Which one is correct - "Committed to help .." or "Committed to helping .."? Consider "I'm committed to help somebody to do something/with something." vs. "I'm committed to helping somebody. to do something/with something."
When should a verb be followed by a gerund instead of an infinitive? 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?
How to stop a sponge cake (chiffon cake) from deflating/sinking? Why do proof authors use natural language sentences to write proofs? I haven't read very many proofs. The majority of the ones that I've read, I've read in my first-year proofs textbook. Nevertheless, its first chapter expatiates on the proper use of English in mathematical proofs, so I suspect that most proof authors do use both English (or another natural language) and formal proof systems for writing their proofs. However, I can't imagine many circumstances where mathematical notation and a formal proof system wouldn't suffice to convey the author's pertinent thoughts.   I suspect that proof authors have good reasons for making use of both English and formal expressions in their proofs, but I can't think of what those reasons are. Why do proof authors use English and formal expressions to write proofs? Are there stylistic rules (or guidelines) that state how, and in what parts of the proof, an author should, and shouldn't, use English? I have installed an Ubuntu server on a VMWare workstation with a space of 20GB storage as seen below;    After the installation I've attached another 40GB worth storage to the existing Ubuntu server installation (seen below);    Now I want to add this 40GB to my / (root) directory or to /var/ directory but my df -h result shows;  root@Userver:~# df -h Filesystem      Size  Used Avail Use% Mounted on /dev/sda1        18G  900M   16G   6% / udev            990M  4.0K  990M   1% /dev tmpfs           400M  308K  399M   1% /run none            5.0M     0  5.0M   0% /run/lock none            999M     0  999M   0% /run/shm none            100M     0  100M   0% /run/user root@Userver:~#   What should I do now? Further, I have only ssh access to the server. Continued fraction of $e^{-2\pi n}$ I found this problem on a well-known problem solving website. It is apparently from Ramanujan.     With   $$\LARGE{a = \frac{1}{1 + \frac{e^{-2\pi}}{1 + \frac{e^{-4\pi}}{1 + \ddots}}}},$$   what is $a$?   The basic methods I know for questions of this type were not helpful to me.  I do not require a full solution, but feel free to post one if you would like. Hints or lecture notes on how to solve problems of this nature would be appreciated.   Keep in mind that I am at an undergraduate level in mathematics. If N and every subgroup of N is normal in G then G/N is abelian . Let $N$ be a normal subgroup of a group $G$ such that every subgroup of $N$ is normal in $G$ and $C_G(N)\subseteq N $. Prove that $G/N$ is abelian.   Here, as usual, $C_G\left(N\right)$ means the centralizer of $N$ in $G$ (i.e., those elements of $G$ that commute with everything in $N$).  I think we need to use that every subgroup of $N$ is normal in $G$ but i can't use .Please help me with Hints. Converting PostGIS point to text causing loss of data? I have a road network and want to test connectivity between the features.  I am having trouble with two specific features, the rest of the dataset is functioning just fine.  When I get those 2 links' start &amp; end locations using ST_StartPoint and ST_EndPoint, the result is that they are slightly different.  However, when I convert the result to text by wrapping it like so:  ST_AsText(ST_StartPoint(geom)) and ST_AsText(ST_EndPoint(geom))  then the results are exactly the same.  Is it possible they are actually off by a tiny amount like .000000001 and the ST_AsText loses a decimal point? I have a dual screen setup on my laptop (using 12.04 LTS) using a HDMI connected display. Everything works fine, but everytime I connect/disconnect the cable I have to go to Sound preferences and change the sound output device manually.  Is there any way to change the sound output device on connect/disconnection of cable, so when I connect my display the sound output is set to HDMI and when I disconnect it the sound goes back to laptop speakers? Why do microcontrollers have so little RAM? Maybe this is more of a perceptional problem, but it seems like microcontrollers have advanced by leaps and bounds in the last 20 years, in almost all regards, higher clock speed, more peripherals, easier debugging, 32-bit cores, etc...  