Xittenn

I'm having trouble with the statement "within irregular shaped polygons (a standard house roof)." Is it a standard house roof or is it an irregularly shaped polygon? I wouldn't call this a knapsack problem there are no weights. I would solve this mathematically using a Lagrange, and this depends entirely on my first question. Are the rooves going to be rectangular or are they going to be mostly complex shapes. I assume that either way you are wanting to cover them as entirely as possible? Can the panels be cut? I am assuming no because you said "homogeneous regular shapes. . .". The math can be a bit tricky, and might require someone to spend some time trying to create a solution that works!

Reminds me of a thread Pangloss had started . . . the Sixth Sense Device - MIT I love the instant access to Amazon comments on books that you might be buying in a store and in person!

@Marat; I am not surprised by a single word that you have said, but I believe that you are seriously skewing the context. I do not have the statistical information on anything and just so I am clear I have seen first hand women who have worked so very hard and have made little gain. I come from work in factories where women represent the minority. I do not know what the exact ratio of 'professional' to 'vocational' is but I am pretty sure that Canada is more largely employed in vocational fields. With men no longer obligated to take care of women, by the modern standard of moral practice, women are often left to fend for themselves. Many women do not meet the standards that are set for positions like waitress or secretary, as these positions are still often given to the better looking women by their male superiors. This leaves many women looking for work in factories. I am very familiar with factory work and I have seen a good many woman trying to make their living off of these jobs. For starters they are far less likely to be hired. Not because of their looks and not because of their abilities; a lot of these jobs really do not require any strength and the women are often better with their hands. They are not hired because men are still in charge and are still hiring men. They feel more comfortable with them and more on a personal level; they are chums. They often rationalize, quite unreasonably, that women are in fact a lesser quality worker. Some still feel that women belong in the home and that their husbands will take care of them. For the girls that do get hired, well, they have to accept the fact that in general they will work just as hard as the men around them and will learn to expect to remain at the bottom. I have seen women spend years in places that have started them at lower wages and have seen men come in and are making more money than them in a matter of months. I've seen guys who come in and are absent 2 of 5 days a week and constantly making mistakes, and they are making almost double that of women doing more work and who are always on time and in attendance. Most recently I was involved in a labour dispute with a company that was doing this to the girls it had employed; the man who was responsible was acting largely on the basis of his personal religion and heritage. I agree that there has to be a proper revision of law and ethics in our modern society. I am disgusted by the cases that do occur and the events that you have mentioned. But seriously, it is pretty bunk that you are disregarding the hurt that a tremendous number of women are still facing in our country(I assume you are Canadian). I believe in making all sides clear but in making your point you have seriously belittled individuals who have had some highly traumatic experiences. Women are still faced with starvation, forced into the sex trade to make sure they have money for their children and many of them live in very pitiful conditions. While on the other hand men of equal stature drink and smoke their lives away, drive their cars and buy whatever the hell they feel like. I really wish the general public would revise its attitude because I too often hear the most horrible of sentiments from one party to another and it is often so misguided and so full of bitterness and completely unfounded; did your daddy tell you that, or maybe Google? :/ I apologize now for anything that I may have said, that may have been wrong or unclear or unprovoked . . ..

In statistics and probability theory, ‹~› means “is distributed as”.

Finch, Steven R. Mathematical constants, Volume 94. Pg 449 describes this as the hyperpower analogue of the harmonic series. He goes on to say that it is in fact divergent; though, it does converge in its odd/even parts. [math] \lim_{n\rightarrow\infty} H_{2n} = 0.65836559922 . . . < 0.6903471261 . . . = \lim_{n\rightarrow\infty} H_{2n+1} [/math] He does not give proof and I am finding it rather difficult to find one for any similar series. Are the same types of proofs, such as the Ratio or Alternating Series proofs applicable to Hyperpower in some way? The Ratio test seems rather easily applied . . . [math] where \: n \geq 1 [/math] [math] \lim_{m\rightarrow\infty} \Xi_{m=0} \left ( \frac{1}{n+m} \right ) [/math] The Number Theory book I have dances around a lot of this but never actually dips into! o.o

Maybe the existence of such a forum would incite the activity! I would like to have discussions on this topic and will maybe one day be capable of actually doing so. In the mean time if others were to discuss issues this would give me more to read. I'm just up-voting the suggestion here.

