Explicit Definition and 147 Threads

Hi, this is a very basic question. I want to know why are implicit functions used, when the purpose of functions is to calculate the independent variable. For example, why would someone write ay + bx + c = 0 as a "straight line function" (sorry for the possible abuse of language, I don't...

This may seem elementary, however I have been unable to find a declarative statement that seems reliable. What is the equation for the red-shift z as a function of distance r to the best of our knowledge? That is z(r)=? Thanks in advance.

explicit form for representing "two spin 1/2 system" Hello, Are there any explicit forms(functions) for representing a "two spin(1/2) particle system" whose states are "proton1 up / proton2 up", "proton1 up / proton2 down", "proton1 down / proton2 up", "proton1 down / proton2 down"? Can it...

Hello, I am trying to model an explicit dynamics model in Ansys, to study impact of different objects. I cannot figure out how to model a composite with several layers in workbench. I have been trying to achieve this for over a week now. I was told that I can model the composite in Ansys...

Or, more aptly titled: Pell Numbers & [ Sophie Germain, Square & Pronic ] Triangular Numbers BACKGROUND RESEARCH Conjecture: Sophie Germain Triangles & x | 2y^2 + 2y - 3 = z^2 (Proven) https://www.physicsforums.com/showthread.php?t=462793 Consider the following form... X = (((z - 1)/2)^2 +...

Express y as an explicit function y^2 +xy = x^2 I was unable to get this this are my steps: Y(x + y) = x^2 X + y = x^2/y X=x^2/y – y………..kindly assist

The time evolution operaton may be written formally as: This is an actual solution to: only in the case that [H(t1),H(t2)]=0 (that is: the hamiltonian commutes in different instants of time) Of course, this includes the case of a time independent hamiltonian. If this is not the case, the...

Homework Statement Find an explicit two-parameter family of solutions for, \frac{1}{3}y^{''} = 2x\sqrt[3]{(y^{'})^{2}} Homework Equations The Attempt at a Solution See figure attached for my attempt at the solution. I've gotten to the point where I could simply expand out...

Homework Statement Determine whether R is isomorphic to S for each pair of rings given. If the two are isomorphic, find an explicit isomorphism (you do not need to show the formal proof). If not, explain why. Homework Equations R= 2x2 matrix, a 0, 0 b, for some integers a,b S= Z x Z...

I authored the articles, http//www.cheresources.com/colebrook1.shtml with parts 2 and 3 in 2004. I'm requesting assistance in updating the explicit equations portions of that series. My problem is that I have been unable to verify the accuracy of the Goudar - Sonnad equation. I have attempted...

I know this is really stupid and it looks like i haven't tried at all but i am genuinely confused about this so any guidance at all would help big time. so here is the question. A steel bar, 70mm long is struck at one end by a heavy mass moving at 20m/s. The impact causes a compression wave...

Homework Statement Given a recursive sequence, use iteration to guess an explicit formula a(k) = 5a(k-1) + k and a(1) = 1 Homework Equations Sum of Geometric Sequence : (r^(n+1)-1)/(r-1)The Attempt at a Solution y(2) = 5*1 + 2 y(3) = 5(5+2) + 3 = 5^2 5*2 + 3 y(4) = 5(5^2 5*2 + 3) + 4 =...

how to identify whether a function is implicit or explicit? advanced thanks.

Homework Statement explicit solution of -2x^2y+y^2=1; 2xydx+(x^2-y)dy=0? The Attempt at a Solution I was able to find that dy/dx=-2xy/(x^2-y) which is the implicit solution of the equation. I pretty much derived both of the equations to make sure they are both equal to one another...

I have derived an explicit formula for the http://mathworld.wolfram.com/EulerZigzagNumber.html" , the number of alternating permutations for n elements: A_j=i^{j+1}\sum _{n=1}^{j+1} \sum _{k=0}^n \frac{C_k^n(n-2k)^{j+1}(-1)^k}{2^ni^nn} For details, please refer to my article in...

http://arxiv.org/abs/1006.4908 An Explicit Embedding of Gravity and the Standard Model in E8 A. Garrett Lisi 14 pages. For peer review and publication in the "Proceedings of the Conference on Representation Theory and Mathematical Physics." (Submitted on 25 Jun 2010) "The algebraic elements of...

