ajb

Perhaps there is still a discrepancy between optical sensitivity and mechanical stability. The detectors were originally built with smaller sensitivity. They were optical upgraded, but mechanically they may not be good enough for very small signals.

Why perhaps?

I mean you have read the literature on this, right? You understand the kind of analysis involved? You do understand how well the signal matches the predictions?

If you really have some evidence that a clear signal from a black hole merger was detected then write a paper.

...but I could not see the picture / apperance which might prove it realistic.

What do you want a picture of?

Anyway, as you are interested in engineering, geometric mechanics with constraints and control theory has been applied to many things including space-craft, underwater craft etc. The methods are also being exploited in economic theory.

You can google more for details.

could you provide pictures of usage.

Pictures? Not really, but you can find textbooks and papers that use these notions.

I meant: for example. I imagined that lightning strikes somewhere between two LIGO-detectors. Maybe they are sensitive enough. There may be other sources, but no earthquake, because the disruption must be of short duration.

I am sure that they took their time in eliminating such things. They kept things quite for a while until the team was happy that they measured something interesting.

For sure, the team did not shout about their results until they were very sure that they measured something real. This took several month. I have no idea if lightning was considered as a possible source, however given two separated detectors and that the signal matches predictions (the classical ring down was observed) I think it is not a plausible source and would be discounted straight away.

Phase spaces in classical mechanics (assuming autonomous) are 6 dimensional - 3 positions and 3 momenta. So classical mechanics and control theory applied to engineering often uses spaces (usually smooth manifolds) of dimension greater than 3.

In physics 4 dimensional manifolds are to be found in relativity theory.

Infinite dimensional spaces are often found in functional analysis as applied to engineering and physics - you already stated Hilbert spaces and quantum mechanics. But other spaces such as Banach and Fréchet spaces also appear.

There are also more general notions of 'spaces' that appear in physics, I am not such if they appear in engineering.

isn't this a bit basic? or ..what its importance?

basic yes, but the point is that we do have binary operations that are not associative.

M ≠ Ø < M , o > provides qualifications below.

 

1) every a,b ϵ M aob ϵ M (closed)

 

2) every a,b ϵ M (aob)oc = ao(boc) (associative)

 

3) e unit element , every a ϵ M eoa = aoe = a

This is the definition of a monoid.

although there exist many many many subjects & titles at algebra , I do not remember we used such sets commonly.

Monoids are not uncommon, but for sure they are less well known that say a group. An example of a monoid are the real numbers with standard multiplication.

I see you are using "Lie Algebra" in your papers

Lie algebras are fundamental in mathematical physics and differential geometry. They are also of great interest from a pure algebra point of view. I would be very suprised if you have not encountered these in your studies - at least just the basics and some simple examples.

what is the usage of this definition : this is "Monoid",but has it importance? )

this set does not provide the last requirement to be group!

Yes, you have defined a monoid. Typically a monoid is a 'group' for which not all the elements have an inverse. So, for the case of the real numbers and muliplication, 0 has no inverse.

Could you give an example for binary operation?

Standard multiplication and addition of real or complex numbers; Group multiplication; vector addition; matrix multiplication... all these are associative.

Non-associative examples include multiplication of octonians and Lie brackets.

Associativity means that you can make sense of a*b*c without having to put in the parenthesis -- that is a*(b*c) = (a*b)*c

is it the same defiition with homomorphism / isomorphism (1-1 ,onto) ?

As long as the domain and range are compatible one can make sense of associativity - so partial binary operations can be associative. For example, when dealing with groupoids where we have a partial multiplication.

He or she has asked for the generic name of binary operations that satisfy f(f(a,b),c) = f(a, f(b,c)). Such binary operations are known as associative binary operations. They can now simply 'google' this for more examples.

I think the word 'function' in the opening post is not correct - rather we have a binary operation.

It is true that composition of functions is associative...

I don't think we are dealing with implicit functions here - the example given in the opening post suggest that we are dealing with binary operations that are associative.

An examples of something that does not satisfy the associative property are Lie algebras.

This is the associative property for a binary operation on a set. For example, standard multiplication of real numbers satisfies this property.

It's not really the done thing these days.

I agree - you can find some older papers with simple hand drawn diagrams (for example Feynman diagrams) and even old papers where the equations are written by hand!

But today with LaTex and simple drawing applications there is little excuse for hand-drawn diagrams.

None of you Satans, who have relied, would pass a standard Reading Comprehension Test.

Insulting the people you wish to engage with is never a good idea.

Anyway, as a science forum - albeit this is the religion section - how could you support the position that we are all Satan and that we are in Hell?

This philosophical/religious point of view seems quite at odds with what the Bible says about the Devil.

So, what is [math]\infty - \infty [/math]?

You are trying to over think this problem...

The function in question is just f(x) = x-x =0 which is defined on the real line. We then want to take the limit as x -> \infty, but as f(x) = constant this limit is just that constant, i.e. zero.

What one has to be more careful with is lim(x) - lim(x) = ? as x -> \infty. This is my point and I think what has confused people.

Yes, 3 is correct - in that n-n =0 and so this limit is 0 - and what others said very early on in this thread.

Why in the world would baldness or hairiness affect whether or not you are confident about yourself?

I think that it can do for many men - why I have no idea.

Anyway, the problem is being over confident in the first place methinks.

A)Could you give such given society's like defined above by Swansont & arete & other scientists and how to aply for CONFERENCE (important)

All scientific and engineering societies sponsor meetings, schools and conferences. You need to think about what you are interested in and find the closest matching event.

B) Do journals accept proposal & trial SCIENTIFIC PROJECTS? (should it be submitted as manuscript or article or review,which one??

Typically no. Some journals may publish methods rather than the scientific conclusions that these methods lead to. People tend not to want to publish proposals anyway - proposals are for the funding people and not journals. That said, it maybe possible to publish some plans for possible future experiments and so on. I don't think what you are talking about really fits that bill.

C) will I have to pay for presentation ,accomodation , tickets for journey?

Typically meetings have fees, you pay for accommodation and travel - or in reality one's grant does that. For students and young researchers there maybe reduced rates and even direct help with some or all of the costs. You should ask the organisers about this.

D) what will happen at the end about assessment ,and whom will assess,will they be scientists(academciian)?? (this will be scientific project) (this last two question are about CONFERENCE))

Assess what exactly?

If the meeting has agreed to publish a proceedings, then usually these are peer-reviewed, but check this carefully for the individual meetings in question.

That is the application I am talking about - I have never used it before. It does not look anything like as advanced as Mathematica, but I expect it will do some donkey work with solving algebraic and differential equations, linear algebra and basic plotting.

ajb ,if you think my expressions was impolite

Not at all... anyway we all feel like shouting at editors and referees. This is normal, but don't do it lol!

I have just installed Maxima on my laptop running Ubuntu. I will have a play with it over the coming weeks.

I was wondering of anyone else here has used Maxima? Are there any annoying features, bugs or other problems you would like to share? Is there anything you particularly like about the system? (The price is one great feature!)

You should not read too much into letters of this kind from editors - just move on and submit to another journal, that is what we usually do. Once I bothered to send an email back saying that one of the editorial reviewers was wrong, just for my own sanity. Of course, that did nothing to change the mind of the editorial team. It sucks, but you get over it and get on with the job.

Anyway... the problem here is that one should avoid trying to think of [math]\infty - \infty = \: ?[/math] Remember that infinity is not a real number and so one has to be very careful here and try to make sense of such thing using limits. Well, for the case at hand there is no real trouble as others have pointed out, x-x =0 and the limit of this as x gets large is clearly zero.