It allows for more processes to be done simultaneously thus allowing for greater throughput in a shorter amount of time. The trick with this question is, complete operations can take multiple clock cycles, so unless the subcomponents of an operation were somehow distributed, the higher frequency processor would finish first. There aren't any processors that can distribute the subcomponents of an operation as these are most often serially dependent. GPUs are a good example of all this where they are specifically designed to distribute a high number of the same operation to be done at the same time over a high number of parallel cores! And what Cap' said

Note that given the generalized case it is in fact insufficient to say where n is odd or even but in fact is the parity of the sum total of the number of terms performing an operation that delineates the effect. [math] where \; n \geq 1 [/math] [math] \lim_{m\rightarrow\infty} (\frac{1}{n})^{(\frac{1}{n+1})^{.^{.^{.^{(\frac{1}{n + m})}}}}} [/math] I wonder what [math] n = 1 [/math] says about the convergence of [math] n > 1 [/math] in the generalization?

I don't see any proof positive of there being convergence ..... http://www.wolframalpha.com/input/?i=plot%20%281%2Fn%29^%281%2F%28n%2B1%29%29%20n%3D2%20to%2050 http://www.wolframalpha.com/input/?i=plot+%281%2Fn%29^%281%2F%28n%2B1%29%29^%281%2F%28n%2B2%29%29+n%3D2+to+50 http://www.wolframalpha.com/input/?i=plot+%281%2Fn%29^%281%2F%28n%2B1%29%29^%281%2F%28n%2B2%29%29^%281%2F%28n%2B3%29%29+n%3D2+to+50 The red average is just that an average of two plots. There is the set of exponential terms which sum to an odd value of total terms. There is the set of exponential terms which sum to an positive value of total terms. I think there is actually evidence that suggests that each converge on their own values ..... I am not sure how to prove this indefinitely in either direction though :/ There is no continuous function that represents this problem, as far as I can tell!

No my algorithm is fine :/ .... but thanks for your solution ... I will be trying in Sage when I finish doing some computer updates .... I am still conflicted about how the plot is achieved where odd/even n starting points are affecting the outcome ...

note that n = 50 and i = n - 1 and i-- <===== the right way .... my numbers were actually the same as yours .... I don't understand why an odd n gives ~.65 and an even n gives ~.69 but I can see how this could converge on the avg. I am sure when I think a little more on it, it will become more clear to me. I accidentally put a bunch of n's where i's should have been :/ i > 1 and i--

I was just using C++, I was installing SAGE to do a better job(I hadn't installed it yet) but Shadow has posted. I am curious about Shadows projected figure and I still plan to double check this in SAGE and maybe a few other places. n = 50 x = 1/n for( i = n - 1; n > 1; n-- ) x = pow( 1/i, x ); I went for large numbers to start which was a little foolish; I was half asleep dammit ! > 9000 I don't get why the value bounces like that :/

It's not an issue of proof, this is not conventional mathematics and this is why this is ambiguous. It's an accepted way of doing things just as 2x really means 2 * x, it is an ugly thing to do but it happens. It is what is called 'implied' . . . . . . . . . . . . . If you wish to maintain conventional mathematics than indeed the answer is 288, but I can guarantee you 100% that this was not the intention. There are a number of other ways that this could have been written that are, statistically speaking, far more likely to have been used. Given the statistics if you answer 288, well you would be someone who ignores their own better judgment; I mean you are questioning this!

Run spybot with administrative permissions, there really isn't any such thing as a registry key that cannot be removed. If spybot is choosing to not remove them there must be some reason. Your questions are very vague and difficult to answer through a forum. If you are not very computer savvy the best bet is to have a technician fix your PC for the few dollars that this will cost, really why waste the hours IMHO.

What is 0.690347126114964 ????? 0.69034712611496429 @ n = 10e10 :| well calculating seems to have been a very bad idea ... double precision and the library used wasn't good enough and I noticed that when I started at n=odd vs n=even I get two different numbers ... I'll have to look at this again in the morning if nobody comes up with a better or more viable solution ...

