Do F1 teams release the original 3D CAD models of their cars?

Question: Do F1 teams officially release the original 3D CAD models of all parts of their F1 cars to the public? Quite definitely, as long as the existing FIA regulations are more or less similar, teams are not bound to release the drawings, but have Ferrari, for example, released the detailed engineering drawings of the 312B (1970 F1 car) or F2004 (2004 F1 car)?
Answer: In general terms no, and why would they?
Sure, there's no real competitive issue going to be caused for the current cars in Ferrari releasing detailed information on the F2004 but there's no benefit for Ferrari as an organisation either.
The older cars might not be racing any more but that makes their designs no less the teams intellectual property. I'm sure Ferrari wouldn't be amused if ACME Cars Inc released their new track day car the EFFTWOOHOHFOUR based on said CAD files for example. Not least because Ferrari has it's own nice little side line charging those with deep pockets a not inconsiderable sum to drive around in their older cars. So the older cars might no longer be competition assets but they can definitely still be commercial assets.
The private market for F1 and "F1-based" car ownership might not be huge in volume terms but there's some eye-watering amounts of money changing hands for these cars - a TDF-One which started life as a 2011 Sauber or Marussia will set you back £1.5million
It's complicated even further by the fact that not every part of the car is even the team's IP either. The majority of the teams don't design and manufacture their own engines, gearboxes, brakes, control electronics, wheels so unless the respective manufacturers of these parts are willing to also release their CAD data such a release by the team is going to have significant chunks missing.
If we step away from the legal and commercial aspects for a moment and look at what such a release would mean for a curious fan. Well assuming the fan could get their hands on the appropriate CAD software to even open the files (I think something like Catia or Siemens NX is what teams will use) is a pretty big stretch, we're talking about something that costs thousands of dollars in licensing costs!
But let's say they've done that - what is the layperson getting from that? If you aren't already in the industry it's not going to mean much to you anyway.
Comment: Although the purpose for which I had asked this question is fulfilled, I feel that for the sake of academics, F1 teams should release 3D CAD models for CFD/FEM analysis in schools and universities such that there is a larger pool of people who can work behind the door away from the track. I am not sure what others have to say on this? Thank you.
Comment: @SuddhasattwaGhosh Whether any team specifically releases CAD models to university departments I don't know but some teams *do* work with academia to a certain extent - Aston Martin and Mercedes (through Mercedes HPP) are both partners/sponsors of Formula Student in the UK for example, and I know that when I was at university at least one team was seeking to recruit new staff from the engineering programme there.


A planet in which Natural elements , emits heat energy - Is Inhabitable?

Question: On my alien planet, many natural elements (Soil, some plants, a certain type of stones...) emit a kind of heat energy.
Will this affect flora and fauna of my planet? Since the natural elements emit some kind of heat energy, is that planet became like a hot oven uninhabitable for hot-blood animals?
Comment: Being cold-blooded merely means that the creature can't regulate its body temperature. It has nothing to do with heat.
Comment: So increasing rate of black body radiation? Because right now, all matter (that is above absolute zero) emits thermal energy. Because as it stands your question can be answered: Yes. see black body radiation.
Answer:
Will this affect other flora and fauna of my planet ?

your race evolved on that planet, and environmental conditions are an evolutionary driver. As such also all other living beings on that planet will be affected.
And since on our planet hot deserts are inhabited both by warm blooded and cold blooded beings, being warm blooded doesn't seem to be an obstacle in populating such areas. Evolution will find a way.
Answer: On planet Earth, the source of heat is Sun. Then heat is distributed and kept by air or water. In many cities, (in summer) temperature reaches 117°F (47°C) in the afternoon for many days. People and animals live there. Some even work on roads or outside. I have seen camels walking on sand at 120°F (49°C).
Is there air and water on your alien planet, which distribute and retain heat? What are the highest and lowest temperatures on the planet?
Assuming that just like a hot city on earth (Turbat-Pakistan, Jazan-Saudi Arabia, Mitribah-Kuwait etc.), temperature on your planet varies from 120°F (49°C) to 90°F (32°C), then it will be hot but not uninhabitable.
But if the temperatures reach like on Mercury or Venus [around 800°F (427°C)], then it could be uninhabitable. There is no life or evolution on Mercury or Venus.


change the uiview background color with code

Question: I would like to change the background color of my app programmatically, not IB. Is it possible to get both a Swift and Obj-C answer.
Answer: You can set the backgroundColor property of whatever view it is you have on screen.
In Objective-C:
self.view.backgroundColor = [UIColor redColor];

In Swift:
self.view.backgroundColor = .red

or if it's the main window you're after,
In Objective-C:
self.window.backgroundColor = [UIColor redColor];

In Swift:
self.window.backgroundColor = .red

Answer: self.view.backgroundColor = [UIColor redColor];

possible colors are :
blackColor
 darkGrayColor
 lightGrayColor
 whiteColor

 grayColor
 redColor
 greenColor
 blueColor
 cyanColor
 yellowColor
 magentaColor
 orangeColor
 purpleColor
 brownColor
 clearColor

Comment: For reference, the list of color can be currently found at https://developer.apple.com/documentation/uikit/uicolor/1621945-clearcolor?language=objc
Answer: For Swift 3, you should do:
self.view.backgroundColor = UIColor.white

Unfortunately, the other answers no longer work in Swift 3.
Answer: If you want to change the background color of the view with code in Swift, you should do instead:
self.view.backgroundColor = UIColor.redColor();

Comment: self is not necessary unless in a clousre
Answer: You can use RGB Color by following code:
UIColor *myColor = [UIColor colorWithRed:(128.0 / 255.0) green:(90.0 / 255.0)
blue:(200.0 / 255.0) alpha: 1];
self.view.backgroundcolor = mycolor;

Comment: Welcome to stack overflow :-)
Please look at [answer]. You should provide some information why your code solves the problem.
Code-only answers aren't useful for the community.
Comment: Disagree with @JimHawkins - the problem with SO is not imperfect contribs like the above (which nevertheless have _some_ merit), it's dishearteningly critical comments, often of newbies.
Comment: @ColinStark - there is at least one good reason for code-only answers: the users english is too bad, but the code is helpful as it is. But code-only answers should not be a default on SO . See also https://meta.stackoverflow.com/q/345719/1988304 . I don't see why my comment should be "dishearteningly"
Comment: First you said "code-only answers aren't useful", then said "the code is helpful as it is... should not be the default". Which is it?

 As for disheartening: well, if a newbie is trying her/his best, makes a contribution that's non-null, and immediately gets a negative "this isn't useful" aka "worthless", they may be discouraged. This has occasionally been my experience. It's also the reputation that SO has acquired.
Answer: For swift based project you can simply type the following and press enter:
self.view.backgroundColor = Color Literal

Here the ColorLiteral property will give you a default white colour which you can change by double clicking on that colour.
You can choose from a list of colour from this popup:


Does capex affect the Income Statement of a company in any form?

Question: I know capital expenditures show up in a company's cash-flow statement, but do they have any effect on its income statement?  That is, does the income statement show only revenue-generating activities?
Answer: No, capital expenses do not directly appear on the Income Statement.  There are indirect effects from CapEx that do show up (depreciation, interest if money was borrowed to fund the capex, etc.) but nothing direct.
From a T-account standpoint, A capital expense is a movement from an asset (cash) to another asset, and thus does not involve any expense or revenue accounts that would show up on the income statement.

When I observe the income statement does it show only the state of the revenue-generating activities of the company?

To be pedantic, the income statement does not show "state". It shows the change over a given time period.  But yes, the income statement shows the changes due to activities that generated revenue, and the expenses that were incurred as a result of those activities.
Answer: The cost of a capital expenditure is "amortized" [~released slowly] over the useful life of the asset. Amortization is also called depreciation. This is because accounting theory tries to line up the 'expense' with the related revenue. In this case, buying an asset today not only generates revenue this year, it also generates it in future years.
ie: If a company buys a delivery van that will last 5 years, and it costs $20,000, then it might have an 'amortization expense' of $4k per year, until $20k has been amortized.
The amortization/depreciation expense translates in a very rough way, into the amount of new capital expenditure the company needs to make, in order to remain at a consistent level of operations. In the example above, if you saw $4k of amortization but $0 new capital expenditures on the cashflow statement, it would imply that the company is not buying new property to maintain the same level of operations. Of course, the amortization expense is just an estimate, and some things last far longer than the amortization period [ie: a new building might be amortized over 20 years, but might actually last 40 years before significant additional capital expenditures are required].
Like everything else with financial analysis, looking at a single number ['amortization'] tells you little. But when looking at competing factors, you learn a little more. Combining amortization with net income and current year capital expenditure spending, tells you a little more about whether the company is growing, or 'coasting'. An example from an unrelated question that was recently posted might be a car rental company. If you saw a significant amortization expense but little capital expenditures, it might imply that the fleet of rental vehicles is old and dying, so perhaps this year's net income amount will be lower next year, after cars start breaking down.


How to stop Gmail app checking emails in background?

Question: Is it possible to stop Gmail iOS app checking email without me asking for it?
I don't need the phone to check for emails while I'm in from of my computer.
Answer: As the GMail app is a third party app not built by Apple, it is not allowed to run in the background to check for mails. So closing the app stops it from checking for mails.
However, it probably will still get notifications about new mails pushed from Google's server. But this notification is not initiated from your phone.
You can switch off notifications for the gmail app in the iPhones settings.app under notifications.
Comment: Thanks, turned notifications for gmail app Off, waiting for mail to check if it worked.
Comment: I have turned off everything there, except for badge and sound. Ant it seems the app still receives some notifications about emails.
Comment: Whith everything off it seems gmail stopped checking my email :) Thanks for the answer.
Comment: The answer was correct in 2013, when I wrote it. On newer versions of iOS you may also need to disable `Background App Refresh`.


How to stop overcrowding?

