Connect XOOM to internet using a USB UMTS Stick

Question: I have bought a XOOM WiFI, and would like to know if it would be possible to connect it to internet using an external USB UMTS Stick (Huawei E122 HSPA USB Stick). I am aware this is not supported out of the box, I would like to know what would entail trying to connect it to a USB key which by default comes with drivers for desktop operating systems.
Comment: I assume USB key = USB WiFi connector? (I'm just not familiar with that usage).
Comment: I updated the question, I'm talking about a HSPA USB stick, one that uses the mobile phone network to connect to the internet
Answer: If you mean a USB ethernet adapter, then if you have one that has [fully open source] drivers in the mainline linux kernel, it may be as simple as recompiling the kernel for your xoom, installing it, and getting one of the USB otg adapter cables people have been using to read usb memory sticks on xooms.  Fortunately the xoom seems more open to modified kernels than their phones.
Once it is available in the kernel, you may also need to figure out how to tell android to use that network interface - notice there's no ifconfig binary (though people have made their own).  You might check with the android beagle board and android x86 projects to see how they initialize ethernet adapaters.
Comment: Hi Chris, thanks for your answer. Unluckily I'm not talking about a ethernet adapter, please look at the updated question.
Comment: Actually that would be the same process, if you can get an open source linux kernel driver for the stick (ie, to use it on an x86 pc) you should be able to build that for android just as for a wired ethernet adapter.  Binary blobs to download to the stick are ok (well, controversial, but not a cross compile issue) but binary only kernel modules will not work unless the manufacturer provides an android-compatible arm version.
Comment: I don't think there is one available, I never developed a driver myself and I guess reverse engineering it from a closed source one would not be straightforward. As I said above the stick I'm talking about is a Huawei E122.
Comment: Well, I wouldn't buy one to use it with an android tablet; but if you already have it, don't give up yet.  First it seems that the USB interface just works as a normal USB-serial converter (so the kernel part should be easy), and the hard part is userspace configuration.  Here's a report from someone claiming to have had made it work on a gentoo linux box: http://forums.gentoo.org/viewtopic-t-840212-start-0.html   It might be worth actually making mini/liveCD gentoo install and repeating his process on a desktop before trying to do it on the tablet.
Answer: As of right now, I'm going to say you can't do this. Android 3.1 just added USB host support, so it is technically possible, though someone would need to build drivers or an application to take advantage of it.
Comment: Thank you very much for the links, the XOOM would be my first android device therefore I'm totally new to all this. This would be technically possible then? And it would entail writing a driver for the USB stick using the Android SDK? The USB stick I'm talking about is Huawei E122, by the way.


What is the trajectory of a photon moving through a vacuum?

Question: Since electromagnetic energy is carried by photons and moves in forms of waves, does it mean that a single photon when propagating through space doesn't follow the straight path but instead always moves up and down, up and down like a wave. If so another question arises the speed of propagation of light in vacuum is fixed meaning that it will always take the same amount of time for it to travel from point A to point B, but if a photon always moves up and down it will also mean that it travels longer distance than the distance between A and B and so it ill travel faster than light propagates, is it even possible, could you please clarify these concepts for me?
Comment: Electromagnetic fields are quantum fields, i.e. they are continuous phenomena, at least at the scale that we have access to. What is not continuous are the possible measurements we can do on them. All measurements on a quantum field will always return quantized values for energy and angular momenta. That's what photons are: quanta. They are not particles that travel on or with the field. Photons show up when the field interacts with matter and only then.
Comment: For a nice visualtization see https://en.wikipedia.org/wiki/Electromagnetic_radiation. Notice that the wave does not have any motion perpendicular to the direction of the propagation, but what oscillates is the intensity of the magnetic and electric fields (as mentioned in the answer by Michael.
Answer:
Since electromagnetic energy is carried by photons and moves in forms of waves, does it mean that a single photon when propagating through space doesn't follow the straight path but instead always moves up and down, up and down like a wave.

The term photon belongs to the realm of quantum mechanics. The photon is  a fundamental elementary particle in the standard model of particle physics. Electromagnetic energy is defined well in classical electrodynamics and it does move this energy as a wave in time and space.
A single elementary particle propagating through space is mathematically modeled by a wavefunction which is a solution of a quantum mechanical equation. This is a complex number function, it has a sinusoidal form but the only physically measurable effect is the probability of getting a "photon" signal at a specific (x,y,z,t). It is the probability that has a sinusoidal dependence in space time, not the photon, as can be seen in the answer here. The energy of the photon is h*nu, where nu is the frequency of the classical wave which will emerge from a large number of such energy  photons.
So it is not possible to talk of a trajectory of a single photon at the microscopic quantum level. It is only macroscopically, when the atomic source is known, and the interaction footprint  of the photon is detected on a screen or a camera that a straight line can be drawn which in effect is the optical ray of the classical em wave.

If so another question arises the speed of propagation of light in vacuum is fixed meaning that it will always take the same amount of time for it to travel from point A to point B, but if a photon always moves up and down it will also mean that it travels longer distance than the distance between A and B and so it ill travel faster than light propagates, is it even possible,

No, it is not possible in vacuum. The photon does not propagate as you imagine, and can only be described by its energy=h*nu and its spin direction. It always travels at c.
In the complicated quantized environment of a medium with an index of refraction the way the photon wavefunctions are related to the emergent classical wave, shows that the individual photon paths, which at the microscopic level are always in vacuum and travel with velocity c, can not be an optical ray. An individual photon impinging on a transparent medium will interact by elastic scatterings with the atoms of the lattice and certainly its path cannot be one straight line. In coherence with the zillions of photons in a classical em wave it is better to discuss the classical paths and let quantum mechanics take care of the individual interactions. A true analysis quantum mechanically needs quantum field theory and is unnecessarily complicated.
Comment: This is the best answer I ever saw! Frequency is not a fundamental property of a photon, but it's energy. E=h*nu is a classical equation, not a quantum one.
Answer: Your confusion comes from combining two different concepts (although they are related). Photon is a discrete particle. A wave is a continuous. You can look at light as a discrete particle or a wave, but if you think of them the way you are thinking of them, things get confusing.

A photon does not travel among the wave's amplitude function. It
travels in all possible paths and we observe one path at a time (And
usually if the path from A to B is simple, the many possible paths
cancel out).
A photon always travels at speed c.
The up and downs
of a electromagnetic wave are the consequences of a photon moving.
They are self inducing oscillations in the electromagnetic field.
You can also think that the ups and downs of an electromagnetic wave can be represented as a photon, which is carrying information about a change in the electromagnetic field at speed c. (A change caused perhaps by moving a charged particle like an electron.)

By the way, if I didn't answer your question, try to think about why we started thinking of light as particles. (The problems that lead to the concepts you are studying). You can start at the photo-electric effect.
Comment: Photons don't travel, at all. A photon is an initial state prepared by a measurement and a final state of a second measurement. There are no "particles" between those states. The only thing "there is" is the quantum field, which is continuous. No offense, but particles that travel all possible paths are about as physical as Santa Clause visiting all houses trough the chimneys during one night. It's not a good physical picture and one should avoid teaching QM that way.
Comment: Would you elaborate in saying "photons don't travel at all" in an answer? @CuriousOne
Comment: There is an answer like that here: http://physics.stackexchange.com/questions/247093/description-of-a-photon-and-quanta. I am glad not many people looked at it, otherwise it would have been voted into oblivion, already. People just can't seem to let go of the photon as an object interpretation.
Answer: Photons can be regarded as stable particles depending on perspective. In the Sun's core hydrogen atoms break down into a mixed plasma which includes protons and deuterium atoms. If these collide they form a helium-3 nucleus and a gamma ray is released. The gamma ray is a highly energized photon. It is very difficult for this photon to escape the Sun as it is surrounded by densely packed protons. It bounces around for a while (maybe a thousand or a million years) before it gets to the surface. Due to losing some energy from collisions with protons the photon will now be in the visible spectrum. Then if it is "aimed" towards Earth it will take about 8 minutes through the vacuum to get here but not in an exact straight line as space-time is curved by all of the matter nearby (planets etc). The photon does not move up and down with the waveform however. The photon is represented by a waveform because that it how we measure it. For us, with our measurements the photon is the waveform. One Wavelength = One Photon. The wave moves as one. If I threw a coat-hanger at you it would not take on the trajectory of its shape. The entire coat-hanger would move as one. Hope this breaks your perception that a photon travels along itself. You don't walk along yourself. All the best.


Which Ubuntu version should I install in a Macbook mid 2009, is going up to the latest version okay?

Question: I have a Macbook mid 2009 and I wish to install Ubuntu in it, just want to make sure which version is good to go in it.
Comment: If the 2002 that I have works fine with it, I don't see any problem with the latest Ubuntu.
Answer: I would reccommend 12.04 (due to increased stability and support), unless you can cope with occasional breakage - then you might consider 13.04 which has been running well for me.
From a hardware perspective, either should work. Burn a DVD or use a USB stick to test it in live mode before committing to the install.
Answer: Firstly you have made the right choice in switching.  I am running the latest 13.10 on a 2009 mac 5,5. Everything is working except the nvidia drivers don't play nice with my backlight control, so instead I am using the xbacklight app.
Installing on a mac can sometimes be a headache, so you may need to find workarounds for various features (like I have mentioned above). Make sure you back up your important data beforehand in case anything goes wrong.
Good luck!


Can fully homomorphic encryption be practical?

