likely to occur. If   we proceed as we did [...] for experiments with a finite number of   possible outcomes,  then we must assign the probability $0$ to each   outcome,  since otherwise,  the  sum  of  the  probabilities,  over    all  of  the  possible  outcomes,  would not equal 1.  (In fact,   summing an uncountable number of real numbers is a tricky business;    in  particular,  in  order  for  such  a  sum  to  have  any  meaning,   at  most countably many of the summands can be different than $0$.)    However, if all of the assigned probabilities are $0$, then the sum is   $0$, not $1$, as it should be.   So if we assigned to each point any probability, and given that there is an (uncountably) infinity number of points, their sum would add up to $&gt; 1$. Learning and using English I'm always confused about what word to use for referring to things that have been described by me a few sentences earlier: "that" or "this".   Confusion comes from the fact that only the equivalent of "this" is always used in my native language for such referring. But I've noticed that in English for such referring "that" is used as often as "this" (or maybe even more often).  Some examples for illustrating (just tried to google something appropriate to convey my idea better):     We assess local... the demographics of the local population. What are the natural traffic drivers in the area. Things like cinemas and pubs and retail and office and all that type of things and we now put together a bit of a matrix and actually give a weighted score to each of the things we know help our business. That helps us decide in a more scientific fashion.   or:     The problem of Cervantes' origin became after that into a tough matter. Some experts believed that the Cervantes from Alcázar, in the times of the Lepanto Battle, was in the age of a child, more concerned about gathering nests and that type of things than about fighting as a soldier.   and for "this":     I believe lot of people who involved fishery industries in Mexico Gulf are suffering now but as for economic issues, U.S government and other countries will support them and give an utmost response to it. Important thing is that we learn from this mistake and make sure this type of things will never happen in the future and protect nature environment thus we have to take this technology to get energy from water very seriously. I really hope this technology will be available and used for everybody as soon as possible.   Is there a rule describing proper usage of these words in cases like this? (or should I have written "..in cases like that"?) I am trying to run the following model:         I(week^2):mutation_status +         (week + I(week^2) | subject_id) ,          data = sim_dat)  This is the output I get from this model. The correlation between week and I(week)^2 is rather high (-0.95) and I was curious to know how I can change my data simulation code to lower that value. I am also having issues with convergence and would love to get thoughts on how to avoid issues regarding convergence. Thank you! Linear mixed model fit by REML. t-tests use Satterthwaite's method [lmerModLmerTest]  Formula: fetal_weight ~ week + mutation_status + week:mutation_status + I(week^2) +  I(week^2):mutation_status + (week + I(week^2) | subject_id) Data: sim_dat  REML criterion at convergence: 114  Scaled residuals:      Min      1Q  Median      3Q     Max  -1.9343 -0.3980 -0.0075  0.4168  1.9928   Random effects:  Groups     Name        Variance  Std.Dev. Corr         subject_id (Intercept)   1.51524  1.2309                          week         61.01832  7.8114   0.16                   I(week^2)   496.20236 22.2756  -0.19 -0.95  Residual                 0.05892  0.2427              Number of obs: 100, groups:  subject_id, 20  Fixed effects:                            Estimate Std. Error       df t value       Pr(&gt;|t|)     (Intercept)                  3.1331     0.4226  17.9961   7.413 0.000000713699 *** week                        -1.2465     3.5210  18.0053  -0.354          0.727     mutation_statusY             0.5061     0.5977  17.9961   0.847          0.408     I(week^2)                   34.5706    10.8146  18.0084   3.197          0.005 **  week:mutation_statusY       -1.0697     4.9795  18.0053  -0.215          0.832     mutation_statusY:I(week^2) 202.5521    15.2942  18.0084  13.244 0.000000000101 *** --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  Correlation of Fixed Effects:             (Intr) week   mttn_Y I(w^2) wk:m_Y week        -0.160                             muttn_sttsY -0.707  0.113                      I(week^2)    0.145 -0.966 -0.103               wk:mttn_stY  0.113 -0.707 -0.160  0.683        mtt_Y:I(^2) -0.103  0.683  0.145 -0.707 -0.966  Code for data simulation: set.seed(123)  # set the seed J &lt;- 20  # number of individuals (clusters) cs &lt;- 5  # number of