Can I create cream of tartar with tartaric acid and potassium hydroxide?

Question: Here in Poland, I have no trouble buying both tartaric acid and potassium hydroxide. I'm having trouble sourcing cream of tartar though, so would it be enough to mix the acid and potassium hydroxide? Or do I need to get them to react in non-powder form and then dehydrate it back down to a powder for storage?
Comment: Can I ask what the application is?  In some recipe applications, tartaric acid might be able to substitute directly for cream of tartar (with quantity adjustments).
Comment: Trouble with K of Na hydroxides is that they *always* pull CO2 from the air, so you get carbonates and bicarbonates diluting your nice clean food-grade base. What you're attempting is feasible, but, because of the carbonate problem, best done using a pH meter rather than calculated quantities of acid and base. I'd make up a saturated stock of tartrate, and slowly drip in an 8 molar stock of KOH in H20, taking care not to let things get too hot. When you think you've added about the right amount of base, let the stuff cool and verify pH 7 w a cheap pH meter (amazon or its like). Then dry.
Answer: Potassium hydroxide is not something you'd want to eat.  It's caustic (the base form of corrosive), and you ABSOLUTELY should not mix an anhydrous (pellet or powdered) form of it directly into food, whether or not you mix it with another powder first.  Also, if you get the proportions off and the acid and base do not fully react, you could end up with a corrosive result.  That's not something you want in food.
The chemical synthesis of potassium bitartrate (otherwise known as "cream of tartar") is relatively straightforward.  Usually, you'd have a solution with a high concentration of tartaric acid, to which you'd add a solution of potassium hydroxide until the salt (potassium bitartrate) begins to precipitate out.  You'd then continue to titrate to obtain maximum precipitate.  Lastly, you'd filter out this precipitate and dry it to have powdered cream of tartar.
But I cannot advise you to attempt this on your own unless you have chemistry training.  First, as another answer points out, industrial chemicals are not generally designed to be "food safe," and although they are relatively pure, the small impurities may not be something you'd want to ingest, depending on how they were manufactured.
Second -- and more important -- it's potentially DANGEROUS unless you know what you are doing.  Read the MSDS sheet on potassium hydroxide, particularly the section on acute health effects.  (Note that the health hazard rating is '3', which is on a scale of 0 to 4, with 4 being the most hazardous.)  You should generally wear gloves and goggles when making a potassium hydroxide solution to begin with.  And even if you safely handle the stuff, you need to ensure it is properly reacted and the resulting cream of tartar properly filtered and dried, or else you could be putting a caustic agent into your food.
Basically, the potential for injury is high if you don't know what you're doing and mess something up.  I wouldn't recommend it for home food applications unless you're a trained chemist.
Comment: A proper chemist would use a pH meter to follow the reaction. About pH 3.5 should be the endpoint: https://en.m.wikipedia.org/wiki/Potassium_bitartrate  Also, you'll likely need more KOH than you expect, as the chemical reacts with CO2 in the air to form potassium carbonate/bicarbonate. An old bottle of KOH can be over 20% by mass carbonates.
Answer: If you attempt this reaction you will want to purify your potassium hydroxide and tartaric acid. With a little research you can usually determine what other substances will be in your industrial grade products, i.e. anti caking agent in the tartaric acid or surfactants in the potash.
From there you can perform a recrystallization to remove some of the contaminates using the different solubility of each chemical. If they are similarly soluble then you may have to perform it several times to make it reagent grade. If you are lucky, the contaminates with be either highly soluble or not soluble at all. Check solubility for distilled water, solvents, alcohols, etc. Sometimes one product will not dissolve in methanol and your desired product does dissolve.
I would recommend you just put all the effort this would take into finding cream of tartar; it is not dangerous, yet tartaric acid is, well, an acid and potassium hydroxide is very dangerous and can cause severe burns. It doesn't make sense that those are easy to come by but not the cream of tartar. You did check the spice aisle at the grocery store, correct? Its sold there as a leavening agent for things like lemon meringue. Be safe and good luck.
Answer: In any case, make sure that the reagents you get are food and/or "internal use" medical grade. Anything else can have poisonous contaminants.
It is unlikely that the dry powders would react to any significant degree; they would only do so at the surface at most. Reactions involving dry powders usually depend on the powder particles being either mechanically getting pulverized finer and finer, or being thermally decomposed into gases or liquids, in both cases by energy released from the reaction itself. But I think you wanted baking powder, not gun powder?


Other ID's appearing in my Mac Store account

Question: Just bought a refurbished Mac Mini, with new SSD and fresh instal of Yosemite. After setup, using my existing IOS Apple account details I updated to El Capitan, added Little Snitch and Firefox. All seemed well, until I started to get notifications that updates were available for software I didn't recognise. Being new to Mac I thought this might be OS based and clicked to upgrade, only to be informed that such upgrades were not authorised for this user. I also saw two unknown e-mail addresses. How do I fix this? Also, if as I suspect, ID's are still associated with the machine, why did the updates (to apps not installed) only show up now? HELP!
Answer: Just in case anyone is interested, I think I solved this. Still not sure why it should be the case, but it seems related to an external USB drive. When that is mounted, I get the notices about app updates I haven't bought and therefore can't  download. Even when the drive is ejected, this persists. However, if I clean boot without the drive or re-boot, all is well.


7500 Watt Manual Transfer Switch has #10 wires, but my well pump is wired with #8

Question: Problem!  I have a 1.5 hp 230 VAC deep well pump on a 30A circuit breaker wired with #8 copper that runs a couple hundred feet to the pump controller.  Pump specs say it draws 9.7 amps and allows 808 feet of #8 service panel to motor.  I now have a Firman H08051 Dual Fuel portable generator (10K/8K gas; 9050/7250 LPG) with the intent to run on propane.  The generator has a L14-30R Receptacle to connect to a Reliance 306CRK Manual Transfer Switch that came with a 10' cable of 4 conductor 10 AWG cable.  The generator inlet box has 3' of #10 wire to the transfer switch, and the transfer switch adds 3' of #10 wire to the service panel.  So the question is, can I power this 30 amp circuit with #10 wire when it's using #8 wire out to the load?  And if I can, what is the best connection going from #10 to #8?
Answer: You should be OK. The ampacity of the 8 ga is 40 amps, but who ever installed it was considering voltage drop over that long a run and used 8ga. A wise precaution and someone who actually followed installation specs...nice!
The ampacity of 10ga is 30 amps and such a short run between the generator and xfer switch won't have any appreciable voltage drop.
Most of the experienced electricians here don't really like the type of transfer switches you are using. They are over-priced for what they do and there are better alternatives, like a mechanical interlock on the main panel between the main breaker and the generator breaker. That way there is very little re-wiring to be done and you can easily pick and choose which, of all your circuits, are powered at one time simply by turning off existing individual breakers.
If you carry on with your xfer switch, there are tons of easy options to connect 8 ga with 10 ga.


How to find which chakra a lingam is consecrated?

Question: In many old shiva temples we can find Lingams with some markings on it. The markings aren't same in every lingam. Are those markings is to identify that the lingam is consecrated for a particular chakra? Is there a way to find which chakra a particular lingam has been consecrated?
Answer: TO HAVE A DEEPER INSIGHT INTO SECRET OF LINGA PLEASE REFFER TO---- KHECHARI KRIYA---BIOLOGY.  Khecheri kriya is to stimulate UVULA (LINGA or PSEUDO PHALLUS or object that resemble a small mini hanging penis) by the TIP OF tongue. Actually in Samadhi one need not do it forcefully rather it shall HAPPEN SPONTANEOUSLY when the tongue clings to the hard palate and abuts UVULA rubbing it to produce MADHU or nector or AMBROSIA.
SEE MADHU IN NATH PARAMPRA POTHI.
Comment: What you mention is about meditation. In temples we find Shiva Linga which has some markings so I wanted to know for which chakra that particular Linga is made for and how to find it by seeing the markings.
Answer: My answer will concentrate on the appearance of the lingas present in the chakras in the Kundalini Yoga. (Though there is not much).

Swayambhu Lingam in Mooladhara Chakra.

Shat-Chakra-Nirupana 1.9-10,13.:

Inside it (the triangle/yoni) is Svayaṃbhu in His Linga-form, beautiful like molten gold, with His head downwards. He is revealed by Knowledge and Meditation, and is of the shape and colour of a new leaf. As the cool rays of lightning and of the full moon charm, so does His beauty. The Deva who resides happily here as in Kāśī is in forms like a whirlpool (have vacuum/depression on the top of the Linga).
Over it shines the sleeping Kuṇḍalinī, fine as the fibre of the lotus-stalk. She is the world-bewilderer, gently covering the mouth of Brahmadvāra/Brahmarandhära by Her own. Like the spiral of the conch-shell, Her shining snake-like form goes three and a half times round Śiva.
By meditating thus on it who shines within the Mūla-Cakra, with the lustre of ten million Suns, a man becomes Lord of speech and King among men, and an Adept in all kinds of learning. He becomes ever free from all diseases, and his inmost Spirit becomes full of great gladness. Pure of disposition by his deep and musical words, he serves the foremost of the Devas.

Bana Linga in Anahata Chakra.:

Shat-Chakra-Nirupana 4.25.:

The Śakti whose tender body is like ten million flashes of lightning is in the pericarp of this (Anāhata) Lotus in the form of a triangle (Trikoṇa). Inside the triangle is the Śiva-Linga known by the name of Bāṇa. This Linga is like shining gold, and on his head is an orifice (bindu) minute as that in a gem. He is the resplendent abode of Lakṣmī (Beauty/Sri).
He who meditates on this Heart Lotus becomes (like) the Lord of Speech, and (like) Īśvara he is able to protect and destroy the worlds. This Lotus, is like the celestial wishing-tree, the abode and seat of Śarva. It is beautified by the Haṃsa, which is like unto the steady tapering flame of a lamp in a windless place. The filaments which surround and adorn its pericarp, illumined by the solar region, charm.

Itara Linga in Ajna Chakra.:

Shat-Chakra-Nirupana 6.33-34.:

Within this Lotus dwells the subtle mind (Manas). It is well-known. Inside the Yoni in the pericarp (of Ājñā Chakra) is the Śiva called Itara, in His phallic form. He here shines like a chain of lightning flashes. The first Bīja of the Vedas, which is the abode of the most excellent Śakti and which by its lustre makes visible the Brahma-sūtra, is also there. The Sādhaka with steady mind should meditate upon these according to the order (prescribed).
The excellent Sādhaka, whose Ātmā is nothing but a meditation on this Lotus, is able quickly to enter another's body at will, and becomes the most excellent among Munīs, and all-knowing and all-seeing. He becomes the benefactor of all, and versed in all the Śāstras. He realises his unity with the Brahman and acquires excellent and unknown powers.[2] Full of fame and long-lived, he ever becomes the Creator Destroyer, and Preserver, of the three worlds.