It is still common to see RAM in the 10's of KB (16/32&nbsp;KB).  It doesn't seem like it could be an issue of cost or size directly. Is it an issue of complexity with the RAM controller above some threshold?  Or is it just that it isn't generally required?  Looking over a parts matrix at a popular Internet supplier, I see one  with 256&nbsp;KB for less than US$8, and then for a few dollars more you can find a few more that are ROMless, but it seems pretty sparse...  I don't exactly have a need for a microcontroller with a MB of volatile storage, but it seems like somebody might... Assume: $p$ is a prime that satisfies $p \equiv 3 \pmod 4$  Show: $x^{2} \equiv -1 \pmod p$ has no solutions $\forall x \in \mathbb{Z}$.  I know this problem has something to do with Fermat's Little Theorem, that $a^{p-1} \equiv 1\pmod p$. I tried to do a proof by contradiction, assuming the conclusion and showing some contradiction but just ran into a wall. Any help would be greatly appreciated. Escape Key in the Chat Does the sum of reciprocals of primes converge? Is this series known to converge, and if so, what does it converge to (if known)?  Where $p_n$ is prime number $n$, and $p_1 = 2$,  $$\sum\limits_{n=1}^\infty \frac{1}{p_n}$$ Using natural deduction to prove that $p \implies q \vdash \lnot p \lor q$ Using only rules of natural deduction, I am trying to prove that $$p \implies q \vdash \lnot p \lor q$$ but am having a lot of difficulty. I was able to prove the other direction.   Could anyone show me or point me to the right direction? Accessing raster attribute table in QGIS? I have some Python code that makes Raster Attribute Tables for GeoTiffs using GDAL.    In ArcGIS I can see these attribute tables fine and they behave how I like (as classifications) but in QGIS the whole concept of an attribute table seems to be missing.    Is there any way to access a RAT in QGIS? While playing Phase Ten, is it legal to pick up the top card of the discard pile and then immediately discard that exact card? Why does $\sum_{k=1}^{\infty}\frac{{\sin(k)}}{k}={\frac{\pi-1}{2}}$? Inspired by  (and far more straightforward, I am guessing), Mathematica tells us that $$\sum_{k=1}^{\infty}\dfrac{{\sin(k)}}{k}$$ converges to $\dfrac{\pi-1}{2}$.   Presumably, this can be derived from the similarity of the Leibniz expansion of $\pi$ $$4\sum_{k=1}^{\infty}\dfrac{(-1)^{k+1}}{2k-1}$$to the expansion of $\sin(x)$ as $$\sum_{k=0}^{\infty}\dfrac{(-1)^k}{(2k+1)!}x^{2k+1},$$ but I can't see how...  Could someone please explain how $\dfrac{\pi-1}{2}$ is arrived at? Seeking block (sub-district) level boundaries for India? I'm looking for block (sub-district) level shapefiles for India. The GADM database only has files for the 2300 Tehsils, whereas I'm looking for the about 5500 Census blocks (sub-districts) for any year possible. How to turn particle emission on/off? Is there a way to animate whether or not a particle emitter is emitting particles at a given point in time?  I'm using the particle system to animate bullets, so basically I'm trying to find a way to say: at frame 150 the gun fires a burst until frame 170, at frame 240 it fires a burst until frame 265, and so on.  I've tried key framing the particle render setting between "object" and "none", but the problem with that is that the hidden particles are still there, so when the render setting switches to "object", the particles that were initially hidden suddenly appear.  I've also thought of putting a plane (not rendered) with a collision modifier in front of the emitter and then moving it when I want the emitter to start emitting particles.  Is there a better way? Duplicate id in list My service is working fine for single record insert when i send bulk records at that time it showing soapenv:ClientSystem.ListException: Duplicate id in list: 01ti0000002gUP1AAM Class.Sample.behaviourOfWebService: line 235, column 1  the error line is Database.upsert(pList)     p.productCode = pCode;    p.name =pName;    pList.add(p);  } every planar graph can be expressed as a union of five edge-disjoint forests How can I prove that every planar graph can be expressed as a union of (maximum) five edge-disjoint forests?  Only thing I can think about is going somehow like the $5$ color theorem but I get stuck in the middle. Or with induction, but still something doesn't fit. Can you help? Integral ${\frac{1}{\pi^2}} \int_{0}^{\infty}\frac{{(\ln{x}})^2}{\sqrt{x}{(1-x)^2}} \mathrm d x$