Question: Fully homomorphic encryption has been implemented by Craig Gentry using ideal lattices.
Can it be applied to data stored on a private cloud setup in practice?
I've seen references here and on other sites that lead to the conclusion that it is very slow.
Comment: possible duplicate of [In what ways does Full or Partial Homomorphic Encryption benefit the cloud?](http://security.stackexchange.com/questions/3728/in-what-ways-does-full-or-partial-homomorphic-encryption-benefit-the-cloud)
Comment: Homomorphic encryption is still more theory than practice.
Comment: I agree it to be more on theory ! But theoretically also they rate FHE to be slowest. Isn't there any mechanism or algorithm to make it more efficient as far as the time latency is concerned ?
Comment: I am well aware of the benefits of the FHE on Cloud. I specifically ask for Practical Implementation of the same. So that cant be a Duplicate.
Answer: There is no proof that FHE cannot be implemented efficiently. It is just that, right now, we do not know how to do it. With currently known algorithms (Gentry's algorithm, with a few known optimizations), it would be extremely slow, which means impractical (and quite far in the "impractical" realm, actually). FHE would have to become thousands of times faster than what can be done today, in order to achieve some kind of generic practicality.
Of course, there are a few specific applications which can already make use, in a very practical way, of homomorphic encryption. Typically voting systems, such as Helios Voting -- these do not need fully homomorphic encryption, and can work with a plain, efficient, partially homomorphic ElGamal.
Comment: Apart from being very slow on time constraints are there any other drawbacks/flaws of a Fully Homomorphic Encryption Scheme ?
Comment: @ShashankBajpai: its slowness makes it unusable; it is difficult to have bigger drawbacks than that... Yet I would add that it is a bit too new for its security to be trusted. My rule of thumb is: 5 years of extensive usage in the field. Right now, for Gentry's algorithm, this 5 year period has not even begun...
Comment: I agree on that 5 year period of usage. @Thomas Pornin: Thanks a lot for the valuable input.
Answer: The answer to this question is already completely covered by these questions:

What is the most practical fully homomorphic cryptosystem?.
What's the State of the Art of Homomorphic Encryption?
In what ways does Full or Partial Homomorphic Encryption benefit the cloud?

Excerpts: "The short answer is that none of them are practical ... yet. But there is a lot of active research, and if we're lucky, maybe that will lead to enough improvements that it might become practical. We'll see."   "
They're too slow for most/all practical applications. No point in considering homomorphic encryption for production use today -- way too slow."
Use the search bar on the upper-right of this site, and on Crypto.SE, to find more information about homomorphic cryptography.


Grub Rescue Windows 7 and Ubuntu 14.04

Question: I have an HP Pavilion p7 1010 with 10GB RAM that's dual booted with Windows 7 Home Premium and Ubuntu 14.04. I tried upgrading Windows 7 Home Premium to Windows 7 Professional, and it said that it did it successfully. But for some reason, it didn't recognize my product key, so I tried to go back to Windows 7 Home Premium using the Recovery Partition. That didn't help solve anything, but when I rebooted, it gave me a message that said "Error: No such partition." It said GRUB Rescue, so something must have happened with the Linux bootloader.
Answer: You might like to use boot repair: https://help.ubuntu.com/community/Boot-Repair (installable via USB live ubuntu)

Grub Rescue Windows 7 and Ubuntu 14.04


Spring XD: "tcp" source outputs byte array instead of string? How to output regular text?

Question: The goal is to read data emitted over the network.
On the data generation side I have an app which spews to stdout.  The content of this data is a JSON string.
Here's what I'm doing (on Linux Mint 17, using an BSD flavored netcat):
data generation:
my_app_which_outputs_json | netcat localhost 9999

In SpringXD: (with xd-singlenode)
xd:>stream create --name tcptest --definition "tcp --decoder=LF --port=9999 | file " --deploy
Created and deployed new stream 'tcptest'

Output:
/tmp/xd/output$ cat tcptest.out
82,117,110, ...  (etc, lots more bytes)

I'm sure this is user error, but not sure what to change to make it right.
I should note that if I do this, it works as expected:
my_app_which_outputs_json > /tmp/somefile.txt
...
xd:>stream create --name filetest --definition "tail --name=/tmp/somefile.txt | file" --deploy

Answer: Following up to your own answer, the converters are currently not configured to understand that a byte[] can be converted to a String with content type application/json.
Of course, even if we configured it to do so, it wouldn't be able to determine if the content really is JSON.
Answer: I added the following to my stream defn and it is now doing what I expected.  I found this in the "Type Conversion" section of the documentation.
stream create --name tcptest \
    --definition "tcp --decoder=LF --port=9999 --outputType=text/plain \
    | file " --deploy

(The newlines and backwhacks are not in my actual code, but are used for readability.)
I also tried ... --outputType=application/json... which did not work.  Not entirely sure why.
Answer: text/plain with a byte[] payload activates a ByteArrayToStringMessageConverter. application/json does not currently. I have created https://jira.spring.io/browse/XD-2512 to address this


Is there any reason not to use the trap door ash receptacle in my fireplace?

Question: I never used this trap door. Presumably, it's to dispose of ash on a regular basis.
Is there any particular reason that using this is a bad idea? There's a door/ access panel in the basement to clean out the accumulated ash, which makes me wonder what the benefit is of using this. I can just fill a bucket and carry ash away every fer fires.
Comment: that is actually the only risk that I can think of ... i don't know if smoldering ashes produce much CO, but you could simply install a carbon monoxide detector
Comment: To keep a fire going all winter one  would use the hatch throughout the day. It's not just quicker to sweep into a low spot than shovel out of the front, it keeps dust out of your living area. I've not seen one that's not pre-filled with ash, so if yours isn't, you get to ride that sucker into the ground before the next folks take over.
Comment: let's see ... someone forgets to close the panel downstairs ... they also leave some flammable material laying near the panel .... you can fill in the rest of the story
Comment: Well, I'd be sure the ash I dropped was cool to the touch. I've been taking it out by hand, in a bucket, a few days after prior fire. But, your point is well taken. It adds a layer of risk to my life. Better to avoid it.
Answer: The benefit is that (with the door below closed as per normal practice) you don't need to wait for anything to cool (it's going into a nice masonry chamber, nothing to burn) and you don't need to carry ash through the house. You dump the ash (hot or cold) down the hole all winter, and when spring comes you shovel it out from the basement and go spread it on your garden (unless you are in an alkali soil area. In acidic soil areas wood ash is quite beneficial to gardens.)
@jstola's nightmare scenario is frankly a bit far-fetched. Those cast iron doors don't just fall open by themselves, and any smoldering combustion byproducts would be filtering up by the trapdoor, into the chimney, and out of the house.
Answer: I use my fireplace heavily in Minnesota's winter, and it doesn't have a trapdoor. I do exactly what you describe, scooping out the ash every couple weeks before lighting a fire. No harm will come to you or any furry animals if you don't use the receptacle.


Auto mounting `NTFS` partition at startup not all options work

Question: I am mounting a Windows 7 Home Premium 64-bit system partition on my Ubuntu 14.04.1 LTS 64-bit installation in order to be able to share data between the two OSs. The problem is that although I explicitly give the option permissions in /etc/fstab file I cannot chmod the files or directories inside the mounted drive. I also experimented with it and noticed if I only supplied permissions option while mounting(after unmounting everything) it and changed into the mount directory I noticed that everything had chmod 777 permissions, but I was able to alter the permission via the chmod command. The command is as follows in the command prompt:
mount -t ntfs-3g -o permissions /dev/sda5 /mnt/DATA/

However, I noticed even when I supplied my uid and gid to own the files the option permissions stopped having an effect. I tried appending and prepending it into the list of options just to make sure, and it turned out that in both cases I was not able to alter the permissions with chmod. The codes I used in command prompt is as follows:
sudo mount -t ntfs-3g -o uid=1000,gid=1000,permissions /dev/sda5 /mnt/DATA/

After unmounting, one more try as follows:
sudo mount -t ntfs-3g -o permissions,uid=1000,gid=1000 /dev/sda5 /mnt/DATA/

Both of these configurations did not allow me to change the settings and the option permissions had literally no effect. In my /etc/fstab file I define the line for mounting the NTFS partition as follows:
# data was on /dev/sda5 always
UUID=01CCA0086DD8A980   /mnt/DATA                 ntfs  auto,users,uid=1000,gid=1000,dmask=022,fmask=133,permissions       0       0

How can I make permissions options work so that I can change the permissions on the go without having to remount the partition totally? I read somewhere in this website it as possible, but I am unsure of how to do it. I would greatly appreciate any comments suggestions on this issue. My full /etc/fstab is as follows:
# /etc/fstab: static file system information.
#
# Use 'blkid' to print the universally unique identifier for a
# device; this may be used with UUID= as a more robust way to name devices
# that works even if disks are added and removed. See fstab(5).
#
# <file system> <mount point>   <type>  <options>       <dump>  <pass>
# / was on /dev/sda6 during installation
UUID=c6cc14c0-aa75-4660-9e45-10a8fadedb64 /               ext4    errors=remount-ro 0       1
# /home was on /dev/sda8 during installation
UUID=30c60dd5-3c79-4e36-8ed7-d8035422f0b6 /home           ext4    defaults        0       2
# swap was on /dev/sda7 during installation
UUID=ffbc51d4-25b3-413f-aed1-14eba0f769c7 none            swap    sw              0       0
# data was on /dev/sda5 always
UUID=01CCA0086DD8A980   /mnt/DATA                 ntfs  auto,users,uid=1000,gid=1000,dmask=022,fmask=133,permissions       0       0

Comment: `permissions` and uses user-mapping, which conflicts with `uid` and `gid`. Pick one and stick with it.
Comment: @muru Sorry I did not understand what did you mean exactly, could you elaborate a bit on that? Did you mean that I cannot use `permissions` with `uid and `gid`? But using it with `user-mapping` is possible. Did I get it right?
Answer: The best method I was able to find is the fstab entry below for the desired NTFS drive:
UUID=473577933B1627FB /media/username/Data\040Drive ntfs nosuid,nodev,nofail,x-gvfs-show 0 0

You will have full permissions to the mounted drive.  This was done on ubuntu 14.10


What is a word similar to "multiplier" but for addition (or subtraction)

