Delta Definition and 1000 Threads

Folks, I am looking for a blower to produce a flow of ~150cfm (~4m^3/min) while pumping H2 pressurized at ~40bar. The blower needs to provide a pressure increase of ~5bar. I am wondering if something like a supercharger blower might work.

I am confusing about the delta G(free-energy change). Could anyone explain me more about the sign of delta G. wat the exergonic and endergonic process mean? also, wat is the relation between the delta G and delta S(entropy)? I know the formula between them, but I don't quite understand Thank you,

why in the problem of dirac delta potential, the integral \int^{\epsilon}_{-\epsilon}\phi''(x)dx is equal to \phi'(\epsilon)-\phi'(-\epsilon)? but \int^{\epsilon}_{-\epsilon}\phi(x)dx is equal to 0 if, for example\phi(x)=e^x then \phi(x)''=\phi(x) but, the firts integral is...

Hi guys Can anybody help me? What is the difference between a delta \delta W and a differential dW? (W a scalar function, for example.) In other words, when shold be used a delta and when a differential? Thanks.

the integral \int_{-\infty}^{\infty} \! f(t)*\delta (t-t_0) * \delta (w-w(t)) \, dt is?? can be \delta (w-w(t)) * f(t_0) ?

Hello, I have just integrated over one variable, x and have now got a delta function \delta(m) where m = constant * (s-s') now I have to integrate over either s or s' but I am a bit confused since if I integrate over say s then the delta function depends on s. Hope I have explained clearly...

I do not know how to execute the problem with the 2x in the problem. Evaluate the integral: \int_{-4}^{4} (x^2+2x+1) \delta(2x) dx

1. Consider a steel guitar string of initial length L=1.00 meter and cross-sectional area A=0.500 square millimeters. The Young's modulus of the steel is Y=2.0 \times 10^{11} pascals. How far ( Delta L) would such a string stretch under a tension of 1500 Newtons? Use two significant figures in...

hey if lim (x-->0) f(x) = L where 0 < |x| < d1 implies |f(x) - L | < e how do i prove lim (x --> 0) f(ax) = L? i know 0 < |ax| < |a|d1 d2 = |a|d1 but the textbook says d2 = d1/|a| help you guyssssssssssssssssssssssssssssssss

Homework Statement Given f(x,y) = DeltaFunction(y - x*tan(theta)) a) Plot function. b) Take Fourier transform. c) Plot resulting transform. Homework Equations Delta function condition non-zero condition DeltaFunction(0) = Infinity Sifting property of delta functions The...

Given: limit of (sin x)/x as x --> 0 and that ε = .01 Problem: Find the greatest c such that δ between zero and c is good. Give an approximation to three decimal places. Equations: 0 < |x - a| < δ 0 < |f(x) - L| < εAttempt: 0 < |x - 0| < δ 0 < | sin(x)/x - 1| < ε 0 < | sin(x)/x - 1| < .01 0...

First of all, let me copy the standard solution from Griffiths, section 2.5, just for the sake of clarity. PotentialV(x) = - \alpha \delta (x) The bound state eigenfunction: \psi (x) = \left\{ \begin{array}{l} B{e^{\kappa x}}{\rm{ (}}x \le 0{\rm{)}} \\ B{e^{ - \kappa x}}{\rm{...

Given the limit of \frac{x^2+2x}{x^2-3x} as x approaches 0 equals \frac{-2}{3} and that ε = .01, find the greatest c such that every δ between zero and c is good. Give an exact answer. 0 < |x-0| < δ 0 < |\frac{x^2+2x}{|x^2-3x} + \frac{2}{3|}| < ε |\frac{x(x+2)}{|x(x-3)} +...

I had just reviewed back the properties of Delta Dirac Function, however I'm having a little confusing about the first property as stated : \delta\left(x-a)\right = 0 if x \neq a, \delta\left(x-a)\right = \infty if x = a;Here is my problem : when integrate over the entire region (ranging from...

Homework Statement Let f: \Re \rightarrow \Re and g: \Re \rightarrow \Re be functions such that lim_{x \rightarrow 1} f(x)=\alpha and lim_{x \rightarrow 1} g(x)=\beta for some \alpha, \beta \in \Re with \alpha < \beta . Use the \epsilon-\delta definition of a limit to prove...

I am trying to see why exactly the momentum eignenstates for a free particle are orthogonal. Simply enough, one gets: \int_{-\infty}^{\infty} e^{i (k-k_0) x} dx = \delta(k-k0) I can see why, if k=k0, this integral goes to zero. But if they differ, I don't see why it goes to zero. You have...

