Dave

At the end of the day, you're always going to have things like the Xserve/high-end G5s coming along with very high-end chips. Remember, the Xeon processor is rather ideal for workstation-based systems (we have one running the Avid at work). I just don't see how the 970 will compete with the stupidly fast advances that the entire x86 camp is making. I would say: "wait and see". We can't gauge how good or bad these systems are going to be before they actually come out. Mathematica looked really stonking running on that machine, so we'll just have to wait and see. Personally, I can't wait to get my hands on one; I'm waiting for them to come out so I can buy a cheap Mac Mini G5

You can watch the keynote speech here: http://www.apple.com/quicktime/qtv/wwdc05/ It makes for very interesting watching

I have to disagree quite strongly. This is a very clever business move by Apple in my opinion. First of all, there's the entire IBM contract. The PowerPC 970 was supposed to be revolutionary in its nature, clocking it to 3GHz+, 64bit etc. However, they were supposed to be at the 3GHz+ mark a year after release - two years later, we're at 2.7GHz. The 970 is a power-hungry, white-hot overbloated piece of poo for the performance you get. Without some significant research on the part of IBM, there's not going to be a PowerBook G5 just because of the huge heat envelope. Of course, besides all of this we have the fact that IBM basically made Steve Jobs (and hence Apple) look bad. On the business end of things, switching to Intel is a good move. They have some good work in the pipeline and I think that OS X could be pretty damn sweet on an x86. Whilst I'm an avid Mac fan, I don't have a problem with the x86 architecture like some do. Tiger has apparently sold about 2m copies, which is not to be sniffed at. People like it because it appeals to them; it's friendly to use and quite intuitive. Apple recognises that by moving to x86, it allows them more room for expansion and possibly marketing out the license to people like Dell. (As an example; they already licensed the iPod out to HP). Now, for what it's worth Apple already went through a rather big shift of architecture back in 1994 when they switched from the Motorola 68k processors to the newer PowerPC 600 series. So they do have some experience, although they made rather a mess of it at the time. However, I think the thing that Apple has definately acknowleged in the past 5-6 years is that you should always try to learn from your mistakes. Anyway, this is all my opinion. If you want a more objective article, have a look at: http://www.theregister.co.uk/2005/06/06/apple_intel_analysis/

No, you can't do that. Once you've registered a domain, you're given complete control over it, including all sub-domains, nameservers, MX records, etc.

There's not a lot to actually get about it tbh. Each TLD has rather a lot of names registered under it (i.e. scienceforums.net, abc.net, othername.net etc). It keeps a record of which machines are supposed to be resolving the domain names. So, when you look up the address for http://www.scienceforums.net, your IP resolver will go along to the root nameservers at .net, and say "hey, who's hosting scienceforums.net?" You then get pointed to the nameservers hosting the domain, and then you say to them "do you have a subdomain called www?" It goes "yeah, the IP address is 38.118.74.97". The point of it all is to enable you to point to a lot of IP addresses. Say that we had 20 different machines each hosting a webserver. It would be a pain if we could only resolve scienceforums.net; it'd be useful to have some kind of name for each machine (i.e. www1.scienceforums.net, www2, ..., www20). Also, say you have an FTP service running on a different machine or attached to a different interface. Then it would be prudent to have ftp.scienceforums.net pointing to that IP instead. Similarly for things like mailservers, etc. Whilst it's not very useful for people running things off of 1 connection, for large corporations it's extremely useful.

No. This isn't a section for doing the homework for you. You need to attempt it, and then maybe we'll give you some hints and advice on where to get going.

Processors with hyperthreading have one physical core and one logical core; it speeds up applications that make use of threading, basically. Not usually. Depends on the processors It's the bit that does the calculating, basically.

Trouble is, you have to pick the right series. For example, [imath](1+x)^{\frac{1}{2}}[/imath] only converges for [imath]|x|<1[/imath]. So if you want to work out [imath]\sqrt{2}[/imath], you can't just stick in x = 1.