Question: I'm trying to create a Coruscant type planet with massive cities.  Any specific way to stop overcrowding? There's always long lines of traffic and millions of civilians walking all over the place.  Any way to evenly distribute the civilian population so that it is not extremely crowded in 1 place?
Comment: Your question is very vague, and not entirely clear. Why might one place get "extremely crowded"? Lack of food/security/etc. in one location versus another? I mean, most people won't go to a place that is super crowded unless they _have to_, so why do you think they would do so? Why not work/shop/live in their own areas? Give us a reason and we might be able to offer a solution.
Comment: Update your question to better explain the issue rather than leaving the information in a comment :-)
Comment: yeah sorry about that i'm new here i mean say if there is a lack of food in other areas or this one area is far more economically stronger and safer than other areas thanks for commenting i appreciate it :)
Comment: Don't be discouraged because your question was placed on hold! Simply flesh out your universe a little bit so that we will be able to answer it more accurately. For example, what sort of government runs this planet? What's an approximate city size and population number? Are the people predominantly well off, or poor, with a rich elite ruling them from super luxurious sectors of the city? What sort of law enforcement can we expect (Western society style, or para military, super harsh types?)? **Basically tell us why people might crowd to a certain area and we will tell you how to stop them.**
Comment: Err... Exactly how do you expect to have an overcrowded (= massive cities) planet without overcrowding?
Answer: For Arbitrary Population Size
If you want a solution for any arbitrary k, where k is the size of the total planetary population, it cannot be done.
All fixed resources have their hard limits. This includes planetary surface area and total planet volume. For sufficiently large k, there comes a point where both resources are exhausted and the planet must be vacated.
The only way out is to impose:

A hard population limit, enforced through legal/punitive measures.
Offshoring requirements for overabundant populations via forced relocation to satellite systems.
Zoning requirements that impose a hard limit on the number of residents within their premises, which, if enforced, will prevent immigration once Coruscant reaches capacity.
Strict temporary visa allotments that prevent overstay longer than a minimum sufficient period.

All of this serves to cap your total population size to a sustainable number, and does not let your planet's support system scale indefinitely.

For Fixed Stable Population Size
Assume now that you only want to be able to support a total population of k, and are willing to exact measures to prevent excess above this. We will proceed on the premise that a stable population has been produced i.e. the birth rate exactly equals the death rate, and your planet's overall population is at an equilibrium.
In order to prevent regional overcrowding, you must first consider the following natural limitations:

Extent of temperate regions on the planet. Assuming your population can only thrive in certain specific conditions, the range of latitudes that lets your population survive greatly affects population distributions.
On Earth, the vast majority of the population - 88%, to be exact - is concentrated within a fairly narrow bound in the northern hemisphere, with over half living above 27 degrees N. This coincides near perfectly with the North Temperate Zone, with an average temperature of 31 degrees Celsius and precipitation of 81 cm.

No one wants to live in unusually harsh conditions, so migration to/from the frigid or excessively hot regions of your planet is limited, assuming an alien physiology similar to that of humans. Since you're modelling your planet after Coruscant, which features an influx of migrants of all sorts of physiological proportions, I presume you cannot make assumptions about your alien physiology just yet, so you have to keep in mind the geography of your world before committing to a plausible solution.
Natural disaster frequency: Regions that suffer from regular natural disasters, such as hurricanes, active volcano eruptions, etc., historically strongly affect populations, precipitating a brain drain that leads to migration elsewhere. Catastrophic once-in-a-lifetime events can exact extraordinary economic costs, all of which alter the shape of population distribution in the short term and may be hard to recover from in the long-term.
Even a planet like Coruscant is bound to suffer from natural disasters. Obviously, the sort of disaster depends strongly on the nature of the planet and its orbiting system  itself: a planet without axial rotation has no day-night cycle and suffers from uneven heating leading to different natural disaster intensities, while a planet with no ozone layer orbiting a yellow star will suffer from radiation leaks.
Resource distribution: A region unable to provide food, shelter, or security for its folks is not going to keep them for long. This ties in somewhat with the point about temperate zones, which typically come bundled with sufficient necessary resources such as food and water, but isn't necessarily connected to them. Some temperate regions may be stripped of vital resources, making them less self-sufficient in their own needs, which in turn exacts a living cost on its inhabitants that may or may not prompt migration. What constitutes a vital resource varies by region and by technology: the abundance of coal, for example, affects how likely a Victorian-era society will be to survive the winter, while coal in a purely geothermal society is no longer as relevant.

You also need to consider the following non-natural limitations:

Economic imperative: The chief reason migration occurs is because of better economic prospects. This is often tied to the resource distribution issue, but not necessarily so: government capitals can and do become urban hubs despite not being located on, for example, a river. On planets that have moved to a currency system and engage in economic systems similar to humans, we may safely assume that economic imperative is sufficient to prompt migration.
I'm going to use economic imperative as a catch-all term for a lot of different things here: tax benefits, industry concentration, and geographic closeness to place of work. These are all economic imperatives from a migrant's perspective, and so it seems to fit.
Economic imperative can be balanced out by considering cost of living. Urban hubs exhibit higher costs of living than rural population centers, so migration between locations is unlikely to occur if the difference between net take-home pay (pay after taxes) and cost of living is identical or less than the migrant's original home. I say unlikely but not improbable: long-term considerations, such as future career prospects, also matter.
Supply chain infrastructure: This is the flip side of economic imperative, and affects cost of living. Specifically, by supply chain infrastructure, I refer to how particular locations solve the problem of resource distribution and allocation. Geographically isolated regions (yes, this is possible even on a Coruscant-like planet: imagine a hub with fewer connections to every other hub than its neighbours) with poor natural resources have to import food and resources, which is more expensive than local home-grown provisions. Poor infrastructure or administrative overhead - say, an electric grid built from obsolete parts or unable to make headway through connections - pushes long-term costs on people.

Any effort to stabilise migration so that population distribution is effectively a constant everywhere must therefore address all of these concerns.
Finally, there is one last concern to take care of:

The nature of your government.
A nanny state would solve all these problems in a completely different way than a democratic state. Likewise, administrative decentralisation (say, each node in Coruscant has its own municipal authority) would prompt different solutions than a centralised authority. A state that advocates free trade over government intervention would expect solutions to come from there. You'll have to play around and mix-and-match with what suits your story best.

Solutions

Take care of geographical inequities first. A city-planet like Coruscant has only way of doing this: massive terraforming.
The eviction of trees and plant-life in favour of concrete may or may not cause a runaway greenhouse effect - therefore, Coruscant must build its own equivalents to regulate its atmosphere. This helps nicely in preventing air-related natural disasters as well. Oceans, rivers, gulfs, streams, etc. may also be drained and replaced in favour of concrete. Coruscant drones also dig deep underground and construct their own synthetic mantle and crust, designed to never shift (preventing earthquakes) and allowing full utilisation of the planet's geothermal energy (assuming an Earth-like molten core). As a neat bonus, we can assume all suitable waste is recycled into the planet's core, providing a near-constant supply of indefinite power.
At this stage, no single region has more resources than any other. Power is centrally managed and distributed to the planet as a whole. With the mantle and crust stripped, living space as fraction of planet percentage has quintupled (say) and all mineral resources are now in the hands of a central authority. With an artificial atmosphere, it is now possible to strictly regulate air-related incidents as well. We have removed the geographic incentive for migration anywhere: every point on the planet is now exactly identical, with no temperate differences or resource differences and natural disasters now tightly controlled.
Now you must ask: with all this massive terraforming removing geographic inequities, it now poses a major supply problem: where do vital resources -like food and water - come from? Answer: it must all be outsourced, shipped to the planet. This brings us to the next part of the answer:
Understand your demographics, and distribute resources accordingly.
Coruscant's problem is that it must support any incoming type of alien, while maximising living space without giving up vital industrial processes (such as power generation). Your aliens may survive strictly on a diet of bugs that have to be imported from a different galaxy altogether, for example, but also want to live in a specific region close to their preferred industry. This means that every point in your city must be able to provide for a possible potentiality.
How your government chooses to handle the resource allocation problem is upto you: if your government is totalitarian, it may simply impose strict controls on migration and forbid people from moving there, monitoring their movements. If your government encourages laissez-faire trade, let corporations bid for the right to handle food distribution for an entire sector - aliens who require a certain set of resources will simply have to make the tough decision to move but afford their own private care.
Either way, your government has to import all of its vital resources from off the planet, since it no longer has any of its own. How it then solves the resource allocation problem depends on your government's strategy. I would also recommend enforcing zoning laws that prevent an excess of people living in a residential area, and I'd even go one step further in banning industrial activity on Coruscant's surface.
Tackle economic imperative. In a landscape of corporations, a particularly large corporation may want all of its employees geographically concentrated in one location. This in turn prompts more people to migrate towards a particular hub, leaving other hubs comparatively impoverished.
Fighting this is a difficult problem, but certainly one way to do it is to organise city architecture better. Instead of designing one massive city with roads and blocks - all of which causes extreme interdependence on each other and has a lot of moving parts - it's much better to break your city up into distinct, self-sufficient municipal regions. I envision giant geodesic domes actually physically demarcating boundaries.
This break-up into zones allows better regulation of industry growth: companies that seek to expand past a certain headcount must apply for separate offices in blocks that are not physically adjacent. This helps regulate population distribution simply by spreading out employees over the entire planet, preventing any single corporation from gaining geographical prominence. Corporations here include universities, research institutes, etc. - any organisation so to speak.
As a side benefit, this self-sufficient block design also pretty much guarantees that emergency services can respond quickly and are able to address the needs of its inhabitants, because each block would ideally have its own hospital, school, etc.

For a Non-stable Population
In addition to the previous list of issues, non-stable populations have their own additional problems:

Uneven age distributions: A population with more old people than young requires a different division of resources than a population with the inverse distribution. More old age homes and hospitals, for example.
Familial considerations: Migration can also be affected by intangibles such as perceptions of better school systems or hospital resources, which, for a non-stable population, can prompt major moves (although utilising a block-by-block system with corporations prevented from choosing adjacent regions can help mitigate this somewhat).

Solving both of these is tricky, and hard, and never guaranteed to work. I will point out though that:

Encouraging the virtualisation of intangible resources is a good first step. Hospitals that admit virtual tele-screened appointments from anywhere across the planet means people can get the same quality of care from all over the world. Likewise, schools that subscribe to MOOC-like patterns are able to provide their content all over the planet, improving their own revenue while preventing major population shifts.

That's all I can say would work for your cause right now.

How to stop overcrowding?