I hope this helps. Prd..


Accessing function in the controller from view

Question: In the view, I have 2 div, one accepts the search parameters and other one displays search results. I have a controller wherein there is function for displaying first div (search parameters) at startup and also function for displaying search results.
I am new to the MVC architecture. My question is, how do I access the search function in the controller after clicking on the search button in first div? Any ideas?
Answer: You have to provide attributes for the controller, [HTTPGET] for search parameters routine and [HTTPPOST] for taking the user input as method parameters and then processing it.


How to make dash load faster in unity-2d

Question: My dash always takes 10-15 seconds to show up. Is there a way to make it stay permanently loaded in the RAM or something so that it shows up faster?
Comment: During login or all the time it hides and then shows?
Comment: How much RAM have you got in your PC?  Are you also attempting to use Compiz?  If you have too little RAM and using Compiz, opening the Dash can take the time you mentioned.
Comment: @fossfreedom My computer has 1GB RAM, and I'm not using compiz. Metacity has compositing enabled, but even when it isn't enabled, fake transparency is used so it still takes the same amount of time.
Comment: very strange... is this Ubuntu 11.10? what CPU and graphics chip/driver are you using?
Comment: @fossfreedom Yes, this is Ubuntu 11.10. I have an old computer, so maybe that's the problem. My processor is Intel® Pentium(R) 4 CPU 1.50GHz and my graphics card is GeForce2 MX/AGP/SSE2.
Comment: There is no way to make it load faster, at least none I know of. Your hard drive may be too slow to load Unity in a timely manner.
Comment: try 12.04, it's faster than 11.10 (11.10 is the slowest OS I ever had)
Comment: @Prasad yes, that's what I'm doing now. I thought I wrote that actually, but maybe it didn't get posted...
Answer:
Yes, this is Ubuntu 11.10. I have an old computer, so maybe that's the problem. My processor is Intel® Pentium(R) 4 CPU 1.50GHz and my graphics card is GeForce2 MX/AGP/SSE2

I think you are correct -- the problem is your CPU is old and very slow and your GPU (graphics card) is also old and doesn't support compositing and other features. This means everything must be rendered in software, and that is a burden for your CPU.
The Pentium 4 CPUs were notorious for providing extremely poor performance compared to what their clock speed was (1.5 GHz, here); for example, the CPUMark below shows that a Celeron M at half-the-speed or 800 MHz (released 3 years later) is faster than a Pentium 4 1.5 GHz:

Unfortunately, the solution to continue using the latest Ubuntu on your current hardware probably involves switching from Unity 2D to a lighter desktop environment such as XFCE or LXDE; perhaps you could try an Xubuntu/Lubuntu LiveCD to get a feel for what kind of performance to expect.
Answer: I really don't know if it will make your Dash open faster as this program makes programs lauch faster and the Dash isn't exactly a program, but you can test it:
sudo apt-get install preload
Preload is a little program that fills your RAM memory with the most used programs/files, so it won't work at the moment of the installation, but within two days using the pc it will take effect as it will memorize the common programs that you use.
Answer: Try
sudo dpkg-reconfigure unity-2d

and see if that speeds it up.
Answer: Okay it sounds like your RAM is definitely going but to make sure run a boot-able program called MEMTEST86 and let it run for a while and see if any errors pop up. If you get no errors that doesn't automatically exclude the troubleshooting the RAM.
But before you go out and buy a new stick check your HDD. There is also another program (boot-able also) called Spin Rite and it checks for problems on your HDD (If this one shows no errors you are good to go, if it does you are in trouble.)
If the Spin Rite passes your next step is to continue troubleshooting your RAM..... Replace it with a new one and see if the condition still exists. If so well stick the other 1GB stick in and now you have 2GB. But to fix the issue we have to narrow it down.
If you have a Graphics Card installed on your system remove it and check to see if condition is still persistent. If so then you know now that it isn't the graphics card and it leaves three final problems.
Go ahead and stick your graphics card back in (if you have one) and look around at the capacitors and resistors on your motherboard and make sure none of them are blown (they will have bulging tops much like a cola that has gotten too hot and expanded.)
If none are then you are left with two options. It is software or it is the processor. Deciding between these two is easy. If you made a backup then time to clean install Ubuntu. Then try it. If problem still persists then you know what your problem is: the processor.
I made this tutorial in chronoaffordableologic order meaning it is cheapest and least expensive to start with what I stated first and work your way down.
Comment: I find that this **chronoaffordableologic** order is off, because reinstalling Ubuntu costs nothing at all, and yet is listed last.
Answer: I don't know if this is of any help to you, but ubuntu-tweak is a great application that seems to load my dash at twice the speed after installing it and tweaking some items. I suggest you run Computer Janitor - enhanced speed performance without OverClocking your processor. ubuntu-tweak with Computer Janitor built in is available in the Software Center.


Inequality of matrix norms

Question: I'm trying to prove that $$\frac{1}{\sqrt{n}}\lVert A\rVert_\infty \leq \lVert A \rVert_2$$ I know that $\lVert A \rVert_\infty = \max_i\lVert a^t_i\rVert$ and $\lVert A \rVert_2 = \sigma_1(A)$ where $\sigma_1$ is the largest singular value of $A$, but I can't seem to connect the two.
Comment: Do you know that $\|A\|_p = \max_{\|x\|_p = 1} \|Ax\|_p$? If yes, hint: Hölder inequality.
Comment: https://math.stackexchange.com/questions/391744/matrix-norm-inequality Doing a little search first wouldn't hurt.
Comment: @Hyperplane it also doesn't hurt to read the question. OP uses $\|A\|_2$ differently from the question you linked.
Answer: I think it is best to reserve $\|A\|_2$ for the usual $2$-norm $\displaystyle \|A\|_2 = \sup_{\|x\|_2 = 1} \|Ax\|_2$.
You can use the singular value decomposition: there exist unitary matrices $U$ and $V$ and a matrix $S$ with singular values of $A$ along the diagonal and zeros elsewhere satisfying $$A = USV.$$
Suppose that $x$ is a vector with $\|x\|_2 = 1$. Then you have $$\|Ax\|_2 = \|USVx\|_2 = \|SVx\|_2 \le \|S\|_2 \|Vx\|_2 = \|S\|_2.$$
Because of its particular form, the $2$-norm of $S$ is its largest entry. Since its nonzero entries are the singular values of $A$, this means $$\|S\|_2 = \sigma_1(A)$$ so that $$\|A\|_2 \le \sigma_1(A) .$$
The fact that $\|A\|_\infty \le \sqrt n \|A\|_2$ is easy to prove, giving you
$$ \frac 1 {\sqrt n} \|A\|_\infty \le \sigma_1(A).$$

Inequality of matrix norms


How Large Would A Gas Giant Appear To Be To The Inhabitants Of An Earth-like Moon Orbiting it?

Question: How large would a gas giant realistically appear to be on an Earth-like moon? I think a movie or two has portrayed them as very large, but that's an exaggeration, right? Depending on the size and orbital distance, is it possible that the gas giant might be barely visible during the day?
Comment: Google found this beauty as the first item in my search: https://spacemath.gsfc.nasa.gov/weekly/10Page51.pdf
Comment: This depends on the sizes of the gasgiant and its moon as well as the distances evolved. You will find a detailed answer with pictures here: https://worldbuilding.stackexchange.com/questions/11505/tidally-locked-gas-giant-moon-brightness-of-the-gas-giant?rq=1 Could thus be also a duplicate. At least you should provide more details in your question (size of moon, gas giant, distances involved, etc.).
Comment: Can be readily calculated. refer to any high school trigonometry text, and plug in the gas giant's diameter and distance.  Considering that Saturn is readily visible from Earth at night, and Jupiter is (usually) the 3rd brightest object in the night sky, after the Moon and Venus, it's going to be visible.
Answer: First, on brightness. Our Moon has an albedo of around 0.1 and is bright in the day sky.  Jupiter's albedo is closer to 0.5, so it would be proportionately that much brighter.  It should be easily visible in an Earth-like atmosphere.
Let's look at our own Solar System for sizes.  Jupiter has a diameter of ~150,000 km.  The Galilean satellites orbit at radii of 420,000, 670000, 1080,000, 1880,000 km.  (All rounded numbers.)  So they are respectively about 3, 4, 6, and 12 Jupiter diameters away.  That gives Jupiter an angular diameter of 20 degrees, 12 degrees, 9 degrees, and 4 degrees respectively. (Compare that to the Moon's 1/2 degree size as viewed from Earth.)
We can do the same calculation for Saturn.  (All sizes in 1000 km.)  Diameter: 120, Ring diameter: 350, Distance to Titan: 1200.  So Titan is 10 Saturn diameters away and 3 ring diameters.  Saturn would be about 6 degrees across and the rings (nearly edge on, of course, so hard to see) around 20 degrees.
So Jupiter ranges from big to really big, but never gets to fills-the-whole-sky big.  Saturn is bigish.
Answer: It would definitely depend on the size of the gas giant, and the distance from the gas giant to the moon. If the moon is distance D away from the world, and the gas giant has an apparent radius of R, then someone standing on the moon would see the gas giant subtending an arc of 2*arctan(R/D).


How to perform RACH attacks on GSM mobile networks?

Question: I am studying various vulnerabilities on GSM networks and would like to know what hardware and software are needed to test such vulnerabilities.
Answer: A full-duplex software defined radio would be useful - it would allow you to send any GSM packet you want, even malformed ones which you won't be able to send with off-the-shelf GSM hardware.
On the software side you can always use custom code to generate your GSM frames, but you can have a look at OpenBTS and OsmocomBB for ready-to-use open source code that handles the GSM protocol. GNU Radio has a module for GSM as well. Wireshark can display captured GSM frames.


