In a relatively short time period I will finally embark on all-grain brewing. I would rather purchase grains online as it is cheaper than the LHBS, but the LHBS won't let me use their crushing equipment unless I bought the grains from them.  I was hoping that there was some hard and fast rules regarding this, like "after 3 days, crushed grains start to lose potency; after 10 days, throw them out."  Does this time frame depend on the type of grain, or are they all about the same?  Is there any (relatively) non-anecdotal evidence in this regard? I.e. did anyone ever purchase 10 pounds of one grain, crush 5 pounds, and brewed n many days later? (Double blind taste tests preferred)
What's the shelf life on crushed specialty grains?
This is a  about Active Directory domain naming.   After experimenting with Windows domains and domain controllers in a virtual environment, I've realized that having an active directory domain named identically to a DNS domain is bad idea (Meaning that having example.com as an Active Directory name is no good when we have the example.com domain name registered for use as our website).   , but I'm still not sure about what other rules there are around naming Active Directory domains.  Are there any best practices on what an Active Directory name should or shouldn't be? I tried this in mysql:  mysql&gt; alter table region drop column country_id;   And got this:  ERROR 1025 (HY000): Error on rename of './product/#sql-14ae_81' to './product/region' (errno: 150)   Any ideas? Foreign key stuff? Integral of $\frac{1}{(1+x^2)^2}$ I am in the middle of a problem and having trouble integrating the following integral:  $$\int_{-1}^1\frac1{(1+x^2)^2}\mathrm dx$$  I tried doing partial fractions and got:  $$1=A(1+x^2)+B(1+x^2)$$  I have no clue how to solve this since it is obvious there is no way to cancel out either $A$ or $B$ to get the other variable. Please guide me.  Thank you. What is the C# equivalent of NaN or IsNumeric? What is the most efficient way of testing an input string whether it contains a numeric value (or conversely Not A Number)? I guess I can use Double.Parse or a regex (see below) but I was wondering if there is some built in way to do this, such as javascript's NaN() or IsNumeric() (was that VB, I can't remember?).  public static bool IsNumeric(this string value) {     return Regex.IsMatch(value, "^\\d+$"); } What can I expect from a Skype interview for PhD admissions? Remote Desktop Session Black after Minimize PROBLEM: When I minimize a remote desktop session and restore it, the remote desktop screen shows up black. This only happens when connecting to a particular computer.   DETAILS: If I start clicking around in the black area, portions of the screen will start redrawing and showing up correctly. For example, if I leave a window open in the remote session and click where that window is located on the remote computer, then that window--and only that window--will redraw, and sometimes a portion of that window won't redraw (usually the toolbar).  And to clarify--the window only has to be minimized momentarily, so it doesn't seem to be a timeout issue. Clicking or typing in the remote session still causes the remote computer to respond appropriately. Disconnecting from the session and reconnecting restores the whole screen image, as does clicking all over the place in the black image (causing each section to redraw).  CONFIGURATION: This problem only happens for me when connecting to a particular computer (a W2K Server box configured to allow remote administration) and only with certain client computers. I've tried 7 different client computers with various versions of Remote Desktop (the OSes were: Win2K, Server 2003, Server 2008, Windows 7 RC, 3 XP) and two of them exhibit the problem (one is one of the XP boxes and the other is Windows 7). Those same computers can RDP to other computers without problem.  RESOLUTION ATTEMPTS: I have tried the following:   Disable the LOCAL screen saver as mentioned on  Turned off bitmap caching in the client, as mentioned on many forums. Updated to version 6.1 of the remote desktop client Using mRemote (I doubted this would work since it uses MS's code for connecting to RDP servers) Turning off all video acceleration.   QUESTION: Any ideas on what is causing this? Using Zorn's lemma show that $\mathbb R^+$ is the disjoint union of two sets closed under addition. Let $\Bbb R^+$ be the set of positive real numbers. Use Zorn's Lemma to show that $\Bbb R^+$ is the union of two disjoint, non-empty subsets, each closed under addition. How do volume control headphones work? A recent question over on  got me to wondering how volume control headphones work.  I don't mean volume control which works by , but the kind of volume control that signals to the device to increase or decrease the signal output.  For instance, according to the , the volume controls are only for apple devices:     Universal Compatibility and Microphone Communication   LP comes with 2 cables for universal compatibility with all modern mobile and audio devices. The 3-Button remote microphone cable is designed for the latest Apple devices, including iPhone®,iPad®, iPod®, and Macbook series. The long audio-only cable and 1/4" adapter is universally compatible with all audio devices and professional equipment.   However this sort of device apparently works with some android phones and the question implies that it works with some computer sound cards on Windows machines too, but not being an Apple buyer (and only recently getting my first smartphone) I haven't seen this sort of thing before. I've done a quick google search, but can't find anything on standards for this technology.   How does this work?   Is it something as simple as shorting left/right/mic channels? If so, could using headphones of this type with equipment that doesn't support this technology, damage that equipment? Is it a serial signal, for instance sent over the mic channel? Does it just require a headphone  connector or a headphone  +microphone TRRS connector?   Does this technique have a name?  