studiot

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.

Thank you. +1

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.

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.

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.

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

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"

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 ?

Thanks for your support for my colourful language, by supplying formally correct terminology. +1

The only General I can think of as a result of your post is General Stanley.

In another thread I have just written Is there anything wrong with this belief ? In true scientific manner I am quite prepared to be shown to be wrong about my belief.

All this seems now to be going well beyond the original posted question, which I believe I have answered within the specified number systems (which do not go as far a C). I will leave you in wtf's capable pen hand to discuss rarified algebraic theory and vocabulary.

You seem to have missed the point of my post. This was that the electrostatic energies of an electron in an atom are many orders of magnitude greater than the gravitational energies. So the electrostatic energies (which are quantised) dominate.

Here is what is inside the front cover of a typical computer book. I assume since you have your book you can find something similar. It not only details the rights and restrictions for the reader, but also acknowledges where the authors used software to generate example pages for the book and example screens from real life.

This is the last thing you should do. Wiley or its subsidiaries are under no obligation to reply to you. Period. You, however, owe the actual copyright holder a duty of diligence to respect that copyright. Copyright arises automatically at the moment of creation of the work. There is no requirement on the creator to announce his or her copyright. If they chooose to do so or hand it to a publisher or other person they may do so. Wiley will certainly have stated the rules of use or restriction on the copyright at the very beginning of the book. However with textbooks that state their aim is to tell you how do do something, their is implied tranfer of enough copyright to perform whatever they tell you. So in a maths book if they said "to add 3027 to 5144 place one above the other and draw a line under the stack. Then add each vertical pair of digits, with carries, starting from the right hand side to form the sum placed under the line," you would be OK to do this as often as you wish. The same if they showed you how to code a macro in Word or use the command line editor. If however the author states in the preface something like "there are new results, never before published" you should at the very least write to them explaing your interest and offering to include an acknowledgement as the originator. Remember you can't copyright an actual idea, only a specific presentation of it.

All of this categorisation goes a lot further into pure maths than I normally like to. But I know you work more on the pure side. Here are two pages from one of my most worn books, I cannot recommend it highly enough. I have made the scans largr than usual becasue they have packed a lot of text into each page. Not only does it provide definitions, but it provides cross references to associated or contrasting terminology to help the reader avoid mixing them up. So see what it has to say about both ideals and rings. Collins Reference Dictionary of Mathematics E J Borowski and J M Borwein

Yes there is a great deal more to algebra than is taught in school, indeed there is more than one 'algebra'. As regards number systems, N and Z do not form algebraic fields N fails for additive inverses and Z fails for multiplicative inverses. Q constitutes a field, that does not contain any irrational or transcental numbers. Since Q is closed under both the binary operations of multiplication and addition, it is impossible to find a sequence of operations that will lead to an irrational or trancendental number. R contains all real numbers, including all the irrational and trancendental ones. It is, of course, a field. As such it also contains (all numbers of the form a + b√2), which therefore correspond to a single number in R The point that Joigus was moving towards is that these 'compound numbers' is that they form a subfield of R wtf is quite correct that the name for this is an extension field. There are many extension fields. Hope this helps clear things up.

You seem to be talking about curve fitting. This is a very important subject in Numerical Methods and Finite Element Analysis. First, taking your example, The points are called collocating point (Which is the technical term for co locating). The approximating function matches the desired function at the given points. However there is, in general, an infinite count of such approximating functions. Let us say we have a third degree approximating polynomial ax3 + bx2 + cx +d Then we can can form a maximum of 4 different simulataneous equations with four points to obtain the coefficients a, b c and d. But conditions may also be supplied in the form of derivatives at specific points. Also I have only mentioned polynomials. Other combinations of elementary functions may be more appropriate. More complicated functions such as Bessel functions may only be approximated in this way. There are no combinations of elementary functions to determine them.

Try Aspargtocin What do you want it for https://pubchem.ncbi.nlm.nih.gov/compound/101920666

How would you provide inputs to this program ? The last time I did this was a vibration analysis of an aero engine and propellor system. Here I digitally recorded the noise generated by the system in a suitable file format for input to a digital spectrum analyser (not an oscilloscope as iNow suggests) and ran it through the spectrum analyser to produce a digital output file both displayable on a computer screen and printable. But you would need to understand the advanced mathematics to make any use of such a system. Tip - a bit of searching will find some freeware spectrum analyser programs you can play with before spending any money.

+1

Do you sit on a 3-legged stool or a 4-legged stool ? They are different so in some circumstances they cannot do the same job. But most of the time the differences don't matter. Does that make them incompatible or 'in conflict' The same can be said of gravity and quantum theory. Which is, at least in part, the difference between continuity and granularity or continuous v discrete systems. We do not know if, at the smallest distances , reality becomes granular or remains continuous, this is still a subject of scientific investigation and debate. Like the stools, the differences between continuous gravity and granular quantisation are unimportant at the atomic scale since the electric forces that hold the atom together are many thousands of times larger than gravitational ones. So the electron keeps 'going round the nucleus' despite any small bumps in the road, just as you keep going on your bicycle, despite small bumps in your road. Does this help ?

I'm glad you have done the right thing and started a new thread instead of pursuing off topic additional thoughts in one of your many existing ones. +1 for encouragement. It is actually very difficult to come up with a satisfactory definition of 'random' , deterministic , causal I don't know if the question in your OP is in your own words or if you have quoted some source you haven't acknowledged. Anyway I have a couple of comments. Firstly casual (the word in the OP title question) and causal are different words with different meanings. Secondly the statement fails to properly distinguish between variables and a single result or outcome. Doing this is important. Now 'random' is an adjective that is meaningless by itself. Your quote applies it to three different nouns (all important in statistical theory) to create mathematically specific instances of the nouns variable, experiment and result. It should also equate outcome with result. Also hidden in the above quote is the distinction between singular and plural. Which introduces another very important concept - probability. Strangely enough you need the idea of limits we started to explore in you unfinished calculus thread. You do not need the whole apparatus of calculus however. Otherwise we are stuck with imprecise statements such as ' a very large number of.....' , without having any idea how large is large enough. OK so he is a definition of 'random' due to Kolmogorov. A result is random is it cannot be obtained by any process that is shorter than the statement of the result itself. so '5' , by itself, is a random number since it is shorter than say (3+2) If you wish to follow this through and understand what how this all fits together you will have to stay focused.

Here is a statement that is so far out it falls into that category of not even wrong. I suggest you learn some very basic Physics before you start playing with electronic components. Is there such I thing as a 32.768 crystal ? I have not heard of one. @Sensei has gone a long way to try to offer some sense +1

So you thought that the rules of both politeness and this forum don't apply to you ? A response typical of those ignorant of the subject they are espousing.