Global settings for enumitem concerning list labels

Question: I want a set of enumerate environments within each other, and a certain order of labels to mark their hierarchy. However, the order is different from the originally provided one, and it burdens my work with extra label=<command>s every time I make lists. How can I change settings globally (for just one document, or for all documents that I use enumitem in) so that I can set the order once for all enumerates? Thank you.
Comment: @K.Paul: Don't change the original sources of a package. You should write an importer package, say `personalenumitem` and use with `\usepackage{personalenumitem}` in your documents -- yes, that involves editing the already existing documents, but will simplify the maintenance of them and it will be a starter for future documents that require your setup
Comment: Did you read the enumitem manual? It explicitly explains hove to set the options globally.
Comment: Welcome to TeX.SX!! Can you please give a [minimal working example](http://meta.tex.stackexchange.com/questions/228) and/or example output to  explain what you want. A MWE should start with a `\documentclass` command, have a minimal preamble  and then `\begin{document}...\end{document}`. If you can post what you are currently doing then this would explain more clearly what you want. At least for me, it is not at all clear what you are trying to achieve. You might also want to look at https://tex.stackexchange.com/questions/452049.
Comment: Well I DID actually read the manual but I guess I'll have to go back to it, and in any case, I'm working on multiple projects that requires the same changes, and I was wondering if I could access the actual `enumitem` package and make some changes. If this cannot be done, I guess I'll just have to manually set every document in the same way.
Answer: For future reference:
Needs the enumitem package.
To change the nth level of labels to a specific form, insert following to preamble:
\setlist[enumerate,n]{label=[form goes here]}


How can I set a maximum and minimum level for a dependent variable?

Question: I have to make sure that a dependent variable I explain using linear regression ranges between a minimum of 0% and a maximum of 30% (it is an investment weight in a portfolio). How should I proceed ?
Answer: A natural tool is the CDF, because by definition its range is 0 to 1. By multiplying a CDF by 30, you get your desired range. In logistic regression, the linear predictor is transformed to a probability using just that (the logistic CDF to be precise).
I'm going to give you some R-code that will let you fit a linear regression and then transform it to a [0, 30] scale using a logistic CDF multiplied by 30. The predictions are nice, but unfortunately the coefficients are a bit more difficult to interpret.
<code>set.seed(123)
x <- rnorm(100) # explanatory variable
y <- 15 + 5*x + rnorm(100) # response taking values between 0, 30

pseudo.p <- y/30 # on the same scale as probabilities
pseudo.log.odds <- log(pseudo.p / (1 - pseudo.p)) # like logistic regression

my.lm <- lm(pseudo.log.odds ~ x)
plot(30 * plogis(my.lm$fitted.values) ~ y) # predicted vs actual
</code>
Answer: Not sure I quite have a handle on your question. I assume the issue is that standard issue with modeling a proportion - you don't want your models to provide predictions <0 or >1. (And I'm thus ignoring the <30% requirement, but if this is important you can just rescale your output to be a proportion of a proportion)
There are a number of standard approaches to this issue. My sense is that the most established is to use a beta distribution. But the optimal approach partly/mostly depends on which is easily implemented in your software of choice. Log link models should work well as well. You can find some more complex approaches listed here:
http://www.stata.com/meeting/germany10/germany10_buis.pdf
Implementation of log models for proportions here:
http://www.ats.ucla.edu/stat/stata/faq/proportion.htm
Recent stackexchange thread:
Generalized linear models with continuous proportions
These are both Stata references, but the concepts are applicable to your software of choice.


Deploying Salesforce Flow with new entry criteria option "Formula Evaluates to True (New)"

Question: I have created a Flow by using the "Formula Evaluates to True (New)" entry criteria option but the ant migration tool is not pulling formula conditions when I try to deploy this flow to another sandbox. Flow is not showing any entry criteria in the target sandbox after the deployment.
Flow in the source sandbox:

Flow in the target sandbox:
Answer: You are executing your metadata retrieval on an old API version that does not provide this new construct. Update your API version to 55.0.
The Ant Migration Tool is obsolete for the vast majority of use cases. While it's not the source of your specific problem, consider migrating to the sfdx CLI, which supports OAuth and a variety of other nice features.
Comment: Agree with David, what you just need to do is to upgrade API version to 55.0


Should storm windows be removed if AC will be on and windows rarely opened?

Question: We generally run our AC most of the day.  I am wondering if it is a detriment to leave the storm windows on (b/c they create a pocket of hot air) or a potential benefit (by reducing the escape of cold air).
Comment: Im no expert here, but the fact you trapped the heat seems important.  Removing the storm window would increase solar radiation inside.  From your question it's also impossible to know if any of the glass have energy efficient coatings.
Comment: An analogy: my attic traps hot air, should I remove my roof?
Answer: It's an intriguing question. On one hand, trapped air is heated through radiation. On the other, it acts as an insulator. Keep in mind that we aren't talking about airflow, but heat flow (by conduction, convection, and radiation).
The answer probably depends on how many of your windows are exposed to the sun, where extreme temperatures are generated between panes. In those cases, the insulation benefit of the second pane is probably outweighed by the efficiency lost due to greenhouse effect.
For those windows which are usually shaded, the second pane creates a trapped-air buffer, which dramatically reduces conduction loss.
I don't think a conclusion can be drawn with the information given. You might update your question to describe the building and property features in more detail. (Don't put it in a comment.)


Name and how to care for this plant?

Question: Can someone please tell me what plant is this and what kind of environment it likes to be in? I noticed the browning tips does it require more dry/humid environment?
Answer: Bromeliad; water sparingly ,mostly in the center of the plant. It will tend to hold water. Temperature above 40 F. I have not noticed them to be sensitive to humidity.

Name and how to care for this plant?


how to convert WIF key return to HEX format

Question: any one knows how to convert WIF key return to hex format please also let me know if the private key is out side range of ecc then how to import it to some wallet ?
Answer: Using this python library (I am the author)
<code>>>> from cryptotools import PrivateKey

>>> prv = PrivateKey.from_wif('5KUkQNKHA9cVmhSyKuNmop7r83DN2fMhPtNUW843Q6JxqRddEVz')
>>> prv.hex()
'db07a0c6c98c7a2b5cdc19cd4431a05908a40424d6d1ff20eac9cb2f9488e12d'
</code>
If the key is too large
<code>>>> PrivateKey.from_int(1 << 260)
</code>
it will throw an error
<code>AssertionError: Key larger than Curve Order
</code>
Comment: thank you mike is there any way to import the private key which fall out of range of elliptical curve
Comment: No. If you have a number that's too large you should first find it's congruent modulo N and then import that
Answer: There is also a bash (or zsh) shell script to convert from WIF to hexadecimal format: https://gist.github.com/GregTonoski/fbe2740391a366add4bfcefded00c5c4
Simply run the script like in the example:
<code>$ bash Bitcoin_WIF_into_hex.bash "L3wB8ytuxNS3SPX2CJnHqK48Zzqj1AnayDTrJomvNPDxuKvHyvpT" > private_key_bitcoin.hex
</code>


What do the Borg eat?

Question: We know Seven of Nine eats after she was severed from the collective. We know the Borg drones recharge/sleep in individual docking stations. Do the Borg drones eat? If so, what do they eat, and how is it ingested?
Answer: In the TNG episode "I, Borg", Hugh was fed by absorbing energy through a port in his arm.  La Forge had to install a matching coupling in the wall of Hugh's cell.  The Borg implants convert energy into glucose and whatever nutrients the Borg's organic side needs to keep functioning.

Crusher : The Borg don't ingest food. Their implants can synthesise any organic molecules the biological tissues require. What
  they need is energy.
Comment: Seven needed to eat because many of her implants were removed after she was separated from the Collective.
Answer: Voyager S6 E2 -- "Survival Instinct" -- has a scene of Seven and other drones gathered around a fire, eating meat that starts to trigger memories in each of their lives before the Borg.
Like Proust's Remembrance. The primal act of eating floods in an existential consciousness and a will to narration, of epic proportions.
I would submit that eating is not only not Borg, but perhaps even antithetical to what is Borg. Regeneration in alcoves or otherwise presumably has some biological component -- perhaps nutrition is IV'd in in some way?
Comment: Hi there. There is part of an answer in here, though mostly commentary; I suggest you [edit] your post to clarify whether Borg's are actually never seen eating, or take a stand against it, stuff like this. This would make for a better answer.
Comment: @Vijay Pattisapu - An anonymous user has attempted to edit this answer. If that person is you, you should use the same account you used to post this answer to edit it; that  way, you won't need to submit the edit for approval by other users for the edit to go through. If you can no longer access your previous account for some reason, you can merge your new account with the old one by following the instructions provided [here](https://scifi.stackexchange.com/help/merging-accounts).

What do the Borg eat?


C#: Can a base class use a derived class's variable in a static function?

Question: Is there anyway of having a base class use a derived class's static variable in C#? Something like this:
class Program
{
    static void Main(string[] args)
    {
        int Result = DerivedClass.DoubleNumber();
        Console.WriteLine(Result.ToString());   // Returns 0
    }
}

class BaseClass
{
    public static int MyNumber;

    public static int DoubleNumber()
    {
        return (MyNumber*2);
    }
}

class DerivedClass : BaseClass
{
    public new static int MyNumber = 5;
}

I'm trying to have it return 10, but I'm getting 0.
Here's where I'm using this: I have a class called ProfilePictures with a static function called GetTempSavePath, which takes a user id as an argument and returns a physical path to the temp file. The path base is a static variable called TempPath. Since I'm using this class in multiple projects and they have different TempPaths, I'm creating a derived class that sets that variable to whatever the path is for the project.
See Also

Why can't I declare C# methods virtual and static?
Answer: Apart from the fact that has already been pointed out... that static variables are tied or bound to the specific class declaring them and cannot be overridden. Overriding/Polymorphism needs instances to work.
Your problem can be solved with a change in design.
string ProfilePictures.GetTempSavePath(SomeType UserId, string sBasePath)

if it just needs these 2 variables to compute the return value, you can keep it as a utility/static method. Now you can feed in different base paths..
Now it seems from your question, that you need to use this class in multiple projects (which have fixed base paths) and kind of hardcode the base path so that you dont have to specify it for each call.
Type/Class hierarchies should be defined based on behavior and not on data. Variables can handle change in data. Hence I'd suggest holding the basepath value as a static member variable, which is initialized from a resource file (DoubleClick your project properties node > Settings > Add a new Settings file > add a new setting called BasePath - string - Application scope - VALUE=C:\Users). Now you just need to tweak the app.config file for each project, no code changes, no hardcoding and not more than one type needed.
public class PathHelper
{
  static string _sBasePath;
  static PathHelper()
  {
     _sBasePath = Properties.Settings.Default.BasePath;
  }

  static string GetTempSavePath(string sUserId)
  {
     // dummy logic to compute return value, replace to taste
     return Path.Combine(_sBasePath, sUserId.Substring(0, 4));
  }
}

