Forms Definition and 448 Threads

Can a plasma be compressed to greater densities than other forms of matter?

Hi, 2-forms are defined as du^{j} \wedge du^{k}(v,w) = v^{j}w^{k}-v^{k}w^{j} = \begin{vmatrix} du^{j}(v) & du^{j}(w) \\ du^{k}(v) & du^{k}(w) \end{vmatrix} But what if I have two concret 1-forms in R^{3} like (2dx-3dy+dz)\wedge (dx+2dy-dz) and then I calculte (2dx-3dy+dz)\wedge...

Hello all, I am looking for exact forms (as real number expressions) of the golden ration that are not rewrites of the one we all know and love, i.e. g.r. = 1/2(5^(1/2)+1) Searches in Google have yielded nothing so far :P

Hello, Suppose I have a vector space $V$ over $\Bbb R$, a quadratic form $f(x)$ over $V$, some basis of $V$ and a symmetric matrix $A$ corresponding to $f$ in that basis, i.e., $f(x)=x^TAx$. Using, for example, the Lagrange method, I can find a change-of-basis matrix $C$ ($x=Cx'$) such that in...

Hi, I saw this problem in my textbook. (Please see attached picture.) So, first of all, my answer to this question would be that since the activation energy is lower than the bond energies, it is very easy to provide enough energy for the process to occur. Most importantly, is my answer...

Hi, I have a faced a research problem where I would need to recover a frame field given its connection forms. More precisely, I begin with an orthonormal frame field (given by data) in \Re^3 written as \mathbf F=\begin{pmatrix}\vec f_1\\\vec f_2\\\vec f_3\end{pmatrix} where \vec...

The idea of this question came from Stephen Hawking on a show on the Discovery channel called "Curiosity: Did God Create the Universe". Stephen Hawking said that energy and space were the only ingredients necessary to create the universe: Do all forms of energy behave like light? Can all forms...

After read this stretch https://en.wikipedia.org/wiki/Closed_and_exact_forms#Vector_field_analogies, my doubts increased exponentially... 1. A scalar field correspond always to a 0-form? 1.1. The laplacian of 0-form is a 2-form? 1.2. But the laplacian of sclar field is another scalar field...

Two questions, really: I’m finding it hard to wrap my head around the connections between k-space and real-space for d-wave symmetry, as well as the connections between “order parameter,” “gap,” “Cooper pair wave function,” and “superconducting wavefunction,” which are all mentioned at various...

Homework Statement If (X,d) is a metric space. I want to show that the set of all open balls and \emptyset form a base.Homework Equations The Attempt at a Solution I know that we need to show that the union of all these sets (or balls) is the whole set. I feel like this is simple yet, I am...

Homework Statement lim_{x -> \infty} \left( \frac{x}{x+1} \right) ^ {x} The Attempt at a Solution So I did e^whole statement with ln(x/(x+1))*x, after that I multiplied that expression by 1/x/1/x, then I go ln(x/(x+1)/1/x, I tried taking derivative of top and bottom but it doesn't help with...

Hi, All: Just curious if anyone knows of any online or otherwise software to help compute the wedge of forms, or maybe some method to help simplify. Not about laziness; I don't have that much experience, and I want to double check; I have around 30 terms ( many of which may cancel out) , and...

Hi, All: I have a quotient map given by the mapping torus (S,h) , where S is a compact surface with nonempty boundary, and h: S→S is a homeomorphism. Let I=[0,1]. The mapping torus ## S_h## of the pair (S,h) is defined as the quotient q: $$ q:S \times I/~$$ , where (x,0)~(h(x),1), i.e., we...

Would the electrochemical reduction of H2 form Hydrogen Anions of H- H2 + 2e- -> 2H- If this is the case, is the following true? H- + (1/2)H2 -> H2

Hi, All: Sorry for the length of the post, but I think it is necessary to set things up so that the post is understandable: I'm going through an argument in which we intend to show that a given vector field [ itex]R_ω [/ itex] (actually a Reeb field associated with a contact form ω) is...

http://www.theverge.com/2013/11/28/5154240/north-dakota-river-ice-circle-is-50-foot-wide

Homework Statement A=1.5495<21.0363°x(22.1009<30.3658°/69.9667<9.1884°) Homework Equations The Attempt at a Solution A=1.5495<21.0363x(22.1009/69.9667(30.3658-9.1884)=1.5495<21.0363(0.3159<21.1774)=(1.5495x0.3159)(21.0363+21.1774)=0.4895<42.2137° Solution above is it correct or I have to...

