Can you be found guilty of unsafe speed for conditions if no unusual conditions existed?

Question: How can you be guilty of driving at an unsafe speed for conditions after an officer testifies in his own words in response to certain questions that you were maintaining a safe distance from the vehicles in front of you and that no unusual conditions existed?
Comment: This seems to be really just a complaint about a specific legal issue that happened to you, not an actual question.
Comment: The law is not meant to be impressed by the legal magic of word wizardry because of intentional ambiguity.
Comment: This question is really about a specific set of facts, and so is difficult to address as a legal question. The answer to the question taken literally is probably 'no', but obviously the court didn't accept the premise that the question takes -- a judgment of fact that is both impossible and pointless to usefully discuss on the Internet.
Comment: There are *always* conditions: road maintenance, vehicle maintenance, traffic levels, position of the sun, etc.  What may be a safe speed for a driver in a well-maintained Bugatti Veryon could be unsafe for a Volkswagen Bus with four bald tires.
Comment: That's obviously not what "Unsafe Conditions" means in regards to that particular offense in CA. But it's certainly the legal way to avoid following your own rules and laws.
Answer: California Vehicle Code chapter 11, division 7, article 1, section 22350:

No person shall drive a vehicle upon a highway at a speed greater than is reasonable or prudent having due regard for weather, visibility, the traffic on, and the surface and width of, the highway, and in no event at a speed which endangers the safety of persons or property.

Section 22358.5:

It is the intent of the Legislature that physical conditions such as width, curvature, grade and surface conditions, or any other condition readily apparent to a driver, in the absence of other factors, would not require special downward speed zoning, as the basic rule of section 22350 is sufficient regulation as to such conditions.

Without knowing exactly what questions the officer was asked, it's impossible to know why you were ticketed and why you were found guilty, but "reasonable or prudent" and "endangers the safety of [others]" covers a great deal of ground.
Answer: Any time you see magic words like "unsafe" or "reckless" or "control" or "reasonable" or "prudent" and it's a cop's word against yours you are going down. Why? Because cops are specially trained to identify when people are being unsafe or are out of control. The reason we have statutes about "safety" are so that cops can use their judgment. They are the experts and they are on the street watching with their expert judgment.
Let's say you come tearing ass out of a parking lot. It's a clear day, there are no cars in sight, and you're burning rubber. You get a ticket for something like unsafe driving, or failing to use caution when moving out of your lane... whatever.
You challenge the ticket and the cop testifies as to what he saw and what his report says - basically that you were driving in an unsafe manner. Now you cross examine the cop. You ask if anyone was hurt, you ask if there was anyone even close enough to be hurt, and on and on and so forth. You're thinking you're Clarence Darrow or the To Kill a Mocking Bird guy because how could you be unsafe if no one got hurt. I mean that's obvious right? Wrong. You were unsafe because the cop said you were unsafe.
The ONLY way you win on something like this is by showing a legal impossibility. For example the statute you were ticketed under was for "unsafe lane movement while changing lanes" and you can show that you did not change lanes.
In your example the cop did not say what you think he said. Or if he did, what he said did not mean what you think it means. Or if it did, it doesn't matter because often in this cruel unjust world judges believe cops. Especially with this subjective stuff. For real man, what would happen if judges started believing untrained citizens over the word of cops? Anarchy and mayhem, that's what. Is that what you want? That sounds like what you want. You better be careful or you're gonna end up on a watch list if you're not already on one. And you're going to take all of us down with you. You should've just paid the ticket. You are being watched.
Comment: oh, the last paragraph.
Comment: lol what the? How is he on a watch list for simply defending himself.
Answer: California Vehicle Code 22350. I was actually in court on the day of this particular incident. The young man asked the officer legitimate questions. I remember he asked about the weather, traffic and visibility conditions. The Officer was annoyed and reluctantly stated it was clear, and no construction or pedestrians dangers were present. When he asked the about the vehicle distance and the officer replied he was maintaining a safe distance, my thoughts were the same as his, and everyone else that was there. Clearly he established through the officers own testimony that no imposing or obstructing conditions existed, and no persons or property were ever in danger. His flawed closing argument of "Well, I couldn't be going faster than cars in front of me" was his fatal mistake. But it still doesn't change facts. He obviously wasn't speeding or he would have been cited for that. 'Unsafe Conditions' is the controlling factor, and no violation for that offense could occur without it.
His real issue is obviously clarity. Not a punishable offense, but definitely a factor.
Comment: So can you explain if and why he was found guilty of 22350?


What is an alternative phrase to "swept under the rug?"

Question: I am writing a poem for my Creative Writing class, and my teacher suggested I find a "more interesting alternative" to one of my lines. For context, my poem is about how dead kids are honored and put on pedestals and "never forgotten," but mentally ill kids are hidden away and ignored by society.
Comment: If you're writing something for credit in a class, shouldn't the words be your own, especially for a creative writing class, in which I assume your work will be judged on your own creativity?
Comment: There's "plastered over" and "papered over".  Also, "filed away".
Answer: "an elephant in the room" comes to mind.
"dead kids are honored and put on pedestals and never forgotten, but mentally ill kids are an elephant in the room."

The expression "elephant in the room", sometimes also "elephant in the living room", means "a big issue everyone is aware of, but which is being ignored, because everybody finds discussion about it uncomfortable". The rationale behind the idiom is that an elephant in a (living) room would be impossible to overlook, but people in the room can nevertheless choose to behave as if the elephant was non-existent.

example sentences from the press:

"Increasing poverty in the world is the western politicians' elephant in the room."
"There were two elephants in the room: one of them Clinton's unspoken near miss with the Feds and the other one her Republican rival, who served as the main target of both Democrats' speeches."
"Race is the elephant in the room when it comes to inequality in America."
"Disability is the elephant in the room that we may all wish to ignore. We may be frightened by disability because it reminds us of our own individual and communal vulnerabilities."
"Racial prejudice is the elephant in the room. It's been whispered for years so let's deal with it: many African Americans have privately complained that..."
"Jerry's family keeps criticizing him for not getting a job, but the elephant in the room that nobody talks about is his meth addiction."
Answer: in limbo as defined by The Free Dictionary.  This phrase, meaning in a state of neglect for an indefinite period of time, dates from the early 1600s.

in a state of neglect; in a state of oblivion; in an indefinite state;
  on hold. (*Typically: be ~; leave something ~; put something ~.) (emphasis added)........
They kept her application in limbo for months.

This phrase is particularly apt for your use -- hiding away mentally ill children -- because, as TFD further states:

... allude[s] to the theological meaning of limbo, that is, a place
  outside hell and heaven to which unbaptized infants and the righteous
  who died before Christ's coming were traditionally consigned.
Answer: Mentally ill kids are consigned to the margins sounds good to me. But, if you are a non-native speaker, I'd recommend mentally ill kids are consigned to the margins of society.
Comment: Welcome to ELU. We are not a programming site but rather a site dedicate to the English language. As such, using code markup to create blue monospaced code is wholly out of place here. The use–mention is best made by setting mentions in italic, although for longer pieces you may wish to use the quote markup style.
Comment: A more common way to say this might be the verb "marginalized."
Comment: I chose this one because it fits my syllable count for the line I need to change. Trying to do eight syllables per line, and "I was consigned to the margins" fits that requirement. The rest were all good though. Thank you everyone for your help!


I think my AirPods Pro got ruined by a firmware update. How can I troubleshoot?

Question: I got my AirPods Pro new four months ago. They worked great until last night. I used them yesterday morning. When I finished the case the pods were each about half charged. I left them by my bed all day, not plugged in to charge, but with the pods in the case and the case closed normally.
I went to use them last night and they acted completely dead. The LED won't light in any circumstances. I open the case and my phone doesn't pop up the battery indicator. I put them in my ears and they make no sound. I hold down the pairing button on the back and they won't pair with other Bluetooth devices or respond to other Bluetooth devices they are already paired with. They won't respond to my iPad that they were paired with either. Completely dead.
I spent most of the day yesterday with my phone about ten feet from the AirPods Pro. I got and installed the iOS 15.0.1 update on my iPhone 12 Pro sometime during the day yesterday. It seems to work fine. I noted last night that a new AirPods Pro firmware update was released the day before yesterday. I believe the firmware update, or possibly the iOS update, somehow bricked my AirPods. I can't think of any other possible thing that would make them suddenly stop working without anything physical happening to them.
Last night I plugged them in to charge. I confirmed that the charging wire was working by plugging it into my phone first. After a few minutes, the AirPods felt a bit warm to the touch in the bottom middle. I assume this was the battery charging. This morning they still felt warm to the touch. I think this is a bad sign. It doesn't take eight hours to charge the batteries. They are still totally unresponsive.
I tried How to reset your AirPods and AirPods Pro, but no luck. I noted that my iPhone and iPad still report the firmware version as 3E751, not the new 4A400 before I did Forget This Device.
Is there anything I can try on my own before calling Apple to get these replaced?
Answer: These are so small, I would research the steps (you did well) and then open a support case. There's not much cost benefit to a repair versus a new purchase, but I think Apple might do a better job recycling than I can so I try to get repair parts personally until the new model is substantially better functionality.


Can we use "that", "those", in a derogative way

Question: Do you have examples of uses of "that" "those", etc... in a derogative way.
Comment: This is a comment because I do not know the grammar. It is done with inflection, "I can't believe you wore *that* to the office." The tone says that it was an inappropriate choice.
Comment: *Those people* is sometimes used when the speaker wants to avoid naming exactly who they're talking about (maybe an ethnic minority), but still imply it.  That lets them criticize a group while not explicitly saying so.   For example, "Those people have no self-respect."
Answer: The question seems kind of broad, but I will briefly talk about it and that.
Imagine two girls, A and B. B is dating a man, C. A thinks C is ugly and not worth dating. Normally, we don't use that to refer to a person. We use the personal pronouns, like him or her. But we can use that to suggest that a person is less than human.  I assume this is widely understood as derogatory.

B shows a picture of C to A.
  A: I can't believe you're going out with that.

That would be stressed.
Imagine further that C comes over to visit A and B. Upon his arrival, A decides that she dislikes C more because, in her opinion, he's dirty and disgusting. We don't normal use it for people. Instead, we use he or she. But it can be used similarly to that above. Imagine that C shakes hands with A. Later, A might say

Ew. I can't believe it touched me.