Hope that made sense
Answer: The problem is that you're re-declaring the static variable in the derived class.  The MyNumber declaration in DerivedClass hides the declaration in the base class.  If you remove that declaration, then references to the "MyNumber" in derived class static functions will refer to the base class variable.  Of course, if you remove the declaration then you can't use a static initializer in the derived class.
You might want to consider requiring users to instantiate an instance of ProfilePictures rather than provide a static function for GetTempSavePath.  That way you could overide the GetTempSavePath method to provide the correct TempPath.  Or, you could simply set the value of the static path value in your derived class constructor.
Although it is possible to use inheritance with static members, you can't relly have polymorphic behavior without a "this" pointer.
Answer: Static members are not virtual, so you can not override them.
When you call DerivedClass.DoubleNumber you are actually calling BaseClass.DoubleNumber as the DerivedClass class doesn't have that method. Also, the use of MyNumber in that method is always going to be BaseClass.MyNumber no matter how you call the method.
What you are looking for is a virtual property that you can override in a derived class. As a virtual member can not be static, you need to use an instance of the class. If it's not practical to keep a reference to the instance, you can use the singleton pattern.
Answer: This kinda works:
public class ClassA
{
    protected static int num = 5;

    public static int GetNum()
    {
        return num;
    }
}

public class ClassB : ClassA
{
    static ClassB()
    {
        num = 6;
    }
}

However, note the difference when you call ClassB.GetNum() before and after instantiating one object. The static initializer doesn't run until you create at least one, so you'll get 5 if nothing has been created, and 6 if at least one object has.
Answer: Provide a virtual method that returns the class static.
class BaseClass
{
    public virtual int GetMyNumber() { return MyNumber; }
}

You might want to use a virtual property instead...
Comment: When I use a virtual method or property, the static function can't access it (Compiler error: Cannot access non-static property in static context)
Answer: Using too much of static members is also not recommended if they are going to encapsulate a logic of an entire object. For example your code can be rewritten correctly in following manner... and this is the most recommended in oops,
class Program
{
    static void Main(string[] args)
    {
        int Result = DerivedClass.Instance.DoubleNumber();
        Console.WriteLine(Result.ToString());   // Returns 0
    }
}

class BaseClass
{
    protected BaseClass(){} // this enforces that it can not be created

    public int MyNumber;

    public virtual int DoubleNumber()
    {
        return (MyNumber*2);
    }
}

public class DerivedClass : BaseClass
{
    // this also ensures that it can not be created outside
    protected DerivedClass(){
        MyNumber = 5;
    }

    // only way to access this is by Instance member...
    public static DerivedClass Instance = new DerivedClass();
}

This is how we access configuration values and many other single instance static objects provided by .Net Library.


Chain rubs on a bigger cog on the cassette. Wrong spacing?

Question: my kids mtb on the smallest cassette cog the chain rubs on the next bigger cog creating a harshness while using this smallest cog. I was looking at it and the spacing between the two smallest gears seems to be smaller compared to the remaining gears on the cassette. My question is this normal? It is a Trek marlin and has never been apart since new. Thanks for any help in advance.
Comment: Can you post a photo? Or even a video? It is quite unlikely that the gap is smaller even though a missing spacer could cause that. It could just be a gear indexing issue. The gap certainly must be measured, e.g. by a caliper, cannot be just eyeballed.
Comment: The spacing between all cogs should be the same. Without photos, hard to say much more.
Comment: Perhaps poor RD adjustment or slightly incompatible parts (chainline-issue) causing the front chainring being located to close to the frame.
Comment: Just one gear at the front? To eliminate thoughts about cross-chaining. I'd be looking at the limit screw as it's one end of the range
Answer: The cogs should be evenly spaced. On a normal Shimano HyperGlide type cassette the smaller cogs should have plastic spacers between them. It's possible whoever installed the cassette forgot the spacer or installed it in the wrong place.
There are two exceptions:

The smallest (11 teeth) cog usually has the spacer "integrated" into the cog, i.e. it's thicker and doesn't need one of the plastic spacers.
The two or three biggest sprockets are often riveted onto a "spider" and don't need spacers either.

Make sure the cogs are evenly spaced and are not loose. If a spacer is missing altogether the lockring probably can't press against the cogs and the cogs will be loose and have play.
Comment: The perceived "spacing" issue could just be an optical illusion because of the tooth positions. When starting out road cycling, I also thought that my 11-speed cassette looks [odd](https://ibb.co/TvYnwyc) but that is just because the first 4 cogs are pretty much lined up while the others are offset and the gear jumps are higher (11-12-13-14-16-18-20-22-25-28-32T for my CS-R7000).
Comment: One that gets me on my recumbents is packed dirt between the smallest ~3 cogs.  It makes things look weird, and eventually prevents the chain from seating well.  Was hard to spot too.


Google IAB V3 multiple devices cache

Question: I've been implementing an inapp-purchase solution using the google iab v3 api, and it works perfectly when buying items on one device, but I have stumbled upon one problem.
If a user has several devices on which he logs on with the same account and uses my app I would expect to have the function billingService.getPurchases(...) return the same list of purchases.
This is not the case, if I make different purchases on two devices the list of purchases is (randomly) updated on each device.
My best guess is that this is related to the fact that the google play billingService does internal caching? But if I try to buy one item already bought on another device I get the error: "You already own this item", but the list/cache is still not updated.
Is there anyone with similar experiences?
Do you know if it is possible to force the billingservice to update against the google server?
Is there any known schedule on when the billingservice updates the cache?
Thanks
Bernt-Johan
Comment: as far as I understand the case,it is matter of refreshing the cache, and it happens generally within 24hrs.
Answer: Simple solution is to launch the Google Play Store App, the internal cache should then be updated.

Google IAB V3 multiple devices cache


Is it possible to render readable screen type at a size of 3px?

Question: I just created an icon in fireworks with a size 17*15 (which is small) and when i try to label the icon the minimum size of the text is 8 pixels which is very big . I want to have a label with text size 3. and I do not want the label to be blurred. It should be at least readable .
Can anyone help me regarding this ?
Answer: Nope. What you are asking for is pretty much impossible. You can't render letterforms with only 3 vertical pixels. There have been attempts at making incredibly small screen type, though. For instance:
http://www.typophile.com/node/61920
That face has a 3px x-height. So pretty small. Is it readable? Not really. But a fun experiment.
Answer: Do you want it small or do you want it readable? Anything smaller than 8 pt won't really be easily readable by anyone using standard (1024x768) screen resolution.

Remember that a logo is supposed to provide a graphic representation and good practice encourages redundancy (i.e. a text label below the icon). So for instance this button:

could mean many things to many people. It could mean:

or

This is 10 point text; probably readable by the majority of folks. 3 point text will look like this:
 and won't really be useful. You are probably much better off having a clean graphic and either labeling it below or providing something somewhere else that explains the (nice and clean) graphics. think the toolbar in Photoshop - most folks who are used to the toolbars know that the little brush is the brush tool, the little pencil is the pencil tool, etc. If you hover over the tool you get a pop-up that actually tells you the proper name, but it's normally not there. This keeps the interface as clean and organized as possible.
Comment: Can I steal the second one for an avatar? For somewhere? :)
Comment: If I said "no" and you still used it, would that be irony? ;-)
Comment: As Mathew points out (in a separate answer), this answer talks about points, when it should be pixels.
Answer: You can have the text at whatever size you like so long as it has a sensible mouseover (with normal screens).
Haven't a clue why people are talking 'pts' here - points are dead tree and not pixels, points have no use to you here as a screen could be 72 or 96 or anything else dpi.
In the early days fonts were on 8x8 monospace fonts. If they could have used less pixels then they would have done. But they did not have dithering and 'cleartype' then, never mind proportional width fonts. With these innovations you can go smaller, but screens have gone up in resolution so legibility is tricky for most people with 8 pixel high fonts. With that in mind, do consider your customers and whether there is any point at all in 3 pixel high text.
Comment: "You can have the text at whatever size you like..." Not if it's to be readable. Only one answer mentions points rather than pixels - this would have been better as a comment there.


Strange glyphs code error

Question: Recently I've noticed that just above the web page logo, strange glyphs appeared. What might be the cause? How to get rid of these.
Comment: Did you check your header.php file for example?
Comment: we don't have enough information to help here.  It looks likes its directly placed in.  When did this start?  Have you tried turning all plugins off and see if it disappears or changing themes?
Comment: Thanks, I've found the plugin which was the cause...
Answer: If there is anything printed above the logo, then in most cases it's caused by some errors in PHP. So somewhere in your theme or in one of plugins there is some bad code that is causing this.
And these characters suggest that they're some badly converted UTF characters or some other characters that are not supported by your font.
From my experience - such problem occurs when site gets infected and malicious code is working not entirely how its author wanted it to...
So I would check your theme and then all other files of that site if they were modified and if they contain some code that doesn't look nice.
Comment: Thanks for that. I've found the plugin which was the cause.
Comment: I'd recommend to check what code was causing this and what that code was doing exactly.

Strange glyphs code error


Proving exponential inequality without calculus

Question: Letting $a$ be a strictly positive parameter, one can use calculus to show that $x^a < \frac{1}{1+a-ax}$ for $x \in [0,1)$. Is there a more direct way of showing this? Perhaps some well known inequality that I am not aware off? Thanks for any tips.
Comment: @Asher2211  $0 \le x < 1$ so $0 \le ax < a$ and $a-ax \ge 0$ so $1+ a-ax \ge 1$ and and $0 < \frac 1{1+a-ax} \le 1$.
Comment: @Asher2211: no, because $\frac{1}{1+a-ax} = \frac{1}{1+a(1-x)}$ and $1+a(1-x) > a(1-x) > 0$ given that $a$ is strictly positive and $x <1$.
Comment: If $a$ is a natural number then if $x = 1-w$ then $x^a = (1-w)^a = 1 - aw +\text{stuff that oscilates between positive and negative but shrinks in absolute value size so the sum is ultimately positive} > 1+aw = 1 + a(1-x) = 1 +a -ax$.  Now just wave your hands about like a banshee and fudge and hem why it can expand to the rational values replacing $x$ and $a=\frac mn$ with $x^{\frac 1n}$ and raising it to the $m$ power and then mutter something about taking limits.
Answer: $$x^a(1+a-ax)=x\cdot x\cdot\dots x(1+a-ax)\leq \left(\dfrac{1+a-ax+ax}{1+a}\right)^{a+1} = 1$$
by simple AM-GM, if $a$ was a positive integer. But then again, you can have weighted AM-GM for real numbers so you can modify this to work for positive real $a.$ But then again, weighted AM-GM, or in general the power-mean equality requires some calculus in its proofs so I am not sure if you can make things any simpler.
Comment: I am interested in establishing a matrix analogue to this inequality. See entry in https://math.stackexchange.com/q/4181023/165163