How to add a Jump Force when I collect a coin

Question: So I have a coin in my scene right now I am it set up as a Trigger and to Disappear when I run into it, i have functional code that always me to Jump when I press space, but I want to only be able to jump after I collect the coin.
Well I don't really know where to start, I'm fairly new started coding 2 days ago. I can't seem to find anything on YouTube.
<code>//-----------This Code allows the coin to disappear when collected-----------

{

    private void OnTriggerEnter(Collider plyr)
    {
        if (plyr.gameObject.tag == "Player")
            gameObject.SetActive(false);
    }

}
//---------------------------This is Jump----------------------------------

 if (onGround)

          {
              if (Input.GetButtonDown("Jump"))
              {
                rb.velocity = new Vector3(0f, 50f, 0f);
                  onGround = false;
              }
          }

      }

    void OnCollisionEnter(Collision other)
    {
        if (other.gameObject.CompareTag("Ground"))
        {
            onGround = true;

        }
    }
</code>
Comment: In your player controller, create a `public Void Jump() {}` method. Move your jumping code in there and put `Jump();` in the `if..."Jump"))` block. Then in your coin code, in the `if...tag == "Player")` block, do `gameObject.GetComponent().Jump();` or whatever your player controller script is called instead of `PlayerController`.
Answer: Define a bool to keep track if a coin is collected and an OnTriggerEnter method in your Player script. I'm assuming you have a tag for coin objects which is called "Coin".
<code>private bool coinCollected = false

private void OnTriggerEnter(Collision other)
{
    if(other.gameObject.CompareTag("Coin"))
    {
        coinCollected = true;
    }
}
</code>
Then modify your jump method:
<code> if (onGround)

      {
          if (Input.GetButtonDown("Jump"))
          {
            rb.velocity = new Vector3(0f, 50f, 0f);
            onGround = false;
            coinCollected = false;
          }
      }

  }
</code>


Effective algorithm to test positivity

Question: Let $f(x_1,\ldots, x_n)$ be a real polynomial in several variables. Is there an effective algorithm to test whether $f$ is positive (or nonnegative) on the whole of ${\mathbb{R}}^n$?
Comment: The existence of an effective algorithm follows from Tarski's
theorem on decidability in real-closed fields. Whether
there's a practcial algorithm is another matter.
Comment: There is an algorithm, by Tarski's theorem. My usual reference for practical aspects of this sort of thing is "Algorithms in Real Algebraic Geometry" http://books.google.com/books?id=ecwGevUijK4C
Comment: By "effective" you mean "reasonably fast" or simply "in theory there is an algorithm"? Also, it is difficult to feed a real number to a computer: do you really want real coefficients or would rational coefficients be enough?
Comment: Thanks everyone for their comments. I'm aware that nonnegative f are sums of squares of rational functions, but i was looking for whether the positivity of f could be checked via some other method not subscribing to sums of squares.
Answer: If by effective you mean "is this computable", then yes, the computational versions of Tarski-Seidenberg such as cylindrical algebraic decomposition give you a finite algorithm. (I suppose this is assuming your polynomial has rational coefficients, or at least algebraic coefficients each given by a polynomial they satisfy along with an interval isolating them from other roots.  I would guess the problem is not computable if your coefficients are given by Turing machines which compute [successively better approximations to] the reals in question, but I'm guessing that's not the problem you're asking about.)
If by effective you mean "can this be done in polynomial time", the answer is probably not; the problem is NP-hard.  In particular, a matrix $A$ is defined to be copositive if $x^T A x\geq 0$ for all elementwise nonnegative column vectors $x$.  That is to say, $A$ is copositive if and only if $\left[\begin{smallmatrix}x_1^2 & \cdots &  x_n^2\end{smallmatrix}\right]A\left[\begin{smallmatrix}x_1^2 & \cdots &  x_n^2\end{smallmatrix}\right]^T\geq 0$ for all real $x$, so checking copositivity is a particular example of the kind of problem you have mentioned.  Murty and Kabadi's 1987 paper shows that checking if an integer matrix is not copositive is NP-complete.  In particular this means that checking nonnegativity is NP-hard even in the degree four case.
If by effective you mean "are there polynomial-time methods that work well in practice", the answer is yes.  In particular one can check sufficient conditions like whether $f$ is a sum of squares of polynomials (and a hierarchy of tighter conditions) in polynomial time using semidefinite programming, and often this allows one to solve such problems.  Such methods often enable one to compute the global minimum of a polynomial and so can often even give a "no" answer despite the fact that they are a priori just sufficient conditions for nonnegativity.  If you are interested in such techniques I would recommend the papers by Parrilo, Lasserre, Nie, etc. and in particular Parrilo's course on MIT OpenCourseWare.
Comment: i will check out what is cylindrical algebraic decomposition.
Answer: In practice, the biggest issue is whether your polynomial is a sum of squares (of polynomials) or not. (It's always a sum of squares of rational functions, but that's not helping.) If it's the case, then the methods of Parrilo et al. can really cut down on the computation time. It's all very well explained on the MIT OpenCourseWare.
Equally valid though would be to produce one point in each connected component of $\{f \neq 0\}$ by cylindrical algebraic decomposition or variants, and test the sign of $f$ on each sample point.
On the other hand, if you want a theoretical result (say for a sequence of polynomials), there is no reasonable general method.
Answer: If you could find an upper bound for degrees of polynomials used in Positivstellensatz I guess you can create an algorithm for this.
You would like to take a look at Positivstellensatz, for instance in the book of Bochnak-Coste-Roy "Real Algebraic Geometry" under Corollary 4.4.3 (this corollary combines Positivstellnsatz, Negativstellensatz and Nullstellensatz for real closed fields). A more abstract form can be found in a German book "Einführung in die Reelle Algebra" by Knebusch and Scheiderer (the book is now freely available for download from the university of Regensburg library: here). You would also like to see the works by Schmüdgen and Putinar on various forms of Positivstellensätze.
Comment: Aren't the degree bounds horrible, though?
Comment: I believe Schmüdgen, Schweighofer and Prestel were addressing this at some point. I think in a paper Schweighofer even introduced some algorithms and discussed the complexity involved. But as this is not my area of expertise, I can't really say much more than this.

Effective algorithm to test positivity


Is it allowed for しち reading of 7 to be used in compound numbers?

Question: I thought that [七]{しち} (7) and [九]{く} (9) readings could not be used in constructing compound numbers, like 71 or 19, and unlike their alternative readings, [七]{なな} (7) and [九]{きゅう} (9), can only be used for numbers 7 and 9. But now I noticed that both readings of 7, [七]{しち} and [七]{なな}, can describe 17th and 27th day of month. What's more, only [九]{く} (9), not [九]{きゅう}, is used to describe 19th day of month. What am I getting wrong?
Answer: You're not getting anything wrong. Cardinal numbers are read one way, and the days of the month are read another way. Just try to memorize the "irregular" readings for the days of the month, as well as the ones for the months of the year, minutes, hours, and counters in general. I find repeating them aloud helps you get them down faster.


Batch Files: List file names and folder names

Question: With cmd or .bat scripts, is there a way to list only file names and folder names? I would like to run a batch file to produce a text file that contains this information.
Suppose I have the following folder:
C:\test\test.bat
C:\test\Doc1.exe
C:\test\Doc2.docx
C:\test\subdir1\Doc3.pdf
C:\test\subdir2\Doc4.txt

I'd love to have an output like this:
Doc1.exe
Doc2.docx
test.bat
subdir1
subdir2

So far, this answer is the closest I could get. With an output of:
Doc1     exe
DOC3~1   DOC
subdir1
subdir2
test     bat

I've tried dir:
dir /b /a-d >filelist.txt

But it didn't get what I wanted. (i.e., it only list file names but not folder names).
Thank you!
Comment: What's wrong with just `dir /b`?
Comment: You're right, dir /b gets what I wanted. Perhaps I confused it with dir /d. Thank you.
Answer: Answer
Exclude the /a-d from your code and it should be exactly what you want it to do.
Also, to get the exact output format you specify, order the return by whether the item is a folder.
Explanation
https://ss64.com/nt/dir.html
/a is to specify an attribute
d specifies to look for directories, and the - is negating the d
so /a:-d means: where attribute is not directory and that parameter is taking away your directories from the list.
A simple dir /b will return all folders and files.
The parameter /o lets you organize the return. /o:g will list folders first in the list, and /o:-g will list them last.
Finally, if you ran dir /b /o:-g > filelist.txt your return would be
Doc1.exe
Doc2.docx
test.bat
subdir1
subdir2

Comment: Thank you for the detailed explanation! I especially appreciate the last part about the g vs -g modifier. I'll be sure to read the info in the link you've provided.