It would be stressed.
Comment: It's not so broad, it's especially about the use of "that", "those", and small words that change the meaning subtly, but especially the ones I mentionned. It's simply open on other examples. If I use "that" + noun, is it the same?
Comment: Oh, you should provide specific examples in your post. _That+noun_ can be derogatory. I will delete this answer soon.


RavenDb server security

Question: I'm hosting RavenDb on server. Database is available using url,for example aaaa.com:90 and everyone has access to it and can add,remove documents from server level. It is possibility to make access to ravendb server  depending on windows authentication?
Answer: If ravendb on IIS7 then you need to :
create new user on server set permission on ravendb/web/data read write and
open iis manager select features/authentication and set windows authentication to enable,
and Anonymous authentication to disable,
do not forget use credential on your application,
Go to RavenDB web site for more information

RavenDb server security


Check if display is powered on in Linux

Question: Is there a way to check if a display is powered on in Linux? I tried xrandr and xset but neither of these two gives me any information about monitor power. Using xrandr I can identify if the vga cable is connected but not if power is connected. I need this because many of our lab systems keeps lying unused just because someone pulls out the power cable or something.
Comment: Have you tried doing [this](http://i.imgur.com/3gq27.png)?
Answer: The ddccontrol package communicates with the monitor and can read or set various parameters, including the power.  At least with my monitor it is capable of turning it on when I have shut it off with the power button.
Comment: It works only with Mitsubishi, NEC and Samsung only but in our lab all monitors are dell monitors. I have tried it and it is not detecting monitor.
Answer: I don't think this is possible with normal VGA monitors. The best you can do is determine if the VGA is hooked up, and use DPMS to make sure the monitor doesn't try to sleep on you. I don't think figuring out if somebody has shut off or unplugged the monitor is something you can get from software.
Comment: This is available in some of the monitors like i said above.

Check if display is powered on in Linux


"These include" or "This includes"

Question: I am writing a user manual and am stuck upon these include and this includes. Do I use This includes when there is only one thing involved? For example, "This includes normal users" and "This includes the front door". And do I use These include when there are two or more things? For example: "These include the lights and doors", "These include administrators and normal users".
Comment: What's the sentence that comes before? That would indicate these or this.
Answer: As Sam said in his comment, the crux is what precedes the "this/these include(s)", not what follows. As a matter of fact, "This includes administrators and normal users" can be just fine, depending on the context.
That said, these can still be a little tricky.  For example:

Several different users can change their own passwords; these include administrators, and normal users.

The "these include" refers to "several different users."  But:

No users are allowed to change their own passwords; this includes administrators, and normal users.

In this case, the "this includes" is singular, because it refers to the single principle that no user is allowed to change a password.

Corruption was uncovered at many levels across the organization; these include both administrators, and normal users.

Here, "these include" refers back to the many levels where corruption was found.
However, instead of trying to figure out the correct usage, a better option would be to use the more all-encompassing including.  In fact, this change seems to improve the sentences:

Several different users can change their own passwords, including administrators and normal users.
No users are allowed to change their own passwords; including both administrators and normal users.
Corruption was uncovered at many levels across the organization, including administrators and normal users.

Get rid of this this, and this problem goes away.
A footnote (to underscore how tricky the this/these choice can be): I could have said, "In fact, these changes seem to improve the sentences..."
Which is correct?  If I am referring to the single hint of replacing the phrase "this includes" with the word including, then "this change seems to improve" is appropriate.  But, if I'm referring to the three individual improvements found in each example, then "these changes" would be better.
Comment: Thanks for the tip for getting rid of decision making. But the single principle part confuses me. The sentence was first 'No users are allowed to change their own passwords', but then it became a single principle: 'No user is allowed to change a password'.
Comment: *Corruption was uncovered at many levels across the organization; **this** includes large-scale bribe-taking as well as petty pilfering*. The choice of *this/these* can actually tell the reader which antecedent is being referenced.
Comment: @fxam: it doesn't matter if you say "_no users are_," or "_no user is_;" the **this** doesn't refer to the user(s), it refers to the single rule that users can't change passwords.
Answer: Well, if

there is only one thing involved

then surely use

This includes

Check here for particular cases of use.

"These include" or "This includes"


Voltage of ESC of ebike to motor

Question:
I have 3 cables (blue,green,yellow) from my ESC to my motor. However I'm confused whether the voltage it provides is AC or DC. Does the nature of the voltage have anything to do with the kind of motor used?
Comment: Your ESC appears similar to the one in [this diagram](https://www.google.com/search?client=firefox-b-d&tbm=isch&sa=1&ei=LJCdXOGMJsih_wT9uq1o&q=red+black+blue+yellow+green+motor+esc+3+phase&oq=red+black+blue+yellow+green+motor+esc+3+phase&gs_l=img.3...92732.96508..97269...0.0..0.58.409.8......1....1..gws-wiz-img.HIP_tiihCqw#imgrc=O8eCiyXoPOehQM:).  If so, you may be able to figure out your remaining wires from it, although I'm used to red black blue being a wiring combo for low(ish) voltage 3 phase, so blue yellow green seems an odd combo to connect to the motor.
Answer: The voltage is more like AC than DC. The waveform is composed of positive and negative pulses. It will be some version of the following:

With regard to the kind of motor used, all types of brushless motors would have a voltage waveform of the type shown as the output of the ESC and terminal to terminal voltage of the motor windings. For motors with an ESC integrated into the motor housing, the motor winding voltage would be seen only inside the motor.
A DC motor with a commutator and brushes would have DC or pulsed DC at the brushes. The voltage across the rotor windings would be DC, but a part of the windings switch polarity as different commutator segments engage the brushes.
Comment: Yes, this is a phase-to-phase measurement as the motor sees.  If a phase is instead measured with a scope grounded at the battery the entire waveform would be positive, at least apart from any inductive decoration.  However there are real safety concerns in probing around in such a system, so it is better kept as a "thought experiment"

Voltage of ESC of ebike to motor


iPhone 3.0 SDK freely availible?

Question: In the United States, is the iPhone 3.0 SDK freely available like how the iPhone 2.x SDK was? I have an application that I wrote in Dashcode and I would like to update it to see if it solves any of the bugs.
Answer: Note: When reading this answer please bear in mind that I have no awareness of 'Dashcode'
You need to have an account with the iPhone dev center but you do not need to be enrolled in a paid iPhone developer program.
Answer: Dashcode 3.0 is included with Snow Leopard (Mac OS X 10.6).  On the DVD, there is a folder called Optional Installs which includes Xcode 3.2 (which includes Dashcode 3.0 as part of the Essentials item).
If you wrote the application with Dashcode, then it was a "Mobile Safari app".  I don't think you'd need any iPhone SDK to work with that kind of an application -- since developers were developing iPhone "web apps" for a year before the SDK existed.  In that case, a new iPhone SDK won't affect your application.
The new Dashcode might help though, as well as samples that highlight new cooperation between browsers and iPhone/iPod Touch hardware.  For instance, check out the Safari/iPhoneOrientation sample (no login required).

iPhone 3.0 SDK freely availible?


How to see encrypted field in System mode?

Question: I can see and use encrypted field in user mode with View Encrypted Data permission. But in System mode it always as "stars" (***********). Is it possible to see it in the System mode as plain text?
Answer: The "view encrypted data" permission is required for the user to see the field value in plain text!
Note you cannot edit this on standard profiles and will require you to clone the standard administrator profile.
An elegant solution is to create a permission set and have the "view encrypted data" permission enabled! Assign the permission set to the users needing it!
A note here is you need to log out and log back in to see this change!
The above is all true if you have classic encryption enabled!
If you have shield enabled then you don't need this permission and one can view this field in plain text as the data is encrypted at rest!
Read more on shield encryption behavior for masked fields below article
https://help.salesforce.com/articleView?id=000315108
Comment: How about in Apex Test classes, I tried assigning "view encrypted data" perm but it still couldn't work? I need it for code test coverage
Answer: Only the users with the permission "View Encrypted Data" enabled on the profile assigned to the user can see the encrypted data.
Answer: I found some workaround for it. I can create Visualforce page and put encrypted field to parameters and then it possible to immediately get this parameter as plain String even in System mode:
<code>PageReference ref = new PageReference('/apex/mypage');
ref.getParameters().put('param', record.Encrypted_Field__c);

String decryptedFieldValue = ref.getParameters().get('param');

//or if you want to get value for example in getter method
String decryptedFieldValue = ApexPages.currentPage().getParameters().get('param');
</code>


Passing Report Criteria with URL Parameters in a Deployment-safe Way

Question: In this question, Jeremy mentioned that it's possible to pass complete report criteria by passing in the pc0, pn0, and pv0 parameters, corresponding to the object's field id, filter operator, and filter value.  I've tried this out, but since field IDs can vary among Salesforce environments, I can't figure out a way to encode the pc0 values in a way that can be safely deployed across environments.  Is there a way to do this?
Comment: possible duplicate of [Custom New Button that creates record of specific type and parent record in Visualforce Controller (No URLFOR!)](http://salesforce.stackexchange.com/questions/9169/custom-new-button-that-creates-record-of-specific-type-and-parent-record-in-visu) You might be successful with some screen-scraping utility that'd visit setup pages and write findings to a List custom setting... Horrible "solution".
Comment: I don't see how this is a duplicate.  There may be similar approaches that could be applied, but that assumes a particular solution to this problem.  These are different use cases, different parts of the Salesforce app, and there may be different approaches to solving the problem.
Comment: For me the root problem is "how to obtain & safely store field Ids" that can be then used in all kind of URL-hacking activities. And until we have a way of learning that (Metadata API doesn't have such capabilities, maybe the new Tooling API...) - we need to obtain them somehow through scraping of either standard forms or setup pages... I think that starting Summer custom settings will be copied to dev sandboxes during refresh so that might be a way.
Comment: @eyescream the metadata api can do it :), I've used it a bunch for generate CSVs with a list of fields which includes the field ID (which is nice for creating links to the field from the sheet) as well as the created by and last modified by id which are absent from the standard retrieve metadata call.
Answer: It's not exactly a solution, but you can take advantage of the fact that sandboxes use the same IDs for fields.  Create the field in production and then create a new sandbox.  You'll then be able to reference the id for the field in the sandbox without worrying that it'll break once it's deployed.  This assumes that you'll need to dynamically pass in the field to the report.
If however, you don't need to dynamically pass in the field to the report, just the filter parameter, just setup the report so it already has the field in place for the first filter and leave the filter value blank.  Then you'll only need to pass in the value to the report and you avoid the whole ID issue in the first place.
Of course, if you're willing to go the extra mile, you could use the List call of the metadata api to get the IDs of the Fields programmatically.  Then you need to post deploy update the IDs with the correct values for the field you're working with.  You can do this with ANT or the Metadata API.
Some example list output from ANT
************************************************************
FileName: objects/Custom_Object__c.object
FullName/Id: Custom_Object__c.Field1__c/00N50000001zXXXXEAU
Manageable State: unmanaged
Namespace Prefix: null
Created By (Name/Id): Joe Blow/00550000000XXXXAAI
Last Modified By (Name/Id): Joe Blow/00550000000XXXXAAI
************************************************************
************************************************************
FileName: objects/Custom_Object__c.object
FullName/Id: Custom_Object__c.Field2__c/00N50000001zYYYYEAU
Manageable State: unmanaged
Namespace Prefix: null
Created By (Name/Id): Joe Blow/00550000000XXXXAAI
Last Modified By (Name/Id): Joe Blow/00550000000XXXXAAI
************************************************************