iphoneOS backgrounding sockets

Question: I've a simple TCP client which connects to a simple TCP server sending the word "ping" every 5 seconds. I read these "pings" using the command read from the standard C socket library.
<code>int numberOfBytes = read(m_clientSocketFileDescriptor,buffer,255);
if (numberOfBytes < 0) {
    error("reading from socket");
}
</code>
I have set the WIFI usage, background sound and background voip values in my application plist file.
I declare my socket to be backgrounded as following :
<code> - (void)applicationWillEnterForeground:(UIApplication *)application
 {
   if (m_clientSocketFileDescriptor) {
         CFStreamCreatePairWithSocket(kCFAllocatorDefault, m_clientSocketFileDescriptor, &m_tcpReadStream, nil);
         if (m_tcpReadStream != NULL) {
         CFReadStreamSetProperty(m_tcpReadStream, kCFStreamNetworkServiceType, kCFStreamNetworkServiceTypeVoIP);
         }
    }
  }
</code>
This works perfectly when i press the home button. My pings are received from the server, and when i wake up my application, all the messages have been received.
My problem is when i use the power button to lock the iPhone screen. The socket is actually closed. My server is receiving a SIGPIPE error, and when i wake up the phone, the read() function says : "Socket is not connecting".
I think it's pretty dumb to have a background socket if this is getting down when the user locks the screen (by default, this happens afer between 1 or 5 minutes), so maybe i'm doing things in a wrong way.
Does anyone managed to overcome this problem ?
Tested on iOS 5.0 with an iphone 3GS & iphone 4.
Comment: Did you try `setKeepAliveTimeout:handler:` as suggested by @DarkDust?

Perhaps there's some preparation to do in `applicationWillResignActive:`?
Answer: You might need to use -[UIApplication setKeepAliveTimeout:handler:]. I guess that if you don't have this handler the OS can assume that your app won't be able to handle any responses to the socket anyway and closes it. See also Apple's Tips for Developing a VoIP app.

iphoneOS backgrounding sockets


How can I transform GCS_WGS_1984 to GCS_North_American_1983?

Question: I need to convert a GCS_WGS_1984 data set to NAD_1983_UTM_Zone_14N. What transformation should I use?
Answer: The transformation to use depends on the area of North America that the data resides in. Definitions for the area of use for the Esri transformations (NAD_1983_To_WGS_1984 in your case) can be found in "geographic_transformations.pdf" in your install directory (mine is at C:\Program Files (x86)\ArcGIS\Desktop10.0\Documentation). Here they are for NAD_1983_To_WGS_1984. Note that the transformations are bi-directional:
NAD_1983_To_WGS_1984_1:  1188:  Canada, Central America, Mexico, and United States (Alaska, CONUS)
NAD_1983_To_WGS_1984_2:  1251:  United States - Alaska - Aleutians
NAD_1983_To_WGS_1984_3:  1252:  United States - Hawai'i
NAD_1983_To_WGS_1984_4:  1308:  United States - CORS ITRF94
NAD_1983_To_WGS_1984_5:  1515:  United States - CORS ITRF96
NAD_1983_To_WGS_1984_6:  1696:  Canada - Quebec
NAD_1983_To_WGS_1984_7:  1697:  Canada - Saskatchewan
NAD_1983_To_WGS_1984_8:  1702:  Canada - Alberta

Comment: For ArcGIS 10, see this technical article: http://support.esri.com/en/knowledgebase/techarticles/detail/21327


How to change a specific third level character? [Ubuntu 14.10]

Question: For example, pressing third level chooser (not compose key, as I posted earlier) + v = @. However, I want third level chooser + v to print #. Is there a way to accomplish this?
Answer: This technique is known as "composing a key".  I write Spanish but on US-keyboard layout,and I use ALT+ any number to make accents, but this also hold many others characters as well.
https://help.ubuntu.com/community/ComposeKey should help you on that - but scroll little further down until you see 'third level'.
Comment: Your link shows how to change compose key combinations. I've tried this (copying and modifying .XCompose, and adding "export GTK_IM_MODULE="xim"" to .Xsession). The changes had no effect. However, I didn't want to change the compose key combinations, but rather a specific third level key. (I thought that the compose key and third level chooser are the same thing.) I've modified my original question accordingly.
Comment: I managed to adjust the compose key combination (copied utf8 compose table to ~/.XCompose and modified it to suit my needs, and added "xport GTK_IM_MODULE="xim"" to the beginning of ~/.profile). Do you have any idea if I can do the same for the third level modifiers?


Survey  article on Intersection Theory

Question: Does anybody knows about good overview on intersection theory.
The book of Fulton has very hard language. Does there exist simple overview on this topic with many examples?
Comment: Have you looked at his book "Introduction to Intersection Theory in Algebraic Geometry"? I recall that being gentler.
Comment: ..but if it's a survey you are after, I'd suggest appendix C of Hartshorne.
Comment: Ravi Vakil's intersection theory notes are also good..
Answer: Eisenbud and Harris are coming out with a book on intersection theory, "3264 and all that", and if you know Harris's style at all, you'll know it's chock full of down-to-earth examples that should be right along the lines of what you're looking for. (Sorry to recommend a book that's not strictly speaking published yet, but it does sound like exactly what you're asking!)
Comment: Just downloaded it. This reference is great. Thanks.
Answer: Dear Klim, when you say "the" book, i suppose you mean Intersection Theory published by Springer . However Fulton has written a much more elementary overview called Introduction to Intersection Theory in Algebraic Geometry, published by the AMS  in their Regional Conference Series in Mathematics , Number 54, which is only 74 page long and quite friendly.
There is also a great survey of Intersection Theory by  Joël Riou here and  Archibald's Master Thesis on Intersection Theory for surfaces there.
Comment: Dear @Joachim, I think "the" book by Fulton is incredibly difficult because of its terseness, even if one has a good knowledge of scheme theory. Personally I have resigned myself to use it as a reference and have given up the hope of reading it from cover to cover, and many colleagues have adopted a similar attitude. I think   Eisenbud and Harris's book mentioned by Arnav in his answer is much more suitable as a textbook.
Comment: The link to Joël Riou's survey is now broken. Anybody can point to a working link?
Comment: Dear Georges, when one is new to intersection theory, would you recommend reading Fulton's introduction book before starting with "the" book by Fulton? Or can one start right away, provided the necessary knowledge of scheme theory is already present?
Answer: This is certainly not an overview of intersection theory as a whole, but for its classical roots I highly recommend:

Steven L. Kleiman, Problem 15: rigorous foundation of Schubert's enumerative calculus. Mathematical developments arising from Hilbert problems (Proc. Sympos. Pure Math., Northern Illinois Univ., De Kalb, Ill., 1974), pp. 445–482. Proc. Sympos. Pure Math., Vol. XXVIII, Amer. Math. Soc., Providence, R. I., 1976.

I found this article to be both completely lucid and completely fascinating -- and I am someone who, in general, has no great interest in intersection theory or (especially) Schubert calculus.

Survey  article on Intersection Theory


Changing border color for multiple cells without changing border Style in Excel 2013

Question: Is it possible though to change all border colors without changing the border style?
I have already tried selecting the line color and going through the cells with CTRL - but this does change the line styles and I have multiple styles I don't want to do from scratch.
Comment: No, I want to change all the border colors - now all my borders (no matter what style - dashed, double, thick - are black. I want them to be gray but I want the styles to remain unchanged
Comment: Have you tried using the line-paint tool to draw the lines in place?
Comment: Unless I misunderstood you - as I have written above - that is not what I want to do. I have a big table with multiple line styles (dashed ones, bold ones, thin ones etc.) and I want them to stay as they are but change their color (from black to gray). What i don't want to do is drawing all the borders from scratch
Comment: You mean, you only want to change the background color of a cell?
Comment: Ah. That is not possible though. The properties of a line are all connected, so changing the line color means changing the line style and thickness too.
Answer: You can change the .colorindex property independently from other properties of the border objects, in VBA:
Sub bordercolor()
    With Selection.Borders
        .ColorIndex = 32
    End With
End Sub

This will only change the border color not the linestyle nor the width. Assign this macro to a key for convenience. 32 denotes a color index value, adjust to your liking. See this article for a description of the border collection if you want to change one specific border only (xlDiagonalDown, xlDiagonalUp, xlEdgeBottom, xlEdgeLeft, xlEdgeRight, xlEdgeTop, xlInsideHorizontal, or xlInsideVertical).
Comment: Contrary to a recent hint, this works as tested in Excel for Windows 2003. This might indicate that in more recent versions of Excel color and line style might not be independent of each other.


Determining whether preferences are rational given a utility function

Question: Alex's preferences: U(x;y)=x-(1/y). Are his preferences rational?
Comment: I know that preferences are rational if they satisfy completeness and transitivity assumptions but I don't know how to apply it in this task
Comment: Please, give me a hint
Comment: Not confident enough to put this as an answer, but I suspect the answer is yes. The utility increases monotonically with both x and y. My only worry is that if y is zero then your utility is minus infinity - presumably this means something like if y is zero you'd be dead. Perhaps y could be something like oxygen.
Comment: @Mick I think this function is more theoretical than realistic.
Comment: The necessary and sufficient condition for consumer demand to exhibit rational preferences is the Strong Axiom of Revealed Preference.  As you have two goods, the Weak Axiom of Revealed Preference is equivalent to the strong axiom.  You can derive Alex's demand function by setting up a Lagrangian (hint for the boundary condition assume Alex spends her entire wealth).  Then using this vector-valued function, you can derive her Slutsky (substitution) Matrix and notice it is negative-semidefinite which is sufficient for the weak axiom to hold.  Hence her preferences are rational
Answer: As long as a preference can be represented by a continuous utility function, it is rational (and continuous). So from the very fact that you're writing down a utility function that is continuous in both $x$ and $y$ (on $(0,\infty)^2$), it follows that the function represents a rational preference (provided that both $x$ and $y$ are positive).
However, if you insist that $y=0$ is part of the feasible choice set, then the preference is not complete. The individual cannot compare a bundle $(1,1)$ with another bundle $(1,0)$ because the utility of the latter bundle is not defined.
Comment: I would assume that $(1,1)$ is preferred to $(1,0)$.  My problem would be that $(2,0)$ cannot be compared to $(1,0)$
Comment: @Henry: If the assumption that allows you to say $(1,1)\succ(1,0)$ is monotonicity, then wouldn't the same assumption imply $(2,0)\succ(1,0)$?  At any rate, the conclusion stands: if $y=0$ is feasible then the preference is not complete.
Answer: Re-order the equation.
$U=x-\frac 1 y\\
x-U=\frac 1 y\\
y=\frac 1{x-U}$
I'm sure you know how to draw that graph:

which you can see has transitivity since the curves do not intersect, convexity, and completeness (excluding the line $y=0$) as $U$ can take on any real number. The 'more-is-better' property follows from Mick's comment that as $x$ or $y$ increases, $U$ unequivocally increases.


