Realtime PCR plate cleaning

Question: Have anyone used realtime PCR, is that the plate for realtime PCR is one-time using or not ? Otherwise how to clean the plate after reaction to prevent wrong result in next time using ?
Comment: ahh... it is usually used only for one round.. but if your experiment is not very sensitive then you can wash it in hot water and autoclave it. (I think they are autoclavable)
Comment: @WYSIWYG thank you so much, can you describe more what matter occur to DNA when they being autoclave ? Are they denatured ?
Comment: nothing happens to the DNA.. it might get damaged but we cant rely on that. autoclaving is just for making it sterile. hot water wash should remove the DNA.. you may use a mild soap/detergent too but make sure that none remains.
Comment: Ok, thank you so much, i hope it will work. Otherwise i will try another way to reuse the tube.
Answer: A possible solution is to use the DNA ZAP solution, which I know many people used in adjacent labs and were happy with for cleaning their DNA free workbench. The product sheet states

When 500 ng of template DNA is dried down in a PCR tube, it is rendered unamplifiable upon treatment with DNA ZAP solutions. Additional experiments demonstrate that the DNA is degraded down to free nucleotides.

Please note that I'm not promoting any specific product here and you can purchase any similar product/technology for your particular application. Obviously the best recommendation is to use new plates for each reaction but this/or a similar product can be an option too although the risk of DNA contamination in a PCR based reaction should be carefully balanced against simply using fresh plates considering the product itself is not free either.
The product sheet provides instruction for cleaning/treating PCR tubes hence I assume you use the same protocol for plates if you have the plate centrifuges available in your lab. You can get rid of the solutions by tapping the plates on a tissue to get the liquid out of the wells.
Comment: Honestly spoken I would never think about re-using the PCR plates. Sure, they are not for free, but the reagents of the assay aren't either. If you blow up one experiment because of a contamination (and you will likely use the same genes in an assay more than once), this is more expensive (plate, reagents, sample preparation) than what you save. Besides that, these commercial solutions aren't free either.
Comment: @Chris I 100% agree! I would personally never re-use anything for any reaction and its just best to use new consumables but just though I provide a possible solution to the OP question, which might also be of interest to others but again I agree with you and I would personally never re-use any consumables specially for reactions such as PCR!
Comment: @Chris I changed the language used in the response to highlight it as a possible solution and not a suggestion and clarified that the best thing to do is to use a new plate.
Answer: One of the claimed virtues of RT-PCR plates is their inability to bind DNA. (See for example the assortment at http://www.fisher.co.uk/product/brand_listing.php/T/Thermo%20Scientific%20ABgene/PCR%20plate ). As such, all you need to do to remove the DNA (genomic, amplified, or primers) is to rinse them. This suggests that rinsing may also work for dNTP.
On the other, many types of RT-PCR plates are made of polycarbonate, which is able to bind protein. I would be concerned about an uneven amount of polymerase sticking to the well. To go around that, you should re-use, in any PCR plate, only those wells that saw polymerase before.
I have no idea whether other molecules bind to the wells, but presumably they fall on the DNA or protein paradigm.
It will cost you only one plates and regents for as little as four reactions to test whether these plates are reusable. In the first run, measure two samples, A and B, for some transcript. Rinse the wells, and measure samples A and B again. If the transcript ratio A/B is the wildly different between first and second attempt, you know you can't reuse them. I would also be concerned if it will take many more cycles to reach the plateau stage at the second attempt. Passing these tests, you may be all set. Failing these tests, you may still be able to use the remaining wells. Let us know.
Comment: Welcome to Biology SE! Can you clarify what you are asking?

Realtime PCR plate cleaning


Corporate Domain-Joined PC Used in China

Question: What would be the disadvantages of allowing a user to travel to China (business trip) using a domain-joined corporate Windows PC as opposed to a non-domain-joined PC?
Answer: It's hard to find any reason why it would be advantageous to sending someone with a non-domain joined PC as opposed to a domain joined PC.
Domain joining a PC has several distinct advantages

Administrator can control update policies to software and anti-virus
Administrators can control firewall settings and VPN tunnels / routing
Policies of all sorts can be forced upon the machine easily and centrally administered (admittedly this can be done with some MDM's)
Full Disk Encryption can be enforced on the PC

I'm not sure why you would think there is any security disadvantage to this machine being domain joined.
SIDE NOTE : Simply working on the Internet in China poses no additional threat to your system than anywhere else in the world. I'm not sure why people have the misconception that as soon as your laptop hits the Internet in China it will be infected with MalWare. Keep your PC locked, don't hand it over to anyone without witnessing what they're doing to it and pay attention to certificate errors and you (or your employee) should be fine.
Comment: Small remark to your sidenote: Paying attention to certificate errors is a good point, but if your browsers trusts Chinese CA's then you might have a problem (e.g. https://en.greatfire.org/blog/2014/oct/apple-and-microsoft-trust-chinese-government-protect-your-communication). The risk for a government-sponsored MITM attack is an additional threat that might happen in China.
Comment: Also, you make the assumption that you have a choice in whether or not you can witness what they do to your laptop.
Comment: I non-concur with your "SIDE NOTE" assertion. What grounds do you base your statement that there is, effectively, a net-zero Internet-access risk differential between given geographical locations?
Comment: @Nick You've twisted my words. I said that the country of China does not introduce threats you wouldn't see elsewhere, *not* that the risk is exactly the in each geographical area. That is, if you think that you're only going to face malice in China (even if it happens to be state sponsored) then you would be mistaken.
Comment: @DKNUCKLES Your rebuttal is the same thing. There are different threats that are unique to connecting to the Internet in China than there are elsewhere in the world. Would you also say that (if it were even possible to do so) connecting your laptop to the Internet in North Korea would pose no difference in potential threats than elsewhere in the world? What about plugging into the Internet at a cyber cafe in Nigeria? Or connecting your laptop to the Internet at a cyber-security conference such as BlackHat? Your premise is fallacious, that's all I'm saying.
Comment: @Nick My rebuttal is not the same thing at all. I acknowledge that different geographical and networks will be higher risk that others, but anyone who is conscious about security should be prudent with operation security no matter where they reside, it should only be "high risk areas" that you describe. I would employ the same OpSec with my critical data and computers in Australia, Switzerland, Canada as I would in China, North Korea or Nigeria. My point is that you should always assume there is a risk and act accordingly.
Answer: On a domain-member PC:
There are cached credentials of one (or more) administrators on the device. There are also cached credentials of any users that have logged into the device. There may be other cached credentials such as mapped drives, etc. on the device. Contents of My Documents, etc. may contain sensitive corporate information that has accumulated over time. An insider (while unlikely) could cripple the organization and/or cause great harm (ahem, Snowden...). These credentials and data can be "confiscated" during a customs inspection or while the user is (for whatever reason) separated from their device.
On a stand-alone PC:
A freshly-prepared laptop with only the required data contents will be immeasurably more prudent for a traveler to any foreign country (not just China) from the standpoint of possible corporate or government espionage. Additionally, if the user is an insider the content they can steal will be limited to that of what the administrators prepared during the provisioning process.
Comment: Credential caching can be disabled.


Installing Eclipse Kepler

Question: I need some help to set up the Eclipse Kepler 4.3 on Xubuntu, I whould like to do it by the command terminal. Which are the right commands?
Answer: First of all, you need to check whether you have java installed on your system. You can check by using the command:
java -version
If java is not installed, then you should install it by doing
sudo apt-get install default-jre
Afterwards, download Eclipse from the download section of the official website (http://www.eclipse.org/downloads/). Remember to choose the correct package for your architecture (32bit or 64 bit). The package will have the name:
eclipse-standard-kepler-SR1-linux-gtk-x86_32.tar.gz
or
eclipse-standard-kepler-SR1-linux-gtk-x86_64.tar.gz
After you have downloaded the correct package, extract the eclipse.XX.YY.tar.gz using
tar -zxvf eclipse.XX.YY.tar.gz

switch to root user:
sudo -i

Copy the extracted folder to /opt
cp -r eclipse.XX.YY /opt

Create a desktop file in the location /usr/share/applications and install it:
gedit eclipse.desktop

Copy the following to the eclipse.desktop file.
[Desktop Entry]
Name=Eclipse
Type=Application
Exec=eclipse
Terminal=false
Icon=eclipse
Comment=Integrated Development Environment
NoDisplay=false
Categories=Development;IDE;
Name[en]=Eclipse

Give the desktop file permission to be executed, run:
chmod +x eclipse.desktop

Run the following command to automatically install it in the unity:
desktop-file-install eclipse.desktop

Create a symlink in /usr/local/bin using
cd /usr/local/bin
ln -s /opt/eclipse/eclipse

For an eclipse icon to be displayed in dash, eclipse icon can be added as
cp /opt/eclipse/icon.xpm /usr/share/pixmaps/eclipse.xpm

Comment: If you MUST have oracle / Sun java then take a look at this: -
https://help.ubuntu.com/community/Java
Comment: You may want to edit your answer and add that.
Comment: Thanks a lot, I will do that... but is there any way to install everything from the command line?
Comment: Sorry I forgot to post the JDK install...    If you not fussed about running OpenJDK then its easy to install this with : -

`apt-get install openjdk-7-jdk openjdk-7-jre`
Comment: If you had Eclipse Indigo installed from Software Center, should you remove that before installing Kepler from source? I followed these instructions with Indigo still in the system. And when I launched Eclipse, Kepler came up not Indigo. So I am not sure if it is still a good ideo to remove Indigo from software center.
Comment: Eclipse has a much better GUI self-installer now for linux - see instructions on their site here: http://www.eclipse.org/downloads/eclipse-packages/?show_instructions=TRUE
Answer: There' a bug that keeps the menu from working see
https://bugs.launchpad.net/ubuntu/+source/unity-gtk-module/+bug/1208019
the work around is to change one line in the eclipse.desktop file
Exec=eclipse

to
Exec=env UBUNTU_MENUPROXY= eclipse

Also I had to make the desktop executable before I did the desktop-file-install in order to make it work.

Installing Eclipse Kepler


JavaFX in the wild?

Question: Does anybody know of any real-world web applications based on JavaFX?  I'm an experienced Java programmer considering starting a website while I'm not at my day job.  I don't have a lot of expertise on the UI side, so I'm looking for the best way to leverage my existing skills to create something that can provide an awesome RIA experience.  Only trouble is, I don't know of any sites that are implemented using JavaFX, since it's so new.  I'd like to see what it's capable of.
Comment: Hi Julie, did you have time to evaluate the "Automagic unit tests for upholding Object method contracts in Java?" (http://stackoverflow.com/questions/190007") ?
Comment: We use it in an industrial-strength inhouse PLM solution.
Comment: To use Java to create the user-interface of a web app, I'd suggest [*Vaadin Flow*](https://en.wikipedia.org/wiki/Vaadin#Vaadin_Flow_(Java_API)).
Answer: Found here quite an interesting stories. Top two listed below.