I got this one! It seems pretty thorough as a reference but it is not a textbook. It is pretty clear and readily understood, some of what might be considered standard notation is a little unusual though i.e. the decimal place. :/

I usually take 2(9+3) to mean (2(9+3)) and not 2 * (9+3) so I think that 48÷2(9+3) is asking for 48÷(2(9+3)) and the answer is 2. This is also the more logical answer given the context and the numbers. I think in general, oversights like this are avoided at all costs in literature and they generally constitute a mistake. It is usually pretty clear the intention and this isn't something you should dwell on; there are better uses for your time. lol

There are robots that make other robots but this is considered general manufacturing process. There are also 3D printers that could print every piece of itself and have it ready for assembly. I guess if you added an amount of robotics to its componentry you could have it assemble itself as well, but there would still remain the question of dyes and ink. It might even be feasible to have a processor making factory inside a PC case! There really isn't anything to say that the equipment necessary to manufacture a cpu couldn't be miniaturized and stored inside a PC case! This isn't something that will probably happen though for a good number of reasons. I think really there are two conditions that might make this an occurrence. On the one hand if an assembly of a variety of nanites were to be developed, this might make this a reality. Or if a piece of equipment was developed that had full mastery of energy and chemistry in which it could take matter and form a solution in a rather small amount of time; a sort of ultimate, do it all, chem lab meets machine shop meets star trek. I don't think these are things we will probably be seeing anytime soon, we can barely keep the machines we do have running properly. But really the whole concept of machines building machines is again, general manufacturing process. They just don't tend to be the same machine self replicating. It's not that they can't, but why waste all of that material to manufacture into a device the ability to replicate itself when this is something that will almost never happen? You could think of it more like an ant colony, machines are born from a queen and there are different machines that play different roles. Giving a computer the ability to upgrade it's own physical cpu would be very expensive!

This is probably too late but like a working example?? [math] \begin{array}{lcl} R_0 = \frac{k_2_0[E]_0}{_0 + K_m} & \; & ( \; 1.1 \; ) \: Michaelis - Menten \; Rate \; Law \\ \\ \\ \\ Where \; _0 >> K_m \; then \; R_0 = k_2[E]_0 = R_{max} & \; & ( \; 1.2 \; ) \\ \\ \\ \\ \frac{1}{R_0} = \frac{1}{R_{max}} + \frac{K_m}{R_{max}} \frac{1}{_0} & \; & ( \; 1.3 \; ) \: Lineweaver - Burk \; Equation \end{array} [/math]

What does the OP propose as a reasoning for such a review of the standard system? Is this an exercise in applications of anholonomic systems? Is this just an interesting observation?

This really isn't something that would happen rather quickly and in a few lines of code. If approached from standard Windows programming methodology then there isn't a means to inject external to the console executable binary, you must modify the source code and recompile. This means that essentially you will have a new console separate from all the rest and if you are to use any of the others your modifications won't apply. A far stretch might be to say that, if maybe if you create a server that monitors your system for active consoles and intercept their callbacks, you could essentially create a transparent window layer that aggregates your I/O and have it do the MARK, COPY and PASTE for you :/

There are a good many drivers that operate effectively at this frequency. With the addition of a horn you could easily achieve a dB of >120dB @ ~100Watts. If you produce your own amplifier/oscillator circuit you should be able to do this for ~$100 less the cost of tools.

By fundamental definition two sets are equal when the elements are the same. This means that no matter how the sets were achieved if the sets are the same they are equal. I have only come across definitions of numbers that are themselves sets, so no matter how one gets to any given number, which is a set, if two instances of the number are the same then they are equal. Again this is fundamental, I don't see any argument to the contrary as this is an agreement on definition by a general majority(I'm terrible in stating proper arguments.) I would also like to point out that in establishing the addition operator there is more than one addition operator each functions over a different field. The prescribed notation in use is merely an abbreviation of the accepted and rigorous representation of the underlying fundamentals. If you wish to create a history dependent solver notation system it is sufficient to say you wish to do so. If this is the case isn't it sufficient to simply write out the steps and store them as a whole, and wouldn't this in essence be considered the proper notation under these circumstances?