Best way to develop a level from Top down image using 3dmax

Question: I have to create a game level from a top down view of an area. I used a plane converted to an editable poly to do the job. I used edges to create the top view of roads, walkways and parks so that i can extrude/edit them later. My problem is the curves in the road look blocky I tried appying mesh smooth modifier on the final model but that interfered with material mapping. Again i tried it on the plane without the extrusions and still the modifier does not work(The roads loose their shape). I know one way to solve the problem is to add more vertices on the curve and transform their location to create a more natural curve but i have a lot of curves so before doing it manually i need to know if there is a tool that refines the curves. Also i need to know if there is a better or proper way of doing the task.
Answer: There are many ways of doing this, depending on what your final result wants to look like, but for the majority they all start with using the line tool - found in the spline section, this tool has the ability to change the control points to bezier, which means you have full control over the curve. You can also adjust the amount of points in the curve between each control point allowing you to make completely smooth curves.
You could draw the entire road (both sides and end caps) with this and apply something like a surface modifier to create a simple flat road.
Or you create a slice of the road's shape, so it includes curbs and paths etc.. you can use the line as a path and loft the shape along it.
Experiment with both methods on a small curve to see what effect works best for your purpose.


How do people initially find the CV site?

Question: What fraction of visitors first find the site via Google, other search engines, links from other sites, tips from friends or colleagues, etc.?
Comment: I reached Cross Validated from Stack Overflow. And I reached SO from a colleague tip.
Comment: I first got to Cross Validated because Rob Hyndman mentioned it somewhere (likely on his blog); it's possible I saw it pointed to by another blog, or on one of the stats groups on reddit (but I'm pretty sure it was a direct message by Rob that I saw so if it was reddit he may have posted there) - this is while it was still in beta. (I was already on SO.) I came and checked out the beta, and made an account at some point or other. Then after a little activity I pretty much forgot about it for a while (nearly 18 months I think). Then I realized I hadn't looked in a long time and came back.
Comment: @Silverfish's answer was quite interesting.  Would still like to hear from anyone with access to site statistics.
Comment: Google sent me here
Answer: I cannot tell you how people first find this site, but I can share some statistics provided I am not too "specific."  During the lifetime of this site (including pre-beta and beta phases, up through the beginning of February 2015, four and a half years in),

A strong majority of visits were referred by search engines.
Half of the rest were referred from other sites.  Most of these were google.com or stackoverflow.com.
The remainder were direct traffic.

Most of the search engine visits used an unknown search term.  The most popular search phrases among those that are known include "statistics stackexchange" and "statistics stack exchange," which perhaps should be considered "direct traffic." But these are a tiny fraction of the new visits.

Here are some related numbers to ponder.  Most of them can be gleaned from information readily available to anybody.
As anyone who looks at our main page can tell, we have had 50,000 questions asked.  The number of answers posted is almost the same.  These are a minuscule fraction of all visits.
I don't have information on the number of comments posted, but would guess there would be several times as many as the number of questions plus answers: perhaps a half million total, just a few percent of all visits.  (Some of us average many comments per visit, btw. :-)
The total number of votes (up, down, accepted, etc.) is roughly 1.5% of the number of visits.
The number of edits is less than 10% of the total number of posts--very few posts are edited by the community.
The vast majority of visits therefore involve passive interaction only: no posting or voting of any kind.
Comment: Thank you very much.  I wonder why and by whom you are enjoined from being more specific on some points.  I'm also curious as to why you don't count google.com as a search engine (did you really mean that?).
Comment: Looking over the last 60 weeks, [comments per week](http://data.stackexchange.com/stats/query/161411/site-activity-and-votegraph) typically run at something around 3-4 times the rate of questions per week (sometimes up to 5x), while they are typically at around 3.5-5 times the rate of answers per week.
Comment: @rolando2 The database separately reports on search engines--of which Google is by far the major contributor--but also lists "google.com" as a "referring site" (albeit with a tiny fraction of the referrals). I couldn't tell you what distinguishes the two kinds of referrals. I am enjoined by the SE team from sharing the "specifics" of the statistics to which I, as a moderator, have easy access.  (But many of these are available, with a little time lag, to anyone willing to write a little SQL transaction against the SE database.)
Answer: Possibly this should be a comment rather than an answer as I do not have access to any site statistics, but judging from traffic levels to questions I have asked or observed, it seems there are several different audiences who come across the content.
I have asked several questions whose viewing figures are low, averaging just a handful of views per day, but almost all those views occurred in a couple of spikes: these occurred when there was activity that promoted the question to the main page for a few hours, or sometimes (e.g. on reporting Welch degrees of freedom) over a couple of days when I put a bounty on. My guess is that most of these viewers were regular SE users, probably registered and occasional contributors on CV.
Questions which make it to the "popular questions" sidebar across SE sites also seem to get a boost in traffic but generally temporary and in the hundreds. I'm guessing the boost mostly comes from SE users who are not CV regulars.
I recently received the "famous question" (10,000 views) for Real life examples of distributions with negative skewness. That came within one year of the question being asked, which judging by other "famous questions" (browse the full list here) is a fairly short but by no means record period of time - some examples take a couple of years to accrue the pageviews. Such traffic is implausible from internally generated traffic and I think it's safe to presume very few readers are registered SE users. In that case it is very likely that the traffic is search engine based: when I search google, that question is 2nd ranked for "negative skew example", 3rd for "skewed distribution example", a front-page result for "skew example" and "negative skew" and has even reached the third page for the very wide search-term "skewed distribution".
This is an indication of the effectiveness of SE at SEO! It also suggests we are writing for different audiences at different times. I think for a lot of the more technical and obscure content our users are basically writing at and for each other. But other content that has a wider and more general audience, which perhaps ought to change the way we approach it. On realising so many people were making use of my question I recently copy-edited it down to make it more useful and readable (~20% reduction in wordcount). While I was tempted to delete some of my initial discussion of examples of symmetric and positively skewed distributions, I realised that since the search engine rank was so high for "skew" and not just "negative skew", for many of the search-engine landers that content might actually have been what they were looking for! Presumably questions like this figuring highly in search results increases awareness of the site but I don't know how this works in terms of conversions to new users.
Other questions have had big spikes in pageviews due to sharing of links on external sites, but at least sharing by our own users seems to only account for a handful of the 369 "famous questions". Compare the publicity badges:

Announcer - shared a link to a question that was visited by 25 unique IP addresses, 249 awarded
Booster - shared a link to a question that was visited by 300 unique IP addresses, 12 awarded
Publicist - shared a link to a question that was visited by 1000 unique IP addresses, 3 awarded

It would also be interesting to know whether such external traffic spikes are temporary. Obviously even CV users could share a "plain" link to the question that doesn't identify them as the referrer, and people who are not registered on CV could not use this option, and none of this is tracked on the badge system. A couple of questions have been reddited for instance.
Comment: It's interesting that in spite of >10000 views on that question, no answer has more than 6 upvotes, and the question only has 10. That does suggest almost all those views are non-active users. At least a few of those viewers will look around and become interested in the site.
Comment: "*I think it's safe to presume very few readers are registered SE users.*" - I think that's a very safe bet. The ["people helped" prototype query](http://data.stackexchange.com/stats/query/253267/people-helped-public-prototype-1) that's planned to be used (likely in some modified form) on the new user pages (whenever they happen) - a measure which is based on views - put me at well over a million "people helped" (and several users have much larger figures than that). There's no way SE registered users generate those sort of stats. Many more people than are currently users are seeing what we do
Comment: @Glen_b I think it's worth distinguishing between "registered users" and more general "users" (i.e. people who use the site, but "lurk" rather than contribute, and are not registered) against a wider pool search-engine arrivals or people who arrive by link, but probably see a smaller fraction of our content. While it's true that "Many more people than are currently users are seeing what we do", my impression is that's concentrated on a very small fraction of questions.
Comment: Yeah, I'd say that's right.
Comment: @Glen_b Just to clarify (though I think you got the impression from my post), I don't simply mean that some questions have more page-views than others - clearly they do - but that the audience composition varies substantially from question to question. Questions which don't rate highly in SEO and are not link targets presumably have almost entirely internal traffic.


Why are there so many specific words for groups of animals?

Question: I found this link to names of the groups of animals. I am confused because there are so many various congregations. Is there any guidance rather than learning by rote if I want to remember them?
Comment: Some of them are just fun to look up & remember, when you're 6 years old. Who couldn't love knowing that it's a murder of crows, or a murmuration of starlings. Some you may know without even realising you know, because they are quite frequently used - a pride of lions, for instance.
Comment: Welcome to English Language Learners. The nature of your question may make it difficult for users to provide a definitive answer. Do note that most of these words for groups of animals are not commonly used in "everyday" English, and many native speakers wouldn't even know most of them without checking a reference book. Some (not all!) of the words that *are* commonly used are flock (for birds), herd (for hoofed animals), colony (for insects and some rodents), and school (for fish).
Comment: @pyobum Yeah, I was writing an answer but it would pretty much say the same thing you just did, adding only that the names are generally only used within the scientific community.
Comment: Onoly about 5 of those phrases are commonly used by the average person. You can probably pick them up as you pick up other phrases in English: exposure to everyday English. If you need to learn more of them, you can memorize some more.
Answer: Most of the group names on that list aren't general knowledge or in everyday use.
If you want an even longer list that includes the terms for the male and female members of the species along with the name for the young and groups, check this out. Many of these aren't general knowledge, either.
Even for animals we talk about a lot, the average person wouldn't know to call a group of cats a clowder.
There are a few that most people know, and a few general-purpose terms that can be used if necessary.

Herd - Useful for most hooved and/or grazing mammals: Cattle, sheep, horses, goats etc. But also elephants, giraffes, hippos.
Litter - Generally used for birth groups of small mammals: Kittens, piglets, puppies etc.
Colony - Used for mostly some insects (ants, termites), bats, penguins, and rabbits.
Swarm - Used for flying insects.
Flock - Used for all birds, regardless of whether in flight or on the ground. Also commonly used for sheep and goats.
Pod - Used for groups of sea mammals: dolphins, whales, seals.
School - Used for groups of fish.