TweetBox
TweetFX
Answer: I think the best example of what JavaFX can do is in the examples on JavaFX.com.
However, it's still early in the JavaFX days thus you will be in pioneer days. Which means there are potential rich rewards to be had, but also - many unknowns.
What I think JavaFX "sweet-spots" are:
1 - If you either have Photoshop skills or are collaborating with someone who is - JavaFX provides the only real platform that lets you take Photoshop and generate a UI. Normally you mock-up in Photoshop and try your best to replicate, JavaFX can leverage it natively.
2 - You get all of the goodies from Java libraries "for free".
3 - Can leverage the UI skills to mobile (those that JavaFX will run on anyway).
However, if you are just wanting to have a Java GUI but would rather wait for more polish on JavaFX - I would recommend grabbing MigLayout & go with Swing on Java 6u10 or later.
Answer: There are a few JavaFX apps from the JavaFX Coding Challenge; my personal favorite is Music Explorer FX.
The new version of Indaba Music's software was written in JavaFX; the old version was in Flash.
Answer: In my personal opinion I would not use JavaFX for web. Simply because HTML5 is crushing everyone in sight. Now, I totally recomend the use of JavaFX for desktop applications.

JavaFX in the wild?


Does the Saura Purana foretell the appearance of Madhvacharya?

Question: Madhvacharya was a Dvaita philosopher who propounded Dvaita philosophy by writing commentaries on Prasthanatrayi. I heard that his appearance was foretold in Saura Purana as an incarnation of a demon named Mukhasura. Now, even Wikipedia article on Saura Purana also says chapter 38 to 40 of Saura Purana attacks Madhvacharya. Is this true?
Comment: attacks?  I don't think that's a correct word to use .. why would a Purana attack someone?
Comment: @Rickross That is what the Wikipedia says.
Comment: Okay I thought it was ur word .. U can use block quote then to quote that part
Comment: I have heard that he's advent is also foretold in the Parashara Smriti
Comment: @Surya Kanta Bose Chowdhury Parasara Smriti? Not possible. Because it is a law book.
Comment: @NaveenKick Sorry. I actually meant "Parashara Samhita" instead of Parashara Smriti.
Comment: Read https://archive.org/details/in.ernet.dli.2015.59469/page/n63
Comment: Madhvacharya is mentioned in Ballitha suhktham some pragnya athma have deleted my answer so im not attaching the same because the question itself is having hidden intentions..
Comment: I guess the attack is a wrong. The right word should be Truth.
Answer: Yes. Saura Purana chapters 38 to 40 contain prophecy of the birth of Madhvacharya and passages which attack Madhvacharya and his philosophy.
These chapters glorify Advaita and Shiva. There are frequent usage of the six darshanas viz  Sankhya, Yoga, Nyaya, Vaisheshika, Mimamsa and Vedanta. There is even  glorification of Advaita. Not only that, there is also a mention of non vedic schools like Charvaka, Bauddha, Mlechha and Jaina dharmas. There is also mention of Shankaracharya, Badarayana Sutras (perhaps Padma Pada also. I couldn't understand the verses which contain the name properly).
These chapters talk about the characteristics of Kali yuga and prophecies that there would be falling down of all the varnas and the situation would be terrible where Brahmins would be uncultured. In chapters 39 and 40, Suta says the back story of birth of Madhvacharya. According to the story, it is said there is an evil minded person named Madhu who was cursed by his Guru was born as Madhvacharya in southern coast of Karnataka (!).
The curse goes to a very specific detail. It mentions that Madhu will be born will write a commentary on Brahma Sutras. Interestingly there is exact mention of the name along with birth place. He would tour countries like Utkala, Maharashtra, West Bengal, banks of Ganga and Godavari preaching his philosophy. As the time in Kali yuga passes, the philosophy preached by him will get popular and the shishyas would be evil too who do Shiva Ninda.
Hence, the Wikipedia claim is correct which says Saura Purana's attack on Madhvacharya.
You can read Saura Purana which is a upa purana of Brahma Purana on wayback machine - Saura Purana ASS.
Comment: @TheDestroyer What do you call it? I have not mentioned the words mentioned in the Purana. They are worse than attack.
Comment: Lol this is why I say these Puranic verses about Adi Shankara, Chaitanya Mahaprabhu and Madhvacharya are interpolated.
Comment: "attack" might not be proper word even if wiki mentions.
Comment: @Sarvabhouma Whatever they might be. Such statements are found in some Puranas. But attack is not proper word.
Answer: I request all readers to read this post completely which has all references for the accusations made on Madhvacharya, please click on the links attached and know complete details about this topic. Let us all embrace the factual realities
Yes. Saura purana, Skanda Purana and even Parashara Samhitha says that Madhvacharya was a demon named Madhu/Mukha who takes his birth in Karnataka's Udupi.
Irrespective of Madhvacharya being accused as a demon by these shastras, there's one more interesting thing common in all of the three predictions. All three Shastras (Saura Purana, Parashara Samhitha and Skanda Purana) predicted that Madhvacharya will be a horrendous hater of Advaita siddantham and Lord Shiva which is true infact. If you carefully read the works of Madhvacharya like Mahabharata tatparya nirnaya, brahma sutra bhashya etc: you'll find that he had been a terrific hater of Lord Shiva and Adi Shankaracharya's followers. He has done Shiva-ninda nearly more than 250 times in his tatparya nirnaya and has fostered hatred about Shaivas and Shaivism in a magnificent and vicious manner. You can check here for all the references from his works.
The Saura purana and Parashara Samhitha accuses that his disciples will be most evil and horrendous haters of Lord Shiva and Non dualistic practices so that they even step into killing and murdering activities. How true is this accusation?.
There was a person called Narayan pandit who was one among the direct disciples of Madhvacharya himself. He has penned works like Manimanjari, Madhvamrutha Maharnava etc: where his mindset is clearly understandable.

Manimanjari:- In this vicious work, Mister Narayana pandit abuses Adi Shankaracharya and his family, disciples and lineage in the maximum way possible, like Shankara was a demon, he had Rudravesha, he was killed by Bhima (referring madhva in his previous birth) etc: and also have abused Shankara's beloved mother Aryamba as a prostitute, Shankara as a sex-addict, the one who died because of STD etc: you can find the complete work here where Madhvas have shamelessly uploaded this work with great respect, the most saddest and hindering thing is that these dirty works are being taught to small children of madhvas in their gurukuls, just like how madarasas train Islamic kids for violence.

Madhvamrutha maharnava:- As Saura purana predicts about Madhvacharya's disciples being murderers, it's authenticity and confirmation will be cleared after one read this work. You can find it here.

Talking about other disciples of Madhvacharya like Vadiraja tirtha, Vijayendra tirtha and the famous Raghavendra swamy whom even secular Advaitins and Shaivas worship today, we can know more facts.

Vadiraja tirtha:- This person was a born Advaitin but later was converted to Madhva
siddantha by people in his village, he in Vayu stuthi abuses Adi
Shankaracharya and his followers as Jackals, dogs etc: This man also
criticised female followers of Advaita Vedanta as prostitutes and
like.

Vijayendra tirtha:- He is another example to completely agree with Saura purana, he's the one who tried to kill Appaya Dixitar who was his contemporary Advaitin rival scholar by appointing killers in Kumbhakonam. This Vijayendra tirtha also have written Shaiva sarvasva khandana where he abuses Bhagavan Sadāshiva is a most horrible way possible insulting Shivalingam etc:

Raghavendra tirtha:- Another famous personality who is considered as some god or deity by some fools was an horrible hate mongerer of Adi Shankaracharya and Lord Shiva. He has written a work called 'Parimala' where he insults Advaitins using abusive language and with a most horrible statement, he ends his work i.e "Lord Shiva gets life and energy by drinking the padarenu (Feet's sweat) of Madhvacharya. But irony is that we'll be constantly seeing many Shaivas of South India also worship this personality unknowingly being influenced by the surroundings.

Irrespective of all these, even Today there are 2-3 official Madhva channels in YouTube where they upload pravachanas of Manimanjari, Madhvamrutha etc: being taught to small children and others. The most surprising element is that neither of the Advaitins or Shaivas are ready to expose this atrocities officially in South India that people get awareness.
Hope it clears everything.
Answer: The Saura Purana texts don't talk about Sri Madhvacharya. The text talks about a certain Brahmin named "Madhu Sharma" who was born in Andhra Pradesh (Sri Madhvacharya was born near Udupi, Karnataka). Madhu Sharma is said to be the disciple of Padmapaada Acharya. (Sri Madhvacharya was born 400 years after Padmapaada Acharya). There's too many such historic discrepancies which clearly indicate that this text is not about Sri Madhvacharya. Moreover, there's too many grammatical errors for the text to be authentic. It's more likely that it's interpolated.
Someone has commented in the thread, " In chapters 39 and 40, Suta says the back story of birth of Madhvacharya. According to the story, it is said there is an evil minded person named Madhu who was cursed by his Guru was born as Madhvacharya in southern coast of Karnataka (!). "
This is untrue. Kindly go through the texts once again. Saura Purana Chapter 39 verse 39 states that a wicked minded Brahmin will be born in central Andhra Pradesh. And there's no mention of any southern coast of Karnataka.
For reference,
तदा"न्ध्रीदेशमध्येतु" दाक्षिणात्यो भविष्यति |
ब्राह्मणो दुर्भगः कश्चिद्विधवाब्रह्मणेतरः || ३९.३९ ||
For more info, please go through this rejoinder by Shri BNK Sharma
"AN ATTACK ON ŚRĪ MADHVĀCĀRYA IN THE SAURA PURĀṆA on JSTOR" https://www.jstor.org/stable/41688222?seq=1
Comment: BNK Sharma was a Madhva writer so obviously he'll defend Madhvacharya and his followers.
Answer: Harihi Om.
The mentioned section in the Saura Puraana is nothing more than an interpolation, which:

Has several factual inconsistencies
Is written in incorrect Sanskrit grammar

In the Saura Puraana's 39th chapter and 54th shloka, there a grammatical error:

तथा तथाऽयमुन्मार्गः शिवद्वेष्टुर्भविष्यति |

The word शिवद्वेष्टुः should have been शिवद्वेष्टा. It should have been in prathama vibhakti, a form of Sanskrit words used to indicate the subject of a sentence, rather than shashti vibhakti, which indicates possession!
Further, there are very basic errors:

The 30th shloka mentions that "Madhu Sharma" would appear in Andhra Pradesh, while in reality, Shripaada Madhvacharya appeared in Karnataka, with zero ancestral links to Andhra Pradesh.
Shripaada Madhvacharya's purvaashrama name was 'Vaasudeva' and he accepted sanyaasa under the name 'Aananda Teertha'. He later also became known as 'Purna Prajna' and 'Madhva', but seldom was his name 'Madhu'.
It was said that he would study under Padmapada, a disciple of Shripaada Adi Shankaracharya, who lived more than 300 years before Shripaada Madhvacharya!
It states that Madhu Sharma was a Shiva-dveshi, but on the other hand the Maadhva sampradaaya is one of the few Vaishnava sampradaayas with the greatest regards for Shri Rudra, even worshiping him! The Pancharaatra Aagamas recommend sharanaagati and sole worship of Shri Vishnu, as performed by Shri Vaishnavas, but Shripaada Madhvacharya wrote his own Aagama Shaastras to include the worship of Shri Shiva, Paarvati Devi, etc., whose worship is not covered in the Pancharaatras.

