Danijel Gorupec

I need to present rounded numbers in my software. For example, after calculating "sqrt(2)", the software could display the result as: "1.414" (it only shows the result to a 'reasonable' precision). How to mark this number as a round-off number? Is there a standard notation in mathematics? From the displayed value it should be immediately visible if the result is rounded or exact. For example, consider the following two cases: 1/8 = 0.125 (the exact value) sqrt(2) = 1.414 (rounded value) If there is no standard way to somehow mark numbers that are rounded, I was thinking to put a dash under (or over) the last digit. Or maybe printing out the last digit in a pale color. What do you think?

This seems logical for non-painted steel... However, if rust is sealed with paint, this effect shuld be much smaller (limited by paint permeability). But it seems that sealing rust with paint does not slow the rusting process.

Hi, How does paint protect steel from rusting? I was thinking that the paint cover physically prevents water from contacting steel. Hovewer, I noticed (on my car, unfortunately) paint bubles indicating rust below them. But the paint cover is still undamaged and I don't know how can rust form below seemingly healthy paint. Could be that paint is not the perfect cover. Probably not. It is only slowing down the rusting process... What confuses me is that painted steel can do good for years (without rust signs), but once it starts rusting it seems that the paint doesn't slow the process any more. Why?

Sure, this is a WYSIWYG editor. Basically you have document area (representing a paper sheet) where you can write your equations. It acts as electronical math notepad.

To edit equations, you can use either mouse or keyboard. I recommand keyboard because, after some time, you will be more efficient..... Just mouse-click anywhere at the document area and the blue blinking cursor will appear. Few quick tips: - use ALT+number as a quick method to add simple exponents (use the ^ for more general exponents) - use the underline '_' to add indexes - use double slash '//' to insert fraction sign - you can use some commands to enter special symbols (similar to LaTeX) like: \sin, \cos, \sqrt, \sum, \int... (hit the space bare after the command to execute it) - use ALT+letter as a quick method to enter greek symbols (another way are commands like: \alpha, \beta...) You can hit F1 for quick help, or download the User's manual from the homepage: http://gorupec.award...m/mathomir.html The Math-o-mir is quite powerful software - LaTeX generator is only the latest addition. Good luck.

Hi all, I added LaTeX export functionality to this windows freeware I am developing. Maybe someone here will find it useful (someone lazy enough to learn LaTeX, but eager enough to learn new GUI). Basically, after you type it in, you select your equation (or just touch it with mouse pointer) and press the F6 to generate LaTeX code. The code is automatically copied into windows clipboard and you are free to paste it anywhere you want. The new beta can be downloaded from here: http://www.datafileh...d-6cea854a.html (515k .zip file containing Mathomir.exe file and an example document. Scanned for viruses.) The setup procedure is not included in this beta - just bare .exe that you can run. Of course, any bug report will be helpful. I can repay you by signing your name into the about box of the next version.

test - software generated code [math]x _{1 ,2 }=\frac{-b \pm \sqrt{{b }^{2 }-4 a c }}{2 a }[/math] test - software generated code [math]\sum _{n =1 }^{x }\frac{x }{n }\sin \frac{2 \pi x }{4 n } \, \; +\, \Gamma ^{2 } \left( g \right) \, +\beta ^{*}+{x _{a }}^{4 }+\, \mathrm{f' } \left( x \right) \, +\sin _{tot }z _{i } \, +1.1 [/math] [math]\sin ^{2 } x \, +\, \mathrm{total } ^{2 } \left( G \right) \, +{\left\{ \begin{array}{c}X _{1 }\\ \vdots \\X _{n }\end{array} \right\} }[/math]

two equations test: [math]\begin{array}{l}a \cdot b \\ a+b \end{array}[/math] (PN: bad. Had to do it as array)

(I am testing latex, but no porn here) test1... [math]a[/math] test2... [math]{a}[/math] test3... [math]123a[/math] test4... [math]123.45\cdot a[/math] test5... [math]123.45\cdota[/math] test 6... [math]123,45a[/math] test7... [math]abc[/math] test8... [math]a \cdot b \cdot c[/math] test9... [math]a_b[/math] test10... [math]{a}_{b}[/math] test11... [math]a_{b}^{c}[/math] test12... [math]{abc}_{d ef}[/math] test 13... [math]a b /c[/math] (PN: not enoguh space between variables 'a' and 'b') test14... [math]a _{b }+3.1 \cdot {10 }^{-12}[/math] (PN: minus sign is a bit too long and exponent should be placed a bit higher) test15... [math]3 \frac{x }{y }[/math] (PN: too much space between fraction line and numerator/denominator) test16... [math]2 \sin x \cos y[/math] test17... [math]2 \, \mathrm{sin }\, x \, \mathrm{cos } \, y[/math] (PN: I had to add \, space to make this look nice) test 18.. [math]a \bar{b }c[/math] test 19... [math]x \mathbf{y }z[/math] test20... [math]a b \mathtt{c }\delta \mathcal{Y } [/math] (PN: \mathcal{} works with uppercase letters only) matrix test1... [math]\left[ \begin{array}{ccc}s & b & c \\ x & y &z \\ a & & \end{array} \right][/math] limes test1... [math]\lim _{x \rightarrow \infty }\left( x +1 \right)[/math] underline/overline test.... [math]\underline{a b}\overline{c d}[/math] sqrt test... [math]\sqrt{x }\sqrt[3 ]{y }[/math] 'd' test... [math]d x[/math] (PN: what about partial derivation sign??)