Question: A multiplier is a number by which another number is multiplied. What do you call a number by which another number is added or subtracted?
Comment: **minuend** minus **subtrahend** equals (directed difference)  ( see at http://www.factmonster.com/ipka/A0881931.html ; but 'difference' is always taken as the absolute value, even when taking a larger from a smaller number, which this doesn't cover)
Comment: It's the **addend**.
Comment: Genius. Does that work for subtraction as well, or is the terminology different? By the way, you should make that an official answer so I can mark it as correct.
Comment: Got it. So for *addition* it's **addend** and for *subtraction* it's **subtrahend**. Thanks!
Answer: There are a couple of mathematical points to make which inform the English involved.
(1) 'Addition' (yes, simple addition!) covers two major operations:
(a) Combination of two elements from a set (a binary operation) (eg 3 marbles + 2 marbles = 5 marbles).
(b) Transformation of one element into another (a unary operation) (eg a 3cm-long worm grows by 2cm )
Both are modelled identically by 3 + 2 = 5, but a transformation arrow with '+2' over the top is fitting for the transformation.
In the first case, addend + addend = sum / total
In the second case, augend + addend = sum / total.
(2) We've had a thread discussing the fact that there is no agreed term for the result of a subtraction; 'directed difference' is used by some.
Answer: There is the multiplier (that which multiplies) and the multiplicand (that which is to be multiplied).
For subtraction there is the subtrahend (that which is to be subtracted) and the minuend (that which is to be diminished).
For division there is the divisor (that which divides) and the dividend (that which is to be divided).
These words with -and or -end are Latin future participles.
Comment: Your answer was a bit more straightforward. For those looking for a quick answer, it might be useful to add another sentence about **addend** in the same format. Thanks!
Answer: Probably, the answer is the "addend" and "subtrahend"


What is this plant with the unusual Leaf

Question:
We live in NSW Australia and was given this plant by a friend, very unusual.
Comment: Please send a few better pictures?  I am seeing a pot of soaked soil?  Have you fertilized?  What type and intensity of lighting does this plant need? Do you know if your friend fertilized?  What type of medium has this plant been having to live within?  Potting soil I hope?  Better picture we'll be able to give you a closer ID but with soaked soil, garden soil in the pot, no fertilizer this plant is on a diminishing life line.  Please tell us more and send a better picture or two!  Thanks!
Answer: This is a Calathea, originally native to Central and South America.  There are many varieties and species as you can see from the picture below. I cannot identify which variety due to the picture quality.
Provide filtered high light and water less in the winter.  Apply dilute fertilizer in the spring.  Propagate this plant by dividing the existing plant into two.


How to tell if compression damping settings are working?

Question: This is an embarrassing novice question ... I got a mountain bike with a fork that has low and high speed compression damping settings. This is the first time I am riding a bike with an air fork. I do not have experience with them. I cannot notice any difference in the fork's behaviour when going from minimum to maximum damping or vice versa. In contrast, I can notice a difference in the rebound setting. Is this normal? How can I determine if it is working correctly?
Comment: There's absolutely nothing wrong with a novice question.  Notice that of the thousands of questions already asked here, noone else has asked the same question.  That's awesome, so welcome to the site!   You might want to browse through the [tour] to learn a bit more, now you have some answers to vote on, and get to pick one as "accepted" once you've tested the suggestions.
Answer: Try taking all the air out so you can feel just the damper's resistance. Low speed compression will be noticeable when doing body movements such as preloading, weight shifting, or braking. High speed compression is for events such as hitting big drops and large square edge impacts. The easiest way to test that is to smash into a square curb (perhaps with a bit of air to prevent fork damage).
Remember that the "speed" here is shaft speed, not bike speed. Shaft speed is how fast the damper shaft is moving through the oil column. Smashing a curb at walking speed is a high shaft speed event, just as pumping through a compression at 40km/h is a low shaft speed event.
Comment: Thank you for the tip. I let most of the air out. I left a little bit because the fork has shortened considerably. I think this is because it has a coil spring instead of a negative air chamber. Between maximum and minimum low-speed compression, I can only tell a hint of a difference, but I am not sure. I also tried to speed up and break, then measure the position of the ring. It is the same (within variation) for minimum and maximum compression. But of course this method is not reliable, so the variation is considerable. Does this sound normal to you?
Comment: @Bright Green The adjustment range is usually pretty wide, so no that's not normal. Next step is to take the lowers off so you can play with the exposed damper shaft, if you're comfortable doing that. Which fork?
Comment: It's a "Suntour Auron 35 RC2-PCS 130 mm". It did have it for over half a year, but as a beginner I didn't notice anything wrong other than being surprised that there is not much of an effect from adjustments. It doesn't feel bad to ride it though ... I should probably look into the warranty.
Comment: @Bright Green If you do get it warranties, consider using Suntour's upgrade program. You can get a better fork for a pretty good deal, especially if you use the warranty as leverage.
Answer: I would pump your fork up to the manufacturers suggested air pressure for your riding weight.  Then determine if this gives you the desired sag.  Sag is the distance into your travel that your body and gear weight cause on the suspension, and is an important baseline to get correct first before any other adjustments.  In an air fork, sag is a function of the air pressure and adjusting air pressure changes the sag. Your riding weight is with the gear, including backpack or hydration pack you would normally ride with. Don't worry if this stuff varies between rides, just generally be at your riding weight when setting sag.  The fork will have a sag indicator o-ring usually on the left, air spring side. To set sag--which should be 25-30% of the full travel of the fork--sit on the saddle and assume your normal riding position. Leaning up on a wall or tree or have another person assist, bob up and down on the fork a few times while holding the brake. This breaks any stiction present. Back to your riding position and take a minute for the suspension to settle in.  Carefully slide the sag indicator o ring down the stanchion until it touches the seal.  Now you must carefully dismount the bike while being careful to not activate the suspension which will cause the sag measurement to be inaccurate.  A bucket or step ladder placed beside the bike helps to be able to get off the bike.  When you're off the bike measure the distance between the indicator ring and the oil seal. For 100mm travel forks it should be 25-30mm.  For 120mm travel forks the measurement is 30-35mm.  If your travel is different, simply multiply the the forks total travel by 25% then 30% to obtain the suggested sag measurement range. To adjust the amount of sag you need to adjust your air pressure. If you are getting under 25% sag, you'll need to decrease air pressure in 5 psi increments until you achieve 25-30%.  Air pressure is adjusted with a special high pressure shock pump attached to the schraeder valve on the top of the left fork leg. (Left/right is defined from the rider's  perspective in the saddle). To remove air, attach pump and use the microadjust button).  If the sag measurement is too high--over 30% of travel--air should be added to the air spring, also in 5-10 psi increments.  I usually leave my pump attached to the schraeder valve while I set my sag. This is for convenience and that I kind of know what numbers I'm shooting for. Some might think it will lead to inaccuracy since there is an additional air volume held within the pump and hose. However the pressure reading is that volume of air in the fork and when you disconnect the hose air remains inside the fork and what you hear is air escaping from the hose and pump. You do need to be off the bike to determine the proper pressure reading, then remount to set sag.
Fox recommends an initial rebound setting of 1/2 the number of total clicks out from fully in. Thus if you have 12 total clicks of adjustment, turn the rebound adjuster fully clockwise (do not force the dial past it's stopping point.  This can damage the Internals or jam the rebound needle making it difficult to adjust). So fully in and then back out 6 clicks (determine the total amount of clicks you have by counting them as you unwind the adjuster out from fully in. Generally it's 12 to 14 clicks).  This is your baseline rebound setting and can be altered as you ride.
Low speed compression controls the damping of smaller, low shaft speed hits and rider movement like controlling peddle bob. You have, again, a number of clicks of adjustment and a good starting point is 1/2 the number of total clicks.  You will want to set all these parameters with any 2 or 3 position ride control lever in full open (counter clockwise) position. In other words, you may have a lever on top of the right fork leg that has "open, medium, firm" or "climb-trail-descend" and you'll want to make adjustments in open or descend mode.
High speed compression is high shaft speeds encountered with larger square edged hits or big drops.  The adjuster on the fork is labled HSC, and again the manufacturer will indicate in the manual or sometimes on a sticker on the fork, what a good baseline setting will be for your weight.
To make adjustments out on the trail, I suggest using a method called  stacking.  This is making adjustments to one parameter at a time, riding over the same section of trail that has a variety of bumps and texture, and determining subjectively how it feels. After your baselines are set, ride the selected trail section, pick an adjustment, and make two clicks either way. I usually go out/counter clockwise with my adjustments. So 2 clicks out on 1 adjuster and ride the trail section again. Determine better or worse ride quality.  If better go 2 more clicks out (or two clicks in the same direction that saw improvement in the ride), ride the trail section again, better or worse? When it comes to the point where the ride wasn't as good. Go back one click and see how that feels.  It's a good idea to write down your settings for a quicker set up after maintenance or someone else was riding and made adjustments.
I've linked to some helpful videos explaining suspension set-up.  The "Tuesday Tune" by Vorsoprung is one of my favorite series on suspension since they get more in depth as to what is going on inside the shock or fork and explain the mechanics behind them. Also, they aren't shy about offering an opinion whether good or bad about a product or issue. This is refreshing in an industry that often has too much influence on what is said about their products.
Fundamentals of high and low speed compression
Setting up a RockShox suspension


Sanding with lathe turning

Question: When sanding with the lathe turning, should speed be increased as finer grit is used?
What speeds should be used for sanding according to grit being used?
Answer: Ah an interesting question.
The first part, 'Should speed be increased as a finer grit is used'
Generally once I've finished turning a piece I do increase the speed a bit for the sanding and I sometimes increase it a bit more when I'm getting really fine sanding almost polishing it.
However, hard numbers unfortunately are difficult for several reasons.  the first and biggest issue it that as the size of your work piece changes so too does an 'optimal' speed.  On top of that some pieces will just fly apart if spun at the faster speed smaller pieces handle with ease.
I have a variable speed lathe and can just adjust the speed with a turn of the dial and I have a habit of moving it up and down as I'm working on it.  For me unfortunately it more what is the fastest SAFE speed to turn this piece.
Making it even harder for me to give you any speed ideas is that the eye that monitors the speed on my machine comes loose quickly and give me no reading, and I have long since given up trying to keep it set.
If you have a lathe like a 5 speed, then my recommendation is generally bump it up one gear after you are done turning.
The single biggest thing I have found for speeding up the sanding process on a lathe is actually not the speed it is turning but the direction. My second lathe I vowed would have a reverse, and it does, it's my favorite feature closely followed by the dial variable speed.
By being able to sand it in reverse you are sanding against the shearing action of the chisels and when you have some tear out it really does sand faster.  I tend to switch the turning direction as I sand, I generally let it run both ways for each grit to get the nicest fastest finish out of the piece.
Answer: There's no definitive answer to either of these.
It's not just that you'll get differing opinions from various turners on a question like this but that the other variables such as species and abrasive type matter hugely.
Additionally is the often-hidden factor in turning, one that is vital to remember at all times: for any given set speed on the lathe the actual surface speed varies with the diameter. So even sanding a single piece such as a bowl or platter at a set speed on the lathe you're not actually sanding at one speed1.
One more factor to bear in mind is that many turners are power sanding, possibly in addition to varying the speed of the lathe, or instead of it. Obviously this greatly complicates the picture.