Shripaada Madhvacharya even wrote a Shiva dhyaana mantra to meditate on Rudra, while performing sandhyaavandana. Shri Vyaasa Teertharu even wrote Stutis for Shiva. Additionally, Svaami Vadiraja Teertha Shripaadagalu, a 16th century Maadhva Vaishnava even established a Shiva temple at Dharmasthala, which is handled by Tattvavadis even today.The only basis for the claim about "hatred" towards Shri Shiva by Shri Madhvacharya, is only the interpolation in the Saura Puraana and some misinterpretations of the Mahaabhaarata Taatparya Nirnaya, done by certain online misleaders.
For this reason, Dr. B. N. K. Sharma jokingly stated:

The interpolator is a fourth-rate Pandit, ignorant alike of history, geography, tradition, art, proportion and philosophy. His only qualification is his prejudice against Madhva.

From this, it is evident that these chapters are interpolations. Additionally, they aren't even found in many manuscripts. Indologist M. Winternitz in his book "A history of Indian literature", footnotes to page no. 536, explicitly states:

The Saura-Purāņa would have been compiled approximately between 1230 and 1250. However, as chapters 38-40 do not occur in all the MSS [Manuscripts], it is more probable that they have been interpolated.

Professor Julius Eggeling in the book "Catalogue of the Sanskrit Manuscripts in the library of the Indian office", Volume 1, Part 6, page no. 1188, stated:

The work [Saura Purana] has been published by Pandit Kāshinātha Shāstri Lele, in the Anandashrama Sanskrit Series (Poona, 1889). It there, however, consists of 69 adhyayas, four of which (viz. 38-40, 68) marked by the editor himself as not contained in some manuscripts.

Therefore, without a doubt, these chapters are interpolations and have been added by some miscreants. The same is likely in the case of other Puraanas defaming other philosophers, such as Shripaada Adi Shankaracharya, which are likely to be interpolated during sectarian conflicts in the recent centuries.
Thank you for reading.
Shri Krshnaarpanamastu.


What determines the order of a finite volume scheme?

Question: I often hear that cell centred finite volume is second order accurate but at the same time I come across notions of high order FVM flux schemes. Is there a distinction between the two? If I were to use something like a first order upwind referencing vs something like a third order MUSCL would that make my entire FVM scheme first or third order accurate?
Comment: You can't really know until you've done the math or measured the convergence rate. You really need/ought to do both.
Comment: Typically, the order of accuracy of your scheme is the lowest order of accuracy of discretisation schemes you use for different terms and stabilisation. For example, if you use an nth-order scheme (n>1) for viscous fluxes but use the first-order stabilisation scheme, then the overall accuracy is only first-order.
Answer: For methods that discretize simultaneously space and time, such as Lax-Wendroff or Upwind with Forward/Backward Euler, you can manually compute the truncation errors (for a sufficiently regular $u$). For instance, the former (LW) is both second order accurate in space and time, while the latter (Euler-Upwind) is only first order accurate.
To obtain overall higher schemes, it is common to split spatial and temporal discretization (resulting in the REA algorithm; see for instance this paper, or chapter 5 of my favorite FVM notes).
For the well-known reconstruction of the trace(cell-face) values by means of piece-wise linear functions and slope limiters you are getting in principle a second order reconstruction. However, around local maxima and minima, the limiters cause the reconstruction to fall back to the $\mathcal{O}(\Delta x)$ case.
Popular even higher reconstruction methods are ENO and WENO.
Then, however you need a time integrator. In general, standard RK solvers do not posess the desired TVD property, so you need some specially designed time integrators.
By choosing reconstruction and time integrator of certain order, you obtain in principle a FVM scheme of that particular order. In practice, however, you may observe a worse rate of convergence since the true solution is often discontinuous, rendering the Taylor-Expansion based way of computing truncation errors inapplicable. Also, as already mentioned above, the limiting step (to get the TVD property) might cause your method to approximate maxima and minima not as accurate as desired.


No water dispensing after replacing Kenmore refrig filter

Question: After replacing the water filter on my side by side refrig (Kenmore model 106.51793 412) water dispenser will not work.  I removed and replaced it several times to make sure it was pushed in fully, still no water.  Reinserted old filter and dispenser still would not work. Water leaking out of water filter housing area at the bottom front of refrig.
Refrigerator is 5 yrs old.
Answer: Posted as a comment by Lisa Powers:
The water filter housing part was worn out. I replaced it and the problem is fixed.


Have 20% equity in house, but bank requires a principal payment for refinance

Question: We are trying to refinance our mortgage.  The mortgage has a balance of $123000.  Our house was appraised at $266000.  If we did the math correctly, we have $53200 in equity which gives us approximately $212000 to refinance.  The bank is requiring a principal payment of approximately $3000.  Why is the bank requiring this, if we have 20% equity?
Comment: *If we did the math correctly*... could you show us this math? If the house is worth $266000 and you only owe $123000, how did you arrive at $53200 in equity and $212000 (nearly double the balance) to refinance?
Answer: The answer that first came to mind is that it's not really a "down payment"; it's "closing costs". There are costs associated with creating a mortgage (origination fees, guarantor fees) which can't be capitalized, because they're needed up front to defray overhead, pay other agencies involved in loan creation, etc. They're not willing to lend you this money, and they can't pay the bills with a little extra equity in your home. They need cash, and so you could have 20% equity or 99%, they'll charge you these costs.
You may not have seen this when you bought the home because it's such a buyer's market that sellers are willing to pay closing costs. If that was the case, all you had to bring to closing the first time around was your down payment and maybe some escrow advances (to cover property taxes, homeowner's insurance, etc). Now, though, there's no other party to pick up those costs, so you have to eat them. It's part of the cost of a re-fi.
Comment: It could also be a combination of closing costs and points that the OP and spouse are being asked to pay, say 1 point ($2120 on a $212,000 mortgage), and about $850 in closing costs for a total of slightly less than $3000.
Comment: The median loan origination fee on a mortgage with 10% down or better is $2,537 just by itself. That pays for required services rendered like the notary, lawyer's fees, document prep etc. Typically, points are traded for interest rate deals - money now for money later - but prime rates are so low that most homeowners are unlikely to accept points.
Answer: If your balance is 123000 and you have appraised at 266000, you theoretically have 143000 in equity.  Are you saying you would like to refinance 80% and keep 20% in equity?  I'm assuming that's what you intended with your question based on the numbers.
20% is not a magic number for a down payment (or remaining equity).  Every lender (and every loan) has different standards.  Your credit may also affect the percentage they want to see.
I would recommend asking the bank about the requirements of the loan.


Can I develop Android applications in Perl?

Question: I know that I can run Perl on Android, but I'm looking to write an app that can be released on Google Play, for anyone to download and run. Is Perl still a viable choice?
Answer: This Google project packages Perl scripts and Perl into a self-contained APK, not requiring any further downloads, that can be uploaded to Google Play:
http://code.google.com/p/perl-android-apk/
It provides Android API access through SL4A - see the following page by one of the authors:
http://www.github.com/damonkohler/sl4a
So yes, Perl is a viable option if it's your preferred language to work with.
Answer: Technically you can release anything that conforms Google Play policy and is distributed in APK form. But in case of perl you'd either have to bundle perl with your app or expect user to have it (barely noone), not to mention UI. My answer is - it's not really best idea and if you can rethink it, you might come up with something requiring less hassle.
Answer: I highly recommend Perl for Android together with SL4A for prototyping applications. From there it isn't too much of a leap to refactor your code to Java, as all the system calls are the same on both platforms.
Knowledge of Java is an excellent new string to your bow, and the basics - mainly that everything is a class - can be learned in an afternoon and can largely be replicated in Perl
Comment: The reason I'd like to use Perl is both the immense CPAN, and that I'm a lot more confident with it. Writing the app in Java instead of Perl (if Perl were available) would take a lot more than an extra afternoon, especially if I wanted the same code quality. Now, if there only was a way to bundle SL4A and my script into an APK...
Comment: @Andreas code quality - it's a good reason. But don't forget about application overall quality.
Comment: @Andreas, there are quite a few Java libraries out there, but without CPAN finding them is a bit harder and brining libraries into your APK file will definitely bloat your app. (No free lunch and all that...) I suggest looking into the Maven project for Java, which provides a huge number of OSS libraries for Java for various purposes. I would still love to have CPAN on Android too.
Answer: The short answer is: no, you cannot use Perl in a deployed, native Android app. There's no practical way to do this. There are ways to sort of do it, but none that are feasible.
As others have pointed out, there are some things like SL4A and such to make prototyping possible and you might even be able to run a real app on your phone, but deploying it to a wide base of phones will be problematic.
For 95% of the apps out there, a Java application of some sort is the best option. Yet, a native Java application is not the only alternative available to you.
Other options include:

You can develop an app that is primarily driven on the server side, which is running Perl. This could be through some sort of socket connection, REST API, or a web-based mobile app wrapped in a thin Java app that installs onto the client. However, your application will only work while the phone or tablet has a working data connection. There are many applications (including my own) that work this way.
You can try out PhoneGap, which uses HTML5 and JavaScript (and Java if you want to extend it to do something PhoneGap doesn't support on Android). This framework also has the advantage of making it possible to run your app on iPhones and other smartphones with very little effort. This also has it's own support base and community separate from Android and Google, if that's a concern.
You can also try Scala, which is a functional language (i.e., more Perlish than Java) that builds to the JVM and has some tools to aid in the construction of Android projects. This is not as mature, not supported by Google, and harder to start, but not Java for those offended by Java.

Ultimately, it should be possible for someone to deploy apps to Perl and I'd love to see that happen. I'm unwilling, though, to spearhead that project.
Update Jan 2014: Sadly, my original answer from August 2012 still applies despite what others have said. The SL4A + perl installed solution is closer, but SL4A does not allow you to actually build native Android applications. It, basically, gives you the ability to build a locally hosted web application that has access to some of the phone's native features. This may serve the needs of some, but certainly not all application developers. I still don't know of a project that will allow you to build a native Android application in Perl.
Answer: Google claims that Perl is supported by the "Scripting Layer for Android" (SL4A).
See here: http://code.google.com/p/android-scripting/
and a Perl apk: http://code.google.com/p/android-scripting/downloads/detail?name=perl_for_android_r1.apk
Comment: I know that I can _run_ Perl on Android. But I'm looking to develop an application that can be neatly bundled in an APK on Google Play.


How do I install JavaFx 2.0 on my mac?

