I have difficulty understanding the following sentence: -Or does it somehow lie behind its properties, supporting them, a solid peg on which they happen to hang. Please help me grasp what the present participle function here, together with why a noun phrase followed by a relative clause stands alone. Thank you!
It is generally taught that  function as adjectives modifying a noun (or pronoun).  In a sentence such as:     A major accident occurred on our bus's route to school, making us late for class.   or     The gas tank exploded, sending shrapnel through the air.   are the participle phrases modifying their preceding clauses? (If not, what are they modifying?)
Match-3 algorithm to fill empty space left from removing matches I am currently creating a match 3 game.   I am at the point where I have objects dropping down in the column when only one item is removed. So if an item is removed, the above item moves into its old position etc.  The problem I am having now is that when more than one item is removed from a column, the items in that column only drop down to the first item that was removed. Instead of filling in both items that were removed it just drops down to fill in the first one.   So basically, if two(or more) items are removed from a column the second, third, fourth, etc positions are left blank.  The way I am designing my game is I am using units of 1. So each item takes up 1 unit by x and 1 unit by y. This means that I can position the items like in a grid, at 0x1, 0x2, etc.   What kind of algorithm could I use to move multiple items down to fill the empty space? Does RSA work for any message M? This is the announcement post of the Stack Exchange Data Explorer. Its answers were meant to iron out the initial glitches 6 to 8 years ago.  If you have found a bug or need support  today with any of SEDEs features, please ask a new question and tag it with   What does it do? Allows you to run arbitrary SQL queries on the data dumps, and share those queries with your friends. Technical details It is hosted on the Stack Exchange infrastructure , the database is hosted on the same SQL Server version all other sites are hosted on. You can use most of the TSQL commands, even create temporary objects (but not User Defined Functions). The controls used are jQuery based, the grid is  . All query results are cached, so sharing a link to a query will not result in the server going in to a tailspin. The query edit control is a slightly modified  control, I also am considering bespin cause the inter iframe communication is nasty complicated. It gives up nice syntax highlighting for queries. Parameters There is support for parameterized queries, to get it to work name your params like ##this##. For example have a . Query name and description A query can have a name and description, to name it lead with a comment, to describe it continue commenting, for example: -- This is my query name  -- This is my description -- I can span multiple lines  SELECT 1  Anonymous users can initially name a query, but can not change the names of any existing queries. Tutorial There's a  which helps you getting started in writing your own SQL queries. Logging in You can use your openid provider to log in, at the moment once logged in we will track the list of queries you execute (giving you basic history support) Also if there are any params named UserId they will be populated automatically if your EmailHash matches the one on the site being queried. Magic columns If you alias an id column with as [Post Link] it will automatically create a link in the result set to the parent site. Similarly if you alias an id column with as [User Link] it will display a link to the user page. select top 10 * from Posts will show you how tags are done. (Magic columns for images is planned) example (most controversial posts:  ) So what are you waiting for, check it out at  Any feedback would be greatly appreciated. I hope to have the login section working fairly soon and allow voting on the best queries and commenting. Featured Queries At the moment, admins have permission to feature interesting queries on this page , I am looking for better ways to manage the huge query list that is building up. After restarting my computer when I am presented with the initial login screen (the light gray one with the restart and shut down buttons), I see only two of my three user accounts.  If I log in with one of these accounts, I can see, and log in to, the third (missing) account by either:   Logging off (Apple > Log Out...) to reach the second login screen (the dark gray one with sleep/restart/shut down buttons) Clicking on the fast user switching menu.   How can I restore this account in the initial (light gray) login screen?  I tried repairing disk permissions to no avail.  If I create a new account, it does show up in the list. If $\operatorname{ran} F \subseteq \operatorname{dom} G$, then $\operatorname{dom}(G \circ F) = \operatorname{dom} F$. Basic mathematical induction regarding inequalities I try to search for lines that start with "1" using   ls -1 | grep ^1*   but it returns lines that do not start with 1. What I am missing here? Fluent and Query Expression — Is there any benefit(s) of one over other? Why my U.S. B1 Visa got refused under 214 (b)? I went for B1 U.S. Visa at the U.S. Embassy in Delhi.   