What speeds should be used for sanding according to grit being used?

What wood are you sanding? What are you sanding with? How big is the piece? Are you power sanding or sanding by hand so to speak? Do you stop between grits to manually sand along the axis? And last but by no means least, what grit progression are you using?
I understand the desire to get some definitive numbers believe me, but you're going to need to determine this sort of thing for yourself.
You might find that for you, as it is for a great many other turners, this is actually a seat-of-the-pants thing and not a numbers game.

1 The inside of a thick-walled bowl is moving noticeably more slowly than the outside, the rim of a platter is moving much faster than closer to the centre, and so forth.
2 This isn't merely laziness or a lack of rigour, wood varies so much you sort of have to vary your approach nearly on a piece-by-piece basis.

Sanding with lathe turning


Where should I expect to find the trap for my in-wall washing machine drain?

Question: I am trying to renovate an older home. The washing machine was installed in the master bedroom closet. The drain runs down inside the wall. I would like to move the machine to the lower level. My question is how far from the drain is the trap located. I can't find a trap in the present set up.
Comment: Does the hose connect inside or outside the wall? A photo would be invaluable here so we're not all speculating.
Answer: It's going to be below the opening in the wall - most commonly, directly below, which means that if you pull out the washer drain hose and insert a long, slightly flexible rod, you should feel  it hit bottom in the trap, and can make a mark to measure where the trap is with respect to the opening in the wall.
If you are concerned that it might be an elbow rather than a trap, be sure the rod is dry and wash has not recently been done so you can see (or not see) the waterline of the trap on the end of the rod.
And, ultimately, you can always rip open drywall and repair it (an unfortunately common method the way services are installed in houses.)
Personally, I'd suggest giving a try to leaving it where it is, if you have not - there's some sort of cultural tendency to put laundry in the basement, as far from where it's generated and stored as possible. It's worth questioning, and saves a lot of hauling if it's near where most of the sheets, towels, and clothes are used and stored. If moving the machine, I'd suggest leaving all the plumbing in place and putting a test plug in the drain opening, rather than removing the plumbing - a future owner of the house might appreciate it, and it's less work.
Comment: You may be surprised to find the trap in the basement, I had a house in Ohio that had a nice laundry and all the traps for the sinks were in the basement, I had never seen that before being from the west coast where basements are rare. Also a laundry chute down to the washer and dryer is a nice idea but agree with Ecnerwal because you have to pack everything up the stairs. Now that I am older I think about such things but liked it in the basement 30+ years ago.


Why are there so many First Congregational Churches in the US?

Question: A simple google earth search turns up hundreds of "First Congregational Churches" all over the U.S. What is the significance of this name?
Comment: @RyanFrame You mean like banks? :-/ (Maybe someone will have creative marketing and name a church "Last X Church"--"the first will be last and the last first".)
Comment: Lack of creativity? You'll get the same with "First Baptist Church", "First Church of the Nazarene", etc.
Comment: I've always assumed that when the Congregational denomination comes to town they call their church "The Congregational Church". When second one arrives, either by growth or (more likely) schism it renames itself "First Congregational Church" to distinguish it from latecomers.
Comment: lol @PaulA.Clayton +1
Comment: I have seen a "Fourth Baptist Church" before
Answer: Assuming you don't know about Congregationalism
Congregationalism is a system of governance where the local church independently and autonomously runs its own affairs. It does not specify any doctrine or hierarchy, which allows for the existence of 'Methodist Congregational' churches and 'Uniting Congregational' churches. There are two major denominations in the US which are Congregational throughout their structure - the 'National Association of Congregational Christian Churches' and the 'Conservative Congregational Christian Conference'.
Congregational churches are usually Protestant although there are also Congregationalist variants of other religious institutions.
As for the "first" bit
I haven't been able to track down any conclusive evidence.
Wikipaedia lists approximately 100 churches called "First Congregational Church" and only 2 called "Second Congregational Church". They are all in the US.
Comment: @user989718 Firstly you should have written that as a comment to my answer, not as a separate answer because it isn't really an answer. It also makes it more difficult to contact you because I am unable to comment on your answer (I'm a noobie like you). Secondly, perhaps denomination isn't the right word however it is certain that 'Congregational' falls into a different category to 'Methodist' or 'Uniting'. For one thing, there are Congregational Methodist churches and Congregational Uniting churches. Have you got an alternative term to define this distinction?
Comment: The "first/second" thing isn't always a sign of a split. Usually it's just an indication of the sequence churches were founded in a given area. First Presbyterian church of Podunkville is just the first Presbyterian church founded there. I've noted some large cities with churches like "43rd Baptist" although usually after the first and second slots are gone people get more creative with names.
Comment: @Caleb Well I guess this is what happens when an Aussie speaks from personal experience online. We just can't help doing things differently...
Comment: Adding information about how the term potentially indicates different things down under vs up top might make an interesting and useful addition to this answer.
Comment: Just to point out, i meant google "earth" search, i'll edit the question to be more specific.
Answer: Congregational churches are part of the Puritan tradition. The English Puritans, who formed a really core part of the New England colonies, distanced themselves from traditional (high) church practice, especially when these were the same as Roman Catholic practices that they disagreed with.
In traditional Christian practice – this definitely dates back to the fourth century (see list of oldest church buildings) – churches were dedicated to a particular saint, or event in the life of Christ (or the Virgin Mary), or some aspect of God. Often, the church might actually be built or house the remains (relics) of the saint to which it is dedicated.
The seventeenth-century Puritans disagreed with this practice, as do their present-day successors. You may see some churches in this or similar streams of tradition named after Christian concepts such as Trinity or Grace, but equally common are neutral names based on the location of the church. "First," apparently, is a pretty obvious choice for the first church in a particular location, if that location is a large city.
Comment: There still exist a few Church of England churches built by the Puritans in England which do not have a patron saint, but are merely (for one example) "Plaxtol Parish Church".


Are reference designs assumed to be license free?

Question: Can I use a reference design from a data sheet in a commercial product without attribution/licensing of any sort?
Answer: In the most general way, yes.
The document will normally have some sort of legal disclosure somewhere. Many companies will have a disclosure that you may not use their method unless you are using the part it was designed for.
Not to get into anything too much legal, if you are doing something small, no worries. If you are doing something very large scale or that you expect to make a large amount of money from, just get a lawyer's opinion, in writing. Then if someone goes wrong you are protected.
If it is a method they patented, and they are disclosing it with the intention of you licensing it, which I have never seen done without an obvious disclosure, then you do not want to use the technique.
Please let me know if there is anything else I can add to make this more clear or more helpful. I am not a lawyer of any sort, please double check with one if there is substantial money at stake.
Answer: In many cases, a reference design will show you how to use a manufacturer's own device. So, they only stand to gain if you use the design and buy their devices.
However, I am not a lawyer.


The size of Copernicus' and Ptolemy's corrections

Question: I understand that both Copernicus and Ptolemy needed epicycles, but one might assume that a heliocentric system would need much smaller corrections to account for the non-circular motion of the planets.  This is however not mentioned as an important reason to favor Copernicus' system. Is this not the case?
Comment: Related: https://astronomy.stackexchange.com/questions/32766/nicolas-copernicus-discovery As I said there, apart from being heliocentric, a key feature of the Copernican system is that it eliminated [equants](https://en.wikipedia.org/wiki/Equant), although it retained epicycles.
Answer: I gather the worse problem for Copernicus was Mercury.  Not only is Mercury's orbit quite elliptical, it has relatively high precession due to the gravitational influence of other planets.
I found a quote attributes to Copernicus in this document (sorry, only direct link available) where he says :

It is interesting to note that Copernicus had difficulty explaining Mercury's motion and once commented that "this planet has .  ..  influenced many perplexities and labours on us in our investigation of its wanderings".

This is apparently originally from this source :

Baum, Richard and Sheehan, William.In Search of Planet Vulcan:  The Ghost in Newton's Clockwork Universe. Plenum Trade, New York. 1997.

The gravitational perturbation of the planets, particularly by Jupiter, and the concept of barycenter for even ideal elliptical orbits required the work of Newton (following Kepler's concept of elliptical orbits) to explain.  Up until Newton there was no solid theory for the motion at all and people were "just" (poor choice of words) trying to find the simplest model.  Copernicus provided a simple model, but also a less accurate one.
Answer: It all depends what you mean by "corrections." Indeed, Copernicus's model is not geocentric, which should mean that it's more precise, except that it wasn't. His model basically is just an adaptation of Ptolemy's model, but "translated" (in the geometrical sense) to have the Sun near the centre, and with slightly different parametres.
Because that's another misconception : Copernicus's model is not heliocentric but rather heliostatic, which means that the Sun is not in the centre, but simply fixed, and near the centre of planetary orbits. The distance between the Sun and the centre of a planet's orbit is its eccentricity, and it is different for each planet.
To top it all off, Copernicus introduced additional epicycles, so his model is actually more complicated than Ptolemy's. For example, Saturn moves on a small epicycle of radius $r' = 285$ (arbitrary) units, which itself moves on the deferent of radius $R = 10,000$ units (the same size in arbitrary units for all planets). This deferent is not centred on the Sun, but $e = 854$ units from it. Finally, the Earth is $r = 1,090$ units from the Sun. One then has four line segments where one starts where the other one ends, and the goal is to find the angle between the two ends, knowing all the other angles. With Jupiter, terms change to $r' = 229$ units, $e = 687$ units, and $r = 1916$ units.
The diagram below shows how it would look like from the northern pole of the ecliptic. All movements are counterclockwise. The two circular blue arrows mean that the two associated movements are done at the same rate, different from one planet to another, and called its anomaly. The values are very close to those in Ptolemy's model.