Homework Statement In Section 5.2 we discussed four equivalent ways to represent simple harmonic motion in one dimension: x(t) = C_1 e^{i \omega t} + C_2 e^{-i \omega t} (1) = B_1 cos(\omega t) + B_2 sin (\omega t) (2) = A cos(\omega t - \delta) (3) =Re C e^{i \omega t} (4)...

On the basis of the eigenvalues of A, classify the quadratic surfaces X'AX+BX+k=0 into ellipsoids, hyperboloids, paraboloids and cylindres. Can somebody help me to solve the problem?

Hi, All: Let w be a contact form , say in ℝ3, or in some 3-manifold M i.e., a smooth, nowhere-integrable 2-plane subbundle of TM. I'm trying to see how to find the Reeb field Rw associated with w. My ideas are: i) Using the actual definition of the Reeb field associated with a contact...

A piece of unidentified element X reacts with oxygen to form an ionic compound with the chemical formula X2O3. Which of the following elements is the most likely identity of X? A) Ba B) Cs C) In D) P E) Zn I am doing exam practice questions...

Hey guys, I am wondering whether there is any book out there that approaches EM field using differential form and on the same or more advanced than Jackson, I have a solid knowledge of differential form and algebraic topology, thanks :D

I’m supposed to prove that if ΣF(v) = -Av^2, where A is a constant, then Δx = m/A * ln (v0/v) by using Newton’s second law in the form ΣF = m dv/dt. I can solve the problem by using the form ΣF = mv dv/dx; however, it’s specifically stated that I’m not allowed to use the law in that form...

In electromagnetism we introduce the following differential form \begin{array}{c} \mathbb{F}=F_{\mu \nu}dx^{\mu}\wedge dx^{\nu} \end{array} Then the homogeneus Maxwell equations are equivalent to: \begin{array}{c} d\mathbb{F} = 0 \end{array} And is nice, but what purpose does this have...

Homework Statement Showthe two forms of the sample variance are equivalent: \frac{1}{n-1}\sum_{i=1}^\n (Yi-Ybar)2 = \frac{1}{n(n-1)}\sum_{i=1}^\n \sum_{j>i}\n (Yi-Yj)2 The first summation is from i=1 to n, the second is i=1 to n and the third is j>i to n. Sorry, I don't know how to format...

Hello MHB, I have been reading a book on Algebraic Geometry by Reid. On page 15, there's a theorem on Quadratic forms. The book doesn't explicitly define what a Quadratic Form is. From Hoffman & Kunze's book on Linear Algebra I found that given an inner product space $V$ over a field $F$, the...

Here are the questions: I have posted a link there to this topic so the OP can see my work.

Can someone please explain how the taylor series would work if x, the given value from the function, is equal to a, the value at which you expand the function? For example, let's take 1/(1-x) as an example. The taylor series for this with a=0 is Ʃ(n from 0 to infinity) x^n. But if we let...

When I start to read the the article called "symmetric bi-linear forms", I face the following sentence. But I don't understand what does the following sentence suggest. Could someone please help me here? We will now assume that the characteristic of our field is not 2 (so 1 + 1 is not = to 0)

That is what I need, Help! I have been working on a project and I can't seem to include the Form app into the Console app and vice versa. Does anyone know how one may do this?

I need to write the lewis dot structure along with the 3 resonance forms for CH3CNS. This is what I had but it was wrong. Not sure what to do. Thanks.

Hi all, I'm testing out a matrix solving program and while it checks out for 2x2/3x3/4x4 I would like to try it out on some larger matrices, but I don't really want to go through the hassle of row reducing a couple of 10x10 matrices to double check my program. Does anyone happen to know of...

Suppose we have a curve, formed by a function f that maps real numbers to real numbers, such that f is everywhere smooth over a subset D of its domain. Let's suppose that, for all x in D, there is a vector space that contains all vectors tangent to the curve at that point, called the tangent...