Mathmatical Induction

Question: Prove, by mathmatical induction, that $5^{2n}$ + $2^{2n-2}$$3^{n-1}$ is divisible by $13$.
I first plugged in n as 1 and showed that the expression is divisible by 13 for n=1.
Then I assumed that the expression was divisible by 13 for n=k and plugged in k. The simplified expression in terms of k was $25^k$ + $\frac{4^n3^n}{12}$. I then plugged in k+1 and got an expression for that. I am unable to show that the sum or difference of the k and k+1 expressions is divisible by 13. How do I proceed?
Answer: $$25^{k+1}+\frac{4^{k+1}3^{k+1}}{12}=25\cdot 25^{k}+12 \frac{4^{k}3^{k}}{12} $$
$$=13\cdot 25^k+12\cdot25^k+12 \frac{4^{k}3^{k}}{12} $$
$$=13\cdot 25^k + 12 \left(25^k+ \frac{4^{k}3^{k}}{12}\right)$$
Comment: **Remark** $ $ that this proof is special case of the proof of the Congruence Product Rule, and it is *much* more insightful to view it in its natural congruence form - see my answer.
Answer: HINT:
For $n=m+1,$
$$f(m+1)=25^{m+1}+4^m3^m=25^{m+1}+12^m$$
$$f(m+2)-25f(m+1)=25^{m+2}+12^{m+1}-25(25^{m+1}+12^m)=-12^m(25-12)$$
$$\implies f(m+2)-25f(m+1)\equiv0\pmod{13}$$
Alternatively, $$f(m+2)-12f(m+1)=25^{m+1}(25-12)\equiv0\pmod{13}$$
By either method, $f(m+2)$ will be divisible by $13$ if $13|f(m+1)$
Now establish the base case i.e., for $n=1$
Answer: Hint $\ \ \ 25^{n+1}\!+12^n =\, (\underbrace{25\!-\!12}_{\large\color{#c00}{=\, 13}})\,25^n + 12\,(\!\!\!\!\!\underbrace{25^n+12^{n-1}}_{\large\color{#c00}{=\, 13\,k}\rm\ by\ induction}\!\!\!\!\!\!)\ $ is divisible by $\,\color{#c00}{13}\ \ $  QED
Remark $\ $ More intuitively, use the Congruence Product Rule to multiply the first two congruences below to deduce the  third, $ $ yielding the induction step $\,P(n)\,\Rightarrow\, P(n\!+\!1)$.
$$ \begin{eqnarray}{\rm mod}\ 13\!:\quad\  25&\equiv&\ \ \ 12\\ 25^n&\equiv&\!\! {-}\!12^{n-1}\ \ \ {\rm i.e.}\ \ \ P(n)\\ \Rightarrow\ 25^{n+1} &\equiv&\!\! {-}\!12^n\quad\ \ \, {\rm i.e.}\ \ \ P(n\!+\!1) \end{eqnarray}\qquad\qquad\qquad$$
The proof in the hint arises in the following mechanical manner: take the standard proof of the Congruence Product Rule in the linked post, then substitute the specific numbers in this problem, i.e. we simply repeated the proof for the special case at hand. Though many such inductive proofs appear to be pulled out of a hat like magic, in fact they are, at heart, instances of congruence arithmetic - exactly as above. Once you learn  congruence arithmetic the problem becomes trivial:  it boils down to $\, (-1)^{n+1}\equiv\, -(-1)^n\ $ since $\ 25\equiv -1 \equiv 12\pmod{13}.$
Comment: Bill, I am a high school student. I am neither familiar with the Congruence Product Rule nor Modular Arithmetic so your answer is much beyond the scope of my knowledge!
Comment: @user140161 The proof in the hint does not use congruences, only very simple arithmetic, accessible to any high-school student. if you later learn congruence arithmetic I encourage you to revisit the Remark. You will be amazed at how it greatly simplifies such matters, bringing to the fore the arithmetical essence of the matter.
Comment: I definitely will, thanks.

Mathmatical Induction


Can Galilean transformation be derived from length invariance?

Question: Given length invariance in Euclidean 3D space between two inertial frames:$$ds^2=ds'^2$$
Can Galilean transformation be derived like Lorentz transformation derived from space-time interval invariance?
Comment: I am not sure, but perhaps one would have to add time to the Galilean "spacetime interval"?
Comment: Since the Galilei group is not a true isometry group for 3 dimensions, I don't think you will be able to do this. The best one can do is obtain the Galilei group as an Inonu-Wigner contraction of the Poincare group (this is more or less what would mathematically correspond to @Jonas his comment).
Answer: The answer is negative, because that invariance property is also valid regarding two reference systems such that one is inertial and the other is not inertial and thus the coordinate transformations are not Galileian.
If we also impose $\Delta t=\Delta t'$, we find  that the admitted transformations are more general than the Galileian ones:
$$t'=t+c$$
$$x'= R(t) x + c(t)$$
where $R(t)$ is an orthogonal matrix depending on time in general and $c(t)$ a tridimensional translation depending on time in general.
Answer: I think what we should start from is not invariance of a scalar $ds^2$, but co(ntra)variance of a $3$-vector. Note that in terms of split-complex numbers the $2$-dimensional Lorentz transformation$$dt^\prime=\gamma(dt-\beta dx),\,dx^\prime=\gamma(-\beta dt+dx)$$satisfies$$dt^\prime+jdx^\prime=\gamma(1-j\beta)(dt+jdx).$$The Galilean equivalent using dual numbers is$$dt^\prime=dt,\,dx^\prime=-\beta dt+dx\iff dt^\prime+\epsilon dx^\prime=(1-\epsilon\beta)(dt+\epsilon dx).$$Note that $\gamma^2(1-j\beta)(1+j\beta)=(1-\epsilon\beta)(1+\epsilon\beta)=1$ is the reason we can invert these transformations, i.e. swap the roles of the two coordinate systems. It also establishes the theories' respective invariances of$$(dt+jdx)(dt-jdx)=dt^2-dx^2,\,(dt+\epsilon dx)(dt-\epsilon dx)=dt^2.$$That $dx$ isn't even in that last expression is a hint of what's about to go wrong.
I'm tidying things up a bit by nondimensionalising a velocity (though this needn't commit us to an invariant speed in the latter transformation family) and making space $1$-dimensional, but you can fix both of those. The important issue is the invariance of quadratic quantities needn't be equivalent to a specific transformation of linear ones in the $\epsilon$-based case, because $\epsilon^2=0\ne1=j^2$. The linear transformation implies the quadratic invariance but, as others have noted, the converse is false, ultimately because dual numbers don't allow division due to their zero divisors. This can be seen as a motive for expecting nature to be Lorentzian rather than Galilean.


Heroku, apparent silent failure of sucker_punch

Question: My app runs on Heroku with unicorn and uses sucker_punch to send a small quantity of emails in the background without slowing the web UI. This has been working pretty well for a few weeks.
I changed the unicorn config to the Heroku recommended config. The recommended config
includes an option for the number of unicorn processes and I upped the number of processes from 2 to 3.
Apparently that was too much. The sucker_punch jobs stopped running. I have log messages that indicate when they are queued and I have messages that indicate when they start processing. The log shows them being queued but the processing never starts.
My theory is that I exceeded memory by going from 2 to 3 unicorns.
I did not find a message anywhere indicating a problem.
Q1: should I expect to find a failure messsage somewhere? Something like "attempting to start sucker_punch -- oops, not enough memory"?
Q2: Any suggestions on how I can be notified of a failure like this in the future.
Thanks.
Answer: If you are indeed exceeding dyno memory, you should find R14 or R15 errors in your logs. See https://devcenter.heroku.com/articles/error-codes#r14-memory-quota-exceeded
A more likely problem, though, given that you haven't found these errors, is that something within the perform method of your sucker punch worker is throwing an exception. I've found sucker punch tasks to be a pain to debug because it appears the lib swallows all exceptions silently. Try instantiating your task and calling perform on it from a rails console to make sure that it behaves as you expect.
For example, you should be able to do this without causing an exception:
task = YourTask.new
task.perform :something, 55


Wireless Redstone Lamp without Command Blocks?

Question: So I want to create a building that shows no Redstone. And one of the problem is the lighting. I really want to see if I could get a Redstone lamp float above ground by 1 block and be able to be turned on/off. I could not get the: "pushing armorstand+minecart into block to activate pressure plate under the redstone lamp" (link) thing working as the armor stand only activated the pressure plate for 2 seconds. Then it stopped for some reason (probably fell down a few pixels or something).
Comment: I think is impossible. I saw something likeyou're asking but the redstone lamp had some redstone arround it.
Comment: What about a fix for the armorstand+minecart trick?
Comment: I don't udesrtand you question... For doing that I think you need command blocks.
Comment: @spund3 This is what I was talking about: [link](https://www.youtube.com/watch?v=gSO4UthRLMQ)

The armor stand only activated the pressure plate for 2 seconds or so.
Comment: Please add more detail such as... where the redstone lamp is in the building (i could answer your question if I knew this)
Comment: BUD piston maybe? (if it's still needed :)
Answer: As far as I know, using:
/setblock x y z lit_redstone_lamp

Is the only way to do this, and the lamp will turn off if any adjacent block update occur, such as blocks placed or items being used on it. It is a bit buggy, but it is the best I can think of.
Answer: Disclaimer: The solutions I have for you take up a lot of space, for redstone lamps, I suggest you think through the build before using it. Also I had to use command blocks (There is no way to do it without the command blocks)
I think that the second method will work best for you but you might want to read them all.
I did make wireless redstone once (not just for a lamp) wireless redstone has become far more easy with the implementation of the summon or fill command.
You will have to make an action trigger, a redstone signal and also trigger an action to revert the first action. (I promise this will make sense)
I don't have minecraft avaiable right now so I can't show screenshots right now but anyway, this is what you want to do.
The summon villager method
Here we will activate a piece redstone dust using a summond villager. this design has the largest reciever but it is lag friendly and easy to understand. Also the reciever can be hidden in any ceiling but not in the floor.
1. Write down the exact coordinates of the redstone dust you use to trigger the lamp. round them off to whole numbers.
2. Add 3 to the Y coordinate.
3. Directly above the redstone dust, of which you just wrote down the coordinates,  place a solid block of your choise and place a pressure plate on this block (either wood or stone, not the weighted ones)
4. Make a 1x2x1 (X,Y,Z) room around the pressure plate so a villager can fit in but can't walk off the pressure plate.
5. Think of a way to kill the villager after he has done his job of activating the pressure plate like using the \kill command, which I suggest you do. put this command on a slight delay. the length that you want your redstone signal to be activated depends on the time between the villager hitting the presure plate and him dying.
Golden Redstone Rule: for every tick of delay your readstone signal is on for 0,1 second making 10 ticks a second of delay
You can achieve this delay by using repeaters bewteen the redstone under your presure plate and the command block that will kill him.
6. Setup your summon command to summon a villager at the coordinates that you wrote down before.
Summing up what will happen
The villager when summond lands on the presure plate, activating the redstone signal below it. this will ,after a short delay set by the repeaters inbetween the redstone signal and the killing mechanism, kill the villager and the redstone signal turns back off.
Problems
There are three problems with this design:
1. The sender and receiver have to be loaded by minecraft to make it work.
2. You will loose track of the redstone signal timing of the sender (the time that the sender signal is on)
3. Summoning the mob might take some time to get him in the right spot if you got the coordinates off (after making a few of these devices you will get the hang of it though)
Solution for problem N.2
The solution to this problem is killing the villager with the same signal as it is summond with. to do this you will have to put a repeater going into the commandblock that summons the villager. leave it at one tick of delay. now before the repeater place a redstone torch in a way that it deactivates by activating your input signal. Now place the commandblock that kills the villager so the torch will activate it. now remove the killing system at the reciever module.
The redstone block setblock method
Here we will power the lamp directly with a setblock command by "setblocking" a redstone block underneath it. this has the smalest reciver of the two (only the redstone block if you destroy it from the sender) also it can be placed anywhere (floor, wall or ceiling) it is a bit harder to understand it though.
1. Write down your coordinates of the block to power and choose the side to power it from (use F3 here to see what side it is)
2.  Subtract or add to 1 to the coordinates depending on the side you want to power the block from (-1 on the Y acces to power it from below) this may require some testing.
3. determine where the sender has to be. Setup you command block to setblock the redstone block in the coordinates you just got. then write in this command block the next command:
setblock X Y Z minecraft:redstone_block 0

