Forms Definition and 482 Threads

Consider int(E.dA)=q/e, guass law relating the electric field to the charge enclosed. One can also derive (using the more mathematical version of guass' law - involving the double integral) this same formuala for a graviational field. Here the permitivitty constant would be replaced by...

How can there be three forms of the double-angle formula for cos 20?

Synthetic DNA on the Brink of Yielding New Life Forms

Homework Statement hey there. i have 3 equations in quadratic form: q1 [x] = x^2 + 2xy + 4yz + z^2 [y] [z] q2 [x] = 2xy + 4yz - 2xz [y] [z] q3 [x] = (x + y + z)^2 [y] [z] 2. What i need to find i have to find the real and complex canoncial forms: The Attempt at a...

hi i just wanted a quick explanation of what a symmetric matrix is and what they mean by the quadratic form by the standard basis? (1) for example why is this a symmetric matrix [1 3] [3 2] and what is the quadratic form of the matrix by the standard basis? (2) also how would i go...

I searched Google and could not find a solution for this. I have a form with a text box and I want to make it so that when I resize the form while the application is running the text box would get resized as well and be "relative" to the size of the form. Any help please?

http://www.sciencedaily.com/releases/2007/11/071122151148.htm ScienceDaily (Nov. 23, 2007) — A team led by the University of Colorado at Boulder and the University of Milan has discovered some unexpected forms of liquid crystals of ultrashort DNA molecules immersed in water, providing a new...

1) Let f: V x V -> F be a symmetric bilinear form on V, where F is a field. Suppose B={v1,...,vn} is an orthogonal basis for V This implies f(vi,vj)=0 for all i not=j =>A=diag{a1,...,an} and we say that f is diagonalized. ============ Now I don't understand the red part, i.e. how does...

[SOLVED] Linear forms and complete metric space Homework Statement Question: Let L be a linear functional/form on a real Banach space X and let {x_k} be a sequence of vectors such that L(x_k) converges. Can I conclude that {x_k} has a limit in X? It would help me greatly in solving a certain...

Q: Suppose q(X)=(X^T)AX where A is symmetric. Prove that if all eigenvalues of A are positive, then q is positive definite (i.e. q(X)>0 for all X not =0). Proof: Since A is symmetric, by principal axis theorem, there exists an orthogonal matrix P such that (P^T)AP=diag{c1,c2,...,cn} is...

Hello everyone, I'm new to this forum. I have a doubt about differential forms, related to the divergence. On a website I read this: "In general, it is true that in R^3 the operation of d on a differential 0-form gives the gradient of that differential 0-form, that on a differential 1-form...

Given the vector space consisting of all bilinear forms of a vector space V (let's call it B) it's very easy to prove that B is the direct sum of two subspaces, the subspace of symmetric and the subspace of skew symmetric bilinear forms. How would one go about determining the dimension of these...

I'm practicing some differential forms stuff and got a bit stuck on something. I'd type it out but the action is very long so it's easier if I just link to where I'm getting it from, this paper http://gesalerico.ft.uam.es/tesis/pablo_camara.pdf Equation (4.20) (pdf page 51) is the IIA action...

I am having problems with understanding the whole concept/how to compute the row-reduced echelon form. Can someone please help me? Thanks

First off, I'm no geometer. I've jumped from looking into QFT from an operator algebra perspective to one looking at it from a differential geometry perspective. It's been a fairly nice ride...modulo the fact that I know very little differential geometry. Thus I have been going through a bit of...

Here's an interesting question. I'm aware of closed forms of cubic polynomials that go through 1 or 2 specific (x,y) points. Are there closed form versions for 3 or 4 points? 1 pt: y = a(x-x_0)^3 + b(x-x_0)^2 + c(x-x_0) + y_0 2 pt: y = a(x-x_0)^2(x-x_1)\ +\ b(x-x_0)(x-x_1)^2 \ +\...

let f:VxV->R be an antisymmetric billinear form in real vector space V, there exists an operator that satisfies J:V->V J^2=-I. i need to prove that the form q:VxV->R, for every a,b in V q(a,b)=f(a,J(b)) is symmetric and definite positive. i tried to show that it's symmetric with its definition...