These are a good starter list.  There are a few others that many people know that are specific to a particular sort of animal:

Pride - Used for lions.
Pack - Used for wolves and sometimes dogs.
Hive - Used for bees.

When in doubt, use something generic like bunch or even group. That's a whole bunch of sheep. That is a nice group of tigers.
Hope this helps!
Comment: Language is defined by how people actually use it, not by some book that claims to be an authority.  The "correct" term is "litter of kittens," because that is what any native speaker would say.  No one except someone trying to look superior or be funny would say "kindle of kittens"
Comment: @WhatRoughBeast My list is designed to be terms that are generally acceptable without forcing someone to memorize 100 different terms.  Saying **Litter of kittens** is perfectly acceptable and is way more common than kindle, even if it's the "correct" term. https://books.google.com/ngrams/graph?content=kindle+of+kittens%2C+litter+of+kittens&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Ckindle%20of%20kittens%3B%2Cc0%3B.t1%3B%2Clitter%20of%20kittens%3B%2Cc0
Comment: Actually, it's a swarm of bees unless they are settled in their hive.  And, according to "The Book of St Albans", it's a kindle of kittens. And if you like "murder of crows", you'll appreciate "an unkindness of ravens".
Comment: @Angew: No, it doesn't.  If someone claiming to be the language-authority makes a change to the language and no one follows it, is that change a part of the language?  Most linguists would say no, it's not.  What happens in the real world is that the "authorities" end up not governing the language, but simply watching it and trying to determine when and how it has changed.  Then they make those changes "official" by writing them down in a book.
Comment: Feel free to edit or remove if you think this is inappropriate.
Comment: Don't forget the crows! They come in murders... ;)
Comment: @PatricHartmann That is certainly a very memorable one! :)
Comment: @Catija : You bet! :) It's at least 15 years that I learnt it through an article. Though I never ever used it a single time in all the years, I never forgot...
Comment: @BlueRaja-DannyPflughoeft That also depends on the language. Some languages (e.g. French, Czech) have an official authority regulating them.
Comment: @BlueRaja-DannyPflughoeft Well, these official bodies control what schools teach, so I would say they *do* control the language in a way. They cannot introduce drastic ad-hoc changes, but they certainly can (and do) mark some phenomena as improper in the language, even if said phenomena are widely used colloquially.
Comment: @Angew: We do the same thing in English :) In school, we learn that 'wanna' is not a word.  However, it's widely used by native speakers in both speech and [writing](https://books.google.com/ngrams/graph?content=wanna&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Cwanna%3B%2Cc0), and even has [its own dictionary entry](http://dictionary.reference.com/browse/wanna).  So is it "a word"?
Comment: To me "That's a whole bunch of sheep." sounds like pure slang and slightly comic.  Don't almost all people know a "flock of sheep"?
Comment: Re: clowder and kindle. Those really are obscure and not even highly educated native speakers will have heard of them in that context. You only need to look at https://books.google.com/ngrams/graph?content=clowder+of+cats%2Ckindle+of+kittens%2Clitter+of+kittens&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Cclowder%20of%20cats%3B%2Cc0%3B.t1%3B%2Ckindle%20of%20kittens%3B%2Cc0%3B.t1%3B%2Clitter%20of%20kittens%3B%2Cc0
However some of the marginally obscure ones are reasonable. A troupe of monkeys for example is arguably the correct term that is used by experts.
Comment: @Lembik native speakers do... And I included flock of sheep in my list. All I was saying at the end is the emphasis that you don't **need** to memorize them and that generic collective terms work just fine.
Comment: This is an excellent answer for any English language learner, aimed at precisely the right level.
Comment: @Agnew and BlueRaja, this is the classic prescriptivist/descriptivist argument. It's been waged by linguists for hundreds of years and will not be solved in a comment thread.
Answer: As others have mentioned, most of the odd-sounding collective nouns derive from a hunting tradition. However, many of them are much more recent inventions, and are meant to be whimsical. This is apparently a long-standing tradition, as the Book of St Albans (AD 1486) has some that are clearly not hunters' tradition!
There is nothing predictable about them, and indeed most of them are not used widely... or used at all outside of the imagination of the person who came up with them. I'm not a biologist, but I'm quite sure that they are not scientific terms (as some have said), and that scientists would only use the common ones, or (scientists being as whimsical as anyone) ones that they deliberately adopted for the fun of it.
It should be said that even those that aren't used may be widely known, simply because lists of these words are popular in works of trivia. For example, it's generally known that a flock of crows is called a "murder"... but I don't remember ever hearing anyone use outside of discussing trivia. In everyday use, I would say (and expect to hear) "flock".
Ones that are used and hence worth knowing for more than just trivia's sake:

A flock of birds
A school of fish
A swarm of insects
A pride of lions
A herd of livestock or other animals in general (especially land mammals)
A flock of sheep
A pod of whales or other cetaceans (and seals?)
A pack of wolves or other animals that hunt in groups

There are definitely others that are used (mob of kangaroos, troop of baboons or other primates, colony of social animals, nest of insects or birds), but you can communicate just fine without ever using them, and if you hear them you can often work them out from context.

Source: my own anecdotal knowledge, and Wikipedia.
Comment: +1 although I could narrow the list to like five: flock, school, swarm, herd, pack; with *group* for everything else. :)
Comment: "but I don't remember ever hearing anyone use outside of discussing trivia" Yes. I have never, ever in casual conversation, or in a technical discussion in a science magazine, heard or read someone say "an exaltation of larks" or "a parliament of owls", except to say, "hey, did you know that there's a special word for a group of X?" Maybe there's some sub-population of English speakers who use them -- okay, I admit, I don't tend to hang around hunters or forest rangers or zoo keepers or anybody who has a lot of contact with animals -- but for all practical purposes I think these are ...
Comment: ... just made-up words that nobody really uses.
Answer: In direct answer to your direct question: no, there is no way to learn them other than by memorizing them. Of course, as has been mentioned, most of the terms which are intimidating you are simply not in wide use, so you really only need to learn a few.
As has been mentioned, the earliest compilation of collective nouns is "The Book of St. Albans" (which was the third book printed in English - I know the Bible was first, but I don't know the second, so don't bother asking), but a really excellent modern book on the subject is James Lipton's "An Exaltation of Larks". At the beginning of the book, he argues that knowing collective nouns of game animals was a status issue among the gentry of the time, and this may have contributed to the proliferation of these terms. Inventing new terms for different animals made the subject more difficult for the uninitiated. It is also true that some collective nouns were inspired by the attributes attributed to the animal's behavior: pride of lions, exaltation of larks (from their song), parliament of owls, murmuration of starlings (from the sound of a flock), ostentation of peacocks, etc. Some terms made sense at the time of formation, but the connection has been lost with changes in usage: "host" refers both to angels and armed men, but nowadays angels have lost their martial connotations and made far less fearsome than they used to be. In at least one case, the usage appears to be an error caused by a scribe: school of fish was not inspired by the fish all facing in one direction, like students in a classroom, but by miscopying the original term, "shoal of fish" which describes their appearance in the water.
As Lipton points out, one of the interesting aspects of English is that anybody can invent a word, and if it becomes widely used it will be recognized as "proper". So the invention of collective nouns can become an exercise in humor, or judgement, or various other attributes. "An abominable sight of monks" is clearly the latter. Lipton also recounts the joke of a number British academics responding to the presence of several prostitutes: "a jam of tarts", "a flourish of strumpets" and "an essay of trollops". And, since anyone can do it, Lipton puts forth a few suggestions of his own. "A wobble of bicycles" is my favorite.
Answer: Those are called terms of venery and they come from English hunting tradition.
In hunters community, referring the groups of specific animals, or specific formations of animals was so common that they've got their unique names.
The need to have so many words for 'herd' may be confusing for modern city dwellers, as well as the need to have various words for 'snow' may be confusing for someone who lives in Mexico. And because of the nature of the language evolution, there's no 'logical rule' to learn them, just like there's no logical rule for modern teenagers' slang.
For an extended list of terms of venery, see here: http://en.wikipedia.org/wiki/List_of_English_terms_of_venery,_by_animal
For a little background see for example here: http://rodchu.blogspot.de/2009/05/collective-nouns-terms-of-venery.html
And there are many questions on EL&U about terms of venery: https://english.stackexchange.com/questions/tagged/terms-of-venery
Comment: Note that "terms of venery" is a subset of collective nouns.


Magento 2: Configure just only for one country

Question: We have a magento 2 store, with more than 20 stores location and they are being separately maintained in the same web site, we do sell only in the country. is there anyway that I could completely get rid of those events where they pop up at certain occasions asking to select country, since we operate only in the country I want to get omitted(hide would be better) each and every event where a customer is being questioned asking for the country.
Comment: As per default magento flow there is no popup where user needs to select country. Country is only needed for shipping and billing information.
Comment: Does it sound like , it pops up ?Nop, what I meant was country selecting field shouldn't be appearing where they're now at.
Comment: Let me appreciate the question first (: Magento provides tons of technical facilities and sometimes we don't need all of them so when we need need only one language or one country or even when we don't need some type of product. Let's say downloadable product. - if we disable all the stuff what we don't need in near future. The output will be very different and fast. And near to perfection.
Answer: General -> Country Options -> Allow Countries (for sales)
Instead to have a default country (Brazil) in cart shipping quotes you have to set it in
Store -> Configuration -> Sales -> Shipping Methods -> (Shipping Module) -> Ship to Applicable Countries [YES]
In Ship to Specific Countries you select the countrys.


Herbicide: glyphosate

Question: Roundup's Glyphosate is very expensive and only available in low percentage in my country.
I was able to find glyphosate online for a lower price and an higher percentage.
It's labeled as Ammonium glyphosate, so what's the difference between Roundup's Glyphosate and Ammonium Glyphosate?
Answer: The "active" form of glyphosate is an acid, but to stabilize it for packaging it is sold as several different salts of the acid. Monsanto's formulations use the isopropylamine salt. Other salts used are mononammonium, diammonium, and potassium.
For efficient use as a herbicide it needs to be mixed with other ingredients such as surfactants and emulsifiers to control the droplet size when it is sprayed, and improve absorption into the plant leaves. For commercial agricultural use, these may be mixed separately with the glyphosate at the time of use.
So the strength and effectiveness of the product, and the correct way to use it, will depend on exactly what you are buying.
Comment: The product "Roundup" has the surfactant included. it is called polyethoxylated tallow amine.
Answer: Timing and weather and age of crop is critical.  My question is why or when does a farmer use spray glyphosate to 'get rid of weeds'.  Weeds have NEVER been on my list of things to do in gardening.  It is just to easy to physically control weeds.  Strength of glyphosate is just not important: it is timing and the species of your target weeds.  Why are farmers so wigged out with weeds?  Seriously, weeds are unable to grow so big and so fast as to harm anything within one season.  Glyphosate got bad mouthed so badly people have no idea what to do.  Weeds have NEVER in 60 years of gardening full time been a problem in my experience.  And we are spraying SPRAYING glyphosate over cash crops?
Adding ammonium allows glyphosate to be sprayed and have it stay sprayed on the same target plants.  Glyphosate is not some plant material killer.  It takes almost a month for the glyphosate to kill a plant roots then UP. During which time one can not plant seeds or starts in that area for 3 to 4 weeks after spraying.  I gotta understand the why of using this herbicide on crops.  Is it just some given ritual?