This is a question about solving Einstein's Field Equations for some simple cases, but I'm not sure how to explain this without analogy. So bear with me for a brief discussion. Consider the electrostatic equation: \nabla^2 V = \rho / \epsilon_0 which show explicitly how the charges source the...

Homework Statement Find a linear ordering of \mathbb{N} \times \mathbb{N} and use it to construct an explicit bijection f : \mathbb{N} \to \mathbb{N} \times \mathbb{N}. Homework Equations The Attempt at a Solution I know how to find a bijection by graphically by drawing the \mathbb{N} \times...

A(0, x) = x + 1 For : x >=0 A(y, 0) = A(y-1, 1) For : y > 0 A(y, x) = A(y-1, A(y, x-1)) For : y > 0, x > 0 Find A(2,x) for x >= 0 I worked this out... but I am wondering if I am right. Let x be 1 and y be 2. From statement 3 : A(y, x) =...

find explicit function or functions corresponding from implicit ,,, Homework Statement 1) 4x^2+9y^2=36 2)xy^2 + (x^2-1)y-x=0 The Attempt at a Solution 1) y=√((36-4x^2)/9)==>6/3√(-4x^2)) = 2√(-4x^2)) and the book answer is ±2/3 √(9-x^2) can someone tell me what's my mistake ? 2) well i...

explicit representation?? I got to show the explicit representation of 2cos(omega)t - 1/4 sin(omega)t = 0. what is this? is this operator notation??

Ok so this is a fairly stupid question I'm sure, but I'm not quite clear about the following: Given a Lorentz transformation we require the following to hold: g_{\sigma\rho}\Lambda^{\sigma}_{\mu}\Lambda^{\rho}_{\nu} = g_{\mu\nu} In other notation this is written: \Lambda^{T}g\Lambda...

Homework Statement I'm reviewing my Fourier transforms (useful in quantum mechanics, in this case 1-dimensional representation), and I'm having a heck of time *explicitly* solving the Fourier transform of \psi(x) = sinc(x) \phi(p) = F \left\{ \psi(x) \right\} = \frac{1}{\sqrt{2 \pi \hbar}}...

Hi there, I'm a new user to the forums (and Calculus) and I 'm hoping you can give me your opinion on my chain rule form below. When learning the chain rule, I was taught two forms. This form: \frac{d}{dx}f(g(x))=f'(g(x))g'(x) As well as the Leibniz form...

Homework Statement If a projectile orbits around a planet and lands after x cycles of the equation: radius[n+1] = radius[n] - (M* v^2 / radius[n]*G*P/radius[n]^2) at a final radius of C. What is the necessary v? The only variable that isn't known at the time of solving is v...

hi all! I'm facing this problem and I can't get a solution, I want to explicit variable m from the following equation, I tried with binomial theorem to break up binomial coefficient but it was useless... can someone help me please? \sum_{i=n}^{n+m}\binom{n+m} {i}p^i(1-p)^{n+m-i} = k...

Hello, I was just reading about implicit vs explicit finite element solvers and have a question about the difference between them. I understand that the implicit solver has a linear approximation step that is used to force equilibrium. My question is does that make the explicit solver...

I thought I would share my recent story and bad luck. I was at the Melting Pot, a nice fondue restaurant. The waitress dropped the boiling pot of oil and it splashed on me. Hurt like the dickens and almost instantly skin peeled. The photo is of day three. I've been keeping it uncovered the...

For the function f given by the equation f(x)=\frac{-2x}{3x-4}, determine where the relation f^-1 is a function. If f^-1 is a function, write an explicit expression for f^-1(x). Need help writing explicit expression. Any guidance?

I've been trying to work my way through some of my lecture notes, and have hit this snag. (n.b. I use k_0 \equiv +\sqrt{\vec{k}^2 + m^2}) We have a(q) = \int d^3 x e^{iqx} \{ q_0 \phi(x) + i \pi(x) \} a^{\dagger}(q) = \int d^3 x e^{-iqx} \{ q_0 \phi(x) - i \pi(x) \} To calculate the...