Hi, I'm seeing that many authors like Griffiths and Halliday/Resnick (I've not seen Jackson and Landau/Lif****z) are deriving the differential form of Gauss's law from the integral form (which is easily proven) by using the divergence theorem to convert both sides to volume integrals and then...

I must comment on the Coulomb force - vectorial & non-vectorial form: F=k*((Q1*Q2)/r^2 ) F=k*((Q1*Q2)/r^2 )*[r] >>>[r] unit vector I know that , in case of vectorial form, I can use superposition principle, and use this form when the direction is important for me. But what's more?

Hi, Earth follws a straight path in 4-d space time.ok.now the Earth moves over the geodesic formed by the sun's gravity.now we also have other 7 planets.So does it mean that the sun forms different geodesic for differnt planets. if my question does make some logic than please explain me.

Hey folks, I'm reading "Symmetry in Mechanics" by S. Singer and I'm stuck on an exercise. It asks to find an antisymmetric bilinear form on R^4 that cannot be written as a wedge product of two covectors. Here are my thoughts thus far: on R^2 its trivial to show that every antisymmetric...

Hi, I don't know if this is the right place to post, but can someone help me understand what differential forms are intuitively? And the wedge product intuitively? And finally, how can they help see the bigger picture of multiple integrals, curls, divergence, gradient, etc. I don't know that...

Greetings, I was wondering what Freud said about the formation of the ego. Like the time of childhood it develops and causes for its formation, thanks.

I am reading some books about differential forms. I don't quite understand what is the geometrical meaning of star (hodge) operator. Can anyone give me a hand please? Leon

Sorry to keep bothering, but I am preparing an exam based on Spivak's book on forms (chapter 7 of tome 1). I need to prove that if \dim V \le 3, then every \omega \in \Lambda^2(V) is decomposable, where an element \omega \in \Lambda^k(V) is decomposable if \omega...

I am looking for some good websites that have proofs involving parallelograms and rhombus'? preferably in statement and reasons format any help would be appreciated. thank you

Hello, I'm interested in starting differential forms, Is this book any good? What audience is it intended for? What prerequisites (E.G. Linear Algebra, Calculus(At what level), etc.) would one need to fully appreciate the scope and depth of information presented in this book? Thanks for...

hi, my question is from Modern Engineering Mathematics by Glyn James pg 177 # 17a Using the exponential forms of cos(theta) and sin(theta) given in (3.11a, b), prove the following trigonometric identities: a) sin(x + y) = sin(x)cos(y) + cos(x)sin(y) and 3.11a is: cos(x) = 0.5*[ e^(jx)...

The question is: Show that on R^2\{0} (without zero), let w=(xdy-ydx)/(x^2+y^2) and show (a) closed (b) not exact. (a) is straightforward, and for (b), the following is the solution lecturer provided. Firstly convert to polar coordinates letting x=rcos(p) y=rsin(p) where p is supposed...

Could someone explain these two concepts? What I need is the big picture of 'why' we need this, roughly 'what' these equations mean, 'where' its used etc Thanks in advance

ello ello! The directions are the following: Rewrite each of the following statements in the two forms \forall x, if ____ then ___ and \forall _____ x, _____ For some reason the latex keeps putting an x for the 2nd form, but it should be Upside down A ______ x, _______ for the...

I just discovered this forum: very very nice! And here's my first question: An exterior p-form is a multilinear antisymmetric map from p copies of a vector space (in particular, a tangent space located at some point P of a manifold) to the reals. Now what could it mean to have an integral of a...