4. Setup another command block to destroy the redstone (either at the reciver for a fixed time or at the sender for a variable time depending on the timing of the sender's input) use this command:
setblock X Y Z minecraft:air 0

The wiring is the same as with the villager summon method
you can also setup two buttons. one for turning on the redstone block, one for turning it of. Just connect one commandblock to one button ant the other command block to another button. this will result in a RS latch style sender.
Problems
1. You might want to turn off the tile drops using:gamerule doTileDrops false. this will turn off all block drops though
2. You might have trouble understanding the way this works (even I sometimes do when it does not work)
3. Calculating the coordinate if you want to power it from the side is hard if you do it for the first time. This is where you will have to experiment.
I hope you can use these designs. I will post some screenshots when I get home tonight
Comment: "Wireless Redstone Lamp ***without Command Blocks***?" Also, I see no reason to use `destroy` in the second case, that just makes everything laggy AF. Lastly, asking someone to turn off tile drops without explaining that that will break survival mode completely is no good at all.
Comment: @MrLemon can't be done, this is the only solution at this time
Comment: @MrLemon your right about the `destroy` thing though, editing
Answer: I'm not sure what you can do with this, but try using a sticky piston attached to a redstone block. I'm not the most experienced with redstone, but I was trying to figure out my own problem when I came across this question.
Comment: Could you provide some more details on how this might work? Even if you don't have much experience with redstone, you can still share some things you have tried that might get the OP one step closer to an answer. Thanks!
Answer: If you are in MC Bedrock you can use the setblock method. I will explain.
The setblock method

Place a repeat command block.
Enter in the following command:

setblock ~ ~ ~ lit_redstone_lamp   **
Apply redstone to the command block.

I use this loads in my worlds.

**Make sure to replace ~ ~ ~ with the coordinates of the block and don't put ** at the end of the command or it won't work.


Detect TOR users with IPv6 exit addresses

Question: I need to redirect visitors to .onion site if they come using Tor Browser. It's okay if they have IPv4 IPs (e.g. 22.214.171.124 belongs to tor exit nodes list). But how to do that in case of IPv6 addresses, for example 2a0b:f4c0:16c:13::1 ?
Is there a similar IPv6 exit list or any programmatic method to tell the address is used by exit node?
Comment: You can try the list at https://www.dan.me.uk/torlist/?exit which contains IPv6 addresses, but I haven't looked into specifically how it's generated. You may also be interested in looking into https://trac.torproject.org/projects/tor/ticket/21952.
Answer: You can get the list of IPv6 addresses of tor exit nodes here (the IPv6 column): https://metrics.torproject.org/rs.html#search/flag:exit%20
Also, there is no programmatic way to tell a regular ip from a tor exit node ip (except for maybe doing a reverse dns lookup on the ip and checking if the domain has the word "tor" in it)
Answer: where I work we have an API that does that, it's in the IDS/IPS services
send a mail to email@example.com and I will get you access


Acid catalysed bond hydrolysis in 3-bromobut-1-ene

Question: I came across this doubt while solving a problem. I can't understand to which path (1 or 2) I should give priority, as both sound equally good to me.
Answer: Without looking up data, I would firstly assume that the $\ce{-CHBrCH3}$ group acts like any other alkyl group, and that path I would be preferred (by Markovnikov's rule). Bromine is electron-withdrawing via the inductive effect, but only very weakly.
I did go and look up data for this particular substrate. The reference is J. Org. Chem. 1936, 1 (4), 393–404. On page 399 the authors describe the addition of $\ce{HBr}$ to the above substrate.

In the absence of air and peroxides, however, 3-bromo-1-butene gives mostly (60 per cent.) 2,3-dibromobutane.

2,3-Dibromobutane is the product arising from path I, which confirms my assumption.
Comment: I don't know whether Markovnik rule can be applied here, but another way to arrive at why 1 is preferred is due to the higher stability of the secondary carbocation than the primary due to inductive effect of alkyl groups and hyperconjugation
Comment: That is precisely the rationale for Markovnikov's rule, so you are saying the same thing I did, albeit in a more detailed fashion. I was rather lazy to type all that out because I assumed whoever was reading it would understand why the rule applies.
Comment: Might be. I had commented because the markovnikov rule I've read talks about the addition of negative part of the addendum while in this case there is no mention of the negative part of the addendum. Though I think OH- can be regarded as the negative part and then we can say that markovnikov rule is applicable.
Comment: But if HBr along with peroxides is supplied then what would be the pathway? Actually this doubt is a part of the problem where HBr + ROOR was added as reagents.
Comment: @DIP If that was part of your question you should have asked it at the start, then I would have known to answer it. ): The same article that I cited describes the addition with peroxides. The selectivity is reversed, as is expected from a radical addition, which proceeds with anti-Markovnikov regioselectivity. The product distribution is 80% 1,3-dibromobutane and 20% 2,3-dibromobutane. [...]
Comment: [...] However, the matter is complicated by the fact that 3-bromobut-1-ene and 1-bromobut-2-ene are in equilibrium under peroxide + HBr conditions (the product distribution is the same for both alkenes). The authors write that it is impossible to conclude which alkene the addition products arise from.
Answer: Primary carbenium ions are very unstable. Typically, they will not form unless the positive charge is very well stabilised — so a benzyl cation ($\ce{Ph-CH2+}$) will form but an ethyl cation ($\ce{H3C-CH2+}$) will not form under ambient conditions.
Secondary carbenium ions are much more stabilised by double hyperconjugation, but they are still subject to rapid Wagner-Meerwein rearrangements to form more stable tertiary carbenium ions. However, if there is a sufficient possibility of stabilisation inherent to the molecule, forming them is no problem. Stabilisation could arise from:

a geminal heteroatom donating an electron pair to delocalise the cation onto said heteroatom
a vicinal group that can donate an electron pair in a similar manner, forming a three-membered ring
a neighbouring double bond that can resonate with the carbocation generating an allyl-type cation

In your case, the vicinal bromine is able to form a bromonium ion as in your path I. Thus, the secondary carbenium ion is reasonably stabilised and will be the major product.
Note that protonation of the double bond is reversible. Protonation leading to the primary carbocation will — if no immediate Wagner-Meerwein migrating hydride is observed — quickly eliminate back to the double bond, further favouring path I.

This observation is a classic example of Markovnikov's rule. It states:

When adding $\ce{H-X}$ to a double bond, the hydrogen will add to that side of the double bond which already has a higher number of hydrogens.

Markovnikov's rule is not strict (e.g. it fails completely for borane addition) but its basis is in the formation of the more stable carbenium ion as first addition step of the mechanism.


Most important things you should do after your VPS server has been "built"?

Question: I'm trying to write a guide with some essentials that one should do after his/her server has finished "building", important things like setting up a secondary user that's non-root, locales, perhaps even disabling a password login and using keys instead. If you do decide to participate mind providing code examples in addition to a small description?
Answer: apt-get update && apt-get upgrade to update package lists and install the latest security updates for packages, and also installing aptitude and relying on it since it handles dependencies better.
Answer: apt-get install locales if you don't already have it installed. type locale and if you see any warnings at the top, do dpkg-reconfigure locales, select your locale ( mine is en_US.UTF-8 UTF-8 ), generate and that should be taken care of, to avoid any locale issues when installing / upgrading packages.
Answer: 1) Enable spoofing protect and syncookies:
spoofprotect=yes
syncookies=yes

2) For server will be enough 3 consoles. Edit /etc/inittab:
1:2345:respawn:/sbin/getty 38400 tty1
2:23:respawn:/sbin/getty 38400 tty2
3:23:respawn:/sbin/getty 38400 tty3
#4:23:respawn:/sbin/getty 38400 tty4
#5:23:respawn:/sbin/getty 38400 tty5
#6:23:respawn:/sbin/getty 38400 tty6

3) Secure OpenSSH
4) Install utils:
aptitude install screen htop

Answer: apt-get install aptitude to grab the front end apt wrapper which handles dependencies far better. After doing so ( or if you already have it ), install some "essential" packages with aptitude install ~pstandard which grabs packages such as perl and dnsutils.


Are $CAT(0)$-polygonal complexes median spaces?

Question: A median space is a metric space $X$ for which for any three points $x, y , z \in X $ there exists a unique point $m$ such that $d(x,m)+ d(m, y)= d(x , y ), d(x,m)+ d(m, z)= d(x , z ), d(y,m)+ d(m, z)= d(y , z )$.
 $CAT(0)$-polygonal complexes are simply connected collections of glued (on their faces) polyhedra of varying dimension such that each link is flag.
Does there exist a metric on $CAT(0)$-polygonal complexes such that they are median spaces (in an analogous fashion to $CAT(0)$-cube complexes)?
Comment: The question is unclear if you don't specify the metric on the polygons. Beware that a CAT(0) cube complex of dimension $\ge 2$, with Euclidean cubes, is not a median space; when endowed with the $\ell^1$-metric on cubes, it is median but not CAT(0)!
Comment: Another remark is that real trees are the only examples of geodesic metric spaces which are both median and CAT(0). It follows from the fact that CAT(0) spaces are uniquely geodesic.
Comment: @user129863: Your edited question is not clear either. What are the restrictions you impose on your new metric? Has it to induce the same topology? Has it to be Lipschitz equivalent or quasi-isometric to the previous metric? Because if you impose no restriction, just transfer a median metric through a bijection with a median space having the same cardinality.
Answer: The question is vague. The median metric defined on CAT(0) cube complexes satisfy two fundamental properties:

For finite-dimensional cube complexes, it is bi-Lipschitz equivalent to the CAT(0) metric.
Any automorphism of a cube complex preserves both the CAT(0) and the median metrics.