The Metadata API returns a FilePropertiesResult which includes the same data as above.
Comment: Not in a retrieve call but in a list call.  At least with ant it returns to a text file, updating the answer with links to list call docs and example output from ant.
Comment: Great ideas, but I don't think it'll work for me.  Sadly, not all sandboxes of the same environment.  And we already use the trick of pre-setting some fields, but have some reports where we want to choose the fields dynamically as well.  We may end up just making several copies of the report.
Comment: Does Metadata include the field IDs?  I've never seen that in the resulting XML before.
Comment: HOLY SHEEET. Awesome :) I wish I could upvote twice. Still means we need to hack around if we want this info in Apex but at least it's not screenscraping of setup pages or "new" standard page layout. But pls fix the link, I think it should be http://www.salesforce.com/us/developer/docs/api_meta/Content/meta_retrieveresult.htm?
Comment: Weird, they've been fixed Stackexchange did some extra helper encoding that broke the earlier links.  I'd clicked the open in navigation link so when people click it they have the full contents next to the page.
Comment: This is great.  It doesn't quite meet my requirements yet on its own, but is probably a key piece of the puzzle.


What decrease of polycount should occur as a function of distance?

Question: What decrease in polycount should occur as a function of distance. I make a terrain and I wounder what is the right formula to keep the "poly size"(the screen size) constant. Or is there some mental flaw in this approach?
Answer: In general when polygons get smaller than one or two pixels in either width or height you can get aliasing from that. This is generally called Geometry Aliasing.
It is most noticeable when the small polygons have significantly different colours to the ones next to them. Different normals can also be a problem because specular highlights will change the colour based on the normal.
The aliasing can be reduced significantly by MSAA as it effectively makes the pixels smaller, but screen space techniques like FXAA aren't very good at fixing it.
Of course the size in pixels on screen of a polygon varies with the camera position, orientation and field of view, so the ideal place to select the poly count is in real time with a shader. Failing that you can estimate it based on standard camera settings and a target screen resolution.
Comment: That is an important part of the decisions I have not thought of. I make a voxel world similar to minecraft but smooth so I would like to make most of the decisions of LOD in the CPU. As soon as I get 15 rep i will up wot this however :).
Answer: From my litte experience with terrain rendering, one of the visually most offensive things that happens when naively reducing the polycount with increasing distance is that -for example- the peaks of mountains can get "cut off" or valleys vanish. This obviously will happen when removing vertices uniformly from the mesh and these landscape features simply aren't positioned conveniently enough to be represented by a vertex in the mesh with reduced detail.
So generally I think you will want to retain the shape or silhouette of the terrain as much as possible. One way to achieve this might be to favor local extreme points in your heightmap. That means when reducing the polycount, you first remove vertices that aren't located in the vicinity of a local extreme point or ridge-line, as those should usually represent the peaks of mountains/hill, the bottom of valleys or any other features that greatly define the overall look of the landscape.
Answer: I don't think there is a right formula, it's more important to keep your frame rate smooth rather than keeping the number of polygons fixed. Most games have some polygons budget that they strive to keep their polygons count below. So I would say change how aggressively your application simplify the terrain based on how good the game performs and how good it looks.
It's important to measure and decide what is needed. polycount is a tangible number just like FPS both are not particularly accurate at measuring your game's performance, and there are other things to measure that govern the GPU time such as fillrate, draw batches.
There are famous terrain rendering algorithms such as ROAM that uses a heuristic approach to determine the best detail/performance ratio.
Comment: I understand your point but what I'm looking for is a good gradient of reduced level of detail over distance. I will have like 10 LODs.
Answer: As @Adam said, one or two pixels is as small as you want to go.  In fact, 1 pixel by 2 pixels is the correct size (unless multisampling, which decouples screen pixels from geometry pixels).
The reason it's correct is that 1x2 yields one pixel for each triangle.  If your polygons are smaller than that, then multiple color outputs must be combined into a single pixel.  The final result will vary depending on subtle changes like orientation.  On screen, that looks like jittering textures.  The pixel will be green one second, then brown, then black, when really is should be somewhat constant or smoothly changing.  There are ways to fight it, but if you have exact control of the polygon count through some form of shader tessellation, aim for 1 pixel per polygon.
In terms of math and the "right formula, rendering is always an application of signal processing. This article is an interesting high-level discussion of what happens to a 1-d signal when sampling varies slightly.   As that article describes, the math is almost a century old.  You would probably drive yourself insane trying to apply this theory directly to your rendering, but it does yield a good rule of thumb: one or two pixels.
And obviously, the problem with bigger polygons:
Comment: The ideal for visual quality may be 1 pixel per tri, but current GPU architectures are massively inefficient with such small triangles, due to quad overshading.  I think the IHVs recommend something like 4 to 8 pixels per tri as a minimum to avoid the performance cliff.
Comment: Ah. Now i remember Nyquist frequency. It was a while back but of course it's the right way to go to. It's exactly something like this I was looking for. As I remember a good rule of thumb is to use 5-10 time as sampling frequency for a system (also indicated by Reed -> IHV). So in other words keep the polygons around 5*5 - 10*10 pixels in size. For a screen of HD 1920*1080 would only require 82000 polygons That's not much and with polygon merging and triangulation that will go down even further with about a factor of 5. Of course you also need to add foliage and decorations so in the en 82000


Definition of "healthy adult" when interpreting FDA recommendations

Question: For healthy adults, the FDA has cited 400 milligrams a day—that's about four or five cups of coffee—as an amount not generally associated with dangerous, negative effects.

What exactly is a healthy adult here?
Comment: Welcome to Medical Sciences! Questions here are required to show results of prior research. As described in the [help] and the reasons mentioned in [this meta post](https://medicalsciences.meta.stackexchange.com/q/411), this demonstrates that you've taken the time to try to help yourself, saves us from reiterating obvious answers, and helps you get more specific and relevant answers. Please [edit] your question with links to or references to what you've found in your search. Otherwise your question may be closed.
Comment: For what it's worth, I found it difficult and not at all trivial to find out what specifically constitutes "healthy adult" in this context. This FDA recommendation is linked to from various news and information sources but does not contain any references to the specific studies or discussions leading to the recommendation.
Comment: I'm guessing that the assumption is someone within the not over- or under-weight, no chronic health conditions, adult category. Though this encompasses a huge range of people from early 20's - late 80s, and I don't know if it would include people with say arthritis or an amputation. Interesting question.
Comment: Collins Dictionary defines healthy as "someone who is well and is not suffering from any illness", which is a rather wishy-washy definition in a science context
Answer: I haven't been able to find a source that identifies what specific set of studies the FDA used to make this determination, and didn't immediately find a more detailed report the one linked here which is clearly meant for the general public as a public health statement rather than consisting of comprehensive professional-level guidance.
There are, however, various review papers that speak of the same 400 mg per day guideline. Because they are reviews of multiple studies, there is no single inclusion criteria for patients. I'll mention just a couple of them here.

Wikoff, D., Welsh, B. T., Henderson, R., Brorby, G. P., Britt, J., Myers, E., ... & Doepker, C. (2017). Systematic review of the potential adverse effects of caffeine consumption in healthy adults, pregnant women, adolescents, and children. Food and chemical toxicology, 109, 585-648. is a systematic review; as such, rather than having a specific "healthy" group they have an inclusion criteria for studies, including control groups from studies comparing to another group that may not be considered "healthy".:

"Healthy" subjects were defined as individuals who were not specifically described as having been hospitalized or diagnosed with disease and/or receiving medical treatment for a disease at the time of the study. As such, studies evaluating a healthy population (which included athletes, military personnel, and pregnant women, unless otherwise noted as unhealthy) were included. Studies in which healthy individuals were included as a control group (or similar) as part of a study on unhealthy populations (e.g., individuals with asthma) were included; however, only information from the healthy individuals was used in the assessment.

I'd say this is a fairly broad definition of "healthy".

Another study, Nawrot, P., Jordan, S., Eastwood, J., Rotstein, J., Hugenholtz, A., & Feeley, M. (2003). Effects of caffeine on human health. Food Additives & Contaminants, 20(1), 1-30., is not as systematic, but again "healthy" populations are defined in contrast to other, specific groups of particular interest. If a study is about arrhythmia, the "healthy" group is people without arrhythmia, if about hypertension, the "healthy" group is people without hypertension. For example:

Clinical  studies  have  shown  that  single  doses  of caffeine<450 mg do not increase the frequency or severity  of  cardiac  arrhythmia  in  healthy  persons, patients with ischaemic heart disease or those with serious  ventricular ectopia (Myers  1998)

(here, healthy means those without ischemic heart disease and without ventricular ectopia, a type of heart arrhythmia)

The effect of caffeine on blood pressure in habitual caffeine consumers and abstainers has been investigated in more than 50 acute and 19 repeated-dose clinical  trials  with  healthy  or  hypertensive  subjects(reviewed by Myers 1988, 1998, James 1991c, Green et al.1996). The results of the acute studies indicate that  caffeine  induces  an  increase  in  systolic  (5–15mmHg)  and/or  diastolic  (5–10 mmHg)  blood  pressure, most consistently at doses>250 mg/person, in adults of both sexes, irrespective of age, race, blood pressure status, or habitual caffeine intake.

