Inverse Definition and 1000 Threads

Is it possible to produce the inverse of a natural radioactive decay? If yes, what would happen? Release energy?

Could I by any way find out average thermal retention of a blackbody that is irradiated with x rays? Since wavelength is inversely propotional to temp, in order to emit and absorb x rays it must be at a fairly high temperature I guess.

Why is the solubility of some solids lower when the solution is heated? I read that it is because the process is exothermic (heat from breakdown is greater than the heat needed for breakdown). But why would having extra heat from outside sources inhibit the dissolving process, wouldn't it only...

And also: y`+2y=2(1-e^-2t) Y(0)=0 y¨-2y`+y = t+e^t y(0)=1 and y`(0)=0 Please help me out here folks ;)

Hi. I`m new here and I need some help with Inverse Laplace Transform: f(t)=5+3t+e^3t g(t)=(t+1)u(t-2) g(t)=(t^2-9t+20)u(t-5) and Laplace Transform: F(s)=1/(s+2)^5 F(s)= 2s^2+10/s(s^2+2s+10) G(S)=2s/s^2+4e^-sso if anywone can please help me:)

Homework Statement In the inverse compton scattering, find the formula of the recoiled electron as a function of the incoming electron Homework Equations The energy of the incoming photon and electron are known. The Attempt at a Solution Starting from this...

Hello everyone, This is probably going to come off as a very silly question. However, I have not had calculus in several years. I was angry that my physics textbook did not have a derivation of Electric Potential Energy. So, I finally came across it, and I see that the integration of the...

Homework Statement 1.\int{\frac{sinx}{1+cos^{2}x}} \, dx 2.\int{\frac{1}{13-4x+x^2}} \, dx Homework Equations Inverse trig identities. The Attempt at a Solution For the first one, I'm not too sure about what to do with the sinx on the numerator and i have tried u-substitution to no avail...

Hello! *Let $f$ be a strictly increasing continuous function on a closed interval $[a, b]$, let $c = f(a), d = f(b)$, and let $g:[c, d] → [a, b]$ be its inverse. Then $g$ is a strictly increasing continuous function on $[c, d]$.* How can it be shown that $g$ is continuous at its endpoints $c$...

Homework Statement Find the inverse of the function: Y=X2-X, X≥½ Homework EquationsThe Attempt at a Solution I've switched X and Y to get: X=Y2-Y Then I've tried several things to get Y alone, but none of them seem to work. I've tried taking a square root, using a log, and several other...

I know we can represent it two different ways. First: \mathbf{B} = \frac{\mu_0}{4\pi}\int_C \frac{I d\mathbf{l} \times \mathbf{\hat r}}{|\mathbf{r}|^2} If we open up unit vector, then it becomes: \mathbf{B} = \frac{\mu_0}{4\pi} \int_C \frac{I d\mathbf{l} \times \mathbf{r}}{|\mathbf{r}|^3} I...

I know for two linear operators $$H_1, H_2$$ between finite dimensional spaces (matrices) we have the relations (assuming their adjoints/inverses exist): $$(H_1 H_2)^* = H_2^* H_1^*$$ and $$(H_1 H_2)^{-1} = H_2^{-1} H_1^{-1}$$ but does this extend to operators in infinite dimensions? Thanks.

I am reading Manfred Stoll's book: Introduction to Real Analysis. I need help with Stoll's proof of the Inverse Function Theorem (IFT) for real-valued functions of one real variable. Stoll's statement of the IFT for Derivatives and its proof read as follows: In the above proof we read: "...

Scaling - Inverse relationship between uncertainty and mass I’m trying to express Heisenberg's Uncertainty Principle in a simplified formula that is not boundary unlimited and still capture what I believe is an inverse relationship between uncertainty and mass - the "scaling hypothesis". I...

Homework Statement find the inverse of r in R = F[x]/<h>. r = 1 + t - t^2 F = Z_7 (integers modulo 7), h = x^3 + x^2 -1 Homework Equations None The Attempt at a Solution The polynomial on bottom is of degree 3, so R will look like: R = {a + bt + ct^2 | a,b,c are elements of z_7 and x^3 = 1 -...

Homework Statement arccot x = (π/2) - arctan x arccot x =/= π arccot x =/= 0 Homework Equations arccot x = 1/arctan x (if x > 0) arccot x = 1/arctan x + π (if x < 0) arccot x = π/2 (if x = 0) The Attempt at a Solution π and 0 are the horizontal asymptotes, the values for which y (sine) cannot...

Homework Statement Calculate the total number of compex multiplications required for the calculation in (b) when FFTs are used to perform the Discrete Fourier Transforms and Inverse Discrete Fourier Transforms.[/B] There were two FFT multiplied together and one inverse FFT of that product to...

