So gravity is a force, and when it pulls on an object the object gains kinetic energy. However, doesn’t this mean that energy is being “created”, since the object gains kinetic energy?  Why doesn’t this violate the first law? It seems that energy is just created and then destroyed (when the object stops moving). Please don’t be too complex in explaining, as I do have some knowledge but am not an expert.  Also, isn’t potential energy not really energy, just a way of keeping track of the energy an object has? Doesn’t that make it not a justifiable response for this?
I would like to know where gravity gets its energy to attract physical bodies?  I know that the law of conservation states that total energy of an isolated system cannot change. So gravity has to be getting its energy from somewhere, or else things like hydropower plants wouldn't be able to turn the power of the falling water into a spinning rotor.  Just to be clear, Lets create an example:  Lets say we have two objects with equal mass close to each other. So gravity does its job and it pulls each other closer, this gets turned into kinetic energy. This is where I'm lost. According to the law of conservation energy can't be created or destroyed and the kinetic energy comes from the gravitational pull so where does the gravitational pull gets its energy.  If that energy isn't being recycled from some where else then that means you have just created energy, therefore breaking the law of conservation.
Simulating a Brownian Excursion using a Brownian Bridge? I have applied recently for a general visitor visa to the UK to spend 10 days during Christmas with my British unmarried partner and it has been turned down.   The Entry Clearance Officer stated on his refusal notice the following:     I note that you have never previously travelled to the UK or any country with similar immigration requirements and you therefore do not have a history of travel and compliance to consider.      You have submitted an employment letter to confirm your occupation in KSA but I am required to also assess your personal, domestic and economic circumstances in determining whether you are genuine visitor travelling to the UK for the period and purpose you state.      You claim an income of SAR ........ per month which equal ........ GBP and from the evidence submitted this appears to be your sole source of income.   I note that this monthly income is reflected on your bank statements. However, the bank statement you have presented show a recent large deposit that are in excess of your stated income and inconsistent with the account history. You haven't provided evidence toward the origin of this recent deposit and in the absence of reasonable evidence I am not satisfied that these bank statements accurately reflect your personal circumstances.      In view of the above, I am not satisfied you have demonstrated that your circumstances are as you claim and therefore I am not satisfied that you're travelling to the UK for the period and purpose you stated. 41(i)and(ii).   Its true that I have deposited that sum of money right before I apply and it was a commission I received from work earlier this month.   So, could you please give me your advice on the above as I am planning to apply again soon. and how to avoid my application being refused again? Give us better search-by-score syntax Variational Derivation of Schrodinger Equation I want to show that for $S,T\in B(H)$ bounded operators on Hilbertspace with $S\geq 0,T\geq 0$ and $ST=TS$,  we have $S+T\geq 0$, and $ST\geq 0$.  $T\geq 0$ means $(Tx,x)\geq 0$.    To me it seems that $((S+T)x,x) = (Sx,x)+(Tx,x)\geq 0$. But for $ST$ i like some help.   There is a theorem in Rudin (12.32) that says that for every $T\in B(H)$ we have an equivalence:   $T$ is positive $\Leftrightarrow$ $T$ is self adjoint, i.e. $T=T^*$ and $\sigma(T)\subset [0,\infty)$.   Since $S, T$ are self adjoint we know that $ST=TS = S^*T^* = T^*S^*$ ($ST$ is selfadjoint since $S,T$ commute). Also I read somewhere that if $S,T $ commute then $\sigma(ST)\subset \sigma(S)\sigma(T)$, but I am not sure if this is true. Clearly I cant prove it, but if it were true by this ''Theorem'' it would follow that $ST \geq 0$.   Is there a more straightforward way? Where can I see my full list of Questions and Answers in my profile page of Stack Exchange Android App? I want to see all my Questions and Answers in a particular SE site -  - profile page through Stack Exchange Android App. How can I see that? When I tried to see that I found only Top Posts(5) and Top Tags. Manually change filetype icons in Windows 7 I'm trying to find the dialog tab in Windows 7 that allows a user to change the icon used for a particular file type.  