I was reading this today:  We look forward to following your progress.  Am I correct in thinking that it is missing a be or that -ing should be removed?  So  We look forward to be following your progress.  or  We look forward to follow your progress.  Interestingly I get the same jarring feeling when reading the examples here
Some verbs are followed by ing, e.g. I enjoy swimming. We can't say I enjoy to swim. Likewise, some verbs are followed by to, e.g. I decided to make a plan.   Which particular verbs are followed by ing and to? Can you please provide a list for that?  Moreover, which verbs can be followed by both without having the meaning changed?
I noticed that I have three warnings when I submitted my Sitemap. They all say this:      When we tested a sample of URLs from your Sitemap, we found that some   URLs redirect to other locations. We recommend that your Sitemap   contain URLs that point to the final destination (the redirect target)   instead of redirecting to another URL.   I'd like to try and resolve this issues but I'm not sure what to do.  Sitemap url for reference: Prove that $\det(M-I)=0$ if $\det(M)=1$ and $MM^T=I$ $M$ is a $3 \times 3$ matrix such that $\det(M)=1$ and $MM^T=I$, where $I$ is the identity matrix. Prove that $\det(M-I)=0$  I tried to take $M$ $=$ $$ \begin{pmatrix}         a  &amp;b &amp; c \\         d &amp; e &amp; f \\         g &amp; h &amp; i         \end{pmatrix} $$   but its expansion is too long. 'help' link is located lower than the other items It shows like this on Firefox 25 and Internet Explorer 11 (minus the red line of course):    Chrome seems to be fine. I have the Basic license for ArcGIS and so I cannot use the collapse dual lines to centreline tool or the river bathymetry toolset by ESSA as they both need an advanced license.   Any idea how I can find the centreline or thalweg of the canyons using another tool which works in the standard version of ArcGIS please? Incorrectly answered 'No' to "Any previous visa refusals..." on a UK Standard Visitor visa application. How can I fix my mistake? I'm from Lebanon and I've been working in Saudi Arabia for nine years. In 2012, I put the money that I collected from my job as a teacher in my father's Lebanese account since I didn't have one in Lebanon. During the interview, my interviewer told me that my application will be rejected because I don't have proof that this money is mine and clearance officer will think someone else gave me the money. I didn't know that I had to bring with me from Saudi Arabia an employment letter and bank statements to prove that this money is mine and I earned it by working in Saudi Arabia. Anyways, my visa did get refused as my interviewer had told me it would be.    Last May, I was granted a US visitor visa Multi Entry for 5 years. I wanted to visit the US in August for 10 days but my mom entered the hospital so I had to postpone it. Now I'm applying for a teacher training program in the UK. I received an invitation letter from Brighton University and so I applied for a UK Standard Visitor visa. After I paid and printed the application, I realized that I answered the question Any previous visa rejections ... with "NO" and I don't know how should I fix this.  Please note that I still didn't give my biometrics, I still didn't use my US visa which I received on May 2016, I paid for my application so I can't amend it online. I'm supposed to give my biometrics and submit my documents this Monday.  If I don't say anything will they check it and refuse me?    Will my US visa be an advantage and they will disregard the previous rejection or should I correct it when I submit my documents this Monday? In many experiments in quantum mechanics, a single photon is sent to a mirror which it passes through or bounces off with 50% probability, then the same for some more similar mirrors, and at the end we get interference between the various paths. This is fairly easy to observe in the laboratory.  The interference means there is no which-path information stored anywhere in the mirrors. The mirrors are made of 10^20-something atoms, they aren't necessarily ultra-pure crystals, and they're at room temperature. Nonetheless, they act on the photons as very simple unitary operators. Why is it that the mirrors retain no or very little trace of the photon's path, so that very little decoherence occurs?  In general, how do I look at a physical situation and predict when there will be enough noisy interaction with the environment for a quantum state to decohere? Limit of Multivariate Probability Density Function as one or more or all variables approach positive or negative infinity Could someone point out a good source or provide justification as to whether the limit of a multivariate probability density function, as one or more or all variables tends to positive or negative infinity, goes to zero.  $$\lim_{x_{1}\to\pm\infty}f(x_{1},x_{2},...,x_{n})=0$$  $$\lim_{x_{1},x_{2}\to\pm\infty}f(x_{1},x_{2},...,x_{n})=0$$  $$\lim_{x_{1},x_{2},...,x_{n}\to\pm\infty}f(x_{1},x_{2},...,x_{n})=0$$  I have found this related question for the univariate case: The reason that I ask is because this is happening to LiDAR, and I am inclined to use lidar because it is easier to read. How do I complete the square from the point I have left off at, and is this correct so far?   I have a normal prior for $\beta$ of the form $p(\beta|\sigma^2)\sim \mathcal{N}(0,\sigma^2V)$, to get:  $p(\beta|\sigma^2)=(2\pi\sigma^2V)^\frac{p}{2}\exp[-\frac{1}{2\sigma^2}\beta^T\beta]$  where $\beta^T\beta$ is   $\sum\limits_{i=1}^p \beta_i^2$.  My likelihood has a normal distribtuion for the data points y of the form $p(y|\beta,\sigma^2)\sim\mathcal{N}(B\beta,\sigma^2I)  $  $p(y|\beta,\sigma^2)=(2\pi \sigma^2V)^\frac{n}{2}\exp[-\frac{1}{2\sigma^2}({\bf y}-{\bf B}{\bf \beta})^T({\bf y}-{\bf B}{\bf \beta})]$  (Note that $\beta$ is a matrix/vector too, \bf does not work.)  To get my posterior for $\beta$ I combined the above, took the exponential parts only, and then expanded to get:  $\exp[-\frac{1}{2\sigma^2}({\bf y}^T{\bf y}-{\bf y}^T{\bf B}\beta-\beta{\bf B}^T{\bf y}-\beta^T{\bf B}^T{\bf B}\beta)]\exp[-\frac{1}{2\sigma^2}({\bf \beta}^T{\bf B})]$.  