Characteristic Definition and 287 Threads

My calculations: ##2a = (2a)^4 = 16a^4 = 16a## ##14a=0## This allows for the characteristic to be 2 or 7. But, e.g., ##3^4 = 81 = 4 ~(mod~ 7)## rather than ##3##. So, the only answer is ##2##. 1. Is this derivation correct? 2. The hint in the textbook says to show that ##2a=0##. How to do that?

I woud like to find the characteristic curves for ##u_t + (1-2u)u_x = -1/4, u(x,0) = f(x)## where ##f(x) = \begin{cases} \frac{1}{4} & x > 0 \\ \frac{3}{4} & x < 0 \end{cases}##. By using the method of chacteristics, I obtain the Charpit-Lagrange system of ODEs: ##dt/ds = 1##, ##dx/ds = 1 -...

I was reading about characteristic x rays. I have a question I did not find an answer for it in the book (Concepts of Modern Physics-Sixth Edition-Arthur Beiser) or in the internet search. My question is: How do the atom in the target (in the x ray production experiment) go to the normal state...

The characteristic equation ## m^3 -6m^2 + 12m -8 = 0## has just one single, I mean all three are equal, root ##m=2##. So, one of the particular solution is ##y_1 = e^{2x}##. How can we find the other two? The technique ##y_2 = u(x) e^{2x}## doesn't seem to work, and even if it were to work how...

Before starting, I will leave the link to the article I am talking about here: http://www.msc.univ-paris-diderot.fr/~phyexp/uploads/LaimantParesseux/aimant2.pdf I am conducting a similar experiment to the one discussed in the paper above. Basically, I am rolling a neodium supermagnet down a...

Can someone provide more information about this method to measure chracteristic impedance using resistance paper?. Kraus' book claims that the characteristic impedance can be measured by simple dc measurement. It even shows a case to mesure the impedance of a coaxial cable with square outer...

intermolecular distance means distance between particles. So, I imagine a sphere. $$\frac{4}{3} \pi d^3 = \frac{V}{N}$$ However, Griffitfhs pictures a box instead, where $$d^3 = \frac{V}{N}$$ And the difference between both models is a factor of ##(4\pi/3)^{2/5} \approx 1.8##, which is...

good evening everyone! Decided to solve the problems from last year's exams. I came across this example. Honestly, I didn't understand it. Who can help a young student? :) Find characteristic equation of the matrix A in the form of the polynomial of degree of 3 (you do not need to find...

dx/dt =1, x(0,s)=0, dy/dt=x, y(0,s) = s, du/dt=(y-1/2x^2)^2, u(0,s)=e^s I did well at the beginning to get x(t,s) =t and y(t,s)=1/2t^2 + s, but got stuck with the du/dt part. You can sub in x=t and y=1/2t^2 +s for x and y to get du/dt = s^2. But that's still three variables, and I can't see...

I found my energies for Potassium. I have 3.3 KeV for the k alpha nd 254.6 ev for L alpha, using z=19 and n=3. Are these values correct? Edit: I found the ratio to be .077

I have the characteristic function of the Cauchy distribution ##C(t)= e^{-(\mid t \mid)}##. Now, how would I show that the Cauchy distribution has no moments using this? I think you have to show it has no Taylor expansion around the origin. I am not sure how to do this.

hello everyone! i have some problem in solution of this problem should i transfert the vertical stree to the horizontal stress and solve it ? problem : The equivalent static stiffness of the soil as an infinite elastic half-space under an infinite strip foundation is given in the vertical...

Image 1: Image 2: I am attempting to learn about transmission lines and am having problems with this homework problem. For part a, I have derived an equation for the maximum electric field within the dielectric. I came up with: with r being the radius and the electric field decreasing with...

Hello, I've carried out an experiment to plot the characteristic curves (Ic vs Vce) for a BC108 transistor and then attempted to find where the load-line intersects those curves. Below are my results: ...as you can see, the load-line doesn't intersect the characteristic curves at all...

Could I get a conceptual answer, supported by math, explaining why coax has less characteristic impedance than open wire feeds?I’m new to EE. Thanks for you patience.

What are the critical Reynolds number for fluid and characteristic length when a cylinder immerses and then rotates in the fluid (The fluid is initially static)? Please suggest the critical number for the transition from concentric flow to laminar and from laminar to turbulent flow. I would...