(here, healthy means "not hypertensive")

More generally, then, I would read a recommendation about "healthy people" to basically be saying "we can't rule out that there are some specific populations that will have negative effects". They can only consider the scope of the studies available to review.
Each individual has a unique combination of health circumstances. If any individual wants advice about their personal caffeine consumption and whether they should use FDA's caffeine guidelines for "healthy" adults or some other guideline, they should ask their own physician. From the FDA's consumer guidelines linked in the OP:

Certain conditions tend to make people more sensitive to caffeine's effects, as can some medications. In addition, if you're pregnant, trying to become pregnant, or breastfeeding, or are concerned about another condition or medication, we recommend talking to your health care provider about whether you need to limit caffeine consumption.
Comment: So; "It depends" is really the answer. Depends on the study and what they defined as healthy in their methodology, which might include groups of people who you might consider unhealthy in another context (e.g. with asthma, but not hypertension).


How to prove $\text{Rank}(AB)\leq \min(\text{Rank}(A), \text{Rank}(B))$?

Question: How to prove $\text{Rank}(AB)\leq \min(\text{Rank}(A), \text{Rank}(B))$?
Comment: The rank of a matrix $A$ which maps $V$ to $W$ is the same as the dimension of the image of $V$, which will be some subspace $U$. $AB$ is the composite of two linear maps. Try tracking the image and its dimension through subspaces as you do one after the other.
Comment: http://math.stackexchange.com/questions/978/how-to-prove-and-interpret-rankab-minranka-rankb
Answer: Hint: Show that rows of $AB$ are linear combinations of rows of $B$. Transpose this hint.
Comment: I know how to prove this but I just hate when someone is clearly asking for help and the answer is, "hint:"
Comment: I understand @Maxim. As you can tell from the vote tallies, the site culture was very different in 2011. The average level of studies of the participants (and the questions) was also a bit higher. This has probably been upvoted as a pithy one-liner rather than pedagogical merits (which still are IMO ok). You are not the only one feeling this way. There is also a "secret" tally of unregistered votes from passers by, who were not eligible to downvote. This answer has raked in a number of such votes. Anyway, if posted today, the *question* would be closed rather speedily.
Comment: (cont'd) Because this is first and foremost a Q & A site, not a help site. And the question does not show any research whatsoever.
Answer: I used a way to prove this, which I thought may not be the most concise way but it feels very intuitive to me.
The matrix $AB$ is actually a matrix that consist the linear combination of $A$ with $B$ the multipliers. So it looks like...
$$\boldsymbol{AB}=\begin{bmatrix}
 &  &  & \\
a_1 & a_2 & ... & a_n\\
 &  &  &
\end{bmatrix}
\begin{bmatrix}
 &  &  & \\
b_1 & b_2 & ... & b_n\\
 &  &  &
\end{bmatrix}
=
\begin{bmatrix}
 &  &  & \\
\boldsymbol{A}b_1 & \boldsymbol{A}b_2 & ... & \boldsymbol{A}b_n\\
 &  &  &
\end{bmatrix}$$
Suppose if $B$ is singular, then when $B$, being the multipliers of $A$, will naturally obtain another singular matrix of $AB$. Similarly, if $B$ is non-singular, then $AB$ will be non-singular. Therefore, the $rank(AB) \leq rank(B)$.
Then now if $A$ is singular, then clearly, no matter what $B$ is, the $rank(AB)\leq rank(A)$. The $rank(AB)$ is immediately capped by the rank of $A$ unless the the rank of $B$ is even smaller.
Put these two ideas together, the rank of $AB$ must have been capped the rank of $A$ or $B$, which ever is smaller. Therefore, $rank(AB) \leq min(rank(A), rank(B))$.
Hope this helps you!
Comment: In your first part how do you say that Similarly, if $B$ is non-singular, then $AB$ will be non-singular. I dont think you can jump to this conclusion at once.
Answer: Since we have $\text{Col }AB \subseteq \text{Col }A$ and $\text{Row }AB \subseteq \text{Row }B$, therefore $\text{Rank }AB \leq \text{Rank }A$ and $\text{Rank }AB \leq \text{Rank }B$, then the result follows.
Comment: please what's Col ?
Comment: It is notation for column space.
Answer: You know that a linear transformation cannot increase the dimension of its domain; i.e. If $T: V\rightarrow W$ is a linear transformation,
$$\dim(T(V))\le \dim(V).$$
Answer: Surely vectors that are in the kernel of $B$ are also in the kernel of $AB$. Vectors that are in the kernel of $A^T$ are also in the kernel of $(AB)^T=B^TA^T$ therefore with the fact that Rank($A$)=Rank($A^T$) and the knowledge that the rank gives you the size of the kernel of a matrix you are done.


Visual Studios 2013 with VM on 12" mac1.3GHz Dual-Core Intel Core M

Question: I'm a non mac user. But I would like to buy the latest mac 12" 1.3GHz Dual-Core Intel Core M. But I need Visual Studios 2013 the requirements are 1.6 GHz or faster processor.
Can this be install in VM and work? Thank you in advance.
Comment: There are several latest Macs - I thin k you mean MacBook. As noted on reviews it is slower than MacBook Air let alone MacBook Pro. As for VS - well I'll bet VS2015 will need more CPU and you will upgrade to that before you upgrade the Mac. As for install yes it will probably install - the question is how well it will run and MS are suggesting not well but depends on how complex your builds are. I think if not pure web based you need more powerful machines (I end up with desktops for this reason)
Comment: Yes, and your absolutely right not doing web on vs. Keeping the desktops it is. Thank you for your answer.
Answer: I guess you are talking about the latest MacBook and not Air or Pro?
VS will probably install and maybe even start, but the MacBook(without suffix) was never invented to be for developers, indeed it isn't even meant to complete any complicated tasks, but only Web and Office, which means that you won't be able to properly work with it.
I can only recommend buying a MacBook Pro which even starts cheaper at 1099$ with a 2.5 Ghz Dual-Core processor.
Comment: Thank you for your recommendation, will keep it in consideration.
Answer: The only way to really know for your workload is to buy it and try it with your projects. In the U.S. and EU, there's a 14 day return policy which should be enough time to test it out. It's got a fast SSD and w/ 8GB of RAM it might be good enough. It has a turbo-burst speed of 2.6Ghz so there are a lot of performance variables in play.


In how many ways can seven people depart a lift on three floors if at least one person leaves the lift on each floor?

Question: Seven people enter a lift. The lift stops at three unspecified floors. At each of the three floors , no one enters the lift but at least one person leaves the lift . After the three floor stops , the lift is empty. In how many can this happen.
What I tried was I created an equation of three variables x,y, z and equated them to 7 .I found the total  no. of solution by using formula (n+r-1)C(r-1) and subtracted the case of occurrence of any x,y,z as zero and subtracted those possibilities from the total solution but I was not able to get the result. Any help would be appreciated. Thanks for advance.
Comment: Are the people indistinguishable?  (I'd presume so).  It is 'stars and bars' except there is a constraint of >0 get out on each floor - how about if you work out how many ways 4 get out on 3 floors, in that way fixing at >= 1 for each floor - using a stars and bars method.
Comment: Can we solve this question by assuming x=0 and y=0 and then using inclusion exclusion principal. And by using the same process of x+y+z=7 and finding the total number of solutions of this equation by the use of the formula.
Comment: I don't see how that would work, x and y cannot be zero
Answer: If there were no restrictions, there would be three choices for each of the seven people, so there would be $3^7$ ways the seven people could depart the lift.  However, at least one person gets off the lift at each floor.  Therefore, we must exclude those arrangements in which fewer than three floors are used as exits.
There are $\binom{3}{1}$ ways to exclude one of the floors as an exit and $2^7$ ways for the people to depart the lift on the remaining floors.
However, if we subtract $\binom{3}{1}2^7$ from $3^7$, we will have subtracted those distributions in which all seven people depart the lift on the same floor twice, once for each way we could have excluded one of the other floors.  Since we only want to subtract these distributions once, we must add them back.
There are $\binom{3}{2}$ ways to exclude two of the three floors and one way for all seven people to exit the lift on the remaining floor.
Thus, by the Inclusion-Exclusion Principle, the number of ways seven people can depart on the lift on three floors with at least one person leaving the lift on each floor is
$$3^7 - \binom{3}{1}2^7 + \binom{3}{2}1^7$$
Answer: The wording of the problem indicates to me that people are to be treated as distinct.
There are just $4$ possible patterns, viz. $5-1-1,\; 4-2-1,\;3-3-1,\;and\;\;3-2-2$
Compute (Choose people ) $\times$ (Permute patterns), for each pattern.
e.g. for the $3-3-1$ pattern, $\binom73\binom43\binom11 \times \frac{3!}{2!}$,
or if you are comfortable with multinomials, $\binom{7}{3,3,1}\binom{3}{2,1}$
Compute similarly for each pattern, and add up. You should get the desired answer of $1806$
Answer: Hint:
Assuming people are distinguishable.
Think of this problem as follows: suppose we have a set with seven elements (the seven people) say $S=\{1,2,3,4,5,6,7\}$. You want to find the number of ways to create a three tuple $(A,B,C)$ (the three floors) of the sets $A,B$ and $C$, where these sets form a partition $\{A,B,C\}$ of the set $S$.
For example
$$\Big(\{1,2\}, \, \{3,4\}, \, \{5,6,7\}\Big)$$
represents the scenario that $1,2$ got off on floor $1$, then $3,4$ got off on floor $2$, and $5,6,7$ got off on floor $3$. Whereas
$$\Big(\{3,4\}, \, \{1,2\}, \, \{5,6,7\}\Big)$$
represents the scenario that $3,4$ got off on floor $1$, then $1,2$ got off on floor $2$, and $5,6,7$ got off on floor $3$.
Since $\{A,B,C\}$ is a partition containing three sets , so each of the set $A, B$ and $C$ are non-empty (this ensures at least one person left at each of the three floors). Once you have the partition
Flaw in your approach:
In your approach you are only counting the number of people stepping out on a floor but person 1 getting out at floor 1 is different from person 1 getting out at say floor 2. Your counting does not take that into consideration.
Answer: Your approach is correct, but subtracting the ones that have x, y or z as 0 makes the problem a bit harder. Instead, consider the following approach:
There are 7 people in the lift. Since at least one leaves the lift at each of the 3 floors, we only decide on the remaining 4. Therefore, the integer solutions of x, y, z such that
x + y + z = 4 where x,y,z $\ge$ 0
And the number of solutions to this problem is found by using your formula.
Answer: The possible combinations are 5-1-1, 4-2-1, 412, 3-3-1, 3-2-2, 3-1-3, 2-4-1, 2-3-2, 2-2-3, 2-1-4, 1-5-1, 1-4-2, 1-3-3, 1-2-4, 1-1-5. In each possible way you need to find the permutations


Ammonium is a weak acid but isn't it considered a strong conjugate acid as a salt's ion?