I am trying to integrate a charge density over a volume in order to obtain a total charge, but there is a delta function involved and I am not entirely sure how to treat it. \rho = q* \delta (\textbf{r})- \frac {q\mu^{2} Exp(- \mu r)} {4 \pi r} Q = \int \rho (\textbf{r})d^{3}r...

Homework Statement given a function defined by f(x,y) {= |xy|^a /(x^2+y^2-xy), if (x,y) cannot be (0,0) and = 0, if (x,y) = (0,0) Find all values of the real number a such that f is continuous everywhere e= epsilon d= delta In order to prove this, I know I need to do an...

Homework Statement What is the (volume) charge density of a ring of radius r_0 and uniform charge density \lambda? Homework Equations The Dirac Delta Function The Attempt at a Solution I've done a few line charge densities of straight wires along an axis (usually z, but on x as...

hello all, i am unaware of how to handle a delta function. from what i read online the integral will be 1 from one point to another since at zero the "function" is infinite. overall though i don't think i know the material well enough to trust my answer. and help on how to take the integral of...

Homework Statement I am really confused in my electrodynamics class. I have the following function. f(x) = \delta (x + \alpha ) + \delta(x -\alpha) How do i convert this into Fourier Tranform ? Those are dirac delta functions on either sides of the origin. Homework Equations...

hi, may someone help me to clarify my doubts... in my work, i encounter diracdelta square \delta(x-x_1)\delta(x-x_2) i am not sure what it means... it seems if i integrate it \int dx \;\delta(x-x_1)\delta(x-x_2) = \delta(x_1-x_2) is either zero of infinity. is this correct? thanks

For a field of 15 T, I calculated the magnitude of the splitting, which was 1.391E-22 J (this is delta E), i.e. delta E = |e| / 2m hbar B_z (m2 - m1) where m2 and m1 are the m_l levels. In order to determine the spacings for the visible lines on the absorption spectra, will that just be...

Homework Statement Suppose f(x) = x2 + x + 1, a = 1, and L = 3. Find a value d > 0 such that 0 < |x - a| < d implies |f(x) - L| < 1/100 Homework Equations The Attempt at a Solution Given 0<|x-1|<d implies 0<|x2 + x + 1 - 3|<1/100 0< x2 + x + -2 <1/100 0<(x+2)(x-1)<1/100 Assume 0<|x-1|<1...

Homework Statement Prove the following states directly using the formal e, d definition \lim_{x\rightarrow 8} \sqrt{x + 1} = 3 Homework Equations The Attempt at a Solution If 0 < |x-8| < d Then 0 < sqrt((x+1) - 3) < e Let e be given 3 < sqrt(x+1) < e + 3 9 < x + 1 <...

Homework Statement I wonder how to deal with the square root of Dirac Delta function, \sqrt{\delta(x)}. Actually, this comes from a problem which asking readers to calculate the wave function of a free particle and of a harmonic oscillator at time t, provided that the wave function at time...

Homework Statement On July 1, 2004, the Cassini spacecraft approached Saturn with hyperbolic excess velocity 5.5 km/s to swing by the planet at the closest approach distance rp = 80,680 km. Compute the impulsive ΔV required for a maneuver performed at the closest approach to Saturn to...

Whats the difference between average velocity and delta velocity? I understand the formulas (ie. Vave = delta displacement/delta time) but I don't understand why you would use one over the other and what the difference is. Thanks for the help.

Homework Statement Suppose A_n is, for all natural numbers n, some finite set of numbers in [0,1] and A_n intersect A_m={ } if m!=n Define f as follows: f(x) = 1/n if x is in A_n and 0 if x is not in A_n for all n. Prove that the limit as x goes to a of f(x) = 0 for all a in [0,1]...

I am supposed to prove that δ'(ax) = (1/a)*(1/|a|)*δ'(x) but I cannot figure out where the (1/a) term comes from. Using the scaling theorem I know that δ(ax) = (1/|a|)*δ(x), but how does this apply to the first derivative and does it explain where the (1/a) comes from?

The problem is to prove that δ'(ax) = (1/a)*(1/a)*δ'(x), where a is a constant. I tried applying the scaling theorem with the formal definition of δ'(x) but I can not get the second (1/a) term. Does anyone have some insight on this problem? Thank you...

Awesome vantage point.

Homework Statement Can anyone remember a decent argument/derivation for the following representation of the delta function. Homework Equations $ \nabla^2 \frac{1}{|r|} =\delta(r)$ (probally up to some multipicative constant $\frac{1}{2\pi}$ or something The Attempt at a...

How would you write an infinite line charge with constant charge per unit length \lambda as a volume charge density using Dirac delta functions? Perhaps in cylindrical coordinates? I'm confused because if you integrate this charge distribution over all space, you should get an infinite amount...