I dropped the $({\bf y}^T{\bf y})$ term, as is not a function of $\beta$.  Putting into one expression without the exponential:  $-\frac{1}{2\sigma^2}(-{\bf y}^T{\bf B}\beta-\beta{\bf B}^T{\bf y}-\beta^T{\bf B}^T{\bf B}\beta+{\bf \beta}^T{\bf B})$.  I know I need to combine the similar terms and get into the form of the multivariate normal distribution, which is what I am aiming for, but I am unsure how to do this? I probably have to add an extra term to the expression to get it into the correct form?  Note: This is not homework, it's a project, but my Bayesian working knowledge is not good at all and so I need to understand the working out. I intend to integrate out the $\beta$ and then the $\sigma^2$ after getting into the multivariate form. Does it feel lately like all questions have already been asked and answered and there is nothing more to do? I think everybody with a history of participation can't help but notice the explosive growth of repeated duplicate questions. The work of looking for duplicates and then closing questions has overtaken the work of actually answering questions.  It's become virtually impossible to ask something which hasn't been yet asked. Lately I feel boredom each time I see a new question and start answering it only to realize after the first written sentence that I have answered similar questions five times over or seen them answered some ten times or more. I know where it's going to be going and what answers with what votes it is going to receive before any answer is even written.  It's obviously not the administration's fault, it is simply so. The questions is, what to do about it? Engaging more moderators to close and close duplicates won't work because it's already starting to repel users who get mad at their questions closed and become afraid of asking more or perhaps just go away.  The original idea of Jeff stated the the site is for questions that can be answered. Meaning no open-ended discussions. When I first read this I had a casual thought - well, and what's gonna happen when they all are asked and answered? Will it become a museum, a monument of wisdom and knowledge or what?  I'm not sure what to do about it. Perhaps deprecation/versioning of older questions so that their new versions can sparkle the tiresome evening...  POSTSCRIPTUM.  I recall Star Trek Voyager episode  when another Q asked Captain Janeway for asylum. He was tired of immortality and wanted to die. They opened a hearing and went on to visit the continuum to evaluate the living conditions there which caused the suffering and the wish to escape it in death. A lifeless picture presented itself to the visitors... a house lone in an open space, two people going about their business, nobody talking. When asked why they were silent, the following was said. It's been so long, all has already been said, all stories told, all jokes are made... there is nothing left to do...  Are we there as well?  UPDATE: Just saw this answer in another question:       Also, some of the core questions got asked early on in the life of the site. Great questions still come around from time to time, but many have already been asked.   Doesn't that confirm my point? Can a person negotiate with banks on CD interest rates? I use a brick and mortar bank for some of my savings. I’d love to get a CD interest rate closer to what Ally or other online banks offer.   Are brick and mortar banks will to negotiate with customers on interest rates? For instance, if I went into a branch and said I’m moving my money to Ally unless the bank matches Ally’s rates, do I have any chance of getting them to? Group theory proof of existence of a solution to $x^2\equiv -1\pmod p$ iff $p\equiv 1 \pmod 4$ I've read through the elementary proof of why there exists a solution $x$ to $x^2\equiv -1\pmod p$ iff $p\equiv 1 \pmod 4$ for $p$ an odd prime. Is there a group theory generalization for this fact as well? I'm wondering if there's a simple way to rewrite this in terms of $k$ and $x$, especially as a polynomial. It seems to me to crop up every so often, especially for $k=2$, when I integrate with trig substitution. But $k=2$ is not so bad, because I can use the double angle formula; it's the prospect of higher values of $k$ that motivates this question.   I think the law of sines may help? Or maybe even De Moivre's theorem, to find the length of the hypotenuse as the length of the angle changes, if we think of the right triangle drawn from $\arcsin(x)$ with side1 = $x$, hypotenuse = $1$, and side2 = $\sqrt{1 - x^2}$ as a complex number, though I'm not sure how that might work. We had a rule check tonight that we couldn't answer. On the Pathfinder wiki I could only find info on natural 20s and 1s in regards to attack rolls and saves in combat.  Do they also apply to skill checks? Why is there a peeking duck in my profile pic? What determines color -- wavelength or frequency? Does an Animagus's animal form change along with their Patronus? In the two examples shown of an Animagus capable of casting a corporeal Patronus (Minerva McGonagall and James Potter) both had the same animal as their Patronus and as their Animagus animal.  Now, it is also shown that extreme circumstances can change one's Patronus. I think the only example of this was Tonks, which turned from a jackrabbit into a wolf in response for her love of Lupin.  If Tonks (or any other wizard who had their Patronus change) had been an animagus, would her animagus have changed as well? What is the Stack Exchange (Staff) process of launching a site? Is there a way to view Google Chrome browsing history past three months ago? I'm trying to find a page I looked at months ago but it looks like it's disappeared off the face of the planet. I thought I would have better luck looking through my Google Chrome browsing history, but I can't see history past September. Can I force Google Chrome to display history further into the past? Can I retrieve the history manually from a directory? Is the history data gone? "Much more easy" versus "much easier"