Thanks for the feedback. I spent quite a while trying to create a padlock icon, but it wasn't coming out properly. I'll give it another shot

Thanks I'm thinking that some of you more techy people out there might want an option to display MathML instead of the normal images. Is there any usefulness for this amongst people, or am I wasting my time? Incidentally, I might be pushing images over to PNG for better transparency. I've found a fix for IE to do proper alpha blending, so I'll try it out next week some time.

My thoughts exactly. There must be life out there somewhere - we just don't have the means to find it yet.

Erm, not quite. The formula you gave is for the triangle numbers. According to that formula, 4! = 10. But 4! = 4*3*2*1 = 24. If you want to define it recursively, you can define it as: [math]n! = n \cdot (n-1)!, \ 0! = 1[/math]

I've made some modifications to the rendering code; they should render a bit crisper and nicer now.

Most components have a pretty wide operating range in terms of temperature. You also have to bear in mind that most places that have computers in them are likely to have some A/C or similar.

OE will do it because it's an MS product. I suspect the reason that they haven't documented the HTTPMail protocol is that they don't want people to use products other than their own to download mail from their Hotmail accounts.

I've never really heard the term vertex used in relation to a circle either. I suspect a mistype.

It should be working fine... I can see the images okay

Hmm, you shouldn't be seeing errors now... I fixed it all up

I think you can go ahead and download the entire Planetmath database if you so desired. I've always found with these things that it easier to start from the ground up, so to speak. Maybe I'll give the entire vBulletin-wiki thing a go. It might turn out okay, you never know

Indeed. [imath]\int x\sin x \ dx[/imath] can be done using integration by parts also.

Another interesting ring that we touched upon in my Algebra course was the ring of differential operators: [math]\mathcal{D} = \{ a_0 + a_1 \frac{d}{dt} + a_2 \frac{d^2}{dt^2} + \cdots + a_n \frac{d^n}{dt^n} \ | \ a_0, \dots, a_n \in C^{\infty}(\R,\R) \}[/math] This isn't a ring under addition and multiplication, but under addition and composition. You can use the rule: [math]\frac{d}{dt} \circ g = g' + g \frac{d}{dt}[/math] You can then use this to solve a lot of nasty differential equations. For example, take a look at: [math]\left[ \left(\frac{d}{dt}\right)^2 +(t + \cos t)\frac{d}{dt} + (t\cos t + 1)\right] f(t) = 0[/math] That's a fairly nasty little equation. But using the rule above, we can see that [imath]1+t\frac{d}{dt} = \frac{d}{dt}\circ t[/imath]. Now we get (if we just consider the operator for a second): [math]\frac{d}{dt} \circ \frac{d}{dt} + \frac{d}{dt} \circ t + \cos t \frac{d}{dt} + t \cos t[/math] You can "factorize" this: [math]\left(\frac{d}{dt} + \cos t\right) \circ \left( \frac{d}{dt} + t\right)[/math] So to get solutions, you need only consider the two, easier differential equations given by: [math]\frac{df}{dt} + f(t)\cos t = 0, \frac{df}{dt} + tf = 0[/math]. Of course, you can get the easiest solution using the second equation.

It's a lot of effort. I played around with the idea myself, but it's a lot of work. I mean, you have to bear in mind that on top of wikipedia and Wolfram, you have Planetmath as well. All of these sites have significant contributions from a lot of volunteers, a lot of whom are graduate level or more. I've been thinking about making some kind of wiki-type system for vBulletin. I think it would go well with the theme of the site, but I'm not so sure as to how much it would actually get used, and how many people would contribute entries. We'll see, I suppose.

I shall deal with it shortly. I'd forgotten I'd put that in, to be honest

This is exactly my point. I suspect that the reason the document is 500 pages long is because there was so much bickering about whether this should be that or where this should be, or the exact wording of stanza 728, etc. To me, the entire consitution was just a big document from the elite saying "This is what we want, now you're going to go along with it". It didn't represent anything the public stood for, and ultimately this is why it got the no vote in France.

Not that I can think of. Plotting is rather a complex business... perhaps some additional checks that I haven't thought of can be implemented. I'll give it some thought.