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Generally, when we talk about moment of inertia, we talk about rotation and inherently, we talk about moment of inertia about an axis. But when we talk about inertia tensor, we calculate about a point. Is there a reason for this difference? Am I missing something? I am new to tensors.

Flux through sphere Homework Statement Given \vec{F}=\frac{\vec{r}}{r^2} and unit sphere, find the flux through the surface of the cube. Homework Equations Surface Integral of F dS=volume integral of Div. F d^3r The Attempt at a Solution After the above formula, I do not have...

So, what exactly is it when people refer to "density" or similar notions when they discuss about Riemann Stieltjes integral. Is it how how fast alpha(x_i) grows? in the interval?

Hi all, Homework Statement Is the difference between riemann stieltjes integral and riemann integral that in riemann integral, the intervals are of equal length and in riemann stieltjes, the partitions are defined by the integrator function? If not so what exactly is it that integrator...

Suppose I rearrange the equations, then P=700-0.125QD [which is fine without reflection and same as QD=5600-QD] But, next P=0.25QS-125 but the graph is for 0.25QS+125. Note the + and _ after QS. It works with reflection. but not normally. Is there a certain convention. I mean am I always...

Hi everyone, I am having hardtime understanding this problem. I have two functions: QD = 5600 – 8P QS = 500 + 4P Why is the graph like the one attached and not the normal mathematical graph where supply curve starts from y=(0,-125)? Do ignore the consumer surplus and producer surplus part. That...

Thank you. That was somehow helpful. It is defined over the set of rational numbers for the relation you specified. Yes, I do not understand much and I find my notes/textbook insufficient. I searched online for some explanations, examples and did not find much information there. Still, thank You.

Homework Statement A solution to a problem has following operation: here, [(a,b)] and [(m,n)] are two equivalence classes. [(a,b)]+[(m,n)]=[(an+bm,bn)] Is not [(a,b)]+[(m,n)]=[(a+m,b+n)]? Can anyone explain it to me? Homework Equations The Attempt at a Solution

Hi Dick, Thank you for your suggestion. I am sorry for not including some point. I am actually looking for algebraic proof. Thank You.

My goal actually is simpler. I have to prove (\stackrel{2n}{k})=\Sigma^{k}_{l=0}(\stackrel{n}{l})(\stackrel{n}{k-l}) I can't properly use latex but hope you can understand it. I wanted to follow the above pattern to prove it, but if there is a simpler method, that would be helpful...

Thank You. That was very very helpful.

:smile: Thank You.

Homework Statement I need to derive the prarametric equation of a certain torus. defined by a unit circle on xz plane with center (a,0) and revolving about z-axis. Homework Equations * I don't know if this is relevant but here is something from wikipedia. Surfaces of revolution give another...

Hi All, Homework Statement This is algebraic proof of Vandermonde's identity: I am having some problem understanding how we reached the second last step and more importantly, last steps from revious steps. src::proofwiki.org I would be grateful if someone would elaborate it clearly...

Thank you.

Homework Statement Do all the preimages on X need to have a (and of course I know only one but) image in Y for the f:x->y to be injective? IS THE FOLLOWING FUNCTION INJECTIVE SINCE ONE ELEMENT OF FIRST DOES NOT HAVE ANY IMAGE Homework Equations The Attempt at a Solution Thank You.

the ordered pairs are equal means that we can write y=y' and x=x' which in tern mean that (x,y)=(x',y') Is this fine. Thank You.

Hi all, Q. A function takes (x,y) and gives (y,x). Is this function injective? For any function to be injective, f(x,y)=f(x',y')=>(x,y)=(x',y'). But here, I get, (y,x)=(y',x') How can I show the function is injective? It appears to be one. Thank You.

Hi Everyone, What are the difference between totally and partially ordered sets? Any examples would help except the fact that one holds reflexivity and another totality. Clarification of this would also be fine. Thank You

Thank You.

I am talking abou this proof: Thank You.

Hi all, This is a beginning step in proving aXb=|a||b|sin(theta) thank you

I was suggested not to use vector projections that are in trigonometric forms. As for the y||=(x.y/x^2).x form, I know that what I can do is find y||=(y.kx/(kx)^2).kx [sorry, k is not bold here] and yperp.=y-xk., I have no idea hence forth.

Homework Statement Let x,y is in Vn, such that x is not equal to zero. Show that you can find vectors y┴ and y// is in Vn such that y=y┴ + y// and y// is parallel to x and y┴ is perpendicular to x. Homework Equations x//y => x=ky x.y=0 if x┴y The Attempt at a Solution I calculated...