One semester I was asked to find the inverse of $\,f(x) \:=\:\dfrac{3x - 5}{2x+1}$ Later, I had to find the inverse of $\,f(x) \:=\:\dfrac{2x+7}{4x-3}$ It occurred to me that a general formula would a handy tool. Especially since I planned to teach Mathematics and I might be teaching this very...

What is higher inverse orders of n, as symbolized by O(n)? Please explain this to me---I am still confused even if googling it.

Homework Statement Don't understand why the inverse jacobian has the form that it does. Homework Equations $$ J = \begin{pmatrix} \frac{\partial{x}}{\partial{u}} & \frac{\partial{y}}{\partial{u}} \\ \frac{\partial{x}}{\partial{v}} & \frac{\partial{y}}{\partial{v}} \end{pmatrix} $$ $$...

Homework Statement Hi! Does anyone know how to solve the inverse of these functions? y=(4x^2+2x-2)/(8x^2-4x+6) y=(x+1)/(x^2) I would appreciate your help with these exercises. The Attempt at a Solution For the first one: 8yx^2-4xy+6y=4x^2+2x-2 For the second exercise: yx^2=x+1 yx^2-x=1

f(x) = 3x^3 + 3x^2+ 2x + 1 ,a = 3 formal is Homework is due tonight and this is the only problem i can't solve Your suppose to 3= 3x^3 + 3x^2 + 2x + 1 , solve for xThe find the derivative of y= 3x^3 + 3x^2 + 2x + 1 , then plug x into that and put it under 1.

Hi guys! I am having a problem in finding the inverse z transform of the given signal. Can anyone help me? I'd appreciate it. Thanks! Here is basically what I did: However, I don't know what to do next. What is the next thing to do? Thanks!

Homework Statement If we shift a curve to the left, what happens to its reflection in the line y = x? In view of this geometric principle, find an expression for the inverse of g(x) = f(x + c) where f is a one-to-one function. Homework EquationsThe Attempt at a Solution Initially I did this...

Hello! (Happy) In my lecture notes, there is this remark: A set $X$ is countable iff there is a $f:X \overset{\text{bijective}}{\longrightarrow} \omega$ iff $X$ is the range of a bijective sequence of lengh $\omega$. $$f^{-1}: \omega \overset{\text{bijective}}{\longrightarrow} X$$ then...

Homework Statement If I measure a sound intensity of 1.0 at distance R from its source, what intensity would I measure at distance 3R in a free, unbounded space? What is the difference in decibels? & If I measure a sound pressure of 1.0 at distance R from its source, what pressure would I...

Homework Statement Dear Mentors and PF helpers, Please help me with this question as my junior asked me but I have some doubts in it: It takes 4 workers to complete repairing the road in 42 days. Suppose that 14 days into the road works, 10 more workers are brought into help out in the road...

Hey! :o Does it stand that the eigenvalues of $A^{-T}A^{-1}$ are the inverse of the eigenvalues of $A^TA$ ?? (Wondering)

Hi, let's say in some experiment with ##Z^0## (eg LEP) you are able to determine the "misidentification" of your particles. Then you can find the efficiency matrix ##M_{eff}## which is given (for ##Z^0## decays to leptons or hadrons): \begin{pmatrix} N_e \\ N_\mu \\ N_\tau \\ N_{had}...

Homework Statement Give the inverse Laplace transform of F(s) = (-3/s) + (e^-4s)/(s^2) + (3e^-4s)/s Homework Equations Inverse Laplace [e^(-cs) F(s)] = f(x-c)u(x-c) The Attempt at a Solution I'll break this into 3 parts. Part 1 - (-3/s) -3/s = -3(1/s) -> inverse laplace of -3(1/s) = -3...

Homework Statement This comes up in the context of Poisson's equation Solve for ##\mathbf{x} \in \mathbb{R}^n ## $$ \nabla^2 G(\mathbf{x}) = \delta(\mathbf{x})$$ Homework Equations $$\int_0^\pi \sin\theta e^{ikr \cos\theta}\mathop{dk} = \int_{-1}^1 e^{ikr \cos\theta}\mathop{d\cos \theta }$$...

Assuming that my understanding is correct, I believe it was Einstein who proposed that gravity is the result of the warping or curving of space-time. My question is this: if gravity, which is solely attractive in nature, is the result of warped or curved space time, then is it possible for the...

Anyone noticed this paper: Square Root of Inverse Metric: The Geometry Background of Unified Theory? Authors: De-Sheng Li, arXiv:1412.2578 ? The author tries to construct the square root of the inverse metric, based on a product of a fermion field and a framefield. Somehow the Standard model...