Question: I'm learning about salt hydrolysis in school and this just jumped out at me. How can $\ce{NH_4^+}$ be both a weak acid and a strong conjugate acid? Since $\ce{NH_4^+}$ is a weak acid it has a strong conjugate base $\ce{NH_3}$. However, as part of a dissolved salt, since $\ce{NH_4OH}$ is a weak base, then $\ce{NH_4^+}$ is considered a "strong" conjugate acid. How can we reconcile these facts? Are the definitions slightly different for a salt ion and a normal acid?
Answer: Just because something is a weak base does not mean its conjugate acid has to be a strong acid. Likewise, just because something is a weak acid does not mean that its conjugate base is a strong base.
The only connection between acidity of an acid and basicity of a conjugate base, henceforth labelled $\ce{HA}$ and $\ce{A-}$, is that they are related by the ion product of water, $K_\mathrm{w}$ by the following equations:
$$\begin{align}\ce{HA &<=> H+ + A-}&\quad K_\mathrm{a} &= \frac{[\ce{H+}][\ce{A-}]}{[\ce{HA}]}\tag{1}\\[0.8em]
\ce{A- + H2O &<=> HA + OH-}&\quad K_\mathrm{b} &= \frac{[\ce{OH-}][\ce{HA}]}{[\ce{A-}]}\tag{2}\\[0.8em]
K_\mathrm{a} \times K_\mathrm{b} &= \frac{[\ce{H+}][\ce{A-}]}{[\ce{HA}]} \times \frac{[\ce{OH-}][\ce{HA}]}{[\ce{A-}]}\\[0.6em]
&= \frac{[\ce{H+}][\ce{A-}][\ce{OH-}][\ce{HA}]}{[\ce{HA}][\ce{A-}]}\\[0.6em]
&= [\ce{H+}][\ce{OH-}] = K_\mathrm{w}\tag{3}\\[1.2em]
\Longrightarrow \mathrm{p}K_\mathrm{a} + \mathrm{p}K_\mathrm{b} &= 14\tag{4}\end{align}$$
Therefore, the sum of the acid and base constants must equal $14$. But if $\mathrm{p}K_\mathrm{a} = 6$, then $\mathrm{p}K_\mathrm{b} = 8$ — meaning the conjugate base of a weak acid is a weak base. This basically mirrors ammonia's case.


is there a certain word to describe these songs?

Question: i've noticed in some songs there will be a part where it sounds like someone speaking from a old television, or just speaking in general and then the music starts playing again. here are some example in songs.
sixteen - no doubt 2:04-2:19
no role modelz - J. Cole 2:42-2:58
temptation - joey badass 0:00-0:18
is there a certain word that categorizes these songs ????
Comment: Voting to keep open because aaliyah is asking for a term for a musical practice and citing examples, not so much asking for analysis/transcription *of* a limited set of songs.
Comment: I don't think there is a term for these specific songs but it is a version of sampling.
Answer: I'm unaware of any word for samples specifically of extended clips of spoken word (besides "sampling", which also covers musical samples and even samples less than a second long). There's certainly not a word for that "categorizes" such songs themselves, because many genres use such extended spoken segments, whether sampling other works or as original material.
There are words for other instances of speech in music, but not specifically the use you're thinking of. In hip hop, skits are extended interludes of dramatic dialogue.

In some 20th-century art song, Sprechstimme describes a sort of half-singing-half-speaking that uses changes in vocal pitch without sticking to musical notes.

Comedic genres have often included "patter" sections; Bobby Darin can spend one minute joking before 30 seconds of singing:

... and the concept comes to an extreme in the genre of "Talking blues," and the comedy-routine-with-a-chorus "Alice's Restaurant":

And of course, opera has a centuries-old love-hate relationship with "talking," resulting in the recitative and eventually musical theatre. (If Hamilton is essentially "through-rapped," with very little dialogue outside of any musical numbers, is it a musical, or a hip hop opera?)


Caps Lock is bugged

Question: I have HyperX Alloy Core RGB keyboard (HX-KB5ME2-US). Sometimes when I turn off caps lock, LED on keyboard is still on. After another press, LED is on, and caps lock is on.
Why is this happening? Is that bug in keyboards firmware or in windows driver? Thanks
Answer: Seems to be an existing problem on this keyboard that exists in its firmware. Users here complain about the same thing, but HyperX support has said they will replace the board if you send it in and they can replicate the problem. This comment offers some solutions if you don't want to send it back and are willing to get a bit technical.

Caps Lock is bugged


On the product $\prod_{1\leq a<b\leq \frac{p-1}{2}}\,\left(a^2+b^2\right)$, where $p$ is prime

Question: Let $p$ be an odd prime natural number.  Define
$$M(p):=\prod_{1\leq a<b\leq \frac{p-1}{2}}\,\left(a^2+b^2\right)\,.$$
Prove that, over the field $\mathbb{F}_p=\mathbb{Z}/p\mathbb{Z}$ (i.e., in modulo $p$),
$$M(p)= \left\{
\begin{array}{ll}
0&\text{if }p\equiv1\pmod{4}\,,\\
+1&\text{if }p\equiv3\pmod{16}\text{ or }p\equiv15\pmod{16}\,,\\
-1&\text{if }p\equiv7\pmod{16}\text{ or }p\equiv11\pmod{16}\,.
\end{array}
\right.$$
The first equality (i.e., that $M(p)=0$ for $p\equiv 1\pmod{4}$) is trivial.  For now (see this thread), we know that $M(p)=\pm1$ for $p\equiv 3\pmod{4}$.  Under my answer in that thread, jpvee found that the claim above holds for prime natural numbers $p$ such that $p\leq  1000$.  Does anybody know whether the claim is true, and if it so, how to prove the claim?
Comment: Quite a lot of the expressions there hint at quadratic reciprocity and the Legendre symbol...
Answer:
Miklos Schweitzer 1962. Problem 4: https://artofproblemsolving.com/community/c7h226675p1257636
Comment: A good find! Nice to learn that I can still make serious headway into a Schweitzer Problem :-)
Comment: @JyrkiLahtonen You are being very nice here :) Though i found the answer, to be honest, i don't understand a thing whats written :)
Answer: Let's assume that $p\equiv3\pmod4$ is a prime. As you already did in the linked thread, we can use the field $K=\Bbb{F}_p[i]=\{a+bi\mid a,b\in\Bbb{F}_p\}$.
By the properties of the norm map $N:K^*\to\Bbb{F}_p^*, N(a+bi)=a^2+b^2$, we know that every element of $F_p^*$ is the image of exactly $p+1$ elements. This is because the norm map is a surjective homomorphism between cyclic groups of respective orders $p^2-1$ and $p-1$.
To get a handle on the constraints on $a,b\in\Bbb{F}_p^2\setminus\{(0,0)\}$ we need to do the following. We have the dihedral group $G=D_4$ of order eight acting as obvious symmetries of the norm form: $(a,b)\mapsto (\pm a,\pm b)$ or $(a,b)\mapsto (\pm b,\pm a)$. It is clear that each orbit of $G$ on $K^*$ contains a unique pair $(a,b)$ such that $0\le a\le b\le(p-1)/2$.
Here the orbits of $(a,b)$ such that $0<a<b\le(p-1)/2$ have full size $8$, but the points $(a,0),0<a\le (p-1)/2$, and $(a,a),0<a\le(p-1)/2$ have orbits of size four only as their stabilizers in $G$ have order two.
So if we write $N_1(x)$ for the number of solutions of $x=a^2+b^2,0<a<b\le(p-1)/2$, $N_2(x)$ for the number of solutions of $x=a^2,0<a\le(p-1)/2$, and $N_3(x)$ for the number of solutions of $x=a^2+a^2$, then we have, for all $x\in\Bbb{F}_p^*$, the identity
$$
p+1=8N_1(x)+4N_2(x)+4N_3(x).
$$
Clearly $N_2(x)=1$ or $0$ according to whether $x$ is a quadratic residue or not. Similarly $N_3(x)=1$ or $0$ according to whether $x$ is two times a quadratic residue or not.
I am fairly sure that the formula follows from these observations and the facts that

the product of all the elements of $\Bbb{F}_p^*$ is $-1$,
the product of all the quadratic reside of $\Bbb{F}_p^*$ is equal to $+1$,
the product of all the elements that are twice a square is equal to $2^{(p-1)/2}=\left(\dfrac2p\right)$ where the Legendre symbol is $+1$ when $p\equiv 7\pmod8$ and $-1$ when $p\equiv3\pmod8$.

The way this shows up in your product is that the factor $x$ occurs in it
$$
N_1(x)=\frac{p+1}8-\frac{N_2(x)+N_3(x)}2
$$
times. If two is a quadratic non-residue, then $N_2(x)+N_3(x)=1$ for all $x$
and $N_1(x)=(p-3)/8$ for all $x$ meaning that your product is $(-1)^{(p-3)/8}$. If two is a quadratic residue, then $N_2(x)+N_3(x)=2$ when $x$ is a QR and zero otherwise. In this case your product is $(-1)^{(p+1)/8}$ because the extra factor from quadratic residues is equal to one.


What questions will be asked in the grave?