This problem is a symmetric delta potential problem that I was given a few days ago and I can't seem to get the gist of it. Question: Find the spectrum and wave functions of a particle in the potential V(x)=G[d(x-a)+d(x-a)] Calculate the transmission and reflection amplitude. Where G can be...

the question is , can a delta function /distribution \delta (x-a) solve a NOnlinear problem of the form F(y,y',y'',x) the question is that in many cases you can NOT multiply a distribution by itself so you could not deal with Nonlinear terms such as (y)^{3} or yy'

Find the value of delta that corresponds to 0.75. Give your value of delta where delta or any positive number will satisfy the conditions . give the answer correct to 3 decimal places, round down if necessary. lim (4+x-3x^3)=2 x-->1

I need to show that: \delta(g(x)) = \sum_k \frac{\delta(x-x_k)}{|g'(x_k)|} where the set {x_k} are the zeros of g(x) and g'(x_k) \neq 0 I'm not really sure where to start for this problem, any clues would be much appreciated!

Given f(x) = x2, L = 4, xo = -2, e = 0.5 find delta. -0.5 < x2 - 4 < 0.5 3.5 < x2 < 4.5 (3.5)1/2 - (-2) < x - (-2) < (4.5)1/2 - (-2) =>|x - xo| < (3.5)1/2 - (-2) ~ 3.87 My text says the answer is 0.12 ? I was convinced that I have been doing these right. Am I?

I know that this question was posted before but I just couldn't get it using another way around. So your comments are highly appreciated. In the textbook, \nabla\bullet\left(\widehat{r}/r^{2}\right)=4\pi\delta^{3}\left(r\right). But when I want to calculate the divergence using Catesian...

Let f(X)=\frac{\sin(2x)}{x} and use a graphing utility to conjecture the value of L = \lim_{x->0}f(x) \mbox{ then let } \epsilon =.1 and use the graphing utility and its trace feature to find a positive number \delta such that |f(x)-l|< \epsilon \mbox{ if } 0 < |x| < \delta . My...

Homework Statement This is Example 5 in Chapter 2.3 of the above mentioned text: Problem: Prove that the \lim_{x\rightarrow2}f(x)=4 if f(x)= x^2 \text{ for }x\ne2\text{ and }f(x)=1\text{ for }x=2 Solution Step 1 Solve the inequality |f(x)-4|<\epsilon to find an open interval...

Homework Statement Evaluate the following sums, implied according to the Einstein Summation Convention. \begin{array}{l} \delta _{ii} = \\ \varepsilon _{12j} \delta _{j3} = \\ \varepsilon _{12k} \delta _{1k} = \\ \varepsilon _{1jj} = \\ \end{array} The Attempt at a...

A positive number epsilon (e) and a limit L of a function f at a are given. Find delta such that |f(x)-L|< epsilon if 0 < |x-a| < delta. \lim_{x->5}, 1/x= 1/5, \epsilon=.05. That implies the following |\frac{1}{x}-\frac{1}{5}|< \epsilon \mbox{ if }|x-5|<\delta. Which implies...

45. A gas sample expands from Vo to 4.0Vo while its pressure decreases from po to po/4.0. If Vo = 1.0m^3 and po = 40 Pa, how much work is done by the gas if its pressure changes with volume via (a) path A, (b) path B, and (c) path C? The p-V diagram can be found at the following addrs on...

I have started studying maths on my own using a University maths book that may not lend itself to self study. So I was hoping someone could help me with the following.abs{sqrt{x}-2} < .05 if 0 < abs{x-4} < delta. I rewrite this as abs{sqrt{x}-2} < .05 if abs{(sqrt{x}+2)(sqrt{x}-2)} < delta...

Find the delta for the given epsilon. lim (1/x) =1 epsilon=.07 x->1 Homework Equations The Attempt at a Solution I got to here .07526 >x-1> -.06542 so what one is me delta??

since dirac delta function is not a literally a function but a limit of function,does it mean that dirac delta function is continuous and differentiable through out the infinity? is there any example of dirac delta function if yes then give meeeeeeee?

I have an example bit I can't quite follow it...? Use epsilon -delta definition of continuity to prove f(x) = 3x^2 - x is continuous at x=2 Ep > 0 and delta > 0 in terms of Ep f(x) -f(2) = 3x^2 - x -(3*2^2 -2) f(x) - f(2) = 3x^2 -x - 10 f(x) - f(2) = (3x + 5)(x - 2) So far so...

Homework Statement I had to do a curve fit on some data and got an equation to the form:Homework Equations F(t) = a_0 + a_1 t + a_2 t^2The Attempt at a Solution Each parameter has an associated uncertainty. I need to integrate F(t) over a range to get I. How do I find the the uncertainty in...