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Everything posted by studiot

  1. I'm sorry I can't make head nor tail of what you want to say here. Google doesn't produce anything relevent for specifically defined functions. https://www.google.co.uk/search?source=hp&ei=Y3CYX5qXH8ubjLsPnfG3yAI&q=+"specifically+defined+functions"+&oq=+"specifically+defined+functions"+&gs_lcp=CgZwc3ktYWIQA1DaDljaDmDkGGgAcAB4AIAB7gGIAe4BkgEDMi0xmAEAoAECoAEBqgEHZ3dzLXdpeg&sclient=psy-ab&ved=0ahUKEwja1KnHvNXsAhXLDWMBHZ34DSkQ4dUDCAg&uact=5 You seem to be talking about restricting the domain a function. Please re-organise your thoughts in your own language and have another go at saying what you mean in English. Do you realise that there are functions that cannot be written in terms of 'elementary' functions? Functions such as elliptic integrals.
  2. I don't know if you like Science Fiction, but the novel by Poul Anderson might cheer you up . It has a positive ending or recycling. Tau Zero.
  3. Yes indeed +1 Have you not heard of Einstein, Cavendish, Wordsworth, even Napoleon made a contribution to Mathematics. Whilst in more recent times most people involved in Science gained their livelyhood from it, in the past a significant majority did not. Some were of independent means (Cavendish), some had other jobs (Einstein) , some had other callings (Wordsworth) , some were elite supported by slaves (ancient Greeks) and so on.
  4. So I have finally conquered the MathML here for tables. Here are the Cayley Tables I referred to earlier. [math]\begin{array}{*{20}{c}} + & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 1 \\ \end{array}[/math] So the rules are 0 + 0 = 0 0 + 1 = 1 + 0 = 1 1 + 1 = 1 These demonstrate the commutative and additive inverse requirements for both 1 and 0. [math]\begin{array}{*{20}{c}} X & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 0 & 1 \\ \end{array}[/math] 0 X 0 = 0 0 X1 = 1 X 0 = 0 1 X 1 = 1 These demonstrate the commutative requirements for 1 and 0 and multiplicative inverse requiremtnts for 1 0 is not required to have a multiplicative inverse.
  5. studiot

    MathML test

    Trying to post a Cayley table [math]\begin{array}{*{20}{c}} + & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 1 \\ \end{array}[/math] [math]\begin{array} + & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 1 \\ \end{array}[/math] [math]\begin{array}{*{20}{c}} + & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 1 \\ \end{array}[/math]
  6. Sometimes in English it is even worse since you need the pronunciation to understand the meaning. What do you think this means? I had a row with my boss at lunchtime.
  7. Now that this thread has reached the wonderful anecdotal climax, many thanks I love it +1, surely the thread can be closed as a repeat of earlier nonsense.
  8. studiot


    I can see my table in the list in the activity tab, but I can't see it in the thread itself. This is even after refreshing the thread in the normal manner for MathML. [math]\begin{array}{*{20}{c}} + & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 1 \\ \end{array}[/math] [math]\left( {\begin{array}{*{20}{c}} + & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 1 \\ \end{array}} \right)[/math] [math]\begin{array} + & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 1 \\ \end{array}[/math] [math]\left( {\begin{array} + & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 1 \\ \end{array}} \right)[/math]
  9. An excellent observation +1. There is one mitigating factor to this however. Submarines are not subject to such severe weight constraints as aircraft so the addition of the necessary strengthening bulkheads is far easier.
  10. studiot