In order to calculate the precise longitude of the planet (angle ♈–Earth–planet), one had to introduce additional lines and points in this drawing. Fortunately for his readers, Copernicus—like Ptolemy before him—drew up tables giving the value of each angle from the time or angle it depended upon, so no real mathematical/trigonometric work was needed from the reader.
Copernicus's model was slow in its adoption, because it did not predict planetary positions better than Ptolemy's—it was actually worse, although astronomers didn't realize it right away—and because, as I said, it was more complicated that Ptolemy's model. Also, it did not introduce anything new: in other words, there was no up-to-then-unexplained phenomenon that Copernicus's model explained successfully.
So, astronomers had the choice of following a simple model that gave good results (Ptolemy's), or a more complicated model that gave basically the same results (Copernicus's)… The choice was easy! Add to that the anonymous preface to De Revolutionibus, which basically said that "the model presented wherein is only a mathematical exercise and does not reflect reality," and you have a recipe for disaster for the new theory.
It's only after Galileo showed, with his telescope, the phases of Venus and the moons of Jupiter, that some people started to be convinced—though there was some scepticism about his telescope, as some people thought it was a gimmick/trick that did not show true things, but that's a story of a different time.
Answer: To the authors of both systems, Mars occasionally seemed to move backward in its orbit, so epicycles were needed to account for this. It was not until Newton discovered the laws of gravity that it was realised that Mars was compelled to move slower than the Earth and therefore was sometimes overtaken by the Earth in the journey around the sun. The impression that Mars was moving backwards was of course an illusion, but still had to be accounted for. Copernicus was unaware of Newton's laws, but at least he realised that the orbits of the planets were heliocentric rather than geocentric. He also realised that Mars had further to travel than the Earth.

The size of Copernicus’ and Ptolemy’s corrections


AD9850 and other DDSs: How to stabilize output gain after low pass filtering?

Question: Recently I got familiar with DDS family of ICs. They are fine and nice to work with but there is a problem with them:
The output made by DAC has harmonics that according to the datasheet they need to be filtered by a low pass filter.
That's not a complicated procedure but I need a very very stable output amplitude for a medical device. As anyone knows by filtering, the output drops by -20dB/decade. It can be managed by setting the threshold frequency higher but has the drawback of harmonic remnants.
My question: Is there any way to stabilize the output amplitude? (by the IC itself or additional output components as an amplifier)?
The output before filtering is like this:
Comment: What frequencies are we talking about?  Where is your signal?  Where are the harmonics?  Also, filter output is very "stable", but it might not have the amplitude you want it to have.
Comment: frequency is around 50-100 MHz. As seen in the picture, this is not a clean sine wave.
Comment: The signals generated should generally be below fclck/2.  If this isn't the case, you will have a very hard time removing the harmonics.  Very specifically, what is your clock frequency, what frequency range are you trying to generate, and what is the frequency of the observed harmonics?
Comment: Also, the 20 dB/decade applies to one pole filters only.  More poles means steeper dropoff, which you likely want, but more phase distortion, which you probably don't
Comment: If you have a spectrum analyzer available, you may find it useful. But I would guess that your 'harmonics' are probably related more to the fundamental of the DDS.
Answer: At the outset, use a crystal of at least 8 times the desired maximum output frequency, to provide a greater gap between desired cut-off and DDS-generated harmonics:
Using a spectrum analyzer will show you that the first big noise harmonic is at crystal frequency / 2. A minor harmonic is also showing up for me at 2x output frequency, but its amplitude is pretty close to the noise floor.
By increasing the crystal frequency to beyond 4x desired output, the first big harmonic which remains at crystal frequency / 2 provides a lot more headroom for the low-pass attenuation curve.
Thus, for a 10 MHz maximum output frequency, I would use either a 80 MHz or preferably a 160 MHz crystal.
After this is done, there are several ways of dealing with the specific requirement:

Use LC filters instead of RC filters for an increase in filter attenuation (filter order) for each filter stage.
Use a 4th or 8th order active low-pass filter consisting of several stages, to increase attenuation per decade. See this paper for some insights: "10 MHz Butterworth Filter Using the Operational Amplifier THS4001"
Use a tightly tracking AGC (Automatic Gain Control) stage after the output, to keep the output frequency at a specific level regardless of filter stage attenuation - within meaningful limits, of course.

With a wideband Voltage Controlled Amplifier such as the Analog Devices AD600 / 602, two stages of AGC, both with a roll-off at 35 MHz (inherent to the IC), can be integrated, thus providing a stable output signal voltage for frequencies up to 35 MHz, while attenuating the 40 MHz or higher clock noise even further, beyond the preceding low pass filter stages. See figure 37 of the datasheet for an accurate AGC from DC to frequency range of interest:

Multi-stage active filtering coupled with an AGC seems to be the simplest way to achieve flat response up to the desired frequency. If you keep the filter stage corner frequencies sufficiently higher than the maximum desired output frequency, phase shift will also be minimal.
Comment: Nice answer! I couldn't understand what that AD590 doing there? As I know it is the thermo-sensor!


Federated Authentication check box for service provider disabled\grayed out

Question: I created an external Identity provider in the wso2 identity server carbon console under Identity Providers. I want to add this identity provider to my Service provider API_PUBLISHER in wso2 identity server carbon console.
 But I see the option Federated Authentication disabled under Local & Outbound Authentication Configuration for the service provider. All other options (Default,Local Authentication and Advanced Authentication) are enabled
Answer: You need to configure a federated authenticator for the external identity provider.
When you created an external identity provider, it needs a defined method to communicate with an actual identity provider like google. Federated authenticators are used for that purpose. Once you configured a federated authenticator for your external IDP, wso2is will allow you to use the external IDP with your service provider.
wso2is supports federated authentication with many popular IDPs including Google, Facebook. It also lets you configure any OAuth2, SAML and WS-Fed based IDP as well.
Comment: There is a checkbox called "
Enable SAML2 Web SSO", under idp -> federated authenticators -> SAML2 Web SSO Configuration. Is it enabled?. If not you have to enable it and check if the problem resolved.
Comment: We are using AWS SSO as external IDP and configured the SAML2 Web SSO Configuration. Still the federated authentication radio box is disabled in the Service provider
Answer: Verify identity provider listed in APIM carbon console if not configure the same in APIM carbon console as you did it in Identity server carbon console. Identity server which you configured under


1950s or earlier book with electrical currents living on Pluto

Question: My first sci-fi book I ever read was in the early 1950's in Europe (probably 1952) and it had 10 stories about a different form of life on every planet, including the sun. All I can really remember is that the life on the sun was organized plasma streams on the sun's outer layers, and the life on Pluto was permanent electrical currents within lakes of liquid helium on the planet's surface. Very imaginative at the time.
Comment: Three old stories about plasma life on the Sun are Clarke's "Castaway" and "Out of the Sun", and Clement's "Proof". I don't know any stories that old about electrical life on Pluto.
Comment: It's too late to be the answer, but Larry Niven had superconductor-based life on Pluto in his early short story "Wait It Out"
Comment: The Niven one is way later than 1952.
Comment: @MikeScott: I think you should post that as an answer; it seems that the OP has conflated two things, one of which is very likely to be the Larry Niven short story you mention.
Comment: The idea of life as electric currents in seas of liquid helium is used by Arthur C. Clarke in his story ["Crusade"](https://scifi.stackexchange.com/a/187696/19561) (1968). You can [listen to it on YouTube](https://youtu.be/Li0TnrRTmM8).
Answer: That is Flight into Space edited by Don Wollheim and published in 1950 by Frederick Fell.
It's subtitled "Great Science-Fiction Stories of Interplanetary Travel" and just as you describe, has a story for the Sun, all nine planets, the Moon and the asteroids.  The Sun creatures (in Sunward by Stanton A. Coblentz) are as you said, but the Plutonians (The Rape of the Solar System by Leslie F. Stone) were not -- in that story Pluto was located closer to the Sun until a war with Mars hurtled it outwards.
Comment: Great find! These are really old stories.


Row operations in matrices of vectors.

Question: In cases where linear dependency or independency of some number of vectors is to be found out, one of the methods is to form a matrix of the vectors of dimensions m×n where the column represents the coordinates of a specific vector and the row represents the coordinates of all the vectors along a specific dimension .This is then multiplied with a coefficient matrix and then equated to 0. Solving such problems involve converting the matrix into its row echelon form via row operations. My question here is,why exactly can we perform row operations on the matrix?It is not like we are multiplying one vector with some scalar and add (or subtracting) which is usually the procedure without using matrices.It is like multiplying coordinates of all vectors along specific dimension with some scalar and performing operations on coordinates of all the vectors along other dimension.This is what is shown in my textbook.why does this work?
Answer: The operations are equivalent to multiplying by elementary matrices which are invertible. Therefore, if E is an elementary matrix,
$$
A\cdot\vec{v} = \vec{b} \iff E \cdot A\cdot\vec{v} = E \cdot \vec{b}
$$
because we can go back by multiplying by $E^{-1}$, and thus the original system is equivalent to the last one which is multiplied by $E$. Repeating this process by multiplying by different elementary matrices leaves us with an upper-triangular matrix which is equivalent to the original.
Esentially, when checking if a vector set is linearly independent, you're searching for non-trivial linear combinations of these vectors that equal zero, which we can compactly express as "does $A\cdot v = \vec{0}$ has non-zero solutions?" where $A$ is a matrix that has the vectors as columns.
Comment: While that is correct.One thing that still doesn't get cleared is that how/why can we do this in case of the vector matrix. Because to solve the problem, we multiply the whole vector with some scalar which involves multiplying all the coordinates of a vector with a  scalar . Row operations quite do the opposite.They change individual coordinates. To solve this,it should've probably been that each row represents an individual vectors' coordinates. Then the operations hold true.
Comment: Hmm, I understand what you're saying, though the traditional method is by [row-operations](https://en.wikipedia.org/wiki/Gaussian_elimination). Nevertheless, you can check by hand yourself that if $v_1,... v_k$ are linearly independent, so are $v1, ... \alpha \cdot v_k$.
Comment: Can u pls type out the last sentence again...I can't make out it just shows $v_1....and a bunch of some other characters
Comment: The last thing I said was that, if you have a set of vectors, multiplying one of them by a scalar will not change their linear dependence (or lack of). This is easy to prove using the definition of linear dependence, see if you can prove it yourself.

Row operations in matrices of vectors.


What is the mass of an electron in the sense of its wave nature?