Sure. A good engineer is, first of all, a practical person. Second, he/she excels in art of guessing (estimating) thus is able to make things in fewer number of tries -> he/she can guess how to simplfy a problem without chaning it too much. World's top engineer is probably an unknown person (except if the question is about top-paid engineer). If you only consider famous historical persons, great science experimentalist are good candidates (M. Farady for example).

On the Wikipedia there is an article http://en.wikipedia.org/wiki/Power-to-weight_ratio Acording to this article , there are electric motors that are comparable to IC (some of them used in hybrid vehicles). It seems that an ordinary motor has low power-to-weight ratio because 'nobody' cares about its weight (price is more important). Obviously, there is a room for power-to-weight ratio improvement if you are ready to sacrifise price or reliability. Still, as Swansont partially said, electric motors need strong magnetic flux, and so (without using superconductivity) must contain bulk of ferromagnetic material - iron. Unfortunately, iron is heavy and electric motors cannot easily compete to IC engines.

Hmm... I cannot give you math equations. It is simply that I feel (guess) that you are overly optimistic regarding 'wind and solar' energy sources. I think that we will need something in addition (nuclear fusion is a candidate). What I know is that harvesting non-concetrated energy is always more expensive than harvesting energy from more concentrated source. Therefore, I expect that wind and solar energy will always be more expensive than nuclear energy (mass production may decrease this difference, but I don't think it can annulate it). Here on west (I am actually in eastern Europe) expensive energy might seem like reasonable price to pay, but what about Africa? Of course, I don't think that fusion can be comercially ready within a decade. 25 years, maybe. However, the possibility that once we will posses as cheap and as powerful energy source as the nuclear fusion is appealing.... I see that humanity is aggresive and energy-hungry. And if we limit ourselves to wind and solar only, we will have to recede a little. At the moment, I think we can only choose from wind, solar, biomass, geothermal and/or nuclear. And only the last one seems plenty enough to sustain our current 'way of life'. (Note that I don't promote it and I would actually like more modest society.) I am talking about 10-20 fold energy consumption increase in next 100 years. (I also think that nuclear fusion will prove much greater benefit to humanity than the Appolo program, therefore we can spend 10 times as much. Only if we decide that this is the way we want/need to go.)

Absolutely enormous, yes... But solvable. I feel that decision to go for it would not be entirely unreasonable, even at this moment. What is needed is another "We choose to go to the Moon" type of speech (possibly on Chinese?). I feel that technology leap would not be any greater than it was for the appolo project.

You are right on this one... I had no idea that output power grew that large. Amazing. Of course, nuclear power plant is also scalable.... The difference between wind and nuclear is that with wind we will have to live 'inside' the power plant (towers will be all around us). While with nuclear, we will isolate the plant outside our everyday living space. Both solutions are possible, I beleive.

Well, I suppose that it depends how we define 'green'. I think that 15TW must produce some footprint on the environment (wind towers visible all over the landscape, solar cells covering the land, road network to many power plants...) I agree that this footprint is going to be tolerable and manageable. But I don't think that it will be any smaller than if we decided to use nuclear energy instead. I personally hope that we will develop both technologies and use them wisely. (btw, I don't think that a 2.5MW wind turbine is 'ordinary one' - sure, it will probably become ordinary in near future. Also, we will have to install more than 15TW (maybe 50TW) to cope with unreliable energy source - the wind. Third, not all land is equally suitable for wind turbines or solar cells and you will have to have some concentration that will increase footprint locally.)

Breeder reactors are not that fuel limited (http://en.wikipedia.org/wiki/Breeder_reactor or http://charming.awardspace.com/plutonium/plutonium.html). As far as I know, there are no comercial breeder reactors today (experimental only). Fusion reactors are not limited in fuel, but are future technology. Posibly not that far future (http://en.wikipedia.org/wiki/ITER). Note that first version of fusion reactors will use fuel that is somewhat limited, but some advanced future version might use pure hydrogen. And we have plenty of hydrogen. I don't think that you can produce 15TW from any source and call it green. Collecting and concentrating that much energy will certainly have much impact on environment. Todays green energy sources are only green because are marginally used. Therefore, I think, only real green technologies are ones that reduce our energy needs (either from reducing intrinsic consumption or from increasing efficiency).