Hello! I think I got something wrong here, maybe someone can help me out. Lets consider a n-manifold. A differential n-form describing a signed volume element will then transform as: f(x^i) dx^1 \wedge dx^2 \wedge \cdots \wedge dx^n = f(y^i) \;\text{det}\left( \frac{\partial x^i}{\partial...

This question comes from trying to generalize something that it easy to see for surfaces. Start with an oriented surface smoothly embedded in Euclidean space. The embedding determines two mappings of the unit tangent circle bundle into Euclideam space. Given a unit length tangent vector,e, at...

Author: John Hubbard, Barbara Hubbard Title: Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach Amazon Link: https://www.amazon.com/dp/0971576653/?tag=pfamazon01-20

Homework Statement find the limit. Homework Equations limit_{x->0+} (x+1)^{cotx} The Attempt at a Solution this is of the form 1^{∞} y = (x+1)^{cotx} lny = cotx * ln(x+1) not sure if this is correct so far.. and what to do next? somehow turn it into a fraction, perhaps?

Hi I am doing coursework relating to resonance in a wine glass, and i am so confused as to where the standing waves are formed, clearly in videos i have watched the wineglass, when exposed to a high amplitude of its resonant frequency (in slow motion) clearly shows the wine glass vibrating...

Homework Statement I have to take the curved space - time homogenous and inhomogeneous maxwell equations, \triangledown ^{a}F_{ab} = -4\pi j_{b} and \triangledown _{[a}F_{bc]} = 0, and show they can be put in terms of differential forms as dF = 0 and d*F = 4\pi *j (here * is the hodge dual...

What are the real life applications of quadratic forms? I have used them to sketch conics but are there any other applications?

What are the real life applications of quadratic forms? I have used them to sketch conics but are there any other applications?

Hello, I have a somewhat conceptual question about differential forms. I have been studying differential forms off and on for some time now and things are starting to come together for me. However, there is an irritating gap in my understanding. Regarding the geometric significance or...

Homework Statement lim{x\rightarrow∞} sqrt(x^(2)+5x+11)-x Homework Equations I know it is of type ∞-∞ The Attempt at a Solution I have worked this problem around to death, and I know I'm supposed to give them a common denominator to get ∞/∞ and use L'Hospital's Rule, but I end up...

Homework Statement This is not actually a homework but a personal work. Here it is: Using the differential forms: F=\tfrac{1}{2!}{{F}_{\mu \nu }}d{{x}^{\mu }}\wedge d{{x}^{\nu }} and J=\tfrac{1}{3!}{{J}^{\mu }}{{\varepsilon }_{\mu \alpha \beta \gamma }}d{{x}^{\alpha }}\wedge d{{x}^{\beta...

Author: Raoul Bott, Loring Tu Title: Differential Forms in Algebraic Topology Amazon Link: https://www.amazon.com/dp/1441928154/?tag=pfamazon01-20 Prerequisities: Differential Geometry, Algebraic Topology Level: Grad Table of Contents: Introduction De Rham Theory The de Rham Complex...

Wiki defines :In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. Yes,all nice and dandy,I get to then express it in terms of matrices and then I find the eigen values and then find the canonical quadratic form,the usual boring linear algebra...

Homework Statement lim ln(x-1)/(x2-x-4) x->2 Homework Equations The Attempt at a Solution Well, I thought that every time I had answers as 0/0, 2/0 or 0/2, for instance, they would constitute as indeterminate forms. I have the answer sheet for this problem. It says "answer: 0/-2 =...

So my calculus professor last semester said that 1∞ is just 1 if 1 is exactly 1. He said that 1∞ is an indeterminant form because the rate of change of x as x approaches 1 competes with the rate of change of ∞ as it gets larger in x∞. He also said that 0/0 is an indeterminant form because the...

So say I have a n-1 form \sum^{n}_{i=1}x^{2}_{i}dx_{1}...\widehat{dx_{i}}...dx_{n} and I want to find the exterior derivative, how do I know where to put which partial derivative for each term, would it simply be?? \sum^{n}_{i=1}...

Hi, I understand the concept of the differential of a (differentiable) function at a point as a linear transformation that "best" approximates the increment of the function there. So for example the differential of a function f : D \subseteq \mathbb{R}^2 \to \mathbb{R} could maybe be df = 8...