Question: I just completed a course in Mechanics and I'm currently doing electromagnetism. I haven't rigorously started QM; or Modern Physics. I read up a few articles on the Wave-Particle duality.
So, how is the mass defined for an electron while it exhibiting its wave nature?
Answer: Mass is mostly a notion which shows up in dynamical interactions, but you can see it in principle in the behavior of the wave. For instance, the dispersion relation for the quantum wave corresponding to a non-relativistic electron (the relation between angular frequency $\omega$ and wave-vector $k$) will be
$$\omega = \frac{\hbar k^2}{2m}$$
This is just a "quantized" version of $E = p^2/(2m)$ with $E = \hbar \omega$ and $p = \hbar k$.
Another example: if you have a photon with energy $E_p = \hbar \omega_p$ radiated by the electron, its energy drops to $E' = E - E_p$ and you can compute that its wave-vector will now be
$$k' = \sqrt{\frac{2 m (\omega - \omega_p)}{\hbar}}$$
All these relations have $m$ figuring in them and for a different $m$ you would get completely different scalings.
For more digging, you can see e.g. the wiki of De Broglie waves.
Answer: The effective mass of an electron,$M$ can be found from its De Broglie wavelength, $\lambda$ which is the wavelength of the electron from its wave nature by the following equations:
$$\lambda=\frac{h}{p}=\frac{h}{Mv} $$
 Where $v$ is the speed of the electron wave- particle and $p$ is its momentum.
The by relativistic effective mass of the electron, M is given by:
$$M=\frac{M_0}{\sqrt{1-v^2/c^2}}$$
Where $M_0$ is the rest mass of electron.
So thus the effective mass in terms of De Broglie wavelength can be found from the first and second equation by:
$$M=\frac{M_0\sqrt{1-v^2/c^2}}{\lambda*v}$$


Can't see hard disks

Question: I'm running alpine 3.2.0 installed on a thumb drive. once I boot my linux box using the usb, I can't see my hard disks, despite having two of them installed. when I run df -h or df -a, i can't see where they are mounted in the file system. Please note that am booting from a flash drive. Please help
Comment: Please provide the output of 'df -h' and 'sudo fdisk -l'
Comment: You have 2 HDs /dev/sda and /dev/sdb. On each there are 2 partitions, so you have /dev/sda1, /dev/sda2, /dev/sdb1 and /dev/sdb2, all marked as linux partitions.
Comment: This is not about Ubuntu. Moreover, you should post text, not pictures for terminal output.
Comment: 'sudo mount /dev/sda1 /mnt' to mount and
'sudo umount /mnt' to unmount the partition again.
Answer: df shows mounted filesystems, not hard disks. To see your hard disks, use parted, fdisk or lsblk. Once you have identified

your disks,
their partitions, and
the filesystems in the partitions

you may mount the filesystems somewhere (that is, mount each filesystem on a directory) and then df will show them. It is not usual for a Linux system to mount hard-disk-based filesystems automatically.
Edit: See Mercy Flicker's comment for the complete details of how the problem was solved.
Comment: Thanks for your help. I tried all your suggestions and I added some to them and it worked. i had to first make a file system to each of the hard disks by running `mkfs.vfat /dev/sda1` and secondly ran `mount -t vfat /dev/sda1 /mnt`. This got my mounting working. I had also to edit my fstab file to make them mount automatic at bootup by adding my hardisks to the fstab file.

Can't see hard disks


Upgrading a 2008 Mac Pro 3,1 2.8 GHz dual quad CPU to the newer 4GHz CPU

Question: Will the early 2008 MacPro dual 2.8 GHz quad core function with the newer Intel 4GHz chips? If so, which ones?
Answer: Nope! As Intel releases new processors, they also release new processor sockets, so the new processors, besides not being supported by the computer, literally won't fit in the computer.
The highest upgrade you'll be able to do is something from the same product line. The highest processor in that line is the X5492, which clocks in at 3.40 GHz. According to this Apple forum, these processors will work, although your fan speed may increase.
If you have never replaced a CPU before, ask someone who has for help and watch some tutorial videos, or take it in to somewhere to get it done for you. As someone who recently completed their first processor replacement, I can testify that forums and videos will be essential to a successful upgrade. Good luck!


MacBook pro 15 inch 2019 screen flickers with purple horizontal lines when iPhone is near my MacBook screen

Question: When i bring my iPhone near my MacBook pro screen, the screen flickers with horizontal lines. I have tested the flickering with iPhone 11 Pro, iPhone XS and iPhone XS Max. All the devices are up to date with the latest software. I noticed that the flickering is not happening when I keep the device at aeroplane mode.
Has anyone encountered this issue?
Answer: This sounds like the MacBook's hardware is very much more susceptible to RF interference than it ought to be. You should never see artefacts such as those. It might be that there is a build fault (e.g. accidental omission of some shielding component), or some other hardware fault that is causing the unusual sensitivity issues.
You should take the computer to an Apple authorised service centre where you can demonstrate the issue for assessment and repair options.
Answer: This is completely normal. It happens on my macbook and another laptop as well, and I have seen it on other macbooks and a TV as well. On the macbook it looks just like your photo.
It only happens if the phone is leaning on the screen and has data activity - the simple solution is to not lean your phone on your screen.
This is the visual equivalent of the audible buzzing you might hear on speakers.


Using pointiness and bevel at same time

Question: I'm making a chair and trying to use pointiness attribute to express the damage of paint at the edges. However the chair has bevel so when I put the bevel on, the corner gets rounder and the pointiness disappear. Is there anyway I can use pointiness as if there was no bevel?
Comment: Check my question here: http://blender.stackexchange.com/questions/60710/hard-surface-modeling-on-cylinder as it may not seems to be related, it is covering some pointiness issue which should apply to your question. You can upload your model to: http://blend-exchange.giantcowfilms.com/ it will be easier to provide good answer.
Comment: This is not possible :-(
Answer: Unfortunately no, I don't think there is a good way to do this.
As far as I know the Pointiness atribute relies on actual final geometry to work, thus can' be faked if the geometry is not really sharp.
For this specific shape You could try and fake it with a gradient texture centered of the object. It's an approximation, but with a little tweaking may achieve good results.
Just add a Gradient node connected to the Generated socket and adjust its positioning with a Vector node by [-0.05,-0.05,-0.05]. You can use a Color Ramp to adjust the progression.
You may also combine by color-mixing several different linear gradients to achieve an effect of a gradient starting from every edge.
Comment: Right thank you for the idea! Maybe that is little too focued on the corner rather the edges. might be better if I draw texture for this :)
Answer: Maybe not this is what exactly what I wanted, but if I put subsurf under bevel, the damages shows up little.

Using pointiness and bevel at same time


Changing Word mail merge data source locations in bulk?

Question: I've just moved a number of Word mail merge files, and a number of Excel spreadsheets that are the data sources for the mail merges, from a Windows XP computer to a Windows 7 computer, and now all the paths for the merge sources are incorrect (used to be c:\documents and settings\user\my documents.... now c:\users\documents....). While I can correct the path of the data source in each file individually, I was hoping that there would be some way of updating the files in bulk, as there are a relatively large number of them. Word 2007 is what is being used, but the documents are all in the previous DOC format (not DOCX).
Answer: I think it's a registry setting you can tweak as described here:

Choose the data source
Word can use a wide variety of data
  sources. The 'Select Recipients' icon
  offers the option to type a new list,
  to use an existing list or to select
  from Outlook Contacts. (Outlook 2007
  still provides the option to start the
  merge from Outlook for even greater
  flexibility - the procedure is
  essentially the same as that for
  Outlook 2003).

If you chose to use an existing
  data source, by default Word 2007 will
  try and connect to a data source in
  the 'My Data Sources' folder. This
  will not help much if the data source
  is a Word or Excel document, for
  example, in some other folder. Don't
  be thrown by the two default entries
  shown in the illustration below,
  simply move to the folder that
  contains your data file and select it.

There is no mechanism included by
  which the My Data Sources folder can
  be set to a different location;
  however, you can set the data source
  folder to a path on the same drive as
  the My Documents folder by means of a
  registry hack. The folder is defined
  at:
<code>HKEY_CURRENT_USER\Software\Microsoft\Office\12.0\Common\DataServices
</code>
Edit the 'MyData' sub key to the
  required folder name (without quotes).
  The start point for the path is My
  Documents and the entry in the data
  key would be a sub folder of My
  Documents, which by default is the My
  Data Sources sub folder. If the
  DataServices key has no entry the
  default setting is used. To move up to
  My Documents enter . (a period/full
  stop). To move up two folders enter ..
  (two periods/full stops). Although I
  have not tested it, the convention is
  one period/full stop for each level,
  so if your My Documents folder is
  buried deeper, in theory at least you
  should be able to add extra
  periods/full stops to take you back to
  the root level of the drive. I regret
  I have not found a way to change
  drives within this mechanism.
This method allow you to move the
  folder to a different path location.
  e.g., here I have My Documents as a
  sub folder of the D: drive i.e. "D:\My
  Documents" thus the default setting
  for the data folder would be "D:\My
  Documents\My Data Sources" . To move
  that data folder to "D:\My Documents"
  you would change the default My Data
  Sources entry for a period/full stop
  to move up a level.

To move to another
  sub folder of My Documents eg "D:\My
  Documents\Merge" simply change the
  default "My Data Sources" to "Merge"

and to move to a different branch of
  the folder structure eg to "D:\Merge",
  add the period/full stop to the path
  as below:

Comment: That looks like it would be handy for creating new documents, but I was looking for a way to update the data source path in *existing* documents, which this doesn't look like it does.
Answer: Try putting a shortcut to the sources you want, inside the My Data Sources folder.  This works for me.  I have the opposite problem now, having just been "upgraded" to Office 10.  I WANT the merge to open "My Data Sources" (where all my shortcuts and directories are) but instead it sends me to a QUERIES folder somewhere in Office14.  I'm no tech wiz, but maybe this registry hack will work if I can get there and figure it out.


