Do I have a couple of questions or a few?
What does “a couple” mean to you, and what does “a few” mean to you?
says that a photon of  to $10^{-62}$ kg has been detected:     10×10−62 kg   Mass equivalent of the energy of the lightest photon   detected [citation needed]   This equates ($mc^2=E=hf=h\frac{c}{\lambda}$) to a wavelength of $\lambda=2.2\times 10^{20}$ m (roughly a million ly)! Can anyone provide a citation for this measurement? And how can such a large wavelength/low energy photon be detected?  Edit  Apart from the quotation (true/false un/reliable un/documented ....), I'd like to learn about the lightest photon detected, or about the instrumental limit: what is the lower limit of energy that can be registerd by an intrument (or the greatest wavelength), and how it is done? For example, can you detect a radiowave of 1 Hz? Uncheck checkboxes by changing particular checkbox state I have custom fields in contacts form named checkbox1__c, checkbox11__c, checkbox12__c, checkbox13__c.  When I check checkbox1__c then I want checkbox11__c,  checkbox12__c,  checkbox13__c to be unchecked.  When I unchecked checkbox1__c then I want checkbox11__c, checkbox12__c, checkbox13__c to be checked.  Is there any way to do this by using validation-rules? If not no way to this by validation-rules, then what is the best way to do this? How to perform hard / cold reboot of iPhone or iPad? How to read a windows registry file using java? How do I join two lists in Java? Define additional math operators to be typeset in roman Mathematical operators, such as function names, should be set in roman type, not italics. Latex already has commands for some operators, including \max, \min, and \log.  How can I define additional such commands? Prove or disprove: For every integer a, if a is not congruent to 0 (mod 3), the a^2 is congruent to 1 (mod 3) Prove or disprove: For every integer a, if a is not congruent to 0 (mod 3), the a^2 is congruent to 1 (mod 3)  SO this is for abstract algebra and I am really struggling with this. Here are some of the definitions and theorems I think would apply.  -an integer a divides and integer b if there is an integer q such that b=aq -Let a and b be integers, with a>0. Then there exist unique integers q and r such that b= aq+r and 0&lt;=r  The question says hint: use 2 cases but I'm not really sure what that means. I'm guessing it wants me to look at it when a is congruent to 0 and when it's not? so i tried to do that but just ended up stuck. below is as far as i got with that attempt  Proof: Case 1 There should be some information about letting variables exist in certain number sets here  assume a is not congruent to 0 mod 3, then 3 does not divide a-0, therefore a-0 does not equal 3q for some q in the integers  I was trying to get this to wind down to thus 3 divides a^2-1 but even tho it seems true (I couldn't find a counter example) I couldn't figure out how to prove it with what I have.  Next i tried reversing it thinking I could contradict it or something.  I think this would be case 2? assume a is congruent to 0 mod 3, then 3 divides a-0 and a-0=3q for some q in the integers, then 3q=a since 0 is the additive identity, therefore 3 divides a,  and again stuck and my brain hurts a little..  Can anyone help me figure out how to work this. Why do I always hear remote train horn at night? This is definitely not an illusion, as many people have the same experience. I have usually lived in places miles away from train stations, which makes it unlikely to hear any train horns during the day. However at night, occasionally train horns can be heard. I hope if any one can explain the physics of this effect, like possibly sound travels faster at low temperature. Does SQLDeveloper support executing scripts? How to prove that $\lim \frac{1}{n} \sqrt[n]{(n+1)(n+2)... 2n} = \frac{4}{e}$ I'd like a hint to show that:  $$\lim \frac{1}{n} \sqrt[n]{(n+1)(n+2) \cdots 2n} = \frac{4}{e} .$$  Thanks. Wizard sickness I remember in an interview, or during a Q&amp;A, Rowling stating that Wizards live longer than Muggles. This got me thinking about Wizard deaths in general, and then deaths being attributed to illness.  So, I ask, has there ever been a Wizard, that has died from something like cancer? Is there anything, even briefly mentioning a Wizard becoming ill?  And finally, are there any illnesses that are exclusive to Wizards? Why don't electrons crash into the nuclei they "orbit"? I need to clip a vector layer to the extent of a raster. It has to be very precise that's why I would not want to draw a polygon myself (and clip the two polygons). There seem to be some ways to clip a raster to a polygon but I have difficulties to find a solution to clip a polygon to a raster. I already tried to create a polygon out of my raster several times in ArcGIS and R, so I could clip the result. But every time it crashes because the raster is to big. There must be a simple way to solve this, and somehow I can just not see it at the moment.  How can I do this using GDAL? Which one is the best option to get the identity value I just generated via an insert? What is the impact of these statements in terms of performance?   SCOPE_IDENTITY()  Aggregate function MAX() SELECT TOP 1 IdentityColumn FROM TableName ORDER BY IdentityColumn DESC Determining the Actual Server Create Date I am interested in determining the ages of all 70+ my servers. I would like to create a growth graph showing when servers and databases were added to the environment either/both monthly or annually. I executed the following query using the SSMS multi-query feature with only partial success.  SELECT [name], create_date FROM sys.databases   It's partial success because the master and model databases return with a date of 'April 8, 2003' when I know that I created some of these servers during the past couple years.  I refresh databases from one server to another several times a week, which appears to be causing issues with the database create date.   Is there a simple method to determine the actual create date for both servers and databases? [Probability]need help to understand the following expression So assume $Y$ and $X$ are exponentially distributed with parameters $y_1$, and $x_1$ respecitively.  assume c is a constant.  I am having huge trouble to understand the integration of the following expression.  $P(Y&lt;c/u(X))$  $=\int_{t}^{\infty}f_X(x)\int_{0}^{c/u(x)}f_Y(y)dydx +\int_{0}^{t}f_X(x)\int_{c/u(x)}^{\infty}f_Y(y)dydx$  where t is the cross-point that $u(x)$ change sign    here $c/u(x)$ is given by the plot below, t is the point crossing the zero:   Confusion:   I don't understand the second integration of the second term "$\int_{c/u(x)}^{\infty}f_Y(y)dydx$", this isn't right because Y an X only defined for y>0, and x>0. So it's the first quadrant in this plot. I was asked this question in an interview.  Lets say we have a correlation matrix of the form \begin{bmatrix}1&amp;0.6&amp;0.8\\0.6&amp;1&amp;\gamma\\0.8&amp;\gamma&amp;1\end{bmatrix}  I was asked to find the value of gamma, given this correlation matrix. I thought I could do something with the eigenvalues, since they should be all greater than or equal to 0.(Matrix should be positive semidefinite) - but I don't think this approach will yield the answer. I am missing a trick.  Could you please provide a hint to solve for the same? Overriding !important style Title pretty much sums it up.  The external style sheet has the following code:  td.EvenRow a {   display: none !important; }   I have tried using:  element.style.display = "inline";   and  element.style.display = "inline !important";   but neither works. Is it possible to override an !important style using javascript.  This is for a greasemonkey extension, if that makes a difference. What is the yield keyword used for in C#? One form of Jensen's inequality is     If $X$ is a random variable and $g$ is a convex function, then   $\mathbb{E}(g(X))\geq g(\mathbb{E}(X))$.   Just out of curiosity, when do we have equality? If and only if $g$ is constant?