Question: I need to use JavaFx on my macbook pro. Im using netbeans 7.1.
Currently when i compile my javafx program that I created on windows it gives me this error.
The J2SE Platform is not correctly set up.
 Your active platform is: Default_JavaFX_Platform, but the corresponding property "platforms.Default_JavaFX_Platform.home" is not found in the project's properties files.
 Either open the project in the IDE and setup the Platform with the same name or add it manually.
 For example like this:
     ant -Duser.properties.file= jar (where you put the property "platforms.Default_JavaFX_Platform.home" in a .properties file)
  or ant -Dplatforms.Default_JavaFX_Platform.home= jar (where no properties file is used)
BUILD FAILED (total time: 0 seconds)
Answer: The latest versions of Java from Oracle have JavaFx 2.x included:
http://www.oracle.com/technetwork/java/javase/downloads/index.html
The stand-alone version of JavaFX for Java 6 appears to be available only for Windows (at least from the official download link).
Answer: If you want to avoid potential litigation by Oracle, the safe choice here would be to install OpenJDK, JDK's fully featured open-source build.
You can get it from https://adoptopenjdk.net/.

How do I install JavaFx 2.0 on my mac?


How to mount USB drive on Ubuntu so that other users can access it?

Question: Yes, this question has been asked before, but as far as I'm concerned it has not been answered satisfactorily. Many answers mention that an extra line in /etc/fstab is required. I don't want to add such a line, because I have several USB drives - which I guess will all need their own line with their own label. It will mess up my /etc/fstab file. FYI: I normally put in only one USB drive at a time. I've tried using chmod, chown but to no avail. I've tried the Gnome disk utility but I don't see how it will allow me to change permissions. I've tried to use pmount. So far the other users on my machine continue getting "permission denied". Why does this seem to be so difficult?
Answer: Maybe you could try passing in umask parameters when mounting?
<code># sudo mount /dev/sda1 /mnt/usb -o umask=000
</code>
chmod/chown wont work because permissions are already determined at time of mount. Most drives are also formatted with FAT32 thus are unable to store UNIX permissions


How to not show search results for the whole Mac?

Question: I am using macOS Big Sur, and notice if I use Finder and navigate to a folder, and search for a file by name, then it shows me results, but is for the whole Mac.  This is really confusing. I will have to remember to click it from "This Mac" back to "FolderName"  How do I make it search within that folder and its sub-folders by default?
Answer: In Finder Preferences, in the advanced tab you have an option to choose where the search starts from.

When performing a search:

Search This Mac
Search the Current Folder
Use the Previous Search Scope
Answer: When you search from Finder you get a window like the following after your search.  For example I went to the folder "On My Mac" and did a search. The results are shown in the image below.

Notice near the top of the image is the word search. Next to that are the phrases This Mac and "On My Mac". This Mac is selected and this displays my result for my Mac. If I click on "On My Mac" then the results for that folder will be displayed.
Comment: OP already states that in the question.


Are browser (firefox) settings/passwords preserved in upgrading Ubuntu 14.04 to 16.04?

Question: I have backed-up my files and am ready to upgrade from Ubuntu 14.04 LTS to 16.04 LTS. I was wondering if my firefox password/history/etc will be preserved or wiped?
Comment: Yes, configs for most applications (including `firefox`) should survive, as long as you backup and restore your `$HOME` properly.  Personally I store `/home` on its own partition on all systems I use, precisely to keep it safe across system upgrades.
Answer: Your complete Firefox profile, including settings, bookmarks, history, passwords, installed add-ons, etc. is stored in your home directory in the folder
~/.mozilla/firefox/<PROFILE-NAME>

where <PROFILE-NAME> is normally composed of 8 random letters and a .default suffix.
There is also the file ~/.mozilla/firefox/profiles.ini though which lists the configured profiles of the user account and defines which one should be used by default when you start Firefox without parameters. You can easily recreate this one, but it's easier if you just back it up as well.
Anyway, if you backed up your complete home directory, all your Firefox user data and settings will be preserved.


Is it possible to calculate Euclidean distance but by using a road network?

Question: Using ArcGIS I want to output a raster for the distance from a set of points, however I want to do this using a road network, as opposed to just using the Euclidean distance function i.e. using Euclidean distance but along a road network as opposed to as the crow flies. Can anyone tell me away of doing this?
Ultimately I'm trying to calculate a cost surface of how much it will cost to transport goods from  supply points to an undefined market i.e not a specific point but anywhere within a region.
Comment: Euclidean distance is a length of crow flight.
Comment: Create a cost surface with roads == 1 and everything else is NoData then use cost distance tool.
Answer: Yes this is possible, but it is most easily done with the Network Analyst Extension. This extension is super in depth, and it will allow you to create routes for more than one driver, adding more than one stop, giving them a predetermined maximum time they can drive, timeframes to be at each location, adding start and end times, etc.
Comment: Thanks - could you tell me which function in Network analyst i need? I've used it a bit but I've only worked out how to calculate buffers from points or distance along the road network. what i'm looking for is a continuous surface.  The only way I've thought of doing it so far is  using brute force, creating a point grid at the required resolution, then using the closest facility function to work out the distance to each point, joining the resultant routes to the incidents in the closest faculty and then converting the points to a raster.  there must be a better way then this though
Answer: Network analyst is one option, but I'd like to suggest a second option, which is using the Cost Distance functions in Spatial Analyst, but restricting the analysis to raster cells that intersect roads.


"love to be with" or "love being with"

Question: My sons have a good friend called Ben. I thought I could say, " My sons love to be with Ben". But when I said it to his mother, she replied to me by saying, "Ben also loves being with them as well." Can't we say "love to be with" or are both "love to be with" and "love being with" correct? Is there any difference between these two?
Comment: Both are fine. It sounds as though Ben's mother was simply reciprocating the compliment.
Answer: You can say both but the nuances are a bit different because of the slightly different meanings. We usually use like to do something when we mean that we like the effect of doing it, or we think it is a good idea to do this thing because of its wider effects:

I like to go to the dentist if my filling needs replacing.

This would imply that it's a sensible thing to do. In contrast, we usually use like doing something when we find the experience itself pleasurable or enjoyable. Consider this version of the sentence:

I like going to the dentist if my filling needs replacing.

This would tend to imply that you were a bit of a masochist! Nonetheless, most of the time there will be little discernible difference in everyday speech. Both of your comments to each other were very complimentary!
Answer: To be with can have connotations of an intimate nature (and is often used as a euphemism), whereas being with is taken at face value.
Answer: " Love to" implies that you like the idea of something, while " love ing" means that you enjoy doing it, it's really happening to you.  I think she just rephrased what you had said, you can use either one.
Answer: Both are acceptable common usage. If there is a subtle difference, I'd say that "I love to be with X" refers more to an ongoing general state of existence, before/during/after the time spent; while "I love being with X" refers to my enjoyment of the specific instances of spending time with X.  BTW don't worry about modifying your grammar according to Ben's mother's model, as there is a potential redundancy in her reply "Ben ALSO loves being with them AS WELL."

"love to be with" or "love being with"


Story probably from 80s where travelers are quarantined in an accelerated time bubble and the attendant lives his entire life in a day

Question: Short story, could have been in Analog, Fantasy and Science Fiction, or Amazing. Basically there is some sort of war with aliens, and disease is being used as a weapon. Travelers to the planet have to go through a month of quarantine which is handled in a time bubble so that it is only a few minutes of real time. Each quarantine has to be staffed, though, so the people staffing the quarantine age most of their life in one day. After his day of service, the attendant emerges as an old man with a vast knowledge (from reading and watching shows) of the present he never experienced.
Comment: Main character's name was Frank. Story starts with him hosting a group of people in quarantine (he wears a special suit to protect him). He detects a faint trace of a suspect biological, and spends a few weeks (experienced) messing with the metabolisms of his guests (hiding the liquor from an alcoholic, etc.) and reveals one of them is a carrier for an engineered alien plague. Earth is saved!
Comment: This is his last period running quarantine, and he musters out. Returning home, we find out he enlisted in order to pay for medical treatment for his younger brother. (Who caught an earlier plague.) He comes back home having aged 52 years in just a few months.
Comment: He's afraid to face his family, and ends up getting picked up by a pair of young women who are probably planning to rob him. But he can speak twip just like they can, knows all the current slang, fashion, music, etc. He asks them to turn off "Starborough Fair" because he's so sick of it; he's heard it, the song it's based on, and the folk song that's based on so many times in the past 52 years. The women catch on that he's a "fast-timer," and their curiosity gets the better of them. Eventually they drop him off at the hospital.
Comment: His father is appalled to see Frank older than he is, but his brother is getting treatment.
Comment: Definitely in Analog, not F&SF or Azimov's. I probably have it in at least one anthology too.
Answer: Short story, could have been in Analog, Fantasy and Science Fiction, or Amazing.
"The Million Dollar Day", a novelette by Kevin O'Donnell, Jr.; published in Analog Science Fiction/Science Fact, October 1987; apparently never reprinted.
Basically there is some sort of war with aliens, and disease is being used as a weapon.

Some considered Abe lucky. He had caught, but survived, one of the plagues released in Bysk's only successful bio-attack on Terra. His bones were melting into cartilage, and his system had reabsorbed most of his brown hair, as well as his fingers and toes, but he had survived. So far.

Travelers to the planet have to go through a month of quarantine which is handled in a time bubble so that it is only a few minutes of real time.

"Right," he said sourly, and cut the connection. He pushed back from his desk, there in his office in the Sirius Wing of the Quarantine & Relay Station a billion kilometers darkside of Pluto. He glared at his chrono. "Damn. Damn, damn, damn! Why did they have to come back early?"
The chrono said nothing but:
Universal Time—4 Jul 2204 1300GMT
Experienced Time—18 Jan 2232 0937
[. . . .]
He slapped the writing surface of the console. The damn monitors worked after all. Halfway to retirement and things had to go wrong.
He had expected to retire at seventeen hundred hours on 4 July 2204 Universal Time. Late spring, early summer of his seventieth year, Experienced Time.
After withholding taxes, BCQ would credit his account with a million dollars, give or take a few cents. Not bad for a universal day's work, even if the day did happen to run a few hours over forty-eight apparent years. And more than enough to pay for Abe's treatment.
[. . . .]
Fradero almost cringed. He had played similar scenes with other Guests many times, and never liked them. This one, though, this one would hurt. "To put it most simply, time in Quarantine moves 260,000 times faster than normal. That means that even though you'll spend one hundred eighty days in here, only about a minute will have elapsed in the outside, real world."

Each quarantine has to be staffed, though, so the people staffing the quarantine age most of their life in one day. After his day of service, the attendant emerges as an old man with a vast knowledge (from reading and watching shows) of the present he never experienced.

"But more than that. For me, Earth is a fossil in amber. I will experience forty-five or fifty years in here, and Terra will not change.When I emerge, I will understand the world of my retirement better than anyone alive except my colleagues."
"But then the carousel resumes its ceaseless spin."
"Of course. But I'll know why it's spinning because I will have had time to study trends and fads and social influences and technological developments and anything else that affects my world."