In Windows XP it would be under the Folder Options properties dialog.    Where is it on Windows 7?  I only want to change the icon of a specific filetype, to anything I want but this tab is no longer present in Folder Options of Windows 7. I have been studying the pronunciation of Greek-derived words in English, and I've found an odd anomaly. There are (at least) two possible pronunciation patterns for plural word-forms that end in -&#8288;mata (which correspond to singular word-forms that end in -&#8288;ma).   Antepenult stress (expected)  It appears that it is always possible to place the stress on the antepenult (third-to-last) syllable, such as:    /ˈlɛmə/, /ˈlɛmətə/  /ˈskiːmə/, /ˈskiːmətə/  /ˌtɛrəˈtoʊmə/, /ˌtɛrəˈtoʊmətə/~/ˌtɛrəˈtɒmətə/  /ˈstɪɡmə/, /ˈstɪɡmətə/   This is what would be expected from  (I believe most or all of these words came through Latin before entering English), since the penultimate "a" in the original Greek words is short.  Maybe Latin vowel quality and stress rules are not very relevant; certainly, few English speakers know about them nowadays. And even with antepenult stress, some of these pronunciations do not seem to follow all of the traditional rules for pronouncing Latin-derived terms in English. I was reminded by some comments in this  that  in antepenult stressed syllables, we would expect tense ("long") vowels to be shortened due to  (TSL), yielding pronunciations like /ˌtɛrəˈtɒmətə/ (which I just noticed is in fact listed in the Oxford English dictionary) and ?/ˈskɛmətə/ (which is not). (Compare to genus~genera /dʒiːnəs/~/dʒɛnərə/, and perhaps opus~opera /oʊpəs/~/ɒpərə/). However, there are other Latinate plural forms that typically don't have trisyllabic laxing (matrices, also I think helices), or where both the lax- and tense-voweled pronunciations coexist (codices, apices), so I guess the apparent lack of it in schemata should not be surprising. (There are even some exceptions to TSL in singular nouns like obesity.)  Penult stress (unexpected)  The other pronunciation seems to exist only for a couple of words, in which the penultimate "a" is commonly stressed and broadened: stigma ~ stigmáta  (listed by both the Merriam-Webster dictionary and the ), and also sometimes schéma ~ schemáta /skiːˈmɑːtə/ (listed only by the ). (Neither the Merriam-Webster dictionary nor the Oxford Learner's Dictionaries list *"lemmáta").  I'm wondering why this pronunciation exists. It's an irregular plural either way, and putting the stress on the penultimate syllable creates a stress change between the singular and the plural forms.  (It's true that all of these words are rare, and some people might pronounce some of their plurals differently. The pronunciations I give here are simply the ones listed in dictionaries.)  The plural form "stigmata" is probably most common in religious or theological contexts (where it refers to the wounds of Christ), so at first I wondered if the penultimate stress was supposed to be closer to the original Greek pronunciation, but according to , the stress is on the antepenult in Greek as well.  So, what's up with this? Did the stress perhaps change in Latin over time, is this a tradition of Greek accentuation that I'm not familiar with, is this a simple matter of ignorance of the original position of the stress that has now become entrenched with time and usage, or is this somehow explainable by established English stress patterns? (For example, do English speakers have some natural preference for a penultimate stress on polysyllabic words?)  If nobody knows of a reason, I suppose I can just put it down to people encountering the word mainly in text, not knowing which syllable to stress, and choosing the penult because it sounds better to them.  (I asked this question a while back on , but nobody knew of any reason.) I've installed VM VirtualBox v. 4.3.8 on my Ubuntu 12.04 LTS (Lenovo G500S with Intel 1005M processor) and I can't configure any 64-bit guest (nor Windows, neither other OS). Inslalation of Win 8.1 64-bit under 32-bit profile obviously fails... My processor supports VT-x technology, but in my BIOS there is no enable/disable option for VT-x. Is there any way to force VirtualBox to support 64-bit guest ? Why we can't implement AES 512 key size? Out of curiosity why we can't implement AES 512 key size?    Please explain somehow i can understand! I'm not an expert. "On their back" or "on their backs"? After the therapy, eight children (43%) became able to crawl/move on their back.   Or should I use "on their backs"?   