Incidentally, is someone could answer this, I can probably look up the rest of the information myself. *8') Is it as standard as it appears, or is everyone just following Apple? Is this something that is patented?   If so, who holds the patent and do they charge a license fee for people to use this technology? If not, is there an open standard for it?    There is some excellent information in  to the question  but it doesn't answer the specifics of how this type of volume (etc.) control works, since it now seems to be rather more common and standard. Show that $\frac 1{1+x+y^{-1}}+\frac1{1+y+z^{-1}}+\frac1{1+z+x^{-1}}=1$ if $xyz=1$ Prove by induction that for all $n \geq 3$: $n^{n+1} > (n+1)^n$ I am currently helping a friend of mine with his preperations for his next exam. A big topic of the exam will be induction, thus I told him he should practice this a lot. As at the beginning he had no idea how induction worked, I showed him some typical examples.  Now he showed me an exercise he was having trouble with, which states that one should prove $$n^{n+1} &gt; (n+1)^n$$  for all $n \geq 3$. I have to admit that I too have trouble showing this inequality, as in all of my attempts, my lower bound is too low. Also, I have not yet figured out, how one gets the $(n+2)^{n+1}$, primarely the number $2$ is a problem. I think this might be solved using the binomial theorem, however, I don't think they have already seen the binomial theorem in school.  Is there an easy method to show this inequality by induction not using the binomial theorem? If no: How can one show it using the binomial theorem?  Thanks for answers in advance. Why does your reflection suddenly turn upside down while slowly walking away from a curved mirror? Many people should have realised, when looking into a concave curved mirror (or even a rather reflective spoon in that fact) at a close distance, you will see a slightly distorted reflection. But as you move further away, the image will suddenly become upside-down.  why is this? How can I ask a person in which order in his family among the siblings? My colleague he have two brothers. I want to know, he is first/second/third son of his parents, ie., the order in the family among their siblings.  I can simply ask     Are you first son of your family?   It simply give some predictions, I don't want to that.  Is there a better way to ask the question? Supersymmetry in Quantum Field Theory Introductory Calculus textbook for physics? Infinite Series $‎\sum\limits_{n=2}^{\infty}\frac{\zeta(n)}{k^n}$ ‎If $f\left(z \right)=\sum_{n=2}^{\infty}a_{n}z^n$ and $\sum_{n=2}^{\infty}|a_n|$ converges then‎, $$\sum_{n=1}^{\infty}f\left(\frac{1}{n}\right)=\sum_{n=2}^{\infty}a_n\zeta\left(n\right)‎.$$ ‎Since if we set $C:=\sum_{m=2}^{\infty}|a_m|&lt;\infty$‎, ‎then‎ $$\sum_{n=1}^{\infty}\sum_{m=2}^{\infty}|a_m\frac{1}{n^m}|\leq\sum_{n=1}^{\infty}\sum_{m=2}^{\infty}|a_m|\frac{1}{n^2}\leq C\sum_{n=1}^{\infty}\frac{1}{n^2}&lt;\infty‎$$ and ‎by Cauchy's double series theorem‎, ‎we can switch the order of summation‎: $$\sum_{n=1}^{\infty}f\left(\frac{1}{n}\right)=\sum_{n=1}^{\infty}\sum_{m=2}^{\infty}a_m\frac{1}{n^m}=\sum_{m=2}^{\infty}a_m\sum_{n=1}^{\infty}\frac{1}{n^m}=\sum_{n=2}^{\infty}a_n\zeta\left(n\right)‎.$$ This shows that $‎\sum_{n=2}^{\infty}\frac{\zeta(n)}{k^n}=\sum_{n=1}^{\infty}\frac{1}{kn(kn-1)}$.  My Questions:  1) It's obvious that $\sum_{n=1}^{\infty}\frac{1}{2n(2n-1)}=\log(2)$, but how can I evaluate $\sum_{n=1}^{\infty}\frac{1}{3n(3n-1)}$?  2) Is there another method to evaluate $\sum_{n=2}^{\infty}\frac{\zeta(n)}{k^n}$? MCP4131: How to know what value resistors to use on the multiplexed SPI IO? There are two aspects here. The first question is related to R1 below:    The datasheet says: "R1 must be sized to ensure VIL and VIH of the devices are met" but gives no formula. So first question:  (1) How does one determine value of R1?  The datasheet gives maximum SPI SCK frequency for this device as 10MHz for 5V supply as given in Tables 1-1 and 1-2. However, for the read operation on the device where the SDI/SDO are multiplexed, the idea is different because:    The point 2 under the Table above says that the max SCK can be increased by using a pull up resistor. About these things I am wondering the following:  (2) Why is max SCK frequency lower for multiplexed SDI/SDO read operation only? (3) If I connect a pull-up resistor it will certainly form a voltage divider with the R1 in the first picture. How do I determine the value of both of these resistors then?  Finally, since the Table 1-1 and 1-2 give SCK Input Frequency for voltage 1.8V to 2.7V as 1MHz rather than 10MHz which applies to 2.7V to 5.5V.   (4) Why is the max SCK lowered at lower supply voltage? Windows 7: Disable Lock Workstation After 10 Minutes Using Group Policy On my Windows 7 PC the system becomes locked after 10 minutes of inactivity. Usually I would find this setting next to the screen-saver configuration. The setting is grayed out, however.  I think this is because of corporate group policy. As I am an administrator on this computer I should be able to reconfigure the group policy setting using gpedit.msc.  What is the group policy setting that I need to change to prevent automatic locking of my workstation?  Edit: I don't have configured a screen-saver. I also want to continue to be able to lock the workstation manually. Is "am" in "I am right" an auxiliary verb? Consider these sentences:     The ice was thick enough to walk on.      They were in a hurry.      There is enough salt in it.      It is freezing.      I am right.   Are the italicized verbs auxiliary verbs?    Update: Let me explain why I asked this question.  The above sentences are from exercise 6 "Auxiliary verbs" from the book .  From the 36 sentences in exercise 6, all except the above mentioned five sentences are indeed sentences that contain auxiliary verbs (may, must, can, will, had, etc.).   So, what happened here? Why are those five sentences in this exercise? Is it an oversight?    View image in full resolution here: With variable length instructions how does the computer know the length of the instruction being fetched? Why does this formulation of Choice not follow from the Comprehension Schema?