Forms Definition and 482 Threads

Secret Chiefs 3 (or SC3) is an avant-garde group led by guitarist/composer Trey Spruance (of Mr. Bungle and formerly, Faith No More). Their studio recordings and tours have featured different line-ups, as the group performs a wide range of musical styles, mostly instrumental, including surf rock, Persian, neo-pythagorean, Indian, death metal, film music, electronic music, and various others.
The band's name was inspired by the "Secret Chiefs" said to inspire and guide various esoteric and mystical groups of the previous two centuries. Spruance has expressed interest in, and drawn inspiration from, various mystical or occult systems such as Sufism, Kabbalah, Hermeticism and alchemy.

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  1. D

    Can \( d \omega = 0 \) Be Concluded from \( \int_{\partial S} \omega = 0 \)?

    if i have \int_{\partial S} \omega=0 by stokes theorem \int_{S} d \omega=0, can i say d \omega=0? even 0 as a scalar is a 0-form?
  2. D

    Physics interpretation of integrals of differential forms

    Be a vector field \vec{F}=(f_1,f_2,f_3) and \omega^k_{\vec{F}} the k-form associated with it , i know if i do \int \omega^1_{\vec{F}} is the same of a line integral and \int \omega^2_{\vec{F}} i obtain the same result of \int \int_S \vec{F}\cdot d\vec{S}, which is the flux of a vector field in a...
  3. T

    Proving Vector Space Axioms for f(x) = ax+b, a,b Real Numbers

    Question: Show that the set of all functions of the form f(x) = ax+b, with a and b real numbers forms a vector space, but that the same set of functions with a > 2 does not. Equations: the axioms for vector spaces Attempt: I think that the axiom about the zero vector is the one I need to use...
  4. K

    Fourier transform - Other possible wave forms

    Hi, I am totally a non-math guy. I had to attend a training (on automobile noise signals) that had a session discussed about Fourier Transform (FT). Let me pl. write down what I understand: "The noise signal observed at any point in the transmission line can be formed using a sum of many sine...
  5. W

    Why only Closed Forms Matter in DeRham Cohomology?

    Hi All, One gets homological/topological information (DeRham cohomology ) from a manifold by forming the algebraic quotients H^Dr (n):= (Closed n-Forms)/(Exact n- Forms) Why do we care only about closed forms ? I imagine we can use DeRham's theorem that gives us a specific...
  6. S

    Showing a function forms a vector space.

    Homework Statement Does the function: 4x-y=7 constitute a vector space? Homework Equations All axioms relating to vector spaces. The Attempt at a Solution x_n for example means x with the subscript n The book says that the function isn't closed under addition. So it continues...
  7. Q

    Different forms of Schrodinger equation

    I got confused when in my book they went from one form of schrodinger equation to another. It doesn't make much sense to me algebraically, probably i have some lacks in complex numbers. Here are the equations: In the second one I think it's implied that above two equations give third and I...
  8. Warpspeed13

    Can a plasma be compressed more than other forms of matter?

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

    What is the connection between 2-forms, determinants, and cross products in R^3?

    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...
  10. mesa

    What are some examples of exact forms of the golden ratio?

    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
  11. E

    MHB Diagonalizing quadratic forms in WolframAlpha

    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...
  12. Y

    Could Silicon-Based Lifeforms Exist?

    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...
  13. U

    Recovering a frame field from its connection forms

    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...
  14. R

    Do all forms of energy behave like light?

    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...
  15. J

    Differential forms and differential operators

    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...
  16. C

    D-wave superconductivity: Functional forms?

    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...
  17. S

    How to prove that something forms a base topologically speaking

    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...
  18. P

    L'hopital's rule, indeterminate forms

    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...
  19. W

    Program Computing Wedge of Differential Forms?

    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...
  20. W

    Conditions for Solution to Pullback Equation on Forms?

    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...
  21. Z

    Electrochemical reduction of Hydrogen forms hydride?

    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
  22. W

    Transversality of a Vector Field in terms of Forms (Open Books)

    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...
  23. zoobyshoe

    50 ft. Rotating Ice Disk Forms in River

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

    Polar Form Conversion for Complex Numbers

    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...
  25. E

    Proving the various forms are equivalent

    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)...
  26. F

    MHB Classify Quadratic Surfaces: Ellipsoids, Hyperboloids, Paraboloids & Cylinders

    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?
  27. P

    Calculating Coefficients of Modular Forms

    Given: f\left(\frac{az + b}{cz + d}\right) = (cz + d)^kf(z) We can apply: \left( \begin{array}{cc} a & b \\ c & d\\ \end{array} \right) = \left( \begin{array}{cc} 1 & 1 \\ 0 & 1 \\ \end{array} \right) So that we arrive at the periodicity f(z+1) = f(z) . This implies a...
  28. W

    Finding Reeb Vector Fields Associated with Contact Forms

    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...
  29. C

    Which Element Forms X2O3 with Oxygen?

    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...
  30. N

    Advanced EM Field Book Using Differential Forms

    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
  31. A

    Different Forms of Newton's 2nd Law

    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...
  32. C

    Why using diff. forms in electromagnetism?

    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...
  33. T

    Show the two forms of the sample variance are equivalent

    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...
  34. caffeinemachine

    MHB A theorem on Quadratic Forms in Reid's Book not at all clear.

    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...
  35. MarkFL

    MHB Solve Calculus Limits w/ Sine Function: Answers to Hey's Questions

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

    Indeterminate forms of Taylor series

    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...
  37. D

    How does the characteristic of a field affect symmetric bilinear forms?

    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)
  38. T

    How to Integrate Console and Forms in a Windows Project?

    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?
  39. M

    Help with lewis structures and resonance forms (CH3NCS)

    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.
  40. Vorde

    Looking for Matricies with their R-Echelon Forms

    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...
  41. Mandelbroth

    Trying to understand derivatives in terms of differential forms

    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...
  42. A

    Do different forms of Green's functions give same result?

    I'm solving Helmholtz equation in a cylindrical coordinate. With boundary conditions be Neumann type, I can write several satisfactory forms of the Green's function, right? (for example, I can make the discontinuity of the derivative of the Green's function in the radial part, or in the z...
  43. K

    Help Me Understand Differential Forms on Riemannian Manifolds

    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...
  44. L

    Connection forms on manifolds in Euclidean space

    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...
  45. micromass

    Calculus Vector Calculus, Linear Algebra, and Differential Forms by Hubbard

    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
  46. W

    How Do You Solve the Limit of (x+1)^(cotx) as x Approaches 0+?

    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?
  47. 0

    Where in a wineglass does the standing wave forms?

    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...
  48. WannabeNewton

    Maxwell's equations differential forms

    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...
  49. matqkks

    MHB Quadratic Forms: Beyond Sketching Conics

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

    Quadratic Forms: Beyond Sketching Conics

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