I also think that batteries will be used in cars. Batteries seem more likely to become individual energy-storage devices than fuel cells with hydrogen tanks. But, to store energy on large scale, it might happen that power companies will use large hydrogen tanks and fuel cells. Today we mostly use pumped-storage hydroelctricity for that purpose. However, in future we will produce more and more energy from 'unreliable' sources (wind, solar) and our need to temporary store energy will much increase - hydrogen could be one solution. After that, the whole new hydrogen-based industry and technology may follow.

I think, no. Energy is not consumed by direction changing. (Of course, such engine will have greater vibrations, and will also have to be heavier/ more robust - therefore probably less efficient, but only indirectly).

Hmm... I am not sure what exactly you are considering the real transformer (or ideal transformer), but... Your equation Ns Is = Np Ip cannot be generally true. Imagine a transformer that has its primary connected to AC voltage source while secondary is open. The primary current will be non-zero, while secondary current will be zero. Your equation will be very wrong. (Note that in this example the primary current is in near 90 degree phase difference to primary voltage and therefore no real power is used by the transformer.) Your equation will be very close to true if the transformer is used as current transformer: Its primary winding is excited by AC current (not AC voltage), while secondary winding is almost short-circuited (that is, AC voltage over the secondary winding is near zero). (Because of secondary current, the short-circuited secondary winding will create flux on its own. This flux will exactly opposite the flux created by primary winding. As flux created by any windings is proportional to I and N, there is your equation.... Why the secondary winding wants to exactly oppose the primary flux? The secondary winding just don't like flux changes - any flux change would create EMF (voltage) and this voltage instantly increases current until the flux change is exactly opposed. Because it is short-circuited, there is nothing else to 'absorb' the EMF.)

I am sorry but I can't understand if you are joking or are just serious... I can see many bad things that happen from stopping and starting the piston in piston engine, but efficiency loss is not one of them. At least not directly. ... About the Mazda Renesis engine... A very narrow consumer group is interested in Wankel, and I think this is where Mazda is aiming. These consumers prefer 'something different' more than pure logic. Mazda Renesis runs at high revs, has specific sound and has specific power/torque curve - this can also be appealing to some people. Marketing could also be reason why Mazda is still offering Wankel engine... In addition, Mazda is the only producer of (useful) Wankel engines in the world and they are probably too proud to end production.

I would like to encrypt exam results for several minutes with public key provided by teacher, so that no student can see results of any other studend while working on the exam.... This feature is not essential for my software, therefore I don't like to bloat the software (neither spend much time for development) by including variable-length-integer-math into it. I can afford to store few hunderds of short public keys into the exam file as a quick solution. If this is nearly enough and makes any sense (I am affraid not - I have no experience on this matter). (The idea is that teacher creates an exam and saves the exam file. While saving the exam file he will have to provide a password. From this password, public keys will be derived and stored into the exam file. Any student can then open the exam file, but after finishing the exam, the software will automatally and inevitably save the file encrypted with the public key. Nobody else, except the teacher that knows the password, will be able to open it.... It seems that Windows CryptoAPI doesn't want to derive asymmetric keys from password (?? Windows can only generate random asymmetric keys??).... To achieve this I am actually using Diffie-Hellman algorithm, not RSA, but I understand that key-sizes are about the same. I asked about RSA, because nobody talks about Diffie-Hellman much.) Yes, I combine (in hopefully smart way) many short keys into single key that is then used for encryption.

Hi, For memory restrictions, I cannot fit RSA key generation algorithm that would generate keys longer than 32 bit. This seems too short even for my application (data only needs to remain secure for 15-20 minutes). The question is: how many 32 bit RSA keys I have to be generate in order to achieve security of single 256 bit RSA key? (BTW, what do you think, how long can a 32-bit RSA key hold when attacked using an average PC? Second? Minute?). Thanks.

I'll be damned, but I simply like your theory! Thumbs up! I read your original post and instantly fall in love with the theory. It is much more exciting than the boring science. (I especially like the idea the tiny Mars will soon inflate to the Jupiter size. Amazing.) Count me in, you have one (rather frivolous) follower.

Michel, I was actually joking because (I felt) this thread went too odd... I have no idea how this artist realy make his stuff (but I like it).

I would agree to 'pile of hot coals' analogy. If you pile uranium up, smaller number of neutrons will skip away and more neutrons will remain for chain reaction (analogly, if you pile coal up, smaller amount of heat will radiate away and more heat will remain for burning). I cannot agree to 'graphite to water' analogy (however, I would agree to 'control-rod to water' analogy). Graphite is used as a moderator and it will assist to chain reaction (it slows down neutrons -> only slow neutrons can break atoms).