Homework Statement [/B] I am trying to determien the characteristic function of the function: $$ f(x)= ae^{-ax}$$ $$\therefore E(e^{itx}) =\int_0^\infty e^{itx}ae^{-ax} dx = a \cdot \frac{e}{it-a} |_0 ^ \infty $$ But I am not sure how to evaluate the integral. Wolfram alpha suggests this...

Do we have reflection when the intrinsic impedance η=E/H between two media are matched but not necessarily the characteristic impedance (assuming a transmission line)? Basically, I have a case here shown below I have two parts with different geometries (this may not be a transmission-line, if...

Hello, A few years ago I heard about a list named the "10 characteristic experiences of physics", may I know if a such list exist? A few years ago, at the physics workshops at the Palais de la découverte, I saw the so-called "triple point of water" experience. The experimenter told us that...

Consider a scattering between two particles a and b that produces two particles c and d: d is stable, while c decays in two other different particles e and f. The first interaction is by strong force (time of interaction ##t_1\sim 10^{-23}s##, which is also the time of generation of c and d)...

Homework Statement I am trying to understand the very last equality for (let me replace the tilda with a hat ) ##\hat{P_{X}(K)}=\hat{P(k_1=k_2=...=k_{N}=k)}##(1) Homework Equations I also thought that the following imaginary exponential delta identity may be useful, due to the equality of...

This thread will be a collection of multiple questions I asked before over different forums. I will start from the beginning, and I hope someone will follow the steps with me, because I did it before alone, and I ended with a numerical integration that is not finite, which doesn't make sense...

Is there a way to find the CDF of a random variable from its characteristic function directly, without first finding the PDF through inverse Fourier transform, and then integrate the PDF to get the CDFÉ

Homework Statement The stability of a spinning body may be explored by using equation (3.40), with no torque components present. It will be assumed here that the spin is about the z -axis and has a rate ωZ = S. Homework Equations $$I_{xx}\dot{ω} - (I_{yy}-I_{zz})Sω_y = 0$$ $$I_{yy}\dot{y} -...

Suppose that ##Y=\sum_{k=1}^KX_{(k)}##, where ##X_{(1)}\leq X_{(2)}\leq\cdots X_{(N)}## and (##N\geq K##). I want to find the characteristic function of ##Y## as \phi(jvY)=E\left[e^{jvY}\right]=E\left[e^{jv\sum_{k=1}^KX_{(k)}}\right] In the case where ##\{X\}## are i.i.d random variables, the...

Suppose I have a random variable whose moments are not defined, can I still use the characteristic function to find the CDF of that random variable?

Homework Statement x2 d2y/dx2 + 3x dy/dx + 5y = g(x)Homework Equations How do we find Characteristic equation for it. The Attempt at a Solution x2λ2 + 3xλ + 5 = 0 λ1 = 1/2 [-x2 + √ (x4 + 20 ) ] λ2 = 1/2[ -x2 - √(x4 + 20) ] I used 1/3 -/+ a √(a2 + 4b) where a = x2 b = 5

Will, I have weird question , when the glass is broken for example, its take some shap like So Why this happen , I mean if i throw a ball on glass does the weakest place are broken ,does this right?

These are the links to the specific product I am looking at and its noise characteristic graph. http://www.emelectronics.co.uk/a20.html http://www.emelectronics.co.uk/graphs/a20graph.htm I understand the graph for the most part, but I am confused about which one of the four filters that are...

The Euler Characterist of the projective plane and sphere is given by V - E + F. V is vertices, E is edges, F is faces. A presentation of the projective plane is {a | aa} and a presentation of the sphere is {b | bb^1} Yet the Euler characteristic is 2 for the sphere and 2-n for the connected...

How can I choose the characteristic linear dimension? For example in pipe it is its diameter, but on a surface is the length, on a flat plane it can be measured as 4A/P. I was having problems determining the characteristic linear dimension for a diffusion problem in a "rectangular" pipe. I don't...

By definition, the characteristic of a field is the smallest number of times one must use the ring's multiplicative identity element (1) in a sum to get the additive identity element (0). Can we use the same rule for the set of natural numbers? If yes, I found a problem, that has something to...

As we know $$Re= \frac{ρ.v.l}{μ}$$ The characteristic length (l) is said to be representative of the problem but according to what should we choose this length? I mean if we want to calculate Reynolds number of a wing of plane, should we choose the length or the width?