P.S. As pointed out incomments by DavidW, there was a sequel, "Fradero Goes Home", which appeared in Analog Science Fiction/Science Fact, May 1988:

Franklin Delano Roosevelt Nikolaites came home hurting, both in his body and in his mind.
He had lived fifty-two years (experienced years, they called them) in the space of one day (a universal day, they called it). He had done it to make money, to defend human civilization, and to learn all he could about the civilization he was protecting. In pretty much that order of priority.
He had succeeded.
He had earned (net of all withholding taxes) a few dollars over a million.
He had prevented seven plague-carriers from reaching Earth in the infectious but asymptomatic state.
He had studied the history and the geography of his planet, the science and the art of his culture, the politics and the economics of his country. He understood the world into which he would retire better, perhaps, than anyone alive.
Seventy (experienced) years old, returning to the town where he had drawn his first breath eighteen (universal) years ago, Fradero hurt, in both his body and his mind.
Comment: Amazing.  How did you find it?  (I was apparently conflating "Million Dollar Day" with "Fradero Goes Home."  I did think that it was a lot of plot/characters for a single short story...)
Comment: Thanks davidw and user14111 ! I havent seen these stories for 30 years... just dug them out for a re-read.


Difference between launchpad.net/ubuntu and packages.ubuntu.com?

Question: What are the difference between launchpad.net/ubuntu and packages.ubuntu.com? Are they both for ubuntu packages?
Thanks.
Answer:
http://packages.ubuntu.com/ provides  you information about all the packages available in the Ubuntu Package archive.
Where you can Search package directories and Search the contents of packages
Visit About this site.
Whereas Launchpad is a unique collaboration and hosting platform for software projects.

It brings communities together — regardless of their choice of tools — by making it
  easy to share code, bug reports, translations and ideas across projects.

https://launchpad.net/ubuntu is registered by "Ubuntu Technical Board" team which support many things like:

Report Bug
Ask a question
Find Source code of project
Distributing Software


Blender Downloads and the information required to

Question: Where can I download a copy of the 'free' (and I use that word loosely in relation to Blender) Blender program without having to give my inside leg measurements, or signing up for a daily collection of spam emails? I don't want the world and everyone else to help me with a few 3d models that I want to use myself. I don't want to receive a 'you may be interested in this...' offer of add-ons or plans for a house, of horse. I just want the program because Daz3D says that I 'HAVE' to use this program. I even have to give my email address so that I can read any answers to this question, presumably because I'm too stupid to re-visit these pages knowing that someone has answered. Oh and my inside leg is 32".
Comment: Honestly, just out of interest, how did you try to download Blender? If I type "blender download" into any of my search engine, the [official download page](https://www.blender.org/download/) is always the first result. If this is difficult for some users, it should be improved, so sharing your story would help.
Comment: I'm also curious because you write "Daz3D says that I 'HAVE' to use this program". Daz3D is a commercial, standalone 3D software. Could it be that you signed up to some Daz3D newsletter? I would be very surprised if Daz3D *requires* you to use Blender. Just to be clear, Blender is not affiliated with Daz3D in any form.
Answer: You can download Blender from the official website www.blender.org. There's absolutely no sign-up required. Blender is truly free software, since it is open source and GPL licensed. More information about Blender and the Blender Foundation can be found on the About page.
The following versions of Blender can be downloaded:

The current stable release
Experimental daily builds of versions currently in development
All past releases of Blender

Please check that your hardware fulfills the minimum requirements for running the current version of Blender. If your hardware is unsupported you may have to use an older version of Blender with lower requirements.


Converting Flash videos to an iPad readble format?

Question: I'm about to launch a site that creates user content using the Flash webcam recording functionality.  My problem is that iPad users can't watch the videos.  How could I create some add-on functionality for iPad users so that they are able to view the videos?
Answer: Have the page displaying the video check the browser agent, and if it's an iPad/iPhone, either change the page's content or bounce the user to a page with the video embedded in a compatible format, such as HTML5. This requires storing the video in both formats on your server (doing conversions during off-peak hours), or doing on-demand conversions (at upload or viewing time). The former means that iPad users won't be able to immediately watch uploaded videos, and your server will have a significantly larger storage requirement to support a potentially small slice of users. The latter is potentially expensive, in terms of both time and server resources, meaning users could end up with a long delay before seeing the content, or that the server performance could grind to a crawl during peak usage.
Alternatively, you could host all your flash video content on YouTube and embed those videos, as the iPad has native support for (only) YouTube flash video. Or, you could display a message to the user stating that they must visit the page with a (third party) app that supports viewing flash videos, such as Skyfire.


Word for a phrase that is very commonly used to describe something

Question: What is a word to describe a phrase such as "Anything can happen", which is often made in reference to baseball.  This is frequently said, but "platitude" and "cliche" aren't the right terms.  What type of phrase is this?
Comment: Why is *cliché* not the right term?
Comment: (And, besides, "anything can happen" refers to [Wednesday](https://www.youtube.com/watch?v=_9BWW6Mb7oA), not baseball.)
Answer: Of the many synonyms on offer, adage is a good fit:

A proverb or short statement expressing a general truth
Answer: It can be described as a set phrase:

(grammar) A common expression whose wording is not subject to variation.

(Yourdictionary.com)
Comment: Or a ***stock phrase***, which [is actually more common](https://books.google.com/ngrams/graph?content=a+set+phrase%2Ca+stock+phrase&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Ca%20set%20phrase%3B%2Cc0%3B.t1%3B%2Ca%20stock%20phrase%3B%2Cc0)
Answer: I would say that such phrases are hackneyed, which the OED defines as:

7a. To make common by indiscriminate everyday usage; to render too
  familiar, vulgar, trite, or commonplace. Also with out, about, upon.

But I also see them as platitudes and clichés.
Answer: You might be referring to an idiom:

"...a phrase or a fixed expression that has a figurative, or sometimes literal, meaning. [...] There are thousands of idioms, and they occur frequently in all languages."
Answer: Saying - A common phrase or expression, esp. a proverb, a maxim, an adage (OED).
Answer: I'm rather fond of colloquialism

a word or expression used in casual language by common people.

yourdictionary.com
Answer: You might want to call it pat phrase.

"as we speak" is a pat phrase that means "at this very moment" or "right now." The Grammar Exchange


libgdx: How do you remove a cell from TiledMap?

Question: I am making a Terraria-style sidescrolling game with an open world. I am using a TiledMap to render all of the tiles. If I want to remove a tile, like if it is broken, how would I stop it from being rendered?
Answer: first we make an instance of map layer that contain the tile that we want to remove
for example:
TiledMap map=new TiledMap();
//lets say we want to remove some tile from layer with index of 0
TiledMapTileLayer layer=map.getLayers().get(0);
//so if we need to remove the tile in layer at position 0,1
layer.getCell(0, 1).setTile(null);
Comment: Cool! I assume I can use setTile for creating new tiles? I think I heard somewhere that you can only set tiles that are already in the map.
Comment: Yes u can creating tiles or even the whole Map in run time , search in google for creating tiled map programmatically
Answer: I'm not to familial with TiledMaps but when I create a proceduraly generated 2d game I use a boolean array and in my render method check if the boolean at the index is true if it is draw the tile if not don't draw the tile. But after reading the javadoc I see that a method removeTileSet(int index) so possibly when you break something get the index and try to removeTileSet(x);


How much coil do I need to heat a given length of pipe (as a function of x,y,z)?

Question: I'm imagining heating some water pipes using heating coils similar to these. Under various conditions, would I need to apply almost continuous lengths of heating coil to the entire length of pipe? Or could I leave "gaps" along the pipe, allowing some sections to be heated by adjacent sections? What other major factors would affect this?
Answer: I've used them.  I've never been happy with them.  If you do use them you need to follow these rules:

If you wrap them you must have the wraps evenly spaced.  You can't have 3 turns per foot at one end of the pipe and 6 turns per foot at the other end.

The temperature sensor (disk on the orange blob) must be pressed tightly against the pipe.

The full length of the pipe must be covered. You can't have 4" uncovered at one end.  This can be a problem if the pipe comes out of the ground.   In this case, dig out 6-10 inches, include that in the tape, and rebury.

You MUST NOT cross the tape over itself.

tape the heat wrap firmly in position.  Even a small air gap between the tape and the pipe is double plus ungood.

Wrap about an inch of flexible foam insulation around it.  The foam underlay for laminate works, as does packing foam for separating dishes.  Bubble wrap works too.  Key here:  Uniformity.

Less insulation means that the heat tape runs more.
Insulation will even out small amounts of non-uniformity in wrapping.
Most of the time they haven't lasted more than a year or two.  I now regard them as a temporary fix while I figure out how to keep the whole space where the pipes are above freezing.
Addition in response to comment:
Failure modes
Cheap switches in the thermostat result either in the tape sticking in the off position, or sticking in the on position.  If the latter, then some spot that is better insulated than the rest, or a place where the turns are closer togehter will overheat and burn out the wire.
Sloppy installation.

If the tape wraps over itself you have a hot spot that melts the insulation and allows wires to touch.  Zot.  Short circuit.  The short usually will destroy enough of the wire that when you reset the breaker all is good.

If the tape is better insulated at one point than where the thermostat is, then on a cold night the thermstat can remain on while the wire gets too hot.

If the tape is NOT in contact with the pipe for several inches, heat is not being removed from that section of the tape.  It gets warmer, eventually melts and the wires burn up.

Note that the wiki article https://en.wikipedia.org/wiki/Trace_heating mentions several other designs that are inherently safer and more durable.  I suggest that you also gooogle "failure mode heat tape" for other leads.


how to prove that the ring of algebraic integers of $\mathbb Q(\sqrt {69})$ is a PID or UFD