Herbicide: glyphosate


Oriented vector bundle with odd-dimensional fibers

Question: Is it true that for every oriented vector bundle with odd-dimensional fibers, there is always a global section that vanishes nowhere?
Answer: No.
Let us consider some vector bundles over $S^4$. Since $S^4$ is simply connected all vector bundles are oriented and rank $k$ vector bundles over $S^4$ are classified by $\pi_{3}(SO(k))$ by the clutching construction (I am glossing over basepoint issues here, but I think it is correct in this setting). Now $\pi_3(SO(1))$ and $ \pi_3(SO(2)=\pi_3(S^1)$ are trivial groups, so there do not exist non-trivial rank $1$ and rank $2$ bundles over $S^4$. What about rank $3$? Well $SO(3)\cong \mathbb RP^3$ and the long exact sequence of homotopy groups of the fiber bundle
$$
\mathbb{Z}_2\rightarrow S^3\rightarrow \mathbb{RP}^3
$$
shows that $\pi_3(SO(3))\cong\pi_3(\mathbb{RP}^3)\cong \mathbb{Z}$. Hence there are $\mathbb{Z}$ different rank $3$ vector bundles over $S^4$.
Only the trivial one admits a non-zero section. If another one admits a section, then the orthogonal complement (a rank $2$ bundle) must be non-trivial, otherwise the bundle is trivial. But our previous computation shows that there are no-nontrivial rank $2$ bundles over $S^4$.
Comment: Moreover an important example (often denoted $\Lambda^2_+$) of a rank $3$ oriented vector bundle with no non-vanishing section is given by the self-dual $2$-forms on the round sphere $S^4$ (any other conformal structure and orientation would do). The reason is that otherwise $S^4$ would admit an (orthogonal) almost complex structure, hence two, one for each orientation ($S^4$ has an orentation reversing diffeo). Considering their only two (exercise) common tangent complex lines at each point, $TS^4$ would split in two rank $2$ subbundles, which is excluded as in this answer.
Comment: @Fredy: Note that the euler class is also zero in this example. But this does not imply that there is a non-zero section.
Comment: @fredy: The map that sends each fiber $v$ to $-v$ is orientation reversing if the vector space is odd dimensional. Hence $e(E)=-e(E)$, so $2e(E)=0$, which in the de Rham theory implies that $e(E)=0$ (but not when the Euler class is defined with integral coefficients).
Comment: Thanks a lot, it's wonderful! I conjectured it to be true in order to solve a exercise from Bott/Tu's GTM 82, "the Euler class of an oriented sphere bundle with even-dimensional fibers is zero, when the sphere bundle comes from a vector bundle". I hope to know why this statement turn out to be true.
Comment: @ThomasRot: Thanks. Can you tell me more details about the proof of that exercise? I seem to lack other tools besides looking for a global section...


Solve $(x+1)3^x > 3^{x+1}$

Question: I'm only at a college algebra level (pre-calculus) and am having a hard time knowing what steps to perform to solve this as x is both an exponent and at the base level.  I put this into a calculator and got x = 2 but I'd like to know how to perform the steps.  I know logs are involved but haven't been able to figure it out.  Here is the problem again $(x + 1)3^x > 3^{x+1}$  Any help is greatly appreciated :)
Answer: HINT:
$3^x>0$ for all $x$. Therefore, you can divide both sides by $3^x$ without changing the inequality. Logs should not be involved in simplifying this inequality.
Also, $3^{x+1} = 3^x\cdot 3^1$
Answer: $$(x+1)3^x>3^x\cdot3$$
dividing by $3^x$ you get:
$$(x+1)\gt 3$$ for $x\gt 2$
Answer: $(x+1)3^x> 3^{x+1}=3\cdot3^x$.
By subtracting $3\cdot3^x$ from both sides we get
$(x-2)3^x>0$
As $3^x$ is a positive real number for every real-valued $x$, we are able to divide both side by $3^x$ leaving us with $x-2>0$ which has the solution of $x>2$.
Answer: Taking from @Vanwij's approach:
We have \begin{align}(x+1)3^x&>3^{x+1}\\
(x+1)3^x-3^{x+1}&>0\\
3^x[(x+1)-3]&>0\\
3^x(x-2)&>0
\end{align}
Let $y=3^x(x-2)$.  The $x$-intercept of the function $y$ is $x=2$.  As such, solving using an interval table, we have
\begin{array}{|c|c|c|c|}
\hline
& 3^x & x-2 & \text{Sign of}\ y \\
\hline
x<2 & + & - & - \\
\hline
x=2 & + & 0 & 0 \\
\hline
x>2 & + & + & +\\
\hline
\end{array}
Since we are looking for $y>0$, the only interval that satisfies the inequality is $\boxed{x>2}$.

Solve $(x+1)3^x > 3^{x+1}$


Confusion regarding mechanism of dehydration of alcohols

Question: 1)Today I came across a problem which asks to find the order of dehydration of 2-hydroxycyclohexanone(1), 3-hydroxycyclohexanone(2),4-hydroxycyclohexanone(3). The answer is 2>3>1 But I thought answer should be 2>1>3 cause in 2 and 3 the product would be conjugated and hence more stable.
2)My second confusion is regarding the pathway taken by such hydroxyketones. Do they follow E1 pathway and form carbocation or do they take some other pathway?

I have provided what I think but I am not sure whether the same mechanism will be followed or not.
Comment: Please substantiate / illustrate your lines of thought by a mechanism drawn.  It needn't be complete, but strengthens the ground to engage in a discussion here.
Comment: I have added a picture of what I think
Answer: I think your mechanism is reasonable.
Coming to rate of dehydration,
In first case Alpha hydroxy ketone will have the least rate of dehydration because a carbocation is formed which is destabilized by Ketone group and even notice there is hydrogen bonding in reactant making reactant more stable and thus rate of dehydration is decreased in first case.
In second case, though carbonation is not stabilized,  here breaking of H will be easier because the H are more acidic being next to electron withdrawing group , so 2 has highest rate .
In third case, since carbocation is not so unstable and even the H is not much acidic. So  3 has moderate rate of dehydration.
Therefore,  rate of dehydration:2>3>1
Answer: Product of all the three compounds would be same. You have missed space tautomerism in the third one.
Besides,charge beside a carbonyl is considered very unstable. Thus, first one is lowest in rate. Third one is placed second because there is an extra step of tautomerism.


Two seforim being taken out

Question: How should two Sifrei Torah be taken out of the ark since one should not do two mitvot simultaneously? Should one person take them both out and give one to the chazzan and then keep one for himself or should one person hand a Sefer Torah to the chazzan and then retrieve the second Sefer Torah? Alternatively, should two separate individuals each simultaneously remove both sifrei Torah at the same time?
Comment: Related: http://judaism.stackexchange.com/questions/9469
Comment: -1 How is this two separate mitzvot?  How is this even a mitzvah at all?
Comment: something to consider is we take out more than one sefer torah on days when there are readings from more than one location in the Torah so to not cause tircha tsibur by keeping everyone waiting while the gabbai scrolls to the next place for leining
Comment: what is your source for not doing two mitzvot simultaneously? Also leining isn't a mitzvah.
Answer: Our minhag is two people come up.  The first person opens the ark, takes out the first Torah, hands it to the chazen, then he takes out the second Torah and hands it to the second person who came up. The first person then closes the ark.
Comment: As I wrote this first person is doing two mitsvot 'chavilos' and therefore my third method would be preferable.

Two seforim being taken out


Elastic Potential Energy of spring

Question: Suppose I stretch an ideal spring by distance $x$ then we know that the potential energy stored in the spring during elongation is $kx^2/2$. Now if I leave the spring it returns back to its natural length instantly and its Potential energy becomes 0. But if no body is attached to the spring where was this Potential energy transferred?
Answer: The idealization of zero mass often presents a contradiction when one looks at the system energy, as the kinetic energy is always identically zero, rendering many work–energy analyses invalid and ineffective.
The idealized spring has no mass and extends and retracts instantly, among other unrealistic qualities. The real spring has mass, extends and retracts over finite time, and snaps back and bounces with internal friction when suddenly released, ultimately dissipating stored strain energy as heat.
Answer:
But if no body is attached to the spring where was this Potential energy transferred ?

A released spring oscillates, with the energy converting back and forth between potential and kinetic energy. Since this is an ideal spring the oscillation frequency is infinite and it is undamped so it oscillates at that infinite frequency forever.

it returns back to its natural length instantly and its Potential energy becomes 0

Indeed, and it then compresses instantly, returns to its natural length instantly, extends instantly, and so on. It is not a realistic motion because ideal springs are not realistic objects.
Answer: If there were an object of mass $m$ attached to the end of the ideal spring then the object would execute SHM with amplitude $x$ and period $T = 2 \pi \sqrt {\frac m k}$. During SHM energy is transferred from potential energy to kinetic energy and back again, so that after time $T/4$ the potential energy in the spring is zero and the kinetic energy of the object is at a maximum.
The motion when no object is attached to the spring can be found by letting $m$ tend to zero. You can see that the period of the SHM would also tend to zero. In the (unrealistic) limit of an ideal spring with zero mass attached to it, we have SHM with amplitude $x$ but period $0$ i.e. SHM with "infinite" frequency.
Answer: After considering the prior answers, I don't even think it would retract, since that would violated conservation of energy. If it was released at $+x_0$, then at any value of with $|x|<x_0$ there would be missing potential energy, with no way to have kinetic energy.
So, it would just oscillate between $\pm x_0$ discretely at infinite frequency.
Of course that doesn't make sense even by the low standards of Newtonian physics, so ideal springs are just abstractions.
It raise the general question of where our abstractions breakdown. For instance: elastic collisions between macroscopic classical objects… which are simply not allowed by special relativity. However, quantum particles are fine with elastic scattering.

Elastic Potential Energy of spring