What I claim is that there exist finite-dimensional CAT(0) polyhedral complexes which do not admit a median metric satisfying the above two points. Indeed, otherwise any group acting geometrically on such a polyhedral complex would act geometrically on a median space. By combining the following observation with the fact that any group acting on a median space with an unbounded orbit does not satisfy Kazhdan's property (T), we conclude that it is far from being true.
Theorem: There exists an infinite group satisfying Kazhdan's property (T) which acts geometrically on a finite-dimensional CAT(0) polyhedral complex.
My guess is that there exist plenty of such complexes. For one example, you can see Caprace's paper A sixteen-relator presentation of an infinite hyperbolic Kazhdan group. There, the polyhedral complex is even CAT(-1). [See Yves' comment below for additional information.]
I suspect that the second point above can be removed, ie., there should exist finite-dimensional CAT(0) polyhedral complexes which do not admit a bi-Lipschitz equivalent median metric.
Comment: You can attribute your theorem to Bruhat-Tits (construction of the building for $SL_3(Q_p)$) and Kazhdan (Property T for lattices therein), and maybe Borel-Harish-Chandra (existence of lattice therein). All three ingredients are $\le 1970$.


How to update PHP syntax file for vim?

Question: I notice the syntax file for PHP for vim is quite out-dated.
Does anyone know where is these syntax file located in Mac so I can do the upgrade?
Answer: Solved myself,
here are the steps :-

locate vim | grep php
turn up is this file /usr/share/vim/vim73/syntax/php.vim
sudo mv /usr/share/vim/vim73/syntax/php.vim /usr/share/vim/vim73/autoload/phpcomplete.vim.orig as backup
download latest php vim file from http://www.vim.org
untar the tarball
copy the php.vim to /usr/share/vim/vim73/syntax/php.vim
Answer: I think the proper solution is to install the updated syntax file locally, in your ~/.vim/syntax directory.
From your answer, you have installed the syntax file in /usr/share/vim, which is system class directory. This is not recommended since this can be erased on system or application update, and you don't know what your modification might conflict with. Instead, you should put all your vim configuration files under your home directory in ~/.vim.
(Sorry if it isn't a proper answer to your problem, but it seems I can't add comment to already posted answers)
Comment: which exactly i already did
Comment: It seems to me what you did is quite a different approach: directly modifying the system version of the file in `/usr/share/vim`. Please reread my answer to understand why it is not the proper way to override the default syntax file.

If you look a possibly up to date syntax file, I suggest you take a look at [StanAngeloff's php syntax plugin](https://github.com/StanAngeloff/php.vim) (or better, if you use many languages: the [vim-polyglot plugin](https://github.com/sheerun/vim-polyglot)).

How to update PHP syntax file for vim?


bottle.py server deployment

Question: I am moving from development to deployment and wonder how can i make my bottle.py application service both HTTP and HTTPS requests, and be multiprocess/multithreaded? I understand I need to use something like cherrypy instead of wsgiref?
Answer: In the Docs there are ideas to increase performance and multi-thread. I use a different folder and port for the deployed version so I can test without disrupting use.
The long text is here and includes pasteserver, and several others.

bottle.py server deployment


MacOS X Server Lion with multi-domain mailserver?

Question: Is a Mac OS X Lion Server capable of servicing multiple e-mail domains? We want to get a Mac to use as a standalone mailserver, but the Apple web site doesn't appear to provide an answer.
Answer: It surely can be done: Mac OS X Server uses Postfix Dovecot to provide e-mail services.
If Apple's documentation does not provide a clear answer as to how you can configure e-mail domains, the documentation for the underlying open-source e-mail services surely will.


How to get answers for long winded questions

Question: Recently I have had to ask a very long question.  The configuration involved is fairly extensive and will require any user to spend a decent amount of time investigating.  Given that I would not expect someone to answer such a question for only 15 reputation, I have put a bounty on it, but I still have not gotten too many responses.  Is there a way I could have written this question better in order to receive more answers?
Here is the link
Comment: Well, honestly? You mentioned that the problem has nothing to do with the marshaller, but that stuff is still in your question. Rip it out, make it easier to reproduce and comprehend.
Comment: I've edited the question with links to the code so that people can read the question itself, the error report, and then decide if they want to check out the configurations (if they are even relevant).  You can roll it back if you feel having the code inline is necessary, but I think you'll get more attention if you let the reader decide when to dig into the details...
Comment: Possible dupe, or at least related: http://meta.stackexchange.com/questions/32695/crafting-complex-questions-in-a-way-to-appeal-to-the-masses
Comment: Thanks for that edit, anything to make the question easier to answer. I have not yet had a chance to update the main body, i will do that now just to make sure that there is no irrelevant information.
Answer: Sometimes people won't read all the way to the bottom of your question to find out all the details.  They may have the answer, but give up reading because the question is so long.  One strategy that I have used is to put an "executive summary" at the top of the question.   This should boil the problem down to just a couple of sentences.  Mark it as such and set it off from the rest of the question so it doesn't look like one long ramble.
Using a summary gets your question out there, right in front.  People who have some insight, then know that they may be able to help and could be encouraged to continue reading.  You might also want to mention the bounty in your summary -- having that message at the bottom of your question seems to somewhat defeat the purpose in your case.
Comment: That's a nice descriptions for the title of a question, I always try to compress my question to fit into the title. Having an summary paragraph is less effective because it's not visible on the questions page.
Comment: @gs: If you start with the summary and it's short enough, it will in fact be visible on the questions page (or as a tooltip on the main page).
Answer: Shorten your question.
Format it well.
Comment: +1 Formatting is important.  I will read a long formatted question, but not one big chunk of text.
Answer:
Executive summary at the top
Bolded specific questions at the bottom
Don't list long files, configurations, code segments, etc inline - provide links so the question is simple and to the point, and anyone that wants detailed information can then dig into the links. (wish we had code folding on the site)
Try to pare your question down to the absolute minimum.
Break it up into several smaller problems/issues/questions if possible and ask them individually in separate questions.
Explain what you've tried, why it didn't work, or why you can't use it if it did work.
Provide only enough information to get people interested in asking you follow up questions - once they're hooked on the problem they may be more likely to spend time researching it.
Answer: At a certain point your question becomes too obscure/specialized and you won't be able to get quality answers to your question.
I think your bounty might work.  Keep checking it, but also keep hammering away at the problem on your own and try to further update the question with any extra information you gather.
Answer: Whilst I'm no expert on Spring I do know that for some technologies it's hard to boil everything down into a single concise paragraph or two, and a couple of code snippets.
The important thing is that you've supplied as much of the configuration data that may be of value as you can, and because of the larger font size used by Prettify on Stack Overflow, this can make some questions look more long winded that they need to be.
I think what you've done is fine. It's a niche problem and perhaps there aren't so many eyes on Stack Overflow looking at this with the level of experience you're looking for.
Answer: If the question is very complicated and there is no way to simplify it, consider waiting a bit and putting a good bounty on it. Usually people spend more time on questions when a bounty is involved.
Answer: Edit them into short questions.


How can I get La Longue Carabine from Corporal Sterling in Fallout NV?

Question: In Fallout New Vegas, I would like to get La Longue Carabine from Corporal Sterling, but am unsure how. I have very low sneak, and it doesn't even appear in his inventory to be stolen, is there any easy way to get this weapon that does not involve angering the NCR?
Answer: An alternative to killing him is to pickpocket the ammo he carries, then fast travel and come back.
When you return he will have the gun in his inventory available to be stolen.
Answer: If you don't want to kill him but don't care about losing a slight bit of rep with NCR, you can try and shoot the gun out of his hands then pick it up. If you do this and travel away from the airport (or Camp Hope, depends on where he got sent) and wait three in-game days, they've forgotten you and everything is back to normal.
Answer: No Negative Karma. No significant NCR loss. Sterling still alive. Clean digital conscience!

Wait until he is sleeping.
Talk to him. This will allow you some time to get away from him before he talks to you, lead him to the front gate because he will not stop following until he says howdy.
Wait until he turns around after the conversation, sneak, (stealth boy almost certainly necessary) -SAVE-
Sneak Critical his weapon. (May take some tries)
He'll draw. Shoot the weapon from his hands. (A few tries here too, may be wise to save again after landing the sneak critical on his weapon with a 4570. After which you should be able to holster your weapon and he should put his down as well. Orris in Freeside has a hunting revolver. You must disarm Sterling while he is holding weapon or it seems to disappear.) After shooting the weapon from his hands he will follow you out of Camp McCarran, and the ends of the earth.
Grab it.
Exit.
He'll follow, but the entire NCR won't be shooting at you, and you can outdistance  him pretty quickly if you holster you weapon, allowing you to fast travel to a repair shop. Because it will be broken.
Answer: I found the easiest way to get it without losing reputation, karma, or even being noticed is to wait until he sleeps in the tent to kill him.
Two of the beds have a point in the corner that you can easily get into. Once you're in there, sneak and use a stealth boy and use a melee weapon on his head (not for extra damage just because it is the point that is closest to you).
I found that it works most reliably with the sword you get by killing Davison in the Reppcon test facility basement, so you can get it during the quest with Manny and the bright brotherhood.
I found this to be a better way of getting the gun than stealing the ammo because at least on Xbox when you pickpocket the ammo from him it just won't give you the ammo, and I'm guessing this just happens if you get caught pickpocketing by anyone.
Thus you can't use that method so the only way to get it is by killing him or finding some way for him to die naturally like by an enemy.
Answer: The only way to get the rifle is by killing Corporal Sterling and looting his corpse.
The best ways to do this without angering the NCR is to use the "Sandman" perk, or get a silenced sniper rifle and shoot him in the head from a position where you can not be seen.
Answer: I have a method that may sound good to anyone who doesn't want to kill the corporal or leave him without his favorite weapon.
Open the console by default it's the tilde key (~) click on the corporal and type showinventory. It will then list everything he has along with the item IDs. Find the carbine in the list, type player.additem (the carbine's ###) 1
Answer: I stole all his ammo for it & fast-traveled then came back. (as stated above) Then I pickpocketed it from him and fast-traveled away from the area before he could take it back. Just as someone else stated above, wait 3 in-game days, so the tensions will have cooled down.
I hate how Sterling's Perception is so high, you can't just pickpocket it from him without getting caught. I tried multiple times (at least 30) and got caught every time. It would be just much easier to kill him or shoot it out of his hand and then high-tail it out of there.
Any of those 3 methods will work. So just choose the one that fits your play style and is easiest for you.
Answer: If you're playing on PC:
I killed him with console commands (open console, click cprl sterling, type "kill") looted his gun, then resurrected him (open console, click sterlings corpse, type "resurrect") and he came back to life, and still had his gun. This could also be a way to duplicate la lounge carabine, because he comes back to life with the rifle on his back! :D
Answer: There's a way to get him to give it to you if you do certain things first. After you waste Cook Cook and help Betty with her trauma Sterling walks up and gives the rifle to you as a reward.
I did it years ago via a post someone made but that has become hard to find because of all the players who would rather kill or rob him.
Comment: This answer is incorrect. Your reward for completing [Three Card Bounty](https://fallout.fandom.com/wiki/Three-Card_Bounty) is 1250 caps, NCR Fame, 750XP and the 1st Recon Team gets moved to Camp Forlorn Hope. Under no normal conditions does Sterling give you his rifle.