Question: I am now reading an article about Euclidean ring and one part is about the integers in $\mathbb Q(\sqrt{69})$. One step needed is to prove that the ring is a UFD (or to prove PID). Since in the article this will be used before the definition of the Euclidean function, the fact need to be proven without using that it is Euclidean.
Comment: Fun fact: this domain is Euclidean but the absolute value of the norm is not the Euclidean function. That's getting a little bit ahead of things, but I'm telling you just in case you wonder why they picked this one for this.
Comment: Suppose for the sake of the example (i guess won't work there) that we are dealing with $\mathbb{Q}(\alpha)$, where $\alpha$ satisfies $x^{5}-x+1=0$, instead, and that we have Minkowski bound 4. Then supposing it's ring of integers is not a PID, every non-trivial class has an ideal $I$ with $\mathcal{O}_{K}/I\cong 2$ or $\mathcal{O}_{K}/I\cong 3$. But then we can reduce the polynomial $x^{5}-x+1$ mod $2$ and $3$ and see that there are actually no solutions, a contradiction. This is to show that even bounds $>1$ can be useful
Comment: For information, see the survey The Euclidian Algorithm in Algebraic Number Fields by Franz Lemmermeyer .
Comment: I don't have an answer for you, but you might find interesting to peak at the class group and Minkowski's "geometry of numbers" theory. He embedds a number field $K$ in a finite dimensional $\mathbb{R}$-vector space $V_{K}$ and proves some results concerning lattices in $V_{K}$. When you put an ideal of $\mathcal{O}_{K}$ inside $V$ through this map, it becomes a lattice and you can apply the theorems. This allows you to prove that in each class of the class group, there is an ideal $I\subseteq\mathcal{O}_{K}$ with bounded index $(\mathcal{O}_{K}\colon I)$, making things a lot easier!
Comment: Once the bound of $(\mathcal O:I)$ can be 1, it is finished.
Comment: The existence of Dedekind-Hasse norm is a sufficient and necessary condition for a domain to be a PID. Is it easy to construct?
Answer: Suppose that the ring is in fact not a principal ideal domain. That would mean we can find a number with at least two distinct factorizations, and the principal ideal generated by that number is the product of ideals that are themselves not principal.
Let's look at $\textbf Z[\sqrt{-69}]$ for just a brief moment. We readily find that $$70 = 2 \times 5 \times 7 = (1 - \sqrt{-69})(1 + \sqrt{-69})$$ and so $\langle 70 \rangle = \langle 2, 1 + \sqrt{-69} \rangle^2 \langle 5, 1 - \ldots$ you get the idea. The class number is $8$, if I'm not mistaken, but since I just wanted to make the point that this ring is not UFD, we're done.
Turning our attention back to $\mathcal O_{\textbf Q(\sqrt{69})}.$ Thanks to Minkowski, it is enough to prove that $\langle 2 \rangle$ and $\langle 3 \rangle$ can be factorized into products of principal ideals. (I was having some connectivity problems yesterday, so I apologize I did not post a complete answer yesterday.)
Anyway, the Minkowski bound for $\mathcal O_{\textbf Q(\sqrt{69})}$ is roughly $4.1533119$, so we just need to look at $\langle 2 \rangle, \langle 3 \rangle, \langle 4 \rangle$.
Since $69 \equiv 5 \pmod 8$, then, by Theorem $10.2.1$ in Alaca & Williams Introductory Algebraic Number Theory, $\langle 2 \rangle$ is prime, and therefore $\langle 4 \rangle = \langle 2 \rangle^2$.
That just leaves us $\langle 3 \rangle$ to concern ourselves with. Since $69 = 3 \times 23$, it's a ramifying ideal: $\langle 3 \rangle = \langle 3, \sqrt{69} \rangle^2$.
However, since $$\left(\frac{9}{2} - \frac{\sqrt{69}}{2}\right) \left(\frac{9}{2} + \frac{\sqrt{69}}{2}\right) = 3$$ and $$\left\langle \frac{9}{2} - \frac{\sqrt{69}}{2} \right\rangle = \left\langle \frac{9}{2} + \frac{\sqrt{69}}{2} \right\rangle$$ it follows that $$\langle 3 \rangle = \left\langle \frac{9}{2} + \frac{\sqrt{69}}{2} \right\rangle^2.$$
We have thus verified that the principal ideals generated by positive integers below the Minkowski bound are either themselves prime ideals, or the squares of prime principal ideals. Therefore $\mathcal O_{\textbf Q(\sqrt{69})}$ is a principal ideal domain, and its numbers factorize uniquely, disregarding multiplication by units.
Comment: You might also want to mention that $$\frac{\frac{9}{2} + \frac{\sqrt{69}}{2}}{ \frac{9}{2} - \frac{\sqrt{69}}{2}} = \frac{25}{2} + \frac{3 \sqrt{69}}{2},$$ which is the fundamental unit.


Search only approved items using KeywordQuery

Question: We have approval workflow for document library & content approval column was set to yes for it.We have used KeywordQuery on the library by creating separate scope.We want to display only approved items in search result for that we have set ApprovalStatus property to Zero in scope rule.but even after adding this propert we are getting pending documents in search result.Also after adding the property ApprovalStatus = 0 ,Item Count shows "error" as its value instead of count.
Pls let me know how to show only Approved items in search result.
Answer: ows_ModerationStatus is the crawled property you are looking for. In my environment, it is not mapped to a metadata property, which is what the keyword search uses. Here is the msdn link to manage metadata properties: MSDN metadata properties. Check to make sure the mapping from moderation status to approvalstatus is set up.
Comment: I did mapping of Approvalstatus with ows_ModerationStatus.
but by adding ApprovalStatus = 0 in scope rule still it is not working.Can you please tell me can I use this property in KeywordQuery & how to use it?
Comment: Did you run a full crawl after setting up the ApprovalStatus metadata property?


What is the ordering of events in Nahum and Jonah?

Question: I was reading the book of Nahum and it was speaking about Nineveh.  Is the book of Nahum foretelling the destruction of Nineveh, for which the people of Nineveh averted by repenting of their sins, or is Nahum talking about an event that happened after Jonah's time?
Comment: This is a good question.  If you don't get the answer you are looking for here, you might try Biblical Hermeneutics, where there are several Jewish experts.  Recently, there was a question on the [dating of Joel](http://hermeneutics.stackexchange.com/q/775/68) that was eye-opening to me.
Comment: Link that question is here: http://hermeneutics.stackexchange.com/questions/932/nahum-and-jonah-ordering-of-events
Answer: Typically, Jonah is dated to the period of Jeroboam, i.e 780 - 750s BC, whereas Nahum is dated to either shortly before (615BC) or after (612BC) the fall of Assyria (and its capital, Nineveh). Thus, Nahum is at least 150 years after Jonah.
So, to answer the question directly, No - Nahum is not the promised vengeance of God against Nineveh promised by God in Jonah.  If it were, then God is not "slow to anger, but abounding in compassion," as Jonah himself points out in chapter 4, nor is the "incomplete ending" of Jonah to any effect.
The key date that differentiates these works, however, is 722BC, when Assyria conquered the northern kingdom of Israel, leaving only the last two remaining tribes of Israel - Judah and Benjamin. Jonah presumes a full, diverse Israel, whereas Nahum is only addressing the remaining "Israel" in the sense that most people think of Israel today.  The fuller complement of Israel would have been more steeped in idolatry and the "sins" people think of today.
When Jonah goes to Nineveh to preach repentance, the amazing thing is that Nineveh does repent, much to Jonah's annoyance.  That generation is completely spared the wrath of God and lives, so to speak, happily ever after.
It isn't for another 150 years (think the time between now and the American Civil War)  that Nahum is writing.  He is fortelling the doom of Nineveh in order to encourage (Southern) Israel from prematurely capitulating to Assyria.  The later parts of 2 Kings and 2 Chronicles tells the stories of Hezekiah and Josiah, set in this time period, and the constant question is whether Israel should rely on God, or trust in some bigger foreign power like Egypt or Assyria, the two big players in the region.  Imagine, for example, you're Belgium just before WWII.  Do you rely on God or make peace with either Germany or France, and you're beginning to get the picture.
As it happens, Egypt itself had fallen shortly before Nahum, and Assyria does fall very shortly after (or if you don't believe in prophecy, before) the writing, so in any case, its good advice.
Unfortunately for Judah, however, Babylon is the instrument of Assyria's departure from the scene, and within only about 40 more years (587 / 586 BC) they will invade Judah itself, thus destroying the last vestige of the kingdom, and sending all the peoples into exile.
Answer: Nineveh (Assyria) repented in 700 something BC and God spared them.  But obviously later generations in Nineveh in 600 something BC were not repentant as their ancestors were. They ended up paying the consequences. A Jew with the name of Nahum said that at one time Jonah and Nahum were next to each in the order of the Old Testament.  Reference Mosiac website at: http://mosaicmagazine.com/observation/2016/03/the-discomfiting-but-urgent-message-of-the-prophet-nahum/
Comment: Welcome to Christianity.SE. For a quick overview, please take the [Site Tour](http://christianity.stackexchange.com/tour). For more on what this site is all about, and on writing good answers here, please see: [What makes a good supported answer?](http://meta.christianity.stackexchange.com/questions/692/what-makes-a-good-supported-answer) and: [How we are different than other sites](http://meta.christianity.stackexchange.com/questions/1808/how-we-are-different-than-other-sites). Meanwhile, thanks for offering an answer here!


Fractional Order Derivative

Question: A friend and I were talking about derivatives, and he asked an interesting question. Since both of us have not taken our calculus courses yet, neither of us were sure of the answer. His question has two parts: 1. can you have a fractional order derivative i.e. could you have $\frac{d^ny(x)}{dx^n}$ where, for example, $n=\frac{1}{2}$? And, 2. can you have a variable as the order of a derivative i.e. $\frac{d^ny(x)}{dx^n}$ where n=some variable? I have doubts as to whether either are even possible, but I decided to post the qestion to find out for sure.
Comment: Yes, this is a thing.  [Fractional calculus](https://en.wikipedia.org/wiki/Fractional_calculus)
Comment: I had a suspicion that fractional order derivatives might be possible. Since the detivative is the rate of change, I suspected you could take, for example, the $\frac{1}{2}$ rate of change.
Comment: See also the "Related" answers (Column to the right of the screen on which your question appears) too.
Comment: Citation : From the 18th century, the beginning of the concept of fractional derivation, that is an operator of derivation of not integer degree, appears in papers of L.Euler, of J.L.Lagrange and, early in the 19th century, of P.S.Laplace and of N.H.Abel. The most striking advances are the ones of J.Liouville in several of it's reports to the Ecole polytechnique in Paris, between 1832 and 1835, then the contribution of B.Riemann in 1847, ... Etc. from page 8 in the article for the general public : https://fr.scribd.com/doc/14686539/The-Fractional-Derivation-La-derivation-fractionnaire
Answer: Oh boy, this is a fun one to answer.  First, yes, these things exist and they fall under a thing called fractional calculus.

To start, let's assume that the functions we are looking at are smooth so that all the normal derivatives exist.
Secondly, we'll also want $\frac{d^a}{dx^a}=D_x^a$, the $a$th derivative w.r.t. $x$.
Third, we want $D_x^aD_x^b=D_x^{a+b}$.  Specifically, $D^{1/2}D^{1/2}=D^1$.
Now, one approach would be to use the limit definition of the derivative:
$$D_x^1f(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}h$$
As we've assumed all these derivatives exist, it suffices to replace these limits with one-sided limits:
$$^+D_x^1f(x)=\lim_{h\to0^+}\frac{f(x+h)-f(x)}h$$
Take the derivative again and you'll get
$$^+D_x^2f(x)=\lim_{h\to0^+}\frac{f(x+2h)-2f(x+h)+f(x)}{h^2}$$
One can then derive the following formula with induction:
$$^+D_x^nf(x)=\lim_{h\to0^+}\frac1{h^n}\sum_{k=0}^n(-1)^k\binom nkf(x+(n-k)h)$$
Since $\binom nk=0$ for every $n-k\in\mathbb N_{>0}$, we have
$$^+D_x^nf(x)=\lim_{h\to0^+}\frac1{h^n}\sum_{k=0}^\infty(-1)^k\binom nkf(x+(n-k)h)$$
Let $h=1/N$ and this becomes
$$^+D_x^nf(x)=\lim_{N\to\infty}N^n\sum_{k=0}^\infty(-1)^k\binom nkf\left(x+\frac{n-k}N\right)$$
This allows an extension to fractional derivatives, where we use generalized binomial coefficients:
$$^+D_x^af(x)=\lim_{N\to\infty}N^a\sum_{k=0}^\infty(-1)^k\binom akf\left(x+\frac{a-k}N\right)$$
However, the above sum has the annoying attitude to be divergent for negative values, hence, we may include an additional parameter to fix that:
$$_b^+D_x^af(x)=\lim_{N\to\infty}N^a\sum_{k=0}^{bN}(-1)^k\binom akf\left(x+\frac{a-k}N\right)$$
This is an extended version of the Grunwald-Letnikov derivative, and as I have previously shown, the above extends to integrals via Riemann sums:
$$_1^+D_x^{-1}f(x)=\lim_{N\to\infty}\frac1N\sum_{k=1}^Nf\left(x-\frac kN\right)=\int_{x-1}^xf(t)~\mathrm dt$$
Pretty cool, right?