Hi, The x-ray consists of the bremsstrahlung spectrum and the characteristic spectrum. We can get x-rays by using Coolidge tube where there are an applied voltage on the tube between the filament and the target. The bremsstrahlung is depeding on the PD between the filament and the target, but it...

Homework Statement Hi, I have the probabilty density: ##p_{n}=(1-p)^{n}p , n=0,1,2... ## and I am asked to find the characteristic function: ##p(k)= <e^{ikn}> ## and then use this to determine the mean and variance of the distribution. Homework Equations [/B] I have the general expression...

Hello, guys. I am trying to solve for characteristic function of normal distribution and I've got to the point where some manipulation has been made with the term in integrands exponent. And a new term of t2σ2/2 has appeared. Could you be so kind and explain that to me, please...

Hi, Does anyone know if there are such characteristics that are tell tale signs of diode degradation? I'm not sure if diodes fail short or open, I'd have thought open, but I'm not sure. I was wondering if as a diode gets old the forward bias voltage might increase? Or the diode power loss per...

How do I go about proving that for two matrices of same size, $M$ and $N$, that the characteristic polynomials of $MN$ and $NM$ are the same? If $M$ and $N$ are inversible, then the proof are very straightforward, for example, I can have $|MN - \lambda I| = |MN - \lambda MM^{-1}| = |M(N -...

The question is : Is it true that two matrices with the same characteristic polynomials have the same trace? I know that similar matrices have the same trace because they share the same eigenvalues, and I know that if two matrices have the same eigenvalues, they have the same trace. But I am...

Homework Statement I have a LED Given: u-i-characteristic curve -> thus the wavelengh It's Part of a curcuit. Also (After the LED) There is a resistance of R (known) An a capacitor, (known) Homework Equations If i have a Voltage of U, how can i find the current Running through the LED and...

Hi, Just curious if someone knows of any Characteristic class used to determine if a manifold allows a Complex structure? It seems strange that Complex Space C^n is topologically Identical to R^{2n} yet I believe not all R^{2n}s ( if any) allow Complex structures. Thanks for any comments, refs...

Homework Statement A lossless transmission line has an inductance of 9.0 nH / m and a capacitance of 3.6 pF / m. a) What is the line's characteristic impedance? b) Calculate the phase constant of a frequency of 1 GHz. Homework Equations Equation of characteristic impedance of a transmission...

Hello all, I'm trying to find the characteristic function of the random variable ##X## whose PDF is ##f_X(x)=1/(x+1)^2## where ##X\in[0,\,\infty)##. I started like this: \phi_X(j\nu)=E\left[e^{j\nu X}\right]=\int_0^{\infty}\frac{e^{j\nu X}}{(x+1)^2}\,dx where ##j=\sqrt{-1}##. I searched the...

Hi all, In an x-ray spectrum, the curve part represents the bremsstrahlung part, and the spikes are the characteristics x-rays. Characteristic x-rays represent a discrete energy. However, in many textbooks, I noticed that the characteristic x-rays are often represented as a peak, which implies...

Hi everyone. I'm trying to derive the formula for the characteristic age of a pulsar. What I'm starting with is the following differential equation. dP/dt=K*P2-n What i think is odd, is several places they say solving this differential equation gives the following solution...

There are characteristic lengths for Reynold's, Grashof, Nusselt, and Biot number but the method of obtaining them is not given in my notes. I would like to know how to do so for a plane wall, cylinder and sphere. Thank you.

An ODE of second order with constants coefficients, linear and homogeneous: Af''(x) + Bf'(x) +Cf(x) = 0 has how caractherisc equation this equation here: Ax^2 + Bx +C = 0 and has how solution this equation here: f(x) = a \exp(u x) + b \exp(v x) where u and v are the solutions (roots) of the...

Homework Statement Which of the symptoms is characteristic for food allergy bumps (pimple) on the face difficulty in breathing flue none of these Homework EquationsThe Attempt at a Solution I'm between the first and second.

Hi all I have the following question that I require help with. 1. Homework Statement A supply fan must deliver 2.5m3s of air against a system pressure of 500 Pa.The selected fir this has a performance characteristic as listed below when running at a speed of 1800 revs/min. i) Plot the system...