Java 8 gives error message with Windows XP.  Can it still be used?  What are the latest issues? Windows xp is no longer supported but will Java 8 still work on Windows XP computers since so many people still have windows xp?
I just went to install Java 8 on my ancient laptop that runs Windows XP SP3.  Java pops up a message:     Java 8 requires a newer version of Windows. You may continue with the installation, but for Java to work as specified we recommend upgrading your computer's operating system.   Will Java fail to work properly on Windows XP? Or is this just Oracle trying to be secure?
When is the product of $n$ subgroups a subgroup? How to prove or disprove following statement :     There are infinitely many primes of the form : $\lfloor \sqrt {3} \cdot n \rfloor $    Note: This is a problem I made myself.  There is a theorem that states :  $\lfloor nx \rfloor = \begin{cases}  n\lfloor x \rfloor, &amp; \text{if } 0 \leq \{x\} &lt; \frac{1}{n} \\  n\lfloor x \rfloor +1, &amp; \text{if } \frac{1}{n} \leq \{x\} &lt; \frac{2}{n} \\  n\lfloor x \rfloor +2, &amp; \text{if } \frac{2}{n} \leq \{x\} &lt; \frac{3}{n} \\  \vdots \\  n\lfloor x \rfloor +n-1, &amp; \text{if } \frac{n-1}{n} \leq \{x\} &lt; 1 \\ \end{cases}$  where $\{x\}$ is a non-integer part of $x$ .  Hence :  $\lfloor \sqrt{3}\cdot n \rfloor = \begin{cases}  n, &amp; \text{if } 0 \leq \sqrt{3}-1 &lt; \frac{1}{n} \\  n +1, &amp; \text{if } \frac{1}{n} \leq \sqrt{3}-1 &lt; \frac{2}{n} \\  n +2, &amp; \text{if } \frac{2}{n} \leq \sqrt{3}-1 &lt; \frac{3}{n} \\  \vdots \\  2n-1, &amp; \text{if } \frac{n-1}{n} \leq \sqrt{3}-1 &lt; 1 \\ \end{cases}$  How can I proceed from here ? The question  got me curious and thinking about the following:   For which $n$ and $k$ are there nontrivial homomorphisms from the symmetric group $S_n$ to the cyclic group $\mathbb{Z}/k\mathbb{Z}$ of order $k$? I'm thinking it might be an open problem. Is this a problem with a known solution? If so, how can we prove it?   Thanks! What is the difference between a "link function" and a "canonical link function" for GLM The ship flying away from Rey in her flashback of being left on Jakku looks like one of the ships in the group that takes her away when she is captured.  If so, and it is a First Order ship that dropped her off, this is an interesting Easter egg. Why is '.' a hard link in Unix? Fluent and Query Expression — Is there any benefit(s) of one over other? I'm studying for a midterm and need some help with proving summation     $$\sum\limits_{k=0}^n\binom{n}{k}2^k = 3^n$$   using the binomial theorem.  This is what I've been thinking so far:   In the binomial theorem, we set $x = 0$ and $y = 2$, so:  $3^n = (x+y)^n = \sum\limits_{k=0}^n\binom{n}{k}y^k$  $ = \sum\limits_{k=0}^n\binom{n}{k}2^k$  Am I getting this correct so far or completely wrong? Any help would be appreciated. Thanks. What constitutes an observation/measurement in QM? Fundamental notions of QM have to do with observation, a major example being The Uncertainty Principle.    What is the technical definition of an observation/?  If I look at a QM system, it will collapse. But how is that any different from a bunch of matter "looking" at the same system?  Can the system tell the difference between a person's eyes and the bunch of matter?  If not, how can the system remain QM?  Am I on the right track? What is Electromotive force (EMF)? How is it related to potential difference? What is  (EMF)? How is it related to the potential difference? Is it created by the potential difference in any conductor? Is it a process? Why is it called force?  Does writing EMF instead of voltage make any difference in AC circuits? (Studying alternating current I found some books using EMF while others used voltage.) Why would a JavaScript variable start with a dollar sign? I quite often see JavaScript with variables that start with a dollar sign. When/why would you choose to prefix a variable in this way?  (I'm not asking about $('p.foo') syntax that you see in jQuery and others, but normal variables like $name and $order) Why doesn't Ubuntu ship an application, or the latest versions of some applications? What reasons are there for applications in Ubuntu not being the most up-to-date, and why are some applications not available, in its  repositories? Getting the class name of an instance? How do I find out a name of class that created an instance of an object in Python if the function I am doing this from is the base class of which the class of the instance has been derived?  Was thinking maybe  might have helped me out here, but it doesn't seem to give me what I want. And short of parsing the __class__ member, I'm not sure how to get at this information. I know they have their adherents, but do more or less esoteric branches of mathematics such as Category Theory and/or Quantum Logic provide powerful tools for new theory development or are they just occasionally-useful presentational frameworks?  More particularly, is it worth investing the time to study these formalisms? "Where" exactly are complex numbers used "in the real world"? I've always enjoyed solving problems in the complex numbers during my undergrad. However, I've always wondered where are they used and for what? In my domain (computer science) I've rarely seen it be used/applied and hence am curious.  So what practical applications of complex numbers exist and what are the ways in which complex  transformation helps address the problem that wasn't immediately addressable?  Way back in undergrad when I asked my professor this he mentioned that "the folks in mechanical and aerospace engineering use it a lot" but for what? (Don't other domains use it too?). I'm well aware of its use in Fourier analysis but that's the farthest I got to a 'real world application'. I'm sure that's not it.  PS: I'm not looking for the ability to make one problem easier to solve, but a bigger picture where the result of the complex analysis is used for something meaningful in the real world. A naive analogy is deciding the height of tower based on trigonometry. That's going from paper to the real world. Similarly, what is it that is analyzed in the complex world and the result is used in the real world without imaginaries clouding the problem?  The question:  is nice but covers a more mathematical perspective on interim results that make solving a problem easier. It covers different ground IMHO. Install Linux from Linux SQL function as default parameter value? I tried changing a default parameter value with this:  ALTER PROCEDURE [dbo].[my_sp] @currentDate datetime = GETDATE()   and all the SQL pre-compiler gave me was this error:     Msg 102, Level 15, State 1, Procedure my_sp, Line 8 Incorrect syntax near '('.   I have already created the procedure. (I'm not sure if that's relevant.) I was using a null default value and checking for that later, but that doesn't seem proper. Can I do this in one line?   Update: I was going off of :      [ = default ] Is a default value for the parameter. If a default value is defined, the function can be executed without specifying a value for that parameter.            Note:     Default parameter values can be specified for CLR functions except for the varchar(max) and varbinary(max) data types.         When a parameter of the function has a default value, the keyword DEFAULT must be specified when the function is called to retrieve the default value. This behavior is different from using parameters with default values in stored procedures in which omitting the parameter also implies the default value.   Am I reading this wrong?  Many thanks. Does a surjective ring homomorphism have to be surjective on the unit groups? Let $n \geq 1$ be an odd integer. Show that $D_{2n}\cong \mathbb{Z}_2 \times D_n$. I define a map $$\phi:D_{2n} \rightarrow \mathbb{Z}_2 \times D_n$$ by $R \mapsto (0,r^{\frac{n+1}{2}})$ and $M \mapsto(1,m)$. Then I am stuck at showing the map is bijective. By the way, do we need to show that $(0,r^{\frac{n+1}{2}})(1,m)(0,r^{\frac{n+1}{2}})^{-1}=(1,m)$ ? If we can prove this, then what can we conclude? Lately I see a blue screen of death a lot and want to know why it appears. Where should I gather the information so the problem can be diagnosed best? Couldn't find anything in C:\Windows\Logs.