Now, the above limit is quite horrendous and truthfully hard to evaluate at any non-integer value.  While the following definition for fractional derivatives aren't much simpler, they are usually more direct for solving.  To begin, we instead look at fractional integrals.
Let us have $_uJ_x^a$ be the $a$th integral w.r.t. $x$ around the point $u$.  That is,
$$_uJ_x^af(x) = \int_u^x \int_u^{\sigma_1} \cdots \int_u^{\sigma_{n-1}} f(\sigma_{a}) \, \mathrm{d}\sigma_{a} \cdots \, \mathrm{d}\sigma_2 \, \mathrm{d}\sigma_1$$
Note that $u$ has an impact on the integral. It is, perhaps, a curious thing, that we have the following formula:
$$_uJ_x^nf(x)=\frac1{(n-1)!}\int_u^x(x-t)^{n-1}f(t)~\mathrm dt$$
which may be proven by induction.  Here, $n!$ is the factorial, where define it through the Gamma function,
$$x!=\int_0^\infty t^xe^{-t}~\mathrm dt,\quad x>-1$$
Quite obviously, the above formula extends to non-integer values.  By repeatedly differentiating, you will find with the help of the fundamental theorem of calculus that
$$D_x^a~_uJ_x^bf(x)\stackrel?=D_x^{a-b}f(x)$$
Unfortunately, the right side doesn't have a $u$, which might be a problem, so we need to include an additional parameter:
$$_uD_x^a~_uJ_x^bf(x)=~_uD_x^{a-b}f(x)$$
Also note that the order is necessary, since
$$f(x)=\frac d{dx}\int_u^xf(t)~\mathrm dt\ne\int_u^x\frac d{dt}f(t)~\mathrm dt=f(x)-f(0)$$
That is, we need to take the integral first, then the derivative.  This leads to a natural fractional derivative:
$$_uD_x^af(x)=\begin{cases}\frac1{(-\{a\})!}\frac{d^{\lceil a\rceil}}{dx^{\lceil a\rceil}}\int_u^x(x-t)^{-\{a\}}f(t)~\mathrm dt,&a\ge0\\\frac1{(a-1)!}\int_u^x(x-t)^{a-1}f(t)~\mathrm dt,&a<0\end{cases}$$
Where $\{a\}$ is the fractional part of $a$.  For example,
$\{\pi\}=0.1415926\dots$
$\{-2.7\}=0.3$
And $\lceil a\rceil$ is the ceiling of $a$.  For example,
$\lceil\pi\rceil=4$
$\lceil-2.7\rceil=-2$
Using this definition, you may find that
$$_0D_x^ax^b=\frac{b!}{(b-a)!}x^{b-a}$$
as a mere example.  Particularly, we have things like
$$_0D_x^{1/2}\sqrt x=\frac{\sqrt\pi}2$$

Of course, there are many many other fractional derivatives out there (indeed, no two fractional derivatives are necessarily the same), so I suggest you browse the Wikipedia more if you are interested, and if you feel ready to do some crazy integrals, try some research.
Comment: I think it may be misleading (at best, incorrect at worst) to say that the fractional part of -2.7 is 0.3. It's more accurate and clear to say that $\{a\} = a \mod 1$ or $\{a\} = a - \lfloor{a}\rfloor$.
Comment: @AlexanderJ93 If you wish, $\{x\}=x-\lfloor x\rfloor$ was what I was defining the fractional part as.
Answer: Let me add this "destructive" answer as an addition. We take a conceptual approach to the "half" derivative $Hf$ of $f$.
What properties should a "half derivative" $Hf$ of $f$ have?

(1) Clearly, we want $HHf = f'$ for all twice half-differentiable functions $f$, so applying the half derivative twice should give the ordinary derivative.
However, there are many ways of defining a suitable half derivative with property (1), so this doesn't give a unique definition of $H$. We need more properties.
The next thing which comes to my mind is
(2) For the ordinary $n$-th derivative, very basic differentiation rules state that
$$(f+g)^{(n)} = f^{(n)} + g^{(n)}\quad\text{and}\quad(\lambda f)^{(n)} = \lambda f^{(n)}.$$
It's only natural to ask for the same for the half derivative. So $H$ should be linear, that is
$$H(f+g) = Hf + Hg\quad\text{and}\quad H(\lambda f) = \lambda Hf$$
for all half-differentiable functions $f,g$ and all $\lambda\in\mathbb{R}$.
(In other words, the set of all half-differentiable functions forms a vector space and $H$ is a linear operator on it.)
So do (1) and (2) give us a unique definition of a half derivative?
Unfortunately, we will see that the answer is "no", as these properties turn out to be contradictory if we additionally demand only the following tiny bit
(3) All constant functions as well as the identity function $\operatorname{id} : x\mapsto x$ are three times half-differentiable.

Let us derive the contradiction from (1), (2) and (3).
For the zero function $\mathbf{0} : x \mapsto 0$ we have by additivity (part of the linearity property)
$$
H\mathbf{0} = H(\mathbf{0} + \mathbf{0}) = H\mathbf{0} + H\mathbf{0},
$$
so subtracting $H\mathbf{0}$ on both sides gives
$$
H\mathbf{0} = \mathbf{0}.
$$
Now for the constant function $\mathbf{1} : x\mapsto 1$ we have
$$
(H\mathbf{1})' = HH(H\mathbf{1}) = H(HH\mathbf{1}) = H(\mathbf{1}') = H\mathbf{0} = \mathbf{0},$$
so $H\mathbf{1}$ is a constant function, say $H\mathbf{1} = (x \mapsto a)$ with $a\in\mathbb{R}$.
Now by linearity
$$ \mathbf{0} = \mathbf{1}' = HH\mathbf{1} = H(x\mapsto a) = H(a\cdot\mathbf{1}) = a\cdot H\mathbf{1} = a\cdot (x\mapsto a) = (x\mapsto a^2),$$
showing that $a = 0$ and therefore
$$H\mathbf{1} = \mathbf{0}.$$
Therefore, by linearity any constant function $x\mapsto b$ with $b\in\mathbb{R}$ has the half derivative
$$
H(x\mapsto b) = H(b\cdot \mathbf{1}) = b\cdot H\mathbf{1} = b\mathbf{0} = \mathbf{0}
$$
Now
$$(H\operatorname{id})' = HH(H\operatorname{id}) = H(HH\operatorname{id}) = H(\operatorname{id}') = H\mathbf{1} = \mathbf{0},$$
so $H\operatorname{id} = (x \mapsto c)$ is constant and therefore its half derivative is $\mathbf{0}$.
This gives the final contradiction
$$
\mathbf{0} = H(H\operatorname{id}) = HH\operatorname{id} = \operatorname{id}' = \mathbf{1}.
$$

Conclusion. For me, there is no convincing concept of a half derivative. Of course, people can define fractional derivatives in this way or another and derive conclusions, but for it being really a "fractional derivative", something is missing (as (1), (2) and (3) cannot all be true), and there is no way out by the above contradiction.
Comment: Deleted my previous comments. I think the real take away here is that fractional derivatives need not commute, meaning $HD \neq DH$. That's the source of the contradiction here more than anything.
Comment: This is indeed underappreciated.
Comment: @CameronWilliams I think property (1) captures the essential meaning of the notion "half derivative": Apply it twice and you get the full derivative. But (1) forces $HD = H(HH) = (HH)H = DH$ where we used in the second step that the composition of mappings is associative. So I don't agree with your "real take away here is that fractional derivatives need not commute", as the commutativity it is a consequence of the essential property (1).
Comment: Ah yeah I should rephrase. You can't have both $HH = D$ *and* power associativity or commutativity between $H$ and $H^2$. That's what I meant. You have to lose something somewhere, making the algebraic theory of fractional calculus very wonky.
Comment: @CameronWilliams is correct. Your post would invalidate the recently published Handbook Of Fractional Calculus With Applications, which consists of 8 volumes from many authors.
Comment: @gciriani Did you find a mistake in my argumentation? I still think it is correct. Of course, I don't claim that my answer does "invalidate the recently published Handbook ...", but I insist that their fractional derivative must violate one of the properties (1), (2) and (3).
Comment: @CameronWilliams $H$ is a map, with the set of half-differentiable functions being its domain. As the composition of maps is associative, necessarily H is "power associative", and $H$ and $H^2$ do commute (on the domain of sufficiently often half-differentiable maps).
Answer: Yes. Fractional derivatives exist.
See for example, this Wikipedia entry on Fractional Calculus.  As I mention in a comment above; there are eight "related" posts about fractional calculus.
Indeed, the order of a derivative need not be in $\mathbb N$.  Rational orders of a derivative exist, as you were suspecting in your post.
And even irrational numbers can be an orders of a derivative.
Answer: Another way to define fractional derivatives
Recall that the exponential function $e^{ax}$ is very easy to derive:
$$\frac{d^n}{dx^n} e^{ax} = a^n e^{ax}$$
Assume that $f$ can be written as a sum or an integral of exponentials (I will here only go for the integral case):
$$f(x) = \int a(\xi) e^{c \xi x} \, d\xi$$
Taking ordinary derivatives and assuming that the derivatives can be moved inside the integral then gives
$$f^{(n)}(x) = \int a(\xi) (c\xi)^n e^{c \xi x} \, d\xi$$
This formula directly generalizes to fractional $n$.
Example
Probably you haven't heard about it yet, but there is something called the Fourier transform. It can be thought of as splitting a function into frequencies (using $e^{i \omega t}$):
$$f(t) = \int \hat f(\omega) e^{i \omega t} \, d\omega$$
The derivatives then become
$$f^{(n)}(t) = \int (i\omega)^n \hat f(\omega) e^{i \omega t} \, d\omega$$
There are some technicalities with defining $i^n$ for rational $n$, but the problems can be overcome.
Comment: There is also fractional integration: https://www.johndcook.com/blog/2012/04/05/fractional-integration/
Comment: And the huge trouble is that it is non-local, well-defined only for some (small) subset of functions, quite different to the differentiable ones. There are other definitions of a fractional derivative, well-defined for some different sets of functions. And in general we'd need it for functions in the limiting case, where it is hard to see if it is well-defined or not.
Comment: The non-locality might be a big problem, but isn't it possible to extend this definition from Schwartz space to tempered distributions by $\langle D^\alpha u, \phi \rangle = (-1)^\alpha \langle u, D^\alpha \phi \rangle$? That $(-1)^\alpha$ is not very well-defined could probably be overcome by demanding continuity in $\alpha$.
Comment: If $(i\omega)^a \in C^\infty(\mathbb{R}^{\color{red}{*}})$ and $T \in D'(\mathbb{R}^{\color{red}{*}})$ then $\langle (i\omega)^a T,\phi \rangle = \langle T, (i\omega)^a\phi\rangle$ is well-defined as well as $\widehat{(i\omega)^a T} = D^a \widehat{T}$ if $\widehat{T}$ exists. Otherwise with $\psi_n(x) = 1-e^{-1/(1-n^2 x^2)}1_{|x| < 1/n}$  then  $ (i\omega)^a \psi_nT $ is a distribution, and we can ask if it converges as $n \to \infty$.
Comment: Not all definitions of the fractional derivative will return $D^te^{ax}=a^te^{ax}$.  As with the second definition provided in my answer, you will find the fractional derivatives of exponential functions result in the [Mittag-Leffler function](https://en.wikipedia.org/wiki/Mittag-Leffler_function).
Comment: On the other hand, you will find that, with the second definition provided in my answer, one has $_0D_x^tx^p=\frac{\Gamma(p+1)x^{p-t}}{\Gamma(p+1-t)}$, and so under sufficient conditions, one could use the same approach as your answer, but instead approximate functions via power series that involve non-integer powers.