OpenGL application not picking up 64bit Mesa OpenGL32.dll

Question: I'm trying to get a 64bit OpenGL application running with MESA compiled in 64 bit.
When compiling both in 32bit it works perfect putting the opengl32.dll and talloc.dll in the same directory as the executable, however, in 64bit the mesa opengl32.dll driver seems to simply pass on the my hardware driver.
If I change the opengl32.dll to any invalid file, the application crashes, which means the file gets read, but passes on to some other driver.
Both of my 32bit and 64bit mesa are compiled in with the same flags, except for changing -x86 to *-x86_64*.
Anyone happen to have a hunch of what could be the problem?
(btw I'm using Visual Studio)
Answer: I can't quite provide an answer, but I can offer an advice.

Verify in the visual studio debugger what opengl32.dll gets loaded (the modules tab).
Step through an OpenGL call to understand how it gets routed (if you built yourself, you can generate symbols).


What is this evergreen plant?

Question: Update 7/22/21
It flowered today, do you recognize this flower?

I got it from a local nursery (USDA Zone 10a) and it was just labeled as an evergreen shrub. What is it and how should I care for it?
Comment: Some kind of escallonia?
Answer: This appears to be Escallonia rubra.
Answer: Looks like a euonymus , usually they are variegated in the landscape trade.
Comment: I searched for euonymus but didn't see any plant flowers like this.

What is this evergreen plant?


Reducing aveiros vs increasing mitzvos

Question: Is it more important to focus on reducing our aveiros than increasing our mitzvos?  Does that depend on anything?
Comment: Psalms 34:15 ס֣וּר מֵ֭רָע וַעֲשֵׂה־ט֑וֹב Mesilas Yesharim perek 6 אחר הזהירות יבוא הזריזות, כי הזהירות סובב על ה"לא תעשה" והזריזות על ה"עשה", והיינו (תהילים לד טו): סור מרע ועשה טוב.
Comment: @Chatzkel that seems like a pretty good answer
Comment: It's the beginning of an answer. It's way more complicated and involved than that. Obviously if one is going to work on first not any aveiros he'll hardly have any time to work on doing more mitzvohs! I mention it as a starting point. There are many who say that by doing mitzvohs that itself will help move away from aveiros
Answer: There is the principle that "doing one mitzvah, leads to performing another mitzvah" - Avos 4:2. However, when one sins, the yetzer hara will do anything in his power to lead a person to performing another sin, G-d forbid. See also: Shaarei Teshuva 1:39, Shelah (Torah Shebikhtav, Re'eh, Torah Ohr).
The Derech Chaim explains:

And that which he said, "since a commandment leads to [another] commandment," is meaning to say that the doing of one commandment is also the beginning of another one, since all of the commandments are one thing. Hence one commandment leads to [another] commandment. For anything that is one is not divisible at all. So when he does a commandment - which is half a thing - that commandment leads to another; until he does all of the commandments, which are one thing. And since the whole Torah is one thing, sins - which are the opposite of the commandment - are also one thing. [So] in the same way that a commandment leads to [another] commandment, so too does a sin lead to [another] sin.

You ask:

Is it more important to focus on reducing our aveiros than increasing
our mitzvos?

Well, let's look at what the above-mentioned Mishnah is teaching us. If a person does one sin, the "reward" of that is another sin, e.g. the yetzer hara tries to convince a person to "just do another sin, it does not matter". G-d helps the one who wants to purify himself, but leaves the "way open" for one who will defile himself, G-d forbid (see: Ikar Tosafos Yom Tov; and sources cited there). However, doing a mitzvah, leads to performing another mitzvah, will lead to rewards and the possibilty to purify oneself. When one does a mitzvah, one gets rewarded. What's the reward? That G-d will help him doing another mitzvah (see: Sefas Emes; Vayikra, Achrei Mot, 5:3).
So, by doing mitzvos and more mitzvos, you'll get more rewarded. You can say that this has a similair effect as reducing aveiros, but how does one do that? By increasing in observing Torah and mitzvos. By doing mitzvos, we create a (stronger) bond with G-d (see: Hayom Yom: Cheshvan 8, Likkutei Moharan 65:7:9, Shelah; Aseret HaDibrot, Yoma, Derekh Chayim, #31).
Why does one sin? Because when does one sin, that leads to another. When one does a mitzvah, he creates a "shell" so to speak, that will protect him from doing aveiros, sins. So, do more mitzvos :).
On a final note, the Lubavitcher Rebbe often expresses the importance of increasing the observance of mitzvos (and Torah study accompanied with tzedakah). See for example in his letter in Igros Kodesh, vol. 10, p.36 (although, the letter was written for a person seeking medical advice, in which the Rebbe also adviced increasing the observance of mitzvos).

וצריך להתייעץ עם רופא מומחה במקצוע שכמה טפולים חדשים חדשו בזמן האחרון המועיל בכגון דא, וכיון שלרובא דרובא הרי זה קשור גם כן עם כח המחשבה, הנה ככל שימעט בשימת לב לאופן דבורו ולא יתרגש מזה שלעת עתה אינו כדבעי, יתוסף בהצלחת הטפול ויוסיף בהטבת המצב, ופשוט שככל שיוסיף בהתמדה ושקידה בלימוד התורה והידור בקיום המצות יתוסף בברכות השי"ת נותן התורה בהמצטרך לו בכלל ובהנ"ל בפרט.
Increase your diligence and assiduousness in your study of Torah and
performance of mitzvos in a most beautiful and meticulous manner
(b'hiddur), as well as your service of prayer.
Understandably, all the above can be done without taking away from
your health; there is enough time in the day to occupy yourself both
in increasing the health of your soul and the health of your body.
When you do so, [i.e., increase your Torah study, performance of
mitzvos, and service of prayer,] you will feel physically better as
well. (translation taken from here)
Comment: thanks for this (and your answer(s) on my other questions recently).  Ksiva v'chasima tova!

Reducing aveiros vs increasing mitzvos


Is there a way that I can sum just the numbers in an entire excel sheet?

Question: I'm trying to set up a sustainable budget excel workbook that I can easily set up the sheets to be named the different categories that I'd like in the summary.  The idea is to add the items from the receipts to the different sheet, within their specific category.  I'd like to be able to have a formula that separates the dates, and text within the sheet to just get the sum of the numbers within that sheet.  Is there an easy way to set up the isnumber formula to exclude dates?
Comment: Unfortunately, Excel sees dates as numbers with special formatting. That's going to make it tricky. If all your currency values are less than a certain value, you can use SUMIF. For instance, 01JAN2000 is 36,526. If all your dates are after that and all the values you want to sum are less than that, you can use `=SUMIF([range],"<36526")`
Answer: Consider the following UDF():
<code>Public Function SuperSum(shName As String) As Variant
   Application.Volatile
   Dim sh As Worksheet, r As Range, v As Variant
   Set sh = Sheets(shName)
   For Each r In sh.UsedRange
      v = r.Value
      If IsNumeric(v) And Not IsDate(v) Then
         SuperSum = SuperSum + v
      End If
   Next r
End Function
</code>
User Defined Functions (UDFs) are very easy to install and use:

ALT-F11  brings up the VBE window
ALT-I
ALT-M opens a fresh module
paste the stuff in and close the VBE window

If you save the workbook, the UDF will be saved with it.
If you are using a version of Excel later then 2003, you must save
the file as .xlsm rather than .xlsx
To remove the UDF:

bring up the VBE window as above
clear the code out
close the VBE window

To use the UDF from Excel:
<code>=SuperSum("Sheet2")
</code>
To learn more about macros in general, see:
http://www.mvps.org/dmcritchie/excel/getstarted.htm
and
http://msdn.microsoft.com/en-us/library/ee814735(v=office.14).aspx
and for specifics on UDFs, see:
http://www.cpearson.com/excel/WritingFunctionsInVBA.aspx
Macros must be enabled for this to work!


Instagram anonymous?

Question: If I have viewed an Instagram account (found on a Google search) could the owner of the account see that I have viewed it (pics and videos etc) if I was logged into Google at the time? Would they be able to see my name as having accessed their account?
Answer: Officially answer is No. There's no way to know if someone has searched for them or visited their profile on Instagram. Just as Facebook doesn't report who has viewed your profile, Instagram doesn't either.
Note: There are so many third party apps who claim that by using those app(s) you can get the list of people who have searched or visited your profile (or photos, videos), but I am not sure how true they are (I have never used any). There are huge chances that they are spam.

Instagram anonymous?


Fire not rendering in 2.78?

Question: I was following the camp fire tutorial on the blender guru YT channel, and i've run into a problem when I try to render my scene. In the tutorial, it says to switch from GPU to CPU for rendering. I can't even see that option in rendering tab though. The fire works just fine otherwise, and i followed the tutorial exactly. Any ideas why the rendering won't work? Thanks in advance!
Comment: GPU support for smoke/fire has been added since that tutorial was made (at least for CUDA/nvidia). Aside from that, I'm not sure I understand what exactly isn't working?
Comment: The problem is that the fire is showing up when I view my scene in solid or  material mode etc, but not in an actual render. If I try to render it, it just shows me a black circle where my emitter is.
Comment: I don't know this work for you or not, but works for me. Just name the attribute node "flame" and everything renders fine! Regards, Addy
Answer: That tutorial, as you can see here, is for 2.73, and since then the Blender UI changed a bit, you can find that option in "file=>user preferences=>system" now (it's called "compute device").
You could also download an old 2.73 from the Blender website, to make it easier to follow the tutorial.
Anyway, remember:

be sure to use "cycles" render before creating the "quick smoke" setup.
save the file in order to enable the cache settings
before rendering, run the simulation from the start (frame 1) since it could need recalculations
if something in the simulation seems to be stuck after some settings change, try also to delete (and thus rebuild) the cache

Also, on the above page you can download a "finished" .blend which could help you understand better.

Fire not rendering in 2.78?


8 yr old Northern Catalpa broke in half due to storm-will it regrow top?