    [math]\begin{array} + & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 1 \\\end{array}[/math]
  11. Read Here https://en.wikipedia.org/wiki/GF(2)
  12. I agree that the OP proposition does not constitute a field, since it does not contain the required inverses. However the smallest field contains just two elements, along with appropriate rules for addition and multiplication. An example would be {1, 0} with a De Morgan/Cayley table.
  13. Thank you for sharing your experiences. We are seeing the resurgence partly because too many folks are not taking it seriously enough. Also partly because too many prominent folks are setting bad examples.
  14. I would suggest to try to concentrate on the here and now. The philosophy of living for the moment (also called mindfullness apparently : ref google). This technique has helped many people.
  15. Here is a quote from the UK Technical Manual of siphonc drainage. Perhaps not all non UK companies do not bear this in mind. http://www.siphonic-roof-drainage.co.uk/images/SRDA_An_introduction_to_siphonic_drainage_Nov2014_lowres.pdf In general such systems must be designed from the outset of the building, especially as 'siphonic' drainage can only work on a flooded roof.
  16. Hopefully I will not be called upon to criticise/analyse these sketches. Where did they come from ? You have repeatedly mentioned siphonic action. I see no siphonic action in those diagrams. Here is Wikipedia on the subject. Please note what they say. I did wonder why the screw drawing carried the screw all the way down the pipe. Surely it would be enough to have a short section of helix to induce the vortex, perhaps combined with an entry baffle. Although entry baffles would surely have been fitted anyway; debris protection is not restricted to 'siphonic' systems of any pedigree. I also wondered if it would be cheaper to simply insert new smaller pipes if the existing ones were hydraulically oversize. After all formed helices don't come cheap.
  17. If you weren't so know-it-all, holier-than-thou rude about this then we could perhaps have a more dignified conversation about a statement you made but falsely attributed to me. When you introduced the unbroken column of water in the pipe I take this to mean that the pipe is full to the brim with water. Therefore there is simply no space left for air, vacuum or anything else. I even talked about a plug of water (as being a continuous segment of the pipe full bore with water) which drops down the pipe. We do not know the pressure conditions below such a plug. If the pipe connects directly to further pipework below then the pressure will be increased, not reduced. If there is a vent then air can escape and this will have a slightly lower standing pressure as that air now has velocity. If there is a long drop then the usual situation is that the air and water become partially mixed and a gurgling of water/air mixture comes out at the bottom. But I repeat that we do not know the conditions of discharge. Equally we do not know the conditions of entry. Water leaving (the bottom or actually any point) of a reservoir of liquid forms various pressure patterns/ regimes depending upon the approach shape of the entry region to the exit. A pipe, for instance, stuck up into the fluid in the reservoir will induce an entirely different exit flow regime from one flush with or even tapered to the walls or floor. There are even tables of coefficients for sharp edged transitions v gradual transitions between pipe and wall/floor. So when I said that you did not provide full details of your barrels I only told you what any fluid mech engineer would have told you. In fact I provided a wide ranging chart for a whole range of different entry conditions at your pipe. Your question was rather like my brother asking me for directions to Newport, without even telling me which continent he was sailing for.
  18. Yes the devil is in the detail. Sorry there was not more of it. +1 I stopped posting in this thread because of the long absence of psyclones and the personal turn of your conversation in respect of matters of which you have no knowledge. FYI I am currently developing (elsewhere) an mathematical model of flow in a similar situation, that of the drip rate of medical giving sets. This is about a pipe stuck into a bag (not a barrel) of fluid and how to achieve a predetermined rate of flow. So yes, I do understand the fluid mechanics of the situation.
  19. Depends what you mean. I have already noted that Z is not a field, but Q is. One problem I find is that so many English words have a specialized meaning in some part of Maths it is difficult know whcih is meant and how to find a substitute when you wnat the general English meaning. Category is just such a word. https://en.wikipedia.org/wiki/Category_theory
  20. The thing about scientists is that they try to (or should try to) include the conditions of applicability in their statements. I did just this when I said A few simpler examples of this are phrases such as "A light inextensible string" "A frictionless pulley" "An incompressible fluid" "If I pour a kettle of boiling water into the ocean it makes no difference to the temperature of the ocean since the energy added is insignificant compared to the heat content of the ocean"
  21. Yes, I anticipated you would think along such lines. You refer to some Popcul thing? Does G & S mean nothing to someone with your handle ?
  22. Thanks for your support for my colourful language, by supplying formally correct terminology. +1
  23. The only General I can think of as a result of your post is General Stanley.
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