Why is Powershell 2.0 installed in the same location as Powershell 1.0?

Question: Does anyone know why Powershell 2.0 is installed in C:\Windows\System32\WindowsPowerShell\v1.0 on a Windows 7 box?
Comment: Powershell v3 in Windows 8 (preview) is in the same place as well...
Answer: It's actually an interesting story in side-effects.
Visual Studio has a fixed list of assemblies in their "Add Reference" dialog.
Anything else has to be browsed for.
Developers tended to browse for this location in the Windows directory, where System.Management.Automation.dll (the assembly that runs most of PowerShell lives)
This made an absolute reference to this location.
Since there wasn't going to be a side-by-side install option with PowerShell (as there is with the .NET framework), the best choice available was to allow people to keep referencing the same assembly, both by path and by StrongName, as they did before.
If this story hadn't have stayed this way, all applications written on top of PowerShell V1 would have to be re-released for V2.
Comment: Isnt this what the GAC is for?
Comment: Oh BTW including your signature on every answer is a waste of space :)
Answer: I just think that, at the very begining, Microsoft team plan to deploy PowerShell versions side by side, just as it's done for the Framework .NET versions. But with the time they decided to support only one PowerShell at the time.
There something even more strange when you use the -version parameter of the command line to choose version 1.0 the var $PSVersionTable is present with PSVersion valued to 2.0. $PSVersionTable is not present in PowerShell 1.0
C:\Program Files (x86)\Microsoft Visual Studio 10.0\VC>powershell -version 1.0
Windows PowerShell
Copyright (C) 2009 Microsoft Corporation. Tous droits réservés.

PS C:\Program Files (x86)\Microsoft Visual Studio 10.0\VC> cd \
PS C:\> $PSVersionTable

Name                           Value
----                           -----
CLRVersion                     2.0.50727.4952
BuildVersion                   6.1.7600.16385
PSVersion                      2.0
WSManStackVersion              2.0
PSCompatibleVersions           {1.0, 2.0}
SerializationVersion           220.127.116.11
PSRemotingProtocolVersion      2.1

If you have a look on var $host which exists on both versions
PowerShell V2.0 (vith version 1.0 or 2.0)
PS > $host
Name             : ConsoleHost
Version          : 2.0
InstanceId       : b6ae2582-c1f4-422a-b057-16458b387f7d
UI               : System.Management.Automation.Internal.Host.InternalHostUserInterface
CurrentCulture   : fr-FR
CurrentUICulture : fr-FR
PrivateData      : Microsoft.PowerShell.ConsoleHost+ConsoleColorProxy
IsRunspacePushed : False
Runspace         : System.Management.Automation.Runspaces.LocalRunspace

PowerShell V1.0
PS > $Host
Name             : ConsoleHost
Version          : 188.8.131.52
InstanceId       : b55940f2-b3b2-4f99-b895-98aac4752369
UI               : System.Management.Automation.Internal.Host.InternalHostUserInterface
CurrentCulture   : fr-FR
CurrentUICulture : fr-FR
PrivateData      : Microsoft.PowerShell.ConsoleHost+ConsoleColorProxy

My opinion is that PowerShell V2.0 is able to run almost all PowerShell V1.0 scripts. Microsoft add some vars and you can get troubles if you have these vars present in you scripts but it's peanuts.
JP
Comment: In Windows 8, it is still in C:\Windows\System32\WindowsPowerShell\v1.0\powershell.exe and $PSVersionTable shows a PSVersion of 3.0.
Answer: I think because PowerShell 2.0 is extremely compatible with 1.0, there was no need to have two different versions on the same machine.  So they put 2.0 over top of 1.0 on XP and Vista systems and most likely decided to keep the same directory for Windows 7.  This is also the same reason the extension is still .ps1 (and .psm1, .psd1).
You could ask the same for Windows 7 x64.  Why are the 64-bit system dlls in a dir called System32 and why do those same 64-bit dlls' names end with "32" e.g. user32.dll, kernel32.dll, etc.  :-)
Comment: Nothing to do with "extreme compatibility", but backward compatibility.


Does EBSCO's "Peer Review" search filter filter out junk journals?

Question: My school's library e-journal search tool uses EBSCO. In EBSCO, one can select "Peer Review" to only show articles from peer reviewed journals. Does this filter have a system for removing junk journals (i.e. journals that receive money to publish work) from the search results or will many junk journals calling themselves peer-reviewed journals still manage to get through the filter?
Comment: Not every journal that receives money to publish is junk. PLoS Biology is for example a well respected journal.
Comment: I'll also add that peer review filter simply restrict the search to peer reviewed articles. What is **junk** is subjective. Non peer reviewed doesn't mean junk, it simply means _non peer reviewed_. See the details of EBSCO peer review definitions in my answer.
Answer: Yes.
However, keep in mind the various (read: broad) definitions of what peer reviewed means. EBSCO uses following definitions:

Blind Peer Reviewed - (or Double Blind Peer Reviewed) - Articles appearing in a journal are sent outside of the journal's publishing or sponsoring organization for review by external reviewer(s), whereby the either author's identity or the reviewers' identity is unknown.
Editorial Board Peer Review - articles appearing in a journal are reviewed by an internal board of editors, not solely by one editor. The author's identity may be known or unknown.
Expert Peer Review - articles appearing in a journal are reviewed by experts (either internal or external to the journal) whose credentials are known and who are experts within the subject matter of the article under review. The author's identity may be known or unknown.

According to EBSCO, you can also restrict your search to peer reviewed articles by suffixing your query with AND RV Y.


Matlab simscape component modification.

Question: I am new to Matlab. I wanted to use Simscape resistor element and want to make it Temperature dependent. However i open the code of the component by view source code. I modify the code but couldn't save it. It gives only option to save as "Save as" . If i save as to new .ssc file then i cannot run that code to generate the component either. Your suggestions and opinion regarding this issue will be appreciated.
Thank you!!
Answer: There are three steps that are required to include a custom simscape component into simulink

Suitable directory tree structure

Simscape expects component source to be listed in a directory structure prepended with "+" and within the MATLAB search path ( file --> set path)
Take for instance /home/USER/Documents/MATLAB is listed in the MATLAB path search list, I can create a custom simscape file hierarchy from here:
/home/USER/Documents/MATLAB/+custom
Within this new directory I can save my simscape part

Build the simscape part.

With a valid Simscape structure existing, a library part can be "compiled" via the ssc_build command
ssc_build +custom
where +custom is the structure that was created. This will create within /home/USER/Documents/MATLAB/ a custom_lib.mdl file, a valid Simulink library that can be opened & your custom part dragged out

Adding a custom library to the main library browser

For this to work a slblocks.m file is required
<code>function blkStruct = slblocks
        % This function specifies that the library should appear
        % in the Library Browser
        % and be cached in the browser repository

        Browser.Library = 'custom_lib';
        % 'mylib' is the name of the library

        Browser.Name = 'My Library';
        % 'My Library' is the library name that appears in the Library Browser

        blkStruct.Browser = Browser;
</code>
http://uk.mathworks.com/help/simulink/ug/adding-libraries-to-the-library-browser.html
Your user library and custom part will now appear in the simulink browser
Comment: Thank you JonRB for your time and suggestions. Your suggestion worked for me, apart from including '+' sign for compiling using command **ssc_build custom** no + sign required for my Matlab version 2014 and 2015.

Matlab simscape component modification.


Why can't a gas be liquified by pressure above its critical temperature?