Interviewer: *Good Morning*. Me: *Good Morning* Interviewer: *What is your designation?* Me: *I am a Software Engineer.* Interviewer: *What is the name of your company?* Me: *It is XXX (I replied).* Interviewer: *What is the name of your client?* Me: *It is YYY (I replied).* Interviewer: *Have you ever been to U.S. before?* Me: *NO* Interviewer: *Have you ever been abroad before?* Me: *NO*   At this point he rejected my Visa with letter mentioning 214 (b) as the reason. I don't know why he actually rejected it.  But, I have decent 2+ years of experience with my company. And, I was going on a business meeting with the client. I would have come back after 2 weeks.  I don't know if re applying will help. Any class of a nonempty $X$ generates a base for a topology on $X$. Theorem Any class $\mathcal{A}$ of subsets of a nonempty set $X$ is the subbase for a unique topology $\tau$ on $X$. That is to say, the finite intersections of members of $\mathcal{A}$ form a base for the topology $\tau$ on $X$. Example Consider $X=\{a,b,c,d\}$ Let $\mathcal{A}=\{\{a,b\},\{b,c\},\{d\}\}$ The finite intersection of members of $\mathcal{A}$ give us: $$\mathcal{B}=\{\{a,b\},\{b,c\},\{d\},\{b\},\varnothing,X\}$$  How is it true that $X \in \mathcal{B}$ ? By definition of subbase, the finite intersection of members of $\mathcal{A}$ are the members of some base $\mathcal{B}$. But for $a_i \in \mathcal{A}, \displaystyle\bigcap a_i \neq X$ for any finite intersection of $a_i$'s. Look: $\{a,b\}\cap\{b,c\}\cap \{d\} \neq \{a,b,c,d\}$ nor do any other intersection of elements of $\mathcal{B}$ result in $X$. Anybody know what's going on here? Why is $X \in \mathcal{B}$? How to avoid modifications during pg_dumpall Logic gate - What will be the second input of each gate? Full:    Cropped   :    In the second image (cropped) which is the same as the first (full) image... why the 1st Gate outputs "0"? Bind an element to two sources I currently have two text boxes which accept any number. I have a text block that takes the two numbers entered and calculates the average.   I was wondering if there was a way I could bind this text block to both text boxes and utilize a custom converter to calculate the average? I currently am catching the text changed events on both text boxes and calculating the average that way, but I am under the assumption data binding would be more efficient and easier. When using \textsc, LaTeX issues warning: Font shape `OT1/cmr/bx/sc' undefined I have a Python  object. What is the best way to subtract one day? Does RSA work for any message M? I decided to read the original RSA paper A Method for Obtaining Digital Signatures and Public-Key Cryptosystem because of a question I had about RSA (which is not the question I'm about to ask, but may be a question on here at some time) and came across something I had never seen before in any textbook description of RSA (Note: this comes from the beginning of ).  for any integer (message) $M$ which is relatively prime to $n$, $M^{\phi(n)} \equiv 1\pmod{n}$  The part I don't recall ever hearing in class, or coming across in a text book, or seeing in any description of RSA I've ever read is that $M$ and $n$ must be relatively prime. So, I decided to play around with a toy example of RSA to see what would happen. I use $p=13$, $q=31$, $e=7$ and $M=2p=26$ (for completeness: $d=103$, $\phi(n)=360$, $n=403$). I observed the following using my toy instance of RSA: $M^e\equiv M\pmod{n}$, $M^e\equiv 0\pmod{p}$ and $M^e\equiv M\pmod{q}$. Do these equivalences hold for all $M,p,q$ when $M$ and $n$ are not relatively prime? How would I prove this? What is the real-world effect of this? How to increase body height? I am an adult, and I want to be taller. I know about many medicines which claim to treat stunted height.  Is there any truth behind these? Asynchronous shell exec in PHP Let $({\Bbb R},{\mathcal A},\mu)$ be the measure space where ${\mu}$ is the Lebesgue measure.  Assume that $\int_{\Bbb R}|f|^pd\mu&lt;\infty$ ($p\geq1$). There is an exercise for proving that       $$\int_{[0,\infty)}pt^{p-1}\mu(\{x:|f(x)|\geq t\})d\mu(t)=\int_{[0,\infty)}\mu(\{x:|f(x)|^p\geq s\})d\mu(s).$$   If one formally let $s=t^p$, then $ds=pt^{p-1}dt$ and one would immediately get the equality above. However, how can I justify it rigorously in the sense of Lebesgue integration?    [Edited] What puzzles me is that I have the "change of variable" theorem for Riemann integration, but all the integrations here are in the Lebesgue sense. Unless one has shown that the integrands are also Riemann integrable, how can I directly use "change of variable"? Are $10\times 10$ matrices spanned by powers of a single matrix? I don't know how to answer this question:     Is there a $10 \times 10$ matrix $A$ such that $$M_{10}(\mathbb{F})=\text{span}\{I,A,A^2,\ldots, A^{100}\}\textrm{,}$$ where $M_{10}(\mathbb{F})$ is the vector space of $10 \times 10$ matrices over $\mathbb{F}$?   I think there is a connection to Jordan normal form.