Question: What are the questions angels will ask from us in the grave and how we will answer them? what are the guiding words from Quran and Hadith in this regard.
Answer: Narrated Al-Bara' ibn Azib:
*We went out with the Messenger of Allah (ﷺ) accompanying the bier of a man of the Ansar. When we reached his grave, it was not yet dug. So, the Messenger of Allah (ﷺ) sat down and we also sat down around him as if birds were over our heads. He had in his hand a stick with which he was scratching the ground. He then raised his head and said: Seek refuge with Allah from the punishment in the grave. He said it twice or thrice.
The version of Jabir adds here: He hears the beat of their sandals when they go back, and at that moment he is asked: O so and so! Who is your Lord, what is your religion, and who is your Prophet?
Hannad's version says: Two angels will come to him, make him sit up and ask him: Who is your Lord? He will reply: My Lord is Allah. They will ask him: What is your religion? He will reply: My religion is Islam. They will ask him: What is your opinion about the man who was sent on a mission among you? He will reply: He is the Messenger of Allah (ﷺ). They will ask: Who made you aware of this? He will reply: I read Allah's Book, believed in it, and considered it true; which is verified by Allah's words. Allah establishes those who believe with the word that stands firm in this world and the next.
The agreed version reads: Then a crier will call from Heaven: My servant has spoken the truth, so spread a bed for him from Paradise, clothe him from Paradise, and open a door for him into Paradise. So, some of its air and perfume will come to him, and a space will be made for him as far as the eye can see.
He also mentioned the death of the infidel, saying: His spirit will be restored to his body, two angels will come to him, make him sit up and ask him: Who is your Lord?
He will reply: Alas, alas! I do not know. They will ask him: What is your religion? He will reply: Alas, alas! I do not know. They will ask: Who was the man who was sent on a mission among you? He will reply: Alas, alas! I do not know. Then a crier will call from Heaven: He has lied, so spread a bed for him from Hell, clothe him from Hell, and open for him a door into Hell. Then some of its heat and pestilential wind will come to him, and his grave will be compressed, so that his ribs will be crushed together.
Jabir's version adds: One who is blind and dumb will then be placed in charge of him, having a sledge-hammer such that if a mountain were struck with it, it would become dust. He will give him a blow with it which will be heard by everything between the east and the west except by men and jinn, and he will become dust. Then his spirit will be restored to him*. (Abi Dawud 4753).
Allah has affirmed this situation in the Quran:
Thus, through a firm word, Allah grants firmness to those who believe, in worldly life and in the Hereafter… (Surah Ibrahim: 27).
Have you ever imagined or feel the fear of such moments, whether the Angel of death will give you the glad tidings of Paradise or the bad news of Hellfire.?
Let's make these words a part of our daily Duas in Prayers as they encompass the entire range of man's worldly and other-worldly objectives:
رَبَّنَا آتِنَا فِي الدُّنْيَا حَسَنَةً وَفِي الآخِرَةِ حَسَنَةً وَقِنَا عَذَابَ النَّارِ۲۰۱
Our Lord! Grant us the good of this world and the Hereafter, and protect us from the torment of the Fire. (Surah Baqarah: 201).
and
رَبِّ هَبۡ لِىۡ حُكۡمًا وَّاَلۡحِقۡنِىۡ بِالصّٰلِحِيۡنَۙ, ۸۳ وَاجۡعَلْ لِّىۡ لِسَانَ صِدۡقٍ فِىۡ الۡاٰخِرِيۡنَۙ ۸۴, وَاجۡعَلۡنِىۡ مِنۡ وَّرَثَةِ جَنَّةِ النَّعِيۡمِۙ
My Lord! Grant me wisdom, and join me with the righteous. Bless me with honorable mention among later generations. Make me one of those awarded the Garden of Bliss. (Surah Shu'ara: 83 to 85).


How would I go about making these seem more like planets?

Question: enter image description here

So I recently created this images in blender using some mapping and some planet maps I got online. My question is how would I go about making these planets appear more realistic. Currently they look like circle no matter which way I angle the camera. Thanks in advance.
Comment: What renderer are you using? Blender internal or Cycles?
Comment: Im using blender render at the moment, would you think it would be better if I tried to do it in cycles?
Comment: Cycles has a more realistic result. But in your case the Blender internal can give almost the same result as Cycles.
Comment: I will edit my answer with a solution for blender internal.
Comment: What is the difference between a flat disc and a sphere? When represented in an image in two dimensions there is no difference: they both become circles. The way we would perceive volume and shape is through light and shadow. If the light is coming from every direction equally or from behind the camera there is no way to understand volume. Add a light source that helps to reveal the spherical shape of your objects.
Answer: For the Internal renderer:

Add a direction light and give your sphere a new material. Turn the Specular -> Intensity down to 0.

And add your texture. Result:

For the Cycles renderer:

Add a directional light. And give the material a diffuse shader like this:

In the Image Texture node you can put your texture. (Don't forget to UV unwrap your spheres)
This is the result without a texture:


How to donate a computer without jeopardizing personal information?

Question: I have an old computer that is no longer working and I want to donate it or perhaps throw it in the trash. However, I don't want people to potentially get my banking account data, usernames/passwords I have entered on the computer, software installed, legal or medical documents, internet browser data, etc. I am going to keep the hard drive, should I do something more to the computer before getting rid of it?
Comment: Two possible option, give computer with new HDD or degaussing will help to remove Magnetic HDD data. degaussing is not possible for SSD. Purging also good but reliable.
Comment: @Infra - Degausing a hard drive will wipe the control tracks, turning the drive into a useless brick.
Answer: Donate your Laptop without a hard driver or replace it by a new one, there a many forensics tools able to restore the deleted data (password, files, visited URLS...)
Deleted files

A common technique used in computer forensics is the recovery of deleted files. Modern forensic software have their own tools for recovering or carving out deleted data.[11] Most operating systems and file systems do not always erase physical file data, allowing investigators to reconstruct it from the physical disk sectors. File carving involves searching for known file headers within the disk image and reconstructing deleted materials.

Data recovery
Comment: The question has been clarified to say that the hard drive is being removed
Answer: You are looking to protect the data from accidental leakage or from someone with limited IT knowledge, such as an administrator who knows how to look at drive space marked as "free" by the operating system but still containing data.
For these purposes, a good low-level wipe should do. A lot of information on the Internet is outdated and claims data can be recovered by this and that method, but the reality is that the increase in data density on drives has rendered most of those methods obsolete.
The easiest way is probably using a bootable CD with Linux and either a dedicated tool or the commandline dd command. Here is a link doing this with Ubuntu and here is a much simpler approach using DC3DD. There are also two questions on AskUbuntu about this.
If you are using dd, I would recommend overwriting it three times. Once with zeroes, once with ones and once with random bytes. Make sure you overwrite the whole disk. While there may be theoretical ways to recover at least partial data after that, they are outside of the capabilities of the threat actors in your described scenario. As long as you don't try to hide data from the Mafia or a spy agency, you should be good.

Update
If you keep the harddrive, then securely erasing it isn't the problem. Make sure there's no built-in SSD that the system might be using for caching (some early SDD-accelerated systems had external caches).
RAM should be impossible to recover to any threat actor in your scenario. You can boot the system from a live CD and run a memory test if you want, which will write and read all the RAM, but that's already overkill.

Addendum:
This is one more reason why you should always have the drive encryption active on all your systems. Then you don't have to worry about data loss.
Comment: A three times wipe is unnecessary.
Comment: The OP syas that the drive is not being given away, so all the advice about the drive is moot, isn't it?
Comment: @schroeder if preventing a data leak is the only reason to keep the drive - it's not necessary. If your adversary is the CIA or the FSB, by all means keep the drive, shred it, degauss the pieces, scatter them to the winds and bury the big pieces in seven different locations on seven continents - but for someone whom you don't even think to be malicious, just maybe a bit curious if an opportunity presents itself, it's not needed to go beyond basic protection measures.
Answer: There are easy and effective free wiping tools such as DBAN https://sourceforge.net/projects/dban/. There's a walk-thru guide at https://www.lifewire.com/how-to-erase-a-hard-drive-using-dban-2619148.
Dban and other tools are generally very simple and effective, however there are specialized edge cases that are possible and verification is left to you.
If you don't have the knowledge to perform your own verification, decide what the very low probability of risk is relative to the hard drive cost you are trying to save. If you still have concerns, just physically destroy the drives.
Update based upon new statement of removing the drives.
The above answer still applies to your drives and any potential reuse.
Nothing else in a typical machine stores persistent personal data, so you should be good to go.
Comment: The question has been clarified to say that the hard drive is being removed


How to interpret parameter estimates correlated with the intercept parameter estimate?

Question: I have performed a regression in SAS and extracted the estimated correlation matrix of the parameters, which includes the intercept. One of my variable parameters has a strong correlation to the intercept parameter. I have not seen this before and want to be sure I understand what it means (if anything). Can anyone provide an intuitive explanation of what it means for a variable parameter estimate to be correlated to the intercept parameter estimate?
Comment: If you're interested in not having that correlation in your estimates, you might consider mean-correcting your $x$'s (in some situations that makes sense to do, sometimes it doesn't). Beware, though - it changes the meaning of the intercept.
Answer: In simple terms, imagine you fix one parameter, say the intercept, and estimate the slope. The question is: as you vary the fixed parameter, will your slope estimate change? It will to some degree, and the strength/direction of the effect is the correlation of the parameters.
Suppose you have a simple linear regression with a positive slope in the first quadrant (x and y are positive). If you begin to move the intercept up the y axis, then your slope will have to correspondingly decrease in order to pass through the data. In this case, the intercept and slope are negatively correlated. In any particular setting, the strength of the correlation will depend on the nature of the data (location, spread, etc.)
Answer: Just in case, the correlation refers to the estimated parameters, and springs from the fact that they are derived using the same data. It does not imply a correlation between the unknown parameters being estimated, which being constants (in the frequentist approach), cannot have "correlation". In that sense, it does not have an "intuitive" explanation because it is a consequence of the estimation procedure itself, and does not reflect some aspect of the real-world phenomenon under study.


What gameplay mechanics are new to Super Smash Bros 3DS?