Question: What is the cause behind a gas being difficult to liquify above its critical temperature no matter how much pressure is applied on it?
Comment: No, it is compressible. Liquids aren't compressible. You are misunderstanding something.
Comment: That's a good question and anyone can give an intuitive explanation of why the liquid gas transition disappears above the critical temperature I would be interested to read it. "Intuitive" is the key word here!
Answer: Consider a fixed mass of, say 10g water in a 100ml container at low temperature. Attractive forces cause most of the water to condense into liquid form, with a density of about 1g/cm3. A tiny amount is in the vapour form, at a very low pressure with an extremely low density.
As we raise the temperature of the water, the molecules begin to move about more, and two things happen: The density of the liquid goes down, and the vapour pressure goes up (therefore the density of the vapour goes up!)
At a certain temperature, the vapour pressure is so high that the density of the vapour is equal to the density of the liquid. At this point the vapour and liquid become indistinguishable. The meniscus (interface. between liquid and vapour) disappears. This is of course the critical temperature.
So that, for me at least, is the best way to think of it. The critical temperature is the temperature at which the density (and all other properties) of the liquid and the vapour become the same.
The molecules are moving about so much that the attractive forces are insufficient to cause them to condense into a liquid form.
Comment: How does the density of the liquid goes down? I think it should remain constant. For example if you heat water , then it's density won't change. Its water after all! Please correct me if i am wrong
Comment: @AaryanDewan The density of liquid at constant pressure does decrease slightly as temperature increases - hence the need for an expansion tank on a car radiator. You make an interesting point, though, because the vapour pressure increases massively with temperature, and that might compress the water. http://www.maplesoft.com/applications/view.aspx?SID=134131 shows that even with the increasing vapour pressure, specific volume of the liquid goes up = density goes down (left end of straight lines) while the specific volume of the vapour goes down = density goes up (right end of straight lines.)
Comment: @AaryanDewan in general, in the real world, if you change the conditions in which a material exists, there will be some change, even if it is not significant. For example as you walk across a wooden floor, you compress it and it deforms (it is because of this that it may creak.) Concrete floors will also compress to an immeasurable extent, so that engineers do not have to consider deformation of floors in the design of buildings (though they will consider the deformation of main structural beams.)
Answer: As the substance approaches critical temperature, the properties of its gas and liquid phases converge, resulting in only one phase at the critical point: a homogeneous supercritical fluid. The heat of vaporization is zero at and beyond this critical point, and so no distinction exists between the two phases. http://en.wikipedia.org/wiki/Critical_point_(thermodynamics)
Comment: Yes, but _why_? (Or at least: _how?_)
Answer: How's this for simple and intuitive?
A gas is separate particles moving around at great distances from each other.  As you compress the gas, the particles get closer together.
The particles of a liquid are in contact with each other, but as you heat it, there is more and more space between them as they zip and jiggle more and more.
The combination of heat and pressure cause both gas and liquid to reach an intermediate point where the distances between the particles are the same.   If there's no difference, there IS no difference.  Gas and liquid merge.
Or how about a simple drawing?
It shows up in an interesting way on the Phase Diagram.  If you were to draw the liquid/vapor line from an angle so you can see the heat of vaporization as the height of a cliff, the cliff gets shorter and shorter and ends at the critical point.
Answer: To have a picture of the critical temperature, let us consider the 3d or 2d Ising model.
It is known that in the absence of an external magnetic field, there is a critical temperature $T_c$. Below $T_c$, the system can either point up or down on average. The up-pointing state can be labelled as the gaseous phase, while the down-pointing state can be labelled as the liquid phase. These two phases are essentially the same phase. The only difference lies in the value of some physical quantity. Here, in the Ising model, it is the magnetization. In the gas-liquid phase transition, it is the density per volume. Like the gas phase and the liquid phase, the up-pointing and down-pointing states can be continuously linked.
For the Ising model, we need to go below some critical temperature to enter the spontaneously magnetized phase; for a cloud of molecules, we also need to go below some critical temperature to have the gas-liquid phase transition.
Comment: The ising modeled particles above the critical temperature would be in which state according to you? Are you saying that an ordered phase transition is only possible at subcritical temperatures, without discussing what happena above it?
Answer: There are not many difference between liquid and gas (vapour):

Liquid is more dense than gas (also has greater viscosity, refraction coefficient, etc)
Liquid is "not compressible"
Liquid has surface tension

The first one is vague (one cannot define a threshold above which the stuff can be called liquid).
The second one is a small lie: any liquid can be compressed, it's just usually too hard to do it.
So what about surface tension? It's caused by the molecules on the liquid-gas boundary being "sucked" into the liquid phase.
When the temperature of the liquid rises, the density decreases, so there are fewer neighboring molecules that suck it inside the liquid. In addition, each molecule has a greater chance to escape, because it has more energy. At some point (critical temperature), pressure is just not enough. The energy of each molecule becomes greater than attraction force from its neighbors (at that temperature and density).
Here you can see the experiment on CO₂.
Answer: Simply put, a liquid stays where it is but a gas fills the space available because the attraction between the molecules in a liquid is usually great enough. Not always, though. The energy of molecules is randomly distributed, and therefore even in a liquid there will be a few molecules with high energies. If they're near the surface, their high energy will allow them to escape - that's why fluids evaporate even if not boiling.
Still, that leaves the question why there's a critical point. Basically, if you increase pressure, you push the molecules closer together, which increases attraction and raises the boiling temperature. But if the temperature is sufficiently high, no amount of pressure will bring them close enough together; energies flat out exceed the possible attraction.
Comment: Does this explain how you can go smoothly from a liquid (below the critical temperature) to a gas (below the critical temperature) without a phase transition by taking a path in the pressure-temperature plane which goes above the critical temperature?
Answer: Simple.
Because beyond Critical temperature the cohesive force can never overcome the internal kinetic energy
Comment: I'll disagree. The question could also have been asked  *"Why can't a liquid be vaporized by rareification above the critical temperature?"*, and then this answer would be "beyond critical temperature the internal kinetic energy can never overcome the cohesive forces". This gives us a contradiction without casting any light on the physics. The difficult, but important truth is that there is no essential difference between liquids and vapors unless you can restrict your considerations to a region of phase space that doesn't included paths around the critical point.
Comment: Welcome to Physics.SE! While I don't disagree with your answer, it is rather short. What is simple to you, who knows the subject already, may not be simple to other readers. Please consider adding more details to explain everything more clearly.
Comment: For instance, you could add a bit explaining about the cohesive forces that bind liquids together; a bit that explains how increased temperature (thus kinetic energy) requires more cohesive force to maintain liquid state; and a bit that explains how there is a maximum cohesion between the molecules, which naturally leads to the understanding of the critical temperature. Of course, these are all suggestions. Feel free to answer in your own way; I'm just pointing out that the answer, as it is, won't be viewed as contributing much of anything to this subject


Why isn't there a "Jon Skeet" tag?

Question: It's 2017 and we don't have a Jon Skeet tag on SO and SE?!
Comment: No. Actually, it has been created quite often and then it gets deleted by regulars (read: the regulars remove it from all questions and then it gets deleted by the system as an unused tag).
Comment: Jon Skeet is just a **normal guy** on the Stack Exchange network with a lot of reps. He doesn't need a tag.
Comment: Case in point: https://meta.stackoverflow.com/posts/320188/revisions  and https://meta.stackexchange.com/posts/71642/revisions
Comment: it sounds like it should be blacklisted
Comment: Feature requests must explain a problem that needs solving. Why do we need this, what benefit does it provide, what is the purpose of the tag?
Comment: I interpreted the request to add the tag as being whimsical (i.e. a joke), but I see that everyone has taken it quite seriously. :)
Comment: @Glorfindel then it should be hard-coded in the SO and SE ;)
Answer: Rather than there not ever being a jon-skeet tag, it seems from the comment by @Glorfindel that:

it has been created quite often and then it gets deleted by regulars
  (read: the regulars remove it from all questions and then it gets
  deleted by the system as an unused tag).

This indicates that the reason there is not a jon-skeet tag is that the community sees no case for its existence and burninates it whenever it is re-created.
Rather than creating it or repeated burnination it seems to me like blacklisting it may be more appropriate.
Comment: @evilReiko Jon Skeet"s iconicity is partly memetic. That is to say, his fame is deserved -- he knows his stuff and explains things very well -- but the meme status is partly because he has meme status, so people talk about his fame, and it becomes a self-reinforcing feedback loop.
Comment: You don't need a tag to search for him, you can search for a user, so that would be redundant. @evilreiko
Comment: Jon Skeet is an icon of SO, and there are many questions/answers targeting himself specifically, "his approach", "his opinion", "his life style", "his questions", "his answers", "his comments", etc. To me (and many others), reading and searching for these has been making me a better programmer. So why not have a tag for such questions!?

Why isn't there a "Jon Skeet" tag?


Best Option for Training Sandbox

Question: I am looking to use a sandbox specifically for Training for SFDC. My client does not want to purchase a full sandbox due to high cost. I would like to have "real data" available for the training. What are the best options for a lower cost sandbox for training with consideration to having a fair amount of user licenses, account/record data, and territory data?
Comment: Might be of interest: http://salesforce.stackexchange.com/questions/48313/possible-approaches-to-dedicated-training-environments
Answer: Sandbox Overview
Here you can see an overview of the existing sandbox types. If you need to have production data in your sandbox environment, you will need to access a Partial Copy Sandbox or a Full Sandbox.
Consequently, about the pricing, there are not so many alternatives.
Answer: I have written a longer question about this some weeks ago. As an unfortunate, there is no really good solution for my taste. Just have a look here:
What is the Best Practice for the right Training Environment?
I'm not happy with this situation and I would really appreciate if some of the Salesforce trainers would share their experience and approaches to setup something with a reasonable effort. My guess is, they still have some blacktab-magic to let it rock.
Especially for the PE customers for me it's bloody work so far with manual preparation and ETL jobs...

Best Option for Training Sandbox


Replace null values with just a blank

Question: I currently have a sql statement that outputs data into an excel document. However, every time there is a cell that doesn't have data, it outputs NULL into the cell. I was wondering if there was a way that I could replace NULL with just a blank space? Someone suggested using coalesce to do this, however I haven't ever had the chance to use it so I will have to do some reading on it. Anyone have any other suggestions?
Comment: What database you are using ? Oracle? Sql Server ? MySQL ?....
Comment: Re: "I will have to do some reading on it": Wouldn't it have made more sense to do that reading *before* posting this question? :-/
Comment: My SQL and I have done some reading and it looks like it may work, but I would like to weigh out my options. For example, someone might have a better idea of just avoiding a coalesce in this situation and just use something else
Comment: Could you please explain what exactly is the cause for "avoiding COALESCE()" ? Except for its ugly name, it still is a standard function (which IFNULL() et.al. are not)
Answer: In your select you can put an IsNull/IfNull round the column.  Not particularly efficient but does what you want.
MS SQL
Select IsNull(ColName, '') As ColName From TableName

MySQL
Select IfNull(ColName, '') As ColName From TableName

Comment: Is it possible to replace null in case when I don't know field name? When I do select * from table?
Answer: IFNULL is an Oracle extension (adopted by many other platforms). The "standard" SQL function is coalesce():
SELECT COALESCE(columnName, ' ') AS ColumnName
FROM tableName;

Comment: @DevinLamothe It is odd, but the Question wanted `just a blank space`. I would prefer an empty string, too.
Comment: This is old, but I'd like to point out your code is inserting a space character into ever "empty" cell, which is very different from an empty string (and, in turn, is quite different from a null).
Answer: Microsoft SQL
UPDATE TABLE_NAME
SET COLUMN_NAME = ''
WHERE COLUMN_NAME IS NULL

NOTE: this will SET, not select the result in your TABLE
Answer: MySQL
select IFNULL(columnName, '') from tableName

IFNULL(expr1,expr2)
If expr1 is not NULL, IFNULL() returns expr1; otherwise it returns expr2. IFNULL() returns a numeric or string value, depending on the context in which it is used.
Answer: SELECT teacher.name, IfNull(dept.name, '') as Dept
 FROM teacher left outer JOIN dept
           ON teacher.dept=dept.id

Replace null values with just a blank