time points (cluster size) gam &lt;- c(0, 0.75, 1.34)  # fixed effects G &lt;- matrix(c(1.75, 0, 0,               0, 0.0125, 0,               0,0,0.0625),              nrow = 3)  # random effect variances (G-matrix) sigma2 &lt;- 0.08  mutation_status &lt;- rep(0:1, each = 5) mutation_status &lt;- rep(mutation_status, times = 10)  X &lt;- cbind(1, seq_len(cs),             (seq_len(cs))^2)  # for each individual X &lt;- X[rep(seq_len(cs), J), ]  X &lt;- X[rep(seq_len(cs), J), ]  X[,2] &lt;- X[,2]*0.05 X[,3] &lt;- X[,3]*0.05  # repeat each row cs times pid &lt;- seq_len(J)  # individual id pid &lt;- rep(pid, each = cs)   # Generate person-level (lv-2) random effects uj &lt;- lmf::rmnorm(J, mean = rep(0, 2), varcov = G)  # Generate repeated-measure-level (lv-1) error term eij &lt;- rnorm(J * cs, sd = sqrt(sigma2))  # Compute beta_j's betaj &lt;- matrix(gam, nrow = J, ncol = 3, byrow = TRUE) + uj  # Compute outcome: y &lt;- rowSums(X * betaj[pid, ]) + eij + mutation_status*X[ , 3]*10 + 3  # Form a data frame sim_dat &lt;- tibble(y, time = X[ , 2], pid, mutation_status) sim_dat &lt;- sim_dat[,c(3,2,4,1)] colnames(sim_dat) &lt;- c(&quot;subject_id&quot;, &quot;week&quot;, &quot;mutation_status&quot;, &quot;fetal_weight&quot;) sim_dat$week_2 &lt;-sim_dat$week*5 + 15  sim_dat$mutation_status &lt;- as.factor(ifelse(sim_dat$mutation_status == 0, &quot;N&quot;, &quot;Y&quot;)) sim_dat$subject_id &lt;- as.factor(sim_dat$subject_id ) #Model Building Why must the eigenvalue of the number operator be an integer? My apologies if this question has already been answered. Using the notation of Sakurai, we have an energy eigenket N and an eigenvalue n.  $$N | n \rangle = n | n \rangle$$  For the number operator $N = a^\dagger a $. My question is precisely why does n have to be an integer. I do understand that it must be positive definite due to the norm condition on $ a | n \rangle $:  $$\langle n | a^\dagger a | n \rangle \geq 0$$  I can see that we can show:  $$ a | n \rangle = \sqrt{n-1} | n-1 \rangle $$ and similarly for $a^\dagger | n \rangle$  Sakurai argues that the sequential operation of $a$ operators leads to the form which he does not write, but I will write here for clarity:  $$ a^k | n \rangle = \left(\sqrt{n}\sqrt{n-1}...\sqrt{n-k+1}\right) | n - k + 1 \rangle $$   Since  $$ a|0 \rangle = 0 $$  the sequence must terminate, but can only terminate if n is an integer. How can we make that jump? Is there a formal mathematical proof that the sequence $\left(\sqrt{n}\sqrt{n-1}...\sqrt{n-k+1}\right)$ will terminate if and only if n is an integer? when calling SCP in PuTTY on my Win7 box, it doesn't let me use C:/, but I also have no idea where on my local machine it will look for files by default. None of program directory or user directory worked. For example, I saved file.txt next to PuTTY.exe, and also in C:\Users\Me but calling SCP file.txt file.txt in PuTTY failed both times with      cp: cannot stat 'file.txt'   So, how do I transfer a file to my server using PuTTY?  EDIT: Also, calling SCP file.txt myserver:file.txt gives a similar error: file.txt: No such file or directory I'm working through Knuth's Metafont Book as preparation for learning Metapost and I'm running into some problems working through his "experiments".  I've installed the latest TeX Live 2013 distribution on my system but I'm having problems.  Here's the code (contained in file io.mf as recommended by Knuth):  mode_setup;  em#:=10pt#; cap#:=7pt#;  thin#:=1/3pt#; thick#:=5/6pt#;  o#:=1/5pt#; define_pixels(em,cap); define_blacker_pixels(thin,thick); define_corrected_pixels(o);  curve_sidebar=round 1/18em; beginchar("O", 0.8em#, cap#, 0); "The letter O";  penpos1(thick,10); penpos2(.1[thin,thick],90-10);  penpos3(thick,180+10); penpos4(thin,270-10);  x1l=w-x3l=curve_sidebar; x2=x4=.5w;  y1=.49h; y2l=-o; y3=.51h; y4l=h+o;  penstroke z1e{down}..z2e{right}             ..z3e{up}..z4e{left}..cycle;  penlabels(1,2,3,4); endchar;   Now, when running the mf command and loading this file, I get a window that is unfortunately empty.  Supposedly a large letter "O" should appear.  $ mf This is METAFONT, Version 2.718281 (TeX Live 2013) **io (io.mf The letter O [79]) *end Output written on io.2602gf (1 character, 1724 bytes). Transcript written on io.log.  $ gftodvi io.2602gf  gftodvi: fatal: tfm file `gray.tfm' not found.   Then, when trying to use the gftodvi command I get the above error.   Any ideas why my "window" that should display the letter "O" is blank/empty? How do I resolve the gray.tfm error? Are the two related?   Note: I'm using Ubuntu 14.04, but the TeXLive installation is NOT from the Ubuntu repository.  I used the installer from  and created a local "portable" installation. Hi I'm traveling to Uzbekistan and have 12 hours layover in Seoul via Korean Airlines. Do I need a visa to go out of the airport for sightseeing? I'm a Philippine passport holder.