Question:
Tree was about 15 ft tall.  It has sentimental value as my mom who passed gave it to us and helped us plant it.  Will it ever look like a normal tree?  thanks
Answer: From my own experience, a new leader will emerge, but you may need to prune back some other branches to encourage the shape you desire.  I would recommend pruning back to the main trunk, instead of tipping the branches, which typically stimulate more branching from the pruned branch.
Comment: thanks for the advice
Comment: Would you prune now or wait until winter so remaining leaves can do photosynthesis / make energy to recover?
Answer: Catalpa will readily regrow.
Catalpa will give you new growth willingly. It's up to you to prune for the shape you want.
Right now, cut the bruised stub cleanly for aesthetics and watch for new growth where you want it.
Remove growth where you don't, because your tree will be bursting with energy to rebuild its chlorophyll-capturing leaf surface.
Comment: I see them grow many leaders , depending on the size of the tree. You will need extensive pruning  to get a single leader tree .
Comment: Not sure what you mean by "never very tall". The relatively mature Northern Catalpa (Catalpa speciosa) a few hundred feet from my house is over 50 feet tall. True that this is not "land of the giants" territory, but plenty tall for a tree in a residential area. University of Minnesota and many other sources give the tree's height at 40-70 feet, with the large range due to environmental conditions. The Southern Catalpa (Catalpa bignonioides) is much smaller, topping out at 40 feet - were you thinking of that species?
Comment: @blacksmith37 ok thanks
Answer: Observation:  We lost half a peach tree once, no idea why it broke.  If you were to look at it today it would take close inspection to find the places branches snapped, the tree looks normal.  (Three separate breaks, I assume the shock of one breaking triggered the others.)
Comment: Welcome Loren, this site doesnt work like a forum and your answer is more of a comment.  It will probably get deleted.  You are welcome to edit it and improve it.
Comment: @RohitGupta I thought I was going to go over the size limit for comments.


Understanding what ij mean in a Double Riemann Sum (Double Integral)

Question: I am having trouble understanding what the ($x^*_{ij} $, $y^*_{ij}$) in this diagram (circled in blue) is explaining. What I do know is that $i$ is the iteration of the $x$ Riemann Sum and the $j$ is the iteration for the $y$ Riemann Sum. What I am having an issue with is understanding why $x$ needs the $j$ and $y$ needs the $i$. Couldn't the $P$ simply be represented as ($x^*_i$, $y^*_j$)?
Comment: Are you sure it's not a typo?
Comment: It's not. It's written like this in multiple textbooks and in multiple examples throughout the internet. Even my Prof. used this notation.
Comment: Have you asked your Prof.?
Comment: Not to be mean, but that question is obvious. If I had access to my professor I would have asked him instead of coming here. Instead of questioning the question could you please be more productive?
Answer: The double index is needed to specify an intermediate point in a partition subrectangle in the most general way for constructing a Riemann sum.
To define the double integral over the rectangle $[a,b]\times [c,d]$, we must first specify a partition $P = (P_1, P_2)$ where $P_1$ is a partition of $[a,b]$ defined by points $a = x_0 < x_1 < \ldots < x_n = b$ and  $P_2$ is a partition of $[c,d]$ defined by points $c = y_0 < y_1 < \ldots < y_m = d$.  The partition $P$ can then be viewed as the collection of surectangles $R_{ij} =[x_{i-1}, x_i] \times [y_{j-1}, y_j] = \{(x,y): x_{i-1} \leqslant x \leqslant x_i, \, y_{j-1} \leqslant y \leqslant y_j\}$ for $i = 0,1,\ldots n$ and $j = 0,1,\ldots,m$.
A Riemann sum is then defined by
$$S(P,f) = \sum_{i=1}^n\sum_{j=1}^mf(x^*_{ij},y^*_{ij})\,(x_i-x_{i-1})\,(y_j - y_{j-1}),$$
where the intermediate point or tag $(x^*_{ij},y^*_{ij})$ can be any point in the closed subrectangle $R_{ij}$. Recall that the theory is that Riemann sums converge to the integral as the mesh of the partition (area of the largest subrectangle in the partition) tends to $0$, regardless of how the intermediate points are selected.
If we had specified the intermediate point for $R_{ij}$ as $(x^*_{i},y^*_{j})$ then the points would not be completely arbitrary in that all $m$ subrectangles with fixed index $i$ and $j$ ranging from $1$ to $m$ would have intermediate points with the same $x-$component $x^*_i$ (as well as a similar constraint on $y^*_j$ for fixed $j$).
Such a constrained specification of intermediate points is not unacceptable -  Riemann sums defiend this way will still converge to the integral.  Nevertheless the Riemann integral can be defined in a much more general way using completely arbitrary points $(x^*_{ij},y^*_{ij})$.
Comment: @Doxyy: Yes that is correct.  It must be free to be any point within the subrectangle and so two indices are required to distinguish it from other intermediate points. That is a requirement for the function to be Riemann integrable.
Comment: Just recall the definition of the Riemann integral in one dimension.  A Riemann sum approximates the area as a sum of rectangles with heights specified by the function values at any points within the subintervals. All such sums must converge. It is not enough for only special sums, say using the left endpoints, to converge.
Comment: Ok, so by specifying $x$ with $ij$ instead of just $i$ gives us the ability to make it a point that is arbitrary within that subrectangle?


Question about site rules

Question: Is the stack overflow site an appropriate place to post several documents of code and say, "here's the problem but I don't know what's wrong with it?"
Comment: Nooooope nope nope nope. You need to be able to isolate your Q to a minimal example. Minimal does mean minimal, so ' several documents'is WAYYYY too much
Comment: You may want to re-read http://stackoverflow.com/help/on-topic and than [edit] your question if help did not cover your case.
Comment: If you don't know how to debug your code, stop everything and learn how.
Comment: I wonder how one could even assume that something like this would be ok on any site on the internet where you don't pay the people to do that. Several files and one should do that for you for free? Wow.
Comment: @Tom I'm a natural citizen of Math exchange, where people are more willing to look through your work and tell you what you did wrong. I know it's a lot of work to look through code so I suspected that it might not fly here.
Comment: I *hope* that also depends on the size of the submitted question and if one posts a block of 150 math formulas  with the question "where is the issue", then it will be "too broad". Especially since this is hardly helpful for future readers since it is unlikely that they will find that question and have the same context.
Comment: That's true. I was surprised at the backlash I got for for asking this question. -13? Yikes! But I realize now I gave a bad impression of the question I wanted to ask. It is not so broad as I let on. I am fairly sure the problem is with pointers and I have a good idea of which class they are located in.
Comment: Also, to more directly address what you said, its less formulas and more proofs. Occasionally I have had a proof that clearly proved something that wasn't true but I didn't know what the problem was. In a case like that, you really have no choice but to post the whole proof and say, "where did I mess up?" But usually, for a professional mathematician, it's relatively easy to spot the error, even when it's complicated. Code is obviously different.
Comment: @Will do you know a good place I can learn to debug code online? I'm still learning to program so that would be really helpful for me :)
Comment: @ZacharyF *"I was surprised at the backlash I got for for asking this question. -13? Yikes!"* This is a meta and these downvotes mostly mean disagreement. So the voters are trying to say: don't do what you've asked about. The answers just used text to say the same. So, nothing to worry about.
Comment: @ZacharyF It all depends on what you are doing.  Interestingly, internet search engines are very effective for locating debugging instructions for the language/tool that you use.  For example, if I search Bing for "how to debug in visual studio" I get this link https://msdn.microsoft.com/en-us/library/sc65sadd.aspx which is the start of an entire guide for learning how to debug code in visual studio.  In addition, you can find wonderful books on amazon about using your IDE.  Simply search for it by name and sort the results by user rating.  Buy the first couple and read them.
Answer: From the close dialog

Questions seeking debugging help ("why isn't this code working?") must
  include the desired behavior, a specific problem or error and the
  shortest code necessary to reproduce it in the question itself.
  Questions without a clear problem statement are not useful to other
  readers. See: How to create a Minimal, Complete, and Verifiable example.

If you aren't familiar enough with your own code to narrow the problem down to a few lines, then no one is going to be able to help you.  Nor is anyone going to be willing to dig through your code base for clues.
Answer: If you don't know what the problem is with it (and you have both the code and the context), what chance do a group of strangers have with even less?
It's important for you as an asker to narrow down as much as possible your specific question, which includes paring down the actual issue as much as you can on your own before asking us.
We don't really appreciate giant code dumps and questions which state, "I don't know what's going on", since it doesn't convey to us anything that we can truly help out with or build on.
So, I would encourage you to include as much information as possible, including narrowing down the problem, before asking.  Who knows - by isolating issues like that, you may stumble upon the answer without having to ask Stack Overflow!

Question about site rules


Unity game compiled in Windows doesn't open in Mac

Question: I created an Unity game in Windows and I wanted to pass it to a Mac computer. I built it for Mac and I uploaded the .app folder to Google Drive as a .rar. Then, I downloaded it in a Mac and I unzipped it. When I try to open it, it shows the error message "Someapp.app can't be opened". It doesn't explain why. I think the problem isn't from Unity because the log file is empty after the error. Can anyone help me?
Answer: I needed to make the actual executable in the .app folder, well, "executable".
Please try:
Open up a Terminal and navigate to your app folder:
cd <PATH_TO_YOUR_APP>/<APP_NAME>.app/Contents/MacOS/
This folder contains the actual executable file which Windows apparently didn't make executable. Let's add the executable flag:
chmod +x <APP_NAME>
Afterwards I could start the app.
Answer: I made the Build for my project for both PC and Mac, however I had massive issues getting the Mac one to actually work. Here is the tutorial I used to make the builds which was suppppper helpful, but it didn't help fix my issue:
https://www.youtube.com/watch?time_continue=3&v=7nxKAtxGSn8&feature=emb_title
I just figured out how to make the Mac build work with a friend and it was a bit of work. Once you follow the video's directions exactly for the Mac version, you can send the file to your Mac but when you do it will be labeled MacOS and then when you try to open it it will most likely fail and say missing application to open.
From what I have learned, this is because the compression actually corrupts the executable file to open it on the Mac. To fix this, you have to use Terminal to navigate your way into the file and unlock the permission settings that were changed due what we believe is from the compression.
I honestly can't remember where I found this code but the navigation part I got from the other answer here, but you need to open up a Terminal and navigate to your app folder:
cd <PATH_TO_YOUR_APP>/<APP_NAME>.app/Contents/MacOS/
and add the following:
chmod -R 777 [applicationName].app
This unlocked the permissions on the application but when the app was opened, we had to allow permission through the Mac firewall to let it run on the computer. Once we approved permission, the app ran no problem.
I hope this helps and I'm by no means a professional with this so but my friend and I can try to help in anyway possible.

Unity game compiled in Windows doesn’t open in Mac