Fractional Order Derivative


What is the difference between I used to vs I'm used to?

Question: May I know what is the difference between I used to vs I'm used to? I have seen both of these words on various media. So please tell me?
Answer: See this duplicate question.
The difference between "I used to" and "I'm used to"
In short, used to refers to an action in the past which is not continued into the present, whereas I'm used to means that you have become accustomed to something.
Comment: Used to means the things I did in the past but don't do in the present. So is the meaning of I'm used to the things I did in the past and do in the present too?
Comment: Not quite... It means things that you you have become _accustomed_ to. In other words, things that you have done often, and now you are in the habit of doing. For example, "I am used to jogging every day." This would mean that I have been jogging every day for a while, and now it is not as much of a chore.
Answer: "Use" means, well, what it means, incorporated an artifice, artifact, feature, function, etc. into an activity.

I used sour milk in the pancakes this morning.

An activity in which you have customarily or habitually engaged in the past is an activity that you have made use of. As I understand it, this is how the expression for "used to do" came into currency. A customary activity that you incorporate into (used in) your activities in the past is an activity that you have used.
It's common (but not guaranteed) to become accustomed to the things you do by habit. Thus, you have probably become used to the things you used to do. It's almost as if being used by a habit makes one accustomed to it. (Note that the form is nominally passive be+"used to".)


Dispersion of Lithium Ions in Nature (Ratio Similar to Isotopes?)

Question: I'm working on a project that identifies average characteristics of different elements. I'm stuck on lithium, I can't find a way to ratio lithium I and lithium II that symbolizes how it is in nature. I tried looking around on the internet but I haven't found any mention of ratios to ions only ratios to isotopes. Does anyone know of anything that might help?
Comment: I'm not entirely sure what you're after.  Are you trying to find  $\ce{Li+:Li2+}$?  It's going to be nearly infinite (or nearly zero, if you reverse it.)  Aside from in plasmas, lithium is almost always in the +1 oxidation state.
Comment: The reference to isotopes in the question is very confusing if you really are asking about the ratio of lithium(I) ions to lithium(II) ions.  Outside of high-energy plasmas, particle accelerators, or the vicinity of stellar cores, there aren't going to be many lithium(II) ions on Earth or in the universe.
Comment: Doesn't really answer the question. If this means anything I could use the ratio in plasma conditions.
Comment: Alright I'm very frustrated, not with this site but with my project, does anyone out there know or understand how lithium ions are dispersed in nature?
Answer: I believe I resolved my problem, the attributes I was looking at was spectra and combining the lines of both ions. The problem was I was comparing data given by two authors that used different units, so what I did, which I think solves my problem, was divide the sums of the given intensity by the emission probabilities for which I received the ratio of Li I to Li II as roughly 33 to 6 or 18% Lithium II. More than I or apparently anyone else thought so I may have still made a mistake, either way thanks to everyone who tried and helped.
Comment: Just to add, the resultant rgb value did match approximately with the hue of a common lithium flame test, so I am confident in my answer, thanks again. I need to start using stack exchange more often.


Why does QEvent::ShortcutOverride event occur?

Question: I have a QMainWindow with an event filter installed.
After I open and close a QDialog the keyboard arrow keys don't respond since QMainWindow receives only ShortcutOverride events instead of KeyPress events.
When I changed the QMainWindow's event filter to handle ShortcutOverride events I got a strange behavior since in my program each key press event is preceded by two shortcut override events (why??).
This doesn't work - events are handled more than once:
<code>bool eventFilter(QObject *, QEvent *event) {
  if(type == QEvent::KeyPress || type == QEvent::ShortcutOverride) {
    QKeyEvent *keyEvent = static_cast<QKeyEvent *>(event);

    switch(keyEvent->key()) {
    case Qt::Key_Up:
    case Qt::Key_Down:
    case Qt::Key_Left:
    case Qt::Key_Right:
      // Do something here
      break;
    default:
      break;
    }

    return true;
  }

  return false;
}
</code>
Why is this happening? Where do those ShortcutOverride events come from?
Edit:
As it turns out, QMainwindow loses focus when the QDialog is opened and never gains it back when the QDialog is closed.
I used setFocus() in the eventFilter of QMainwindow and it seems to do the trick.
Answer: Lost focus is exactly the reason for not getting any keyboard events after a dialog opens up. The solution you suggested is probably the best fix for this issue.
As for ShortcutOverride events, they come for every keypress because any key or combination of keys can be registered as a shortcut. This event gives you an option to cancel shortcut handling, if needed. It has to be processed at the earliest possible moment when the engine doesn't know yet if the pressed key is going to be used as a shortcut or not. Thus the event is generated for all key presses "just in case". You may read more here: https://wiki.qt.io/ShortcutOverride
Answer: It is happens when a key press in child is made. It is used to for overriding shortcut key handling (QKeyEvent).
refer http://qt-project.org/doc/qt-4.8/qevent.html#Type-enum
Comment: In my case, the child (QDialog) is destroyed and still the shortcut override event is triggered.


Popup NSColorPanel?

Question: Is it possible to make an NSColorPanel 'Pop Up', almost like a popup menu, from the NSColorWell?
I don't like how it's implemented as a palette, as it's sometimes not  obvious which NSColorWell it's associated with.
Thanks!
MT
Answer: No, you'd need to create your own color inspector and color well. To get it to pop up above your existing control, you'd need to create a child window and attach it to your existing window. The color palette controls would go in the child window.
However, I'd recommend you avoid doing this. The existing color palette mechanism is time-tested and works across multiple applications.

Popup NSColorPanel?


Shopify billing api charges for sellers

Question: New here and i hope i am in the right place to ask my question. We are having problem with submitting our app to Shopify App Store.
We have an app where people can create their own designs on our physical products and sell. So we can produce their products and dropship to their customers. There are many apps to that.
Problem is they forcing us to use Billing API for our product charges. They take 20% of commission which our margin is not that much. We are wholesaler and we our margin is super low. We use (well we were planing to use) Stripe for products charges, which is 2.9 % commission.
And Shopify Apps Team member is keep asking me my margin, and says: "We are requiring that all apps use the billing API, but I might be able to make an exception since it seems like your business model isn't compatible. If an exception is made, you will be required to sign a revenue share agreement based on your margins"
All other App (in our business line)they charge their customers with 3th party payment processors and i have spoken with some of them they say they never heard about it and they don't share any revenue (apart from membership fees) with Shopify.
Any idea about this?
Thank you so much for you help.
Answer: Shopify is charging 20% of the cost of the app not 20% of the cost of your finished products. I don't know if your app can be free and still in the app store but from what you have written free would work since you will actually make your money on the goods. Just bill normally for the orders you receive

Shopify billing api charges for sellers


How can I upload multiple files with drupal 7?

Question: I'm making a drupal 7 module that contains a form and I would like to upload multiple files in a row. Currently I'm using a managed_file type of input field.
<code>$form['attachment'] = array(
                            '#title' => t('Attachment'),
                            '#type' => 'managed_file',
                            '#default_value' => variable_get('attachment', ''),
                          '#upload_location' => 'public://perm/',
                            );
</code>
This gives me the upload button, but only lets me upload one file. Is there a way I can tell this form to upload a file and still keep the option for a second upload open?
Answer: check out the new ajax system, it's pretty easy to implement, it should allow you to trigger an ajax callback once the file has been selected to add additional file fields to the form dynamically, just google "drupal 7 ajax" and you'll find dozens of examples
Answer: have you checked to see if this is what you need? http://drupal.org/project/multiupload_filefield_widget


Why do I get this error when trying to build Clang from source?

Question: I have checked out the current tip-of-tree from the various Clang 'git' mirrors as described in the getting started page here:
  http://llvm.org/docs/GettingStarted.html
I then follow the instruction to generate the make files using CMake, like so:
  cmake -G 'Unix Makefiles' /Path/To/LLVM-Repository
This fails to configure with the following error - what is going wrong?
CMake Error at tools/clang/CMakeLists.txt:480 (add_custom_target):
  add_custom_target cannot create target "install-libclang-headers" because
  another target with the same name already exists.  The existing target is a
  custom target created in source directory
  "/Users/alisdairm/Repositories/llvm/projects/clang/tools/libclang".  See
  documentation for policy CMP0002 for more details.
Answer: This is most likely a double-checkout of the Clang repository, once into the llvm/tools directory (correct) and a second into the llvm/projects directory (error).
The solution is to delete the copy of the Clang repository in the llvm/projects directory, and then everything should configure and build correctly.


Correlation in electron gas

Question: In the textbooks that I read (namely Ashcroft/Mermin , Marder, etc.) it seems that a distinction is made between the correlations in electron gas and a Couloumb interaction between the electrons. What is exactly meant by the concept of correlations? How is that connected to the interactions in electron gas, and how does the screening enters the picture?
Answer: According to my limited understanding of density functional theory. Coulomb interaction is one of the correlation effects. Besides Coulomb interaction, there are interaction due to Pauli exclusion principle and change of kinetic energy compared with that of non-interacting electron gas.
Answer: It would be useful to have the exact reference in the text where "correlation" is mentioned, but I would argue that correlation is a word which characterizes the collective behavior of electrons in certain circumstances. Such circumstances are varied, but imply that their behavior (and that may be spatial dynamics, but also spin dynamics or other quantities) is not independent. Examples include Coulomb interactions: such interaction mar for instance prevent double occupation of a site in a solid if it is strong enough. The Pauli exclusion principle also imposes constraints on the spin arrangements, thereby inducing correlations between the spins of electrons of a lattice. Other spin spin interactions such may induce ferromagnetism or antiferromagnetism on a lattice, which is another form of correlation.
As a conclusion, there is indeed a difference between correlation, which is a general description of the behavior of electrons, and the interaction or other phenomenon (not necessarily an interaction) which generates it.

Correlation in electron gas