Question: Are there any gameplay differences between the current Smash Bros. and Super Smash Bros. Brawl? For example, did they get rid of tripping, or is still a mechanic in Super Smash?
Comment: I purged the unnecessary comments here - we are not here to judge intent of any user. Be nice, guys, and if you can't be nice, be civil. Please.
Answer: There are a few major new/changed mechanics that we currently know of:

Random tripping has been removed; forced tripping is still in.
You cannot grab a character if you've thrown them in the last second (no chaingrabs).
There is no longer a difference in edge actions upon reaching 100% damage.
Edgehogging has been removed; instead, the incoming character will steal the edge from the current occupant.
It appears that swimming has been removed; characters will just fall through water as in Melee.
Directional influence has been revamped. In previous games, you could change the angle of your knockback by holding perpendicular to it. In SSB4, you instead add a vector in your holding direction, which can alter both your angle and your distance.
Characters at high damage deal slightly more knockback.
Comment: Shields are weaker, but regenerate faster.
Perfect shield is easier to perform. (increased sweet spot)
Comment: Swimming has not been entirely removed. On some stages like Delfino Plaza (available on WiiU) you can still swim. And Vectoring was changed in some early update so its more like DI again


Google App Engine with ClientLogin Interface for Objective-C

Question: I'm experiencing the same problem in this previous stackoverflow.com post.
Specifically, I seem to be able to get the "Auth" token correctly, but attempts to use it in the header when I access later pages still just return me the login page's HTML.
Following links related to this post, I've determined that you need to make a subsequent call to this URL.
A call to the URL will then give you an ACSID cookie which then needs to be passed in subsequent calls in order to maintain an authenticated state.
When requesting this cookie, I've read various posts saying you need to specify your original auth token by appending it to the query string such that:
?auth=this_is_my_token

I've also read that you should set it in the http header as described in google's documentation such that a http header name/value is:
Authorization: GoogleLogin auth=yourAuthToken

I've tried both approaches and am not seeing any cookies returned. I've used Wireshark, LiveHttpHeaders for Firefox, and simple NSLog statements trying to see if anything like this is returned.
Below is the code snippet I've been using.
NSURL* url = [NSURL URLWithString:[NSString stringWithFormat:@"http://yourapp.appspot.com/_ah/login?auth=%@", [token objectForKey:@"Auth"]]];
NSHTTPURLResponse* response;
NSError* error;
NSMutableURLRequest *request = [[NSMutableURLRequest alloc] initWithURL:url];
[request setValue:[NSString stringWithFormat:@"GoogleLogin auth=%@", [token objectForKey:@"Auth"]] forHTTPHeaderField:@"Authorization"];
NSData * data = [NSURLConnection sendSynchronousRequest:request returningResponse:&response error:&error];

//show me all header fields
NSLog([[response allHeaderFields] description]);

//show me the response
NSLog(@"%@", [[[NSString alloc] initWithData:data encoding:NSASCIIStringEncoding] autorelease]);
NSArray * all = [NSHTTPCookie cookiesWithResponseHeaderFields:[response allHeaderFields] forURL:[NSURL URLWithString:@"http://yourapp.appspot.com/_ah/login"]];

//show me all cookies
for (NSHTTPCookie *cookie in all)
{
    NSLog(@"Name: %@ : Value: %@", cookie.name, cookie.value);
}

I hope you can use ClientLogin for Google App Engine code.
Answer: Adding sample code to this question because someone contacted me directly about my solution. Note that you must set the "service" parameter equal to "ah" on the initial token request.
Initial Request of Token [done synchronously] NOTE: the "service" parameter is set to "ah" and the "source" is just set to "myapp", you should use your app name.
//create request
NSString* content = [NSString stringWithFormat:@"accountType=HOSTED_OR_GOOGLE&Email=%@&Passwd=%@&service=ah&source=myapp", [loginView username].text, [loginView password].text];
NSURL* authUrl = [NSURL URLWithString:@"https://www.google.com/accounts/ClientLogin"];
NSMutableURLRequest* authRequest = [[NSMutableURLRequest alloc] initWithURL:authUrl];
[authRequest setHTTPMethod:@"POST"];
[authRequest setValue:@"application/x-www-form-urlencoded" forHTTPHeaderField:@"Content-type"];
[authRequest setHTTPBody:[content dataUsingEncoding:NSASCIIStringEncoding]];

NSHTTPURLResponse* authResponse;
NSError* authError;
NSData * authData = [NSURLConnection sendSynchronousRequest:authRequest returningResponse:&authResponse error:&authError];

NSString *authResponseBody = [[NSString alloc] initWithData:authData encoding:NSASCIIStringEncoding];

//loop through response body which is key=value pairs, seperated by \n. The code below is not optimal and certainly error prone.
NSArray *lines = [authResponseBody componentsSeparatedByString:@"\n"];
NSMutableDictionary* token = [NSMutableDictionary dictionary];
for (NSString* s in lines) {
    NSArray* kvpair = [s componentsSeparatedByString:@"="];
    if ([kvpair count]>1)
        [token setObject:[kvpair objectAtIndex:1] forKey:[kvpair objectAtIndex:0]];
}

//if google returned an error in the body [google returns Error=Bad Authentication in the body. which is weird, not sure if they use status codes]
if ([token objectForKey:@"Error"]) {
    //handle error
};

The next step is to get your app running on google app engine to give you the ASCID cookie. I'm not sure why there is this extra step, it seems to be an issue on google's end and probably why GAE is not currently in their listed obj-c google data api library. My tests show I have to request the cookie in order sync with GAE. Also, notice I don't do anything with the cookie. It seems just by requesting it and getting cookied, future requests will automatically contain the cookie. I'm not sure if this is an iphone thing bc my app is an iphone app but I don't fully understand what is happening with this cookie. NOTE: the use of "myapp.appspot.com".
NSURL* cookieUrl = [NSURL URLWithString:[NSString stringWithFormat:@"http://myapp.appspot.com/_ah/login?continue=http://myapp.appspot.com/&auth=%@", [token objectForKey:@"Auth"]]];
    NSLog([cookieUrl description]);
    NSHTTPURLResponse* cookieResponse;
    NSError* cookieError;
    NSMutableURLRequest *cookieRequest = [[NSMutableURLRequest alloc] initWithURL:cookieUrl];

    [cookieRequest setHTTPMethod:@"GET"];

    NSData* cookieData = [NSURLConnection sendSynchronousRequest:cookieRequest returningResponse:&cookieResponse error:&cookieError];

Finally, I can post json to my gae app. NOTE: the snippet below is an async request. We can handle responses by implementing didReceiveResponse, didReceiveData, didFailWIthError.
NSURL* url = [NSURL URLWithString:[NSString stringWithFormat:@"http://myapp.appspot.com/addRun?auth=%@", mytoken]];
    NSMutableURLRequest* request = [[NSMutableURLRequest alloc] initWithURL:url];
    [request setHTTPMethod:@"POST"];
    [request setHTTPBody:@"my http body";

    NSURLConnection *connectionResponse = [[NSURLConnection alloc] initWithRequest:request delegate:self];
    if (!connectionResponse) {
        NSLog(@"Failed to submit request");
    } else {
        NSLog(@"Request submitted");
    }

Comment: It's a Cocoa thing... "The URL loading system automatically sends any stored cookies appropriate for an NSURLRequest unless the request specifies not to send cookies. Likewise, cookies returned in an NSURLResponse are accepted in accordance with the current cookie acceptance policy."
Comment: I don't see how anyone could figure this out from Google's documentation.  Thanks very much for the experimentation.
Answer: Check out the code that does this in the official SDK. The latest SDK release even has it split into its own file.
Comment: Same issue. Here's what I don't understand, if i just plug: http://myapp.appspot.com/_ah/login?continue=http://myapp.appspot.com/&auth=my_auth_token_i_just_got

into a browser, shouldn't i see the cookie get set???
Answer: 1st  - thanks for the great post it really got me started.
2nd - I have been slugging it out with my app, trying to POST to the GAE while authenticated.
This is the request is built when POSTing, once you have acquired the authtoken:
    NSMutableURLRequest *request = [[[NSMutableURLRequest alloc] init] autorelease];

[request setURL:[NSURL URLWithString:url]];
[request setHTTPMethod:@"POST"];
[request setValue:postLength forHTTPHeaderField:@"Content-Length"];
[request setValue:@"image/png" forHTTPHeaderField:@"Content-Type"];
[request setHTTPBody:postData];

[request setValue:authtoken forHTTPHeaderField:@"auth"];  // <-- the magic

mattb
Answer: I created a few obj-c classes for implementing ClientLogin, including support for Google App Engine:
http://github.com/cameronr/GoogleAppEngineAuth
Answer: Note that Google has recently changed the way authorization failure is indicated. They used to place an Error token in the response. Now they just return a 403 (Forbidden) status. This broke my code!
Answer: Thank for this post and especially the answer from Keith but it does not works for me.
Even if it seems ok for me ... very strange.
I check this post (How do you access an authenticated Google App Engine service from a (non-web) python client?) which talk about doing the same thing in python. I test it and it works.
And the objective C code proposed by Keith is really similar to the python code.
But when I try to get the "Auth" token authData contains Error=BadAuthentication.
Some one got an idea about possibles problems ?
Comment: ok my problems is just that parameter of the request (email, passwd, ....) have to be "encoded". Like what is done in python with "urllib.urlencode". Not found yet how to done that in objc but should be ok.

sorry
Answer: Using HOSTED_OR_GOOGLE is wrong, and I will explain why.
There are two kinds of accounts in the Google world. The ones you create for GMail, etc are "Google" accounts. The ones you create for Apps for Domains are "Hosted" accounts. You can use a Hosted Account email to make a Google Account, thus creating an email address that is associated with both kinds of accounts.
Your Google App Engine app can be configured to work with (1) Google Accounts or (2) Hosted Accounts for a particular domain.
Assume that we are developing an app for Google Accounts. A user enters in an email address that is associated with a Google Account and a Hosted Account. Google will use their Google Account for the login. This all works fine.
Now, if we use ClientLogin with this same email address and use HOSTED_OR_GOOGLE for the account type, login will be successful, but it will use the Hosted Account, since the Hosted Account takes precedence. As I mentioned above, you cannot use a Hosted Account for an app that expects a Google Account. So the authentication will not work.
So, when using ClientLogin to authenticate with a Google App Engine app, you need to use GOOGLE for the account type if the app is for Google Accounts, or HOSTED for the account type if the app is for a domain.