Homework Statement Find an explicit formula for the sum of the series, given that the formula for any term in the series is \frac{1}{2n(n+3)} Homework Equations The Attempt at a Solution

Homework Statement Determine an explicit formula for the sum of n terms for the given series: 1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5} Homework Equations The Attempt at a Solution I calculated the first 5 terms for the sum sequence and got: 1, \frac{3}{2}...

I am trying to use a explicit FDM for transient 1d conditions with linear elements for specific diffusion equation: ds/dt=D(x)*d2s/dx2+R(s) the problem is that I am using different, nonlinear functions describing diffusion constant D(x) and reaction rate R(s). The diffusion parameter is...

I am sure this is a stupid question but can someone give me the equations for r(t) and theta(t) for an orbit an inverse square law (treating the central mass as being at rest). The books always seem to only give r(theta) i.e. the shape of the orbit but not the actual time evolution. Is it ever...

I'm wondering if someone can give me an example of an everywhere defined unbounded operator on a (separable for simplicity) Hilbert space in a "constructive" manner. Since it's unbounded, simply a dense definition (i.e. on an orthonormal basis) wouldn't work since you can't extend it by...

I'm trying to understand something that's coming from my Marion & Thornton (4th edition 1995 on p. 264 in a section titled "Conservation Theorems Revisited"). The topic is conservation of energy and introduction of the Hamiltonian from Lagrange's equations. We're told that the Lagrangian...

Hi, Is there an explicit formula for the eigenfunctions of the harmonic oscillator? By explicit, I mean "not written as the nth power of the operator (ax-d/dx) acting on the ground state". Thanks.

Say I have a funciton sin(theta - phi) theta and phi are both time-dependant. How do I take the time derivative of this function? Is there a general notation or do I have to assume theta = w1t and phi = w2t and go with that?

Hi! This is my first post...I've a little question about a mathematical issue I found in the passage from explicit to implicit equations of a dynamical system. How to demonstrate that?? http://pixhost.eu/show_big.php?/share/2007-01-19/doi.jpg Thanks to all

Hello everyone. I got the hard part of the problem done with help from another forum member, and i transferred it into a gemeotric sum, which i will show below but I'm confused on the following directions that my profressor wrote: I checked in the section he was talking about and to my...

What would an explicit or analytic formula for a homeomorphism between a circle and a square be? Or a disc and [0,1] x [0,1]?

Hello everyone, yet another obscure problem on web work. No examples like this in the book nor did the professor go over it so i was wondering if someone can let me know what exactly they are wanting me to do! Find an explicit or implicit solutions to the differential equation...

How do u find an explicit formula when given an integral of a function. For example, the integral from 0 to x of tg(t)dt=x+x^2, how do u find the forumla for g(t)?

I have a lot of trouble trying to figure out the explcit forumla of a series of numbers. I can see the pattern in a recursion forumla, however. 2, -4, 8, -16, ... Is a multiplication of -2 to the term before it. Which is cake to write in a recursion forumla. But what about an Explicit...

Problem f(x) = \frac{x}{1-x-x^2} = \sum _{n=1} ^{\infty} f_n x^n By writing f(x) as a sum of partial fractions, find an explicit formula for the nth Fibonacci number. My work \frac{x}{1-x-x^2} = \frac{-4}{(2x + \sqrt{5} + 1)(2x - \sqrt{5} + 1)} = \frac{A}{2x + \sqrt{5} + 1} +...

As part of proving that d/dt <p> = <-Del V> you have to use the fact that < dp/dt> = 0 when p is not an explicit function of time. I'm not clear on what this means. Any insights to share? From classical mechanics, if there is a potential V = -k/r then there will be a force on a particle...

for this post, let N = {1, 2, 3, ...}. Q: explicitly write down a closed form bijection with domain N and range N x N. (no need to prove its a bijection... just write down the formula.) this may lead you off track, but the way i did it was to first find a formula from N x N to N and then...