Homework Statement Q. Define an order relation (x,y)<(j,k) if and only if x+k<y+j Homework Equations x<y means x+a=y and viceversa The Attempt at a Solution I have no idea. To show it is equivalence relation, I simply show that it is reflexive, transitive and symmetric. but how do I...

Thank You.

Verbal Part: We know that for any value of an integer, we can find two integers such that the smallest of those two integers is the first integer. i.e. for every integer n we can write integers n and n+a where, a>=0. which gives min{n,n+a}=n. Specific example would be for n=100, we can write...

Yes, definitely I mean for any integer, that's possible unless n=infinity which I believe does not belong to Z. So, does verbal proof suffice? Thank You. :-)

Sorry, that I forgot the first part. It is defined for all f:ZXZ gives z. So c0 domain is set of all integers. I am supposed to prove it not just explain. Thank You.

And, is the following the right way to show that the function is surjective? f(x)=y, x=f^-1(y) f(f^-1(y))=x Is this why it is called right invertible?

Homework Statement Is the minimum function defined by f(a,b)=min{a,b} surjective or injective? Homework Equations a function is injective f(x)=f(y) always implies x=y. a function is surjective if for every y in codomain, there exists an x in domain such that f(x)=y. The Attempt at...

Someone said zE[x] and zE[y] cannot imply [x]=[y]. It is indeed true if equivalent relation does not exist. What happens when the equivalence relation x~y does exist as in above example. So, is the first part of proof correct in the light of this comment? I am totally new and just had one/two...

is it better now? To Prove [x]=[y] iff x~y Here, First we take x~y and prove [x]=[y]. Then we take x is not ~y but [x]=[y] and arrive at x~y. Firstly, For any element zEX and zE[x] we know there exists a relation z~x Sincem z~x and x~y, we can write from law of transitivity, z~y which...

I got it. I have to prove if a=>b and then if b=>a. Is first part correct then?

Here is my solution, From the definition of equivalence class, we suppose any z such that, [x]={z\inXlx~z} holds. - - - - - - - - - - - - - - - - -(i) for every such z, since, x~y and x~z=z~x [property of symmetry] we write from law of transitivity, z~y exists. Thus, we can now...

I will try it now. Thank You. dpa

Yes, that is it. Still, I have no idea how to prove equivalent classes as equal.

Hi voko, I did not understand that either. That is the exact statement in the Homework question. I assumed it simply meant x=y. Can you help me if it is x=y? Thank You.

Equivalence Principle: A hint on how to start! Hi, I have no idea where to start. 1. Statement Problem Let X be a non empty set with a equivalence relation ~ on it. Prove that for all x,y\inX, [x]=[y] if and only if x~y. Homework Equations For the Equivalence Relation to exist, it...

Hi Windowmaker, So do you suggest I take courses like Real Analysis and Topology in addition to my major if I want to go to graduate school to study economics? Thank you.

Thank you all. I really appreciate your comments.

Hi all, I am majoring in electrical engineering as an undergrad student and minoring in economics. I want to go to graduate school to study economics. During my undergrads shall I write papers/do research in economics or will that in engineering be fine too considering graduate admissions in...

is bumping a bad ettiquette?

Hi all. This is strange question. Is publication of poetry during UGRADs helpful or will it hurt if I mention it while applying to graduate school in engineering, especially in extremely competitive programs like MIT? Thank You.

Hi all, I have a little out of track question and I was forced to consider this after reading FQXI Essay competition title Is Reality Digital or Analogue and Kant's Critique of Pure reason simultaneously. If I am not wrong, according to Kant, there are limits of pure reason. Is not the...

Hi all, :shy: I have a bit out of track question and may be this shall go to philosophy section. On one hand, I often see posts where some amateur/non physicist posts some speculative idea or hypothesis. Others go onto argue or suggest not to merely speculate and argue like I read...

I definitely don't know much but then just like wavelength of any object's wave from wave particle duality decrease with increase in mass, can we not conclude that degree of other quantum mechanical phenomena shown decreases in similar fashion? And hence no clear demarkation exists.

Well, First there arose a interesting question of how entropy increases when particles due to gravitation form huge mass. I guess i read john baez's online page. Heat/energy so forth concept was applied to explain it. Then, Taking its reverse, does not receeding of galaxies then decrease...

quantum mechanical phenomena are microscopic phenomena and exactly anti intuitive. Is it not wrong to imagine as in schrodinger's cat case that cat is in superposition of different states. Living and dead. Cat is macroscopic and has no such thing as quantum state to exhibit superposition...

Ah! The paper is just age old which I don't know, I just stumbled upon while searching about what graviton-graviton scattering is. It might not have been important one, but here it is: ===================================== Infrared behavior of graviton-graviton scattering John F. Donoghue1 and...