Transformed continuous variable Z-Score to Percentile

Question: I had a non-normal distribution of my variable of interest which required log10-transformation to reduce outliers. This was then standardized, to a mean of 0 and sd of 1 (z-score?). I now want to obtain percentile values from the standardized values. For example, how do I obtain the 75th percentile of my variable given I know it was not normal to begin with and even after log10-transformation it is not normally distributed. Thanks for insight.
Comment: I think so since all the transformations you mentioned preserve rankings
Comment: So you have large number of observations of the said distribution? Sample percentile won't work for you?
Comment: ~450 observations. Can you expand on sample percentile? In it's standardized and transformed version, getting the  Xth percentile is straightforward?
Comment: 75th percentile = upper quartile.
Answer: Let's say you have an RV $X$. Your transformations are all included in this function which result in another RV $Y = f(X)$. My understanding is that you'd like to know what the 75th percentile of $Y$ is. If that's the case, you could just use the samples (450 observations of $\hat Y$) to get an estimate.
Answer: You may have started with data somewhat similar to the 450 observations
in the vector w, which are summarized below using R:
summary(y);  sd(y)
Min.  1st Qu.   Median     Mean  3rd Qu.     Max.
 914    27299    83975   380413   220675 16507340
[1] 1381348  # sd

The transformation $W = \log_{10}(Y)$ gets rid of some of the skewness, and
considerably reduces the number of boxplot outliers.
 w = log10(y);  summary(w);  sd(w)
  Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
 2.961   4.436   4.924   4.930   5.344   7.218
[1] 0.7004566  # sd

Finally, we transform to get a random variable $Z$ with $E(Z) = 0$ and $SD(Z) = 1.$ That is. $Z = \frac{W - \bar W}{S_W}.$ [The histogram shows that $Z$ is not normal.]
z = (w - mean(w))/sd(w)
summary(z);  sd(z)
      Min.   1st Qu.    Median      Mean   3rd Qu.      Max.
 -2.810906 -0.705027 -0.008336  0.000000  0.590705  3.265995
 [1] 1  # sd

Notice that the the summaries have given sample upper quartiles (75th percentiles throughout:  220675 for $Y,$ 5.344 for $W,$ and 0.590705 for $Z.$
Because the transformations have not changed the order of the observations,
the sample quartiles are related according to the transformations:
$\log_{10}(220675) = 5.344$ and $(5.344 - 4.930)/0.700 = 0.591.$
 log10(220675)
 [1] 5.343753
 (5.343753 - mean(w))/sd(w)
 [1] 0.5907055

With a sample as large as $n = 450,$ sample quartiles should not be
very far from population quartiles.  Because of the way I simulated the
data, I know that the exact 75th quantile of the distribution of the $W$'s
is 5.457, which is not far from the upper quartile 5.344 of the observed values of $W.$  Of course, a larger sample size would tend
to give a better match between sample and population upper quartiles.
qgamma(.75, 50, 10)
[1]  5.457062

One style of 95% nonparametric bootstrap confidence interval
for the population 75th percentile is $(5.27, 5.41).$ Unfortunately,
our sample of 450 observations was an 'unlucky' one, with an unusually
low 75th percentile, so this CI does not quite include 5.457. [I could have started over with a different seed to get a 'more cooperative' sample of 450, but it is wrong to give the impression that 95% CIs are 100% CIs.]
set.seed(2019)
d.re = replicate(2000, quantile(sample(w, repl=T),.75))
quantile(d.re, c(.025, .975))
    2.5%    97.5%
5.267784 5.413533


What is going on at point A of this velocity-time graph of a bouncing ball?

Question:
I was wondering what the ball is doing physically at point A -- is it as soon as the ball hits the floor? If so, what about the section of the graph after point A? Is the ball just coming to a rest?
Comment: I cannot reconcile that drawing with the position, velocity, or acceleration of a bouncing ball.  Do you have more detail of how you came by it?
Answer: It may be a velocity-time graph, but if so, it doesn't represent anything like a bouncing ball.  So describing what is happening at some point may be difficult.
Under the influence of gravity alone, all objects near the earth's surface have a near-constant acceleration.  On a velocity-time graph, a constant acceleration would be a constant slope.  So a bouncing ball would show most areas with a similar slope, and a few discontinuities from the bounces (which are periods of very high acceleration).
But your graph shows some areas where the slope is positive, and some areas where the slope is negative.  That's not how bouncing balls behave.
At point A, there is no large acceleration as would be seen during a bounce.  Instead it's like gravity has suddenly reversed.
Answer: It's hard to say for sure, since it's not clear what assumptions have gone into the creation of the graph. I would expect the upward slopes to be quite steep as the ball very rapidly changes from travelling towards the floor (negative velocity) to travelling away from the floor (positive velocity).
If we assume a fairly idealized system (no energy lost on each bounce and practically instantaneous bounces) you might see something like this:

As you can see, any point where the velocity jumps from negative to positive is where the ball bounces off the ground. If the ball is losing energy on each bounce, the yellow line should show similar slopes, but the amplitude would decrease on each bounce. You can also see that the acceleration during the bounces should be extremely high, so your graph showing essentially equal slopes is a bit strange.
To answer your questions:

Point A should be where the ball bounces.
The slope you see after point A should be where the velocity goes
positive and the ball starts to rise again. If the ball actually came to rest   after the section of negative velocity, my assumption would be that it stuck to the floor for some reason.
Answer: The graph looks like the velocity of a ball rolling on the floor and bouncing sideways between two walls. The line is straight (I presume that is what you meant to draw), which means there is no acceleration between two bounces. The corners are sharp, which means the reversal is sudden. A perfectly sharp corner on the graph would mean that an infinitely large force deflected the ball in an infinitely short time interval.
This is something of an idealization. A bouncing ball does not really instantly reverse direction. If you look in detail, you would see the ball flatten as it slows to a stop, and regain its shape as it springs back.
But in many cases, the details of what goes on in the collision are not important. People just want to know what was the velocity between collisions. While the collision is not instantaneous, it is usually quick. The idealization makes life simpler. It allows you to treat the velocity as constant between the end points. This is usually not far off. For ordinary purposes, it is good enough.


iPhone requesting password for different Apple ID when updating apps after updating iOS

Question: My iPhone 5 was updated to iOS 8.3 with a different computer. Now the apps I downloaded before the updates by computer was made, are now bothering me a lot. Any time I want to update them, my iPhone asks me to enter the password for the Apple ID of that computer I used to update it.
Comment: Then you need to wipe it & go back to your original computer & restore from your own latest backup. You have, by the sound of it, hybridised your device to someone else's ID.
Answer: The computer you used to upgrade iOS was apparently signed into a different Apple ID when you upgraded your device. The thing that doesn't make any sense is that the Apple ID signed in on the computer shouldn't matter - you should have to sign-in on the device with a a different Apple ID for it to matter.
That said, you can try signing out of the App Store on the device (App Store app > bottom of the Featured tab > tap on the button that says "Apple ID: xxxx@xxxx" > Sign Out), then sign back in with original Apple ID.


Car chugs along after jump start but no lights work

Question: Today I was leaving work and my car didn't start so I had it jumped by a coworker. I was driving on and noticed that my gauges weren't working and my lights weren't turning on. It also chugs along and sounds like the engine wants to die as well as didn't accelerate when stepped on the gas pedal. Made it home,  I don't know how,  and when I parked it it died in me.
It's a 2005 ford escape v6 2wd amd just two days ago bought a brand new battery so does anyone know what is the problem?
Answer: The new battery is flat.
Why is the next question. When you replaced the old battery did you have the charging system checked, or did you just replace the old battery as it was flat and you thought it was defective.
I suggest that you charge the new battery, once it is fully charged then you can check the alternator and make sure it is charging.
Comment: Yes I was late to work and just replaced it so didn't check my alternator or anything else. Going to get the battery charged up and then check it out at autozone or O'Reilly s
Answer: I don't hope the person who jumped started the car used a calibrated 12V-14V output, if more your system could be burned, or partially... Sy son had a similar situation, at garage with problem, they tried to start it so many times the battery down, jump started and burned out the CPU on the carlights didn't work and a series of more problem.. Start up using a quick start-up machine could bring more problems,.. hope your are not having the same problem... could be interesting to check the output in Volts are in range..
Comment: Well the headlights did turn on when I have it in park but turn off when I turn the key to start but it was a simple jump start one try with cables so hopefully no problems


Furnace starts to light then goes out

Question: My furnace will light one burner the first time for a few seconds then go out. The second time it will light maybe 3 burners for a few seconds, then go out then the blower will come on...I replaced the flame sensor but no help.
Comment: What make and model is this furnace?
Comment: Can you please include more details? For example, make/model of furnace and type of thermostat? It might also help to know how old the furnace is, what size gas line is going to it (if it's on natural gas), whether the combustion air intake is close to an obstruction, how long you've had the issue...
Comment: You may have dust on the burners/venturi which keeps the gas/flame from spreading from one burner to the next. Is the single burner that lights the same one where the flame sensor is mounted?
Answer: I had the same thing happen with my furnace and I had to have the blower replaced. A very expensive lesson to learn about changing filters often.
The tech told me that if it tried to start and did not pick up on any air movement it would automatically shut off the furnace.
The lack of full air flow first burned out the blower and then I lack of the blower operating kept the furnace from firing.
Answer: As others have indicated, specify your make/model of your furnace. However, based on your short description, I'd take a look at your flame sensor. This is the same exact problem I experienced when my sensor failed (it gets covered in carbon over time). You can test it, by turning your furnace off completely (power and all), disconnect your sensor, "scrape" it with a sharp knife, but don't gouge it at all (your just scraping the black carbon off of the sensor), plug it back in, and let your furnace fire up again. Does it happen again? If not, you need a new sensor (it will likely fail in 1-2 weeks again).  disclaimer: If your not at all comfortable with any of this, don't do it, and call an hvac tech.
Comment: I would add to make sure the flame sensor is touching the flame sometimes air flow moves the flame away from the sensor and this can shut down the flow, but usually the pilot will go out when this happens
Comment: Best to use steel wool on a flame sensor to remove buildup.
Comment: Yup, steel wool would be better (not sure why I never thought of that)...
Answer:
will light one burner the first time for a few seconds then go out. The
second time it will light maybe 3 burners for a few seconds

A multi-burner furnace has an ignition source near one end of the burner array and a flame sensor at the opposite end. The flame is supposed to begin at the ignition source, hop from one burner to the next across the array, and ultimately ignite the burner where the flame sensor is located. This has to happen within just a second or two. If it only goes part way across then the sensor correctly detects no flame and causes the gas to shut down.
There is a thin "wing" that connects a small ribbon of gas/flame between the central part of one burner and the next. (This part has a formal name but I don't remember what it is!) Dust can accumulate in this "wing" area, preventing proper flow of gas, which impairs the ability for the flame to propagate from the first burner to the last burner. (photo: airaceheatingandcooling.com)

Often a bit of vibration while the gas is flowing will cause the dust to dislodge. In other words, whack the burner assembly with a wrench or hammer. (Remember the memes about the repairman going into the basement and banging on the pipes?) If it doesn't clear readily, one can remove this formed sheet metal portion and wash it with water. Take care to shake or dry all the water droplets out of that thin wing area; droplets left in there will cause even more blockage than the dust did!
If you do the whack-while-burning method you'll notice that the normally-blue flames flash a bright orange. The change of color is caused by the dust burning. With each successive strike you'll notice less orange in the flame because there's less dust being knocked loose each time.

Furnace starts to light then goes out