Homework Statement take inverse laplace of: 6/[s^4(s-2)^2] Homework Equations 6/[s^4(s-2)^2] The Attempt at a Solution I used partial fractions. I was wondering if It could be manipulated to where I could use the laplace table?

Homework Statement Find H(s) = \frac{Y(s)}{X(s)} \frac {d^2y(t)}{dt^2} + a\frac {dy(t)}{dt} = x(t) + by(t) Homework EquationsThe Attempt at a Solution [s^2 + as - b] Y(s) = X(s) H(s) = \frac{1}{s^2+as-b} I assume the inverse is a sign or a cosine but unsure which one.

Homework Statement find the inverse laplace Homework Equations L^(-1)[(s+1)^2/(s+2)^4] The Attempt at a Solution included in attachment. the top problem, #20.

Homework Statement Let ##f : G \rightarrow H## be an epimorphism from a group ##G## to ##H## and let ##h \in H##, then ##f^{-1} (h) = g ~ker(f)##. Homework EquationsThe Attempt at a Solution So, if I understand the problem correctly, we are trying to find a epimorphism which has a rule such...

Inverse Laplace transform \mathcal{L}^{-1}[F(p)]=\frac{1}{2\pi i}\int^{c+i\infty}_{c-i\infty}F(s)e^{st}dp=f(t) Question if we integrate along a straight line in complex plane where axis are Re(p), Im(p), why we integrate from c-i \ínfty to c+\infty? So my question is, because Im(p) are also...

Homework Statement Find the inverse Fourier transform of X(ejw = 1/(1-ae-jw)2 using the convolution theorem. Homework EquationsThe Attempt at a Solution I tried finding the partial fraction coefficients but without success.

Hello, everybody. I am currently working on deriving solutions for Stokes flows. I encounter a multidimensional inverse Fourier transform. I already known the Fourier transform of the pressure field: \tilde{p}=-\frac{i}{{{k}^{2}}}\mathbf{F}\centerdot \mathbf{k} where i is the imaginary unit...

Homework Statement Division by s Equals integration by t: For this problem use the following property (see relevant equations) to find the inverse transform of the given function: F(s) = \frac{1}{s(s-1)} Homework Equations L^{-1}(\frac{F(s)}{s}) = \int_{0}^{t} f(\tau)\,d \tau The Attempt...

Hi! (Wave) Could you give me a hint how I could show that if $f$ is a function, that is $1-1$, then, it stands that: $$(\forall x \in dom(f)) f^{-1}(f(x))=x$$ ? (Thinking)

Homework Statement Hi there! I have a data set of r (independent variable) and E (electric field strength) (dependent variable). The question asks for a non graphical method to show if there is an inverse square law relationship between the two data sets. -- My attempt: I picked the equation...

Hi all What if instead of charges and a surface, we were given a set of charges and image charges and have to find the surface, how would you do that? This is actually part of my homework but I'm pretty sure he doesn't want us to prove it mathematically (the case is obviously a sphere) so I...

Homework Statement ...(2 , 3) A = ...(1 , 3) Find the trace of A^(-1) Homework Equations (a , b)......(d , -b) ...^(-1) = (ad-bc)^(-1)* (c , d).......(-c, a) The Attempt at a Solution .....(3 , -3) A^-1 = 9* .....(-1. 2) (In mod 26) ... (1, -1) = ... (-9...

Why exactly is there no such thing as an inverse factorial function? Now I am fully aware of the fact that the factorial function (##f(x) = x!##) is not one-to-one, since both 0! and 1! equal 1. But can't we circumvent this by restricting the domain of f such that it only includes values of x...

I seem to recall reading a geometry method that showed zero to be the inverse of infinity. Can you give me a reference for that?

After working a homework assignment which required sketching effective potential energy for the gravitational/coloumb forces, I went and looked at a few effective potentials for inverse cube and inverse quartic (not sure if this is the right word; 1/r^4 force) forces, with inverse square and...

Homework Statement Determine which of the formulas hold for all invertible nhttp://msr02.math.mcgill.ca/webwork2_files/jsMath/fonts/cmsy10/alpha/144/char02.png n matrices A andB A. 7A is invertible B. ABA^−1=B C. A+B is invertible D. (A+B)2=A2+B2+2AB E. (A+A^−1)^8=A8+A−8 F...

Homework Statement the problem is to find the inverse of a 3x3 matrix using LU Decomposition with C++ command, with the numbers designated. in my case, my numbers for the matrix are '306 410 780' #include <stdio.h> #include <iostream> #include <stdlib.h> #include <math.h> using namespace std...