Singular because each child only has one back, or plural because we're dealing with eight backs? Why is there a mismatch between size reported by LVM and the size reported by df -h? I'm new to LVM and have been very confused by this:  I am transfering a large file to a partition that I thought had about 1.5 terabytes of space on it.  Near the end of the transfer, rsync exits with an error claiming that the partition is full.  I investigate and find the following:  $ sudo lvm lvs   LV        VG     Attr   LSize   Origin Snap%  Move Log Copy%  Convert   home      system -wi-ao  97.66G                                         log       system -wi-ao  48.81G                                         log.audit system -wi-ao   9.75G                                         root      system -wi-ao 341.59G                                         swap      system -wi-ao   4.88G                                         temp      system -wi-ao  97.66G                                         var       system -wi-ao   1.46T     This seems to imply that /var (the partition that I'm transfering to, has the amount of storage I expect.  However, then I see:  $ sudo df -h Filesystem            Size  Used Avail Use% Mounted on /dev/mapper/system-root                       331G  1.3G  313G   1% / /dev/mapper/system-temp                        95G  188M   90G   1% /tmp /dev/mapper/system-var                        95G   90G     0 100% /var /dev/mapper/system-home                        95G  188M   90G   1% /home /dev/mapper/system-log                        48G  264M   45G   1% /var/log /dev/mapper/system-log.audit                       9.5G  340M  8.7G   4% /var/log/audit /dev/sda1              99M   25M   70M  26% /boot tmpfs                 8.0G     0  8.0G   0% /dev/shm   I'm guessing this has something to do with the volume being resized at some point.  While I have reliable backups, I'd rather not interrupt services for the time it will take to get the backup and restore.  Thus, is there anyway to make the filesystem seen by the OS match the space available according to lvm without losing data? sf:INVALID_OPERATION: INVALID_OPERATION: testLevel of NoTestRun cannot be used in production organizations While deploying code in vsCode from sandbox to production I get the below error      sf:INVALID_OPERATION: INVALID_OPERATION: testLevel of NoTestRun cannot   be used in production organizations   As per the error, I need to change the value of testLevel but I am not able to find where and how can I change it to RunLocalTests  Could someone please help me to change the value of testLevel in vsCode How do you install Google Chrome on Ubuntu? Can you re-equip equipment to the same creature? Why would one suppress the intercept in linear regression? In a number of statistical packages including SAS, SPSS and maybe more, there is an option to "suppress the intercept". Why would you want to do that? How do I prove or disprove $X \times (Y \cup Z)= (X \times Y) \cup(X\times Z)$  for all sets $X$, $Y$, and $Z$? I'm lost on the steps here. Why does the Stern–Gerlach quantum spin experiment conflict with classical mechanics? My understanding of the Stern–Gerlach experiment is that neutral (0 total charge) particles are sent through a non-homogeneous magnetic field, with the expectation that the field will push that particle's path higher or lower on a detector because of the collective spin of that particle. While the detector can detect particles in a two-dimensional surface, the results of the experiment are that particles appear in only two localized areas directly above the path of the particle stream, or directly below the path of the particle stream - spin up or spin down. The conclusions from these measurements are that the particle, when measured, will always have about the same magnitude.  Why does this not follow from classical mechanical theory related to magnetism? If you shot a magnet through a similar apparatus, I would expect the magnet to be rotated to align with the magnetic field in some way which, at high enough field strengths relative to the mass of the magnet, would cause us to measure basically the same magnitude as if the magnet entered the apparatus pre-aligned with the field.  How is my explanation incorrect? Does the equivalence $$\neg\neg (P \rightarrow Q) \leftrightarrow (\neg\neg P \rightarrow \neg\neg Q)$$ hold in propositional intuitionistic logic? In propositional classical logic the equivalence holds obviously since $P \leftrightarrow \neg\neg P$. However, the similar-looking implication $\neg\neg (P \vee Q) \rightarrow (\neg\neg P \vee \neg\neg Q)$ is . The validity of the backward implication comes up in  as well. Is there any way to create a simple txt file without opening the terminal? Is there any way to create a text file without using the terminal at all?