Find a solution to the equation if possible. Give the answer in exact form and in decimal form. 1 = 8cos(2x + 1) - 3 1 = 8tan(2x + 1) - 3 I don't know how to do this one.. but I know how to do the simpler ones like.. 2 = 5sin(3x) 2/5 = sin(3x) (sin-1(2/5)) / 3 = 0.137172 Those...

Rotating water forms a parabola - why?? I've done some experiments involving rotating a beaker of water, and then measuring the height of the parabola that forms. I am now trying to explain this in my write up, but there are some things that I am simply not understanding, and any help would be...

Why is 1^\infty an indeterminate form? If you keep multiplying 1 by itself doesn't the answer stay 1?

Has anyone ever read or used this book http://www.chapters.indigo.ca/books/item/books-978048665840/0486658406/Tensors+Differential+Forms+And+Variational+Principles?ref=Search+Books%3a+'Tensor+Differential+Forms' Is it any good?

What would be an experiment i could prefrom to show how different forms of energy are converted into electrical impulses?? Simple ones Thanks Nath

Well I'm getting pretty frustrated by this problem which arose in my research, so I'm hoping someone here might set me on the right track. I start with n random variables x_i, i=1..n each independently normally distributed with mean of 0 and variance 1. I now have two different functions...

I decided earlier this week that I was going to compute by hand the genus of an elliptic curve. I've had a miserable (but enlightening!) time! I eventually stumbled upon the trick in Shafaravich: I should be looking at the rational differential forms, and counting zeroes & poles of things...

Do concentrated forms of light, such as a laser, have mass?

A while back in maths we were introduced to the linear equation in two forms: a x + b y = c (1) y = m x + c (2) Now I can use both forms of these, but I was told that: y = m x + c \Leftrightarrow a x + b y = c where m = \frac{a}{b} Thiis can't be right can it? As: a x + b y = c b...

Whats isoamyl? Hi i have a quick question I'm supposed to show how isoamyl propanoate is fromed. I know that this is esterification and that one of the reactants is propanoic acid but i don't know what the alcohol isoamyl is? I tried searching on google and all i get is test questions:mad: Plz help

I'm new to quantum mechanics, i.e. the type of QM you don't learn through books by Brian Greene :biggrin: . I know there aren't any derivations for an operator associated with an observable and they are usually defined in a certain form. So why do they have those particular forms. Was it trial...

Recently, I've begun to study the Geometric Algebra approach to differential geometry (Hestenes[84]) and although I do not claim to be an expert in this area (not at all!) I'm really starting to like what I see. It seems a major problem with the differential forms approach is that it...

They have been around for some time now, but where did the idea of little green men come from, or the big eyed hairless Ivan type, how many different alien forms are there ?

Calcium is essential in the prevention of bone loss. This is particularly important for women who are approaching menopause as they're susceptible to osteoporosis. I'm not sure what age women should begin incorporating more calcium into their diet but I do know that they need more after...

I need to come up with female replacements for the following male words. For instance, as she replaces he and Queen replaces King. man son prince lord my lord your lordship The replacements should have the same general meaning, but it doesn't need to be exact. The problem is that the...

I am working a problem: Find the polar form of the equation 6x^2 + 3xy + 6y^2 = -3 I have run this 4 separate times and have come up with 4 different answers. PLEASE HELP! r^2= 6 over -6 - 3sin(theta)cos(theta) r^2=-3 over 6 - 3sin(theta)cos(theta) r^2=9 over 6 +...

let f:U \rightarrow R^n be a differentiable function with a differentiable inverse f^{-1}: f(u) \rightarrow R^n . if every closed form on U is exact, show that the same is true for f(U). Hint: if dw=0 and f^{\star}w = d\eta, consider (f^{-1})^{\star}\eta...

Who has any litterature about non-linear differential forms, especially for example if I would like to compute the following : (dx\wedge dy)(dx\wedge dy\wedge dz) is it equal to (dx)^2\wedge (dy)^2\wedge dz ?? Thanks in advance.