Characteristic Definition and 287 Threads

Homework Statement I am trying to figure out following problem. Let A ⊂ R. Then we can define the characteristic function: \begin{align} \chi_A : R → \{0, 1\}, x = \begin{cases} 1 & \text{if } x \in A \\ 0 & \text{else } \end{cases} \end{align} Let a be bigger than 0. I am...

In an experiment one observes the characteristic Ka X-rays of two elements at energies of 6.930 and 7.478 eV. The higher energy line is due to Ni. What element is responsible for the lower energy line?

Solve the following Cauchy problem using the Method of characteristic curves: $x_1u_{x_1}+x_2u_{x_2}=\alpha u$ in $\mathbb{R}^{+}\times \mathbb{R}^{+}$ $u(x_1,1)=g(x)$ for all $x_1\in \mathbb{R}^{+}.$ Find the local solution for the problem.Hello. I get as solution $g(s)=s$, I want to know if...

Homework Statement Hello. This should be rather easy. I am trying to figure out what the Characteristic length I should use in calculating the grashof number for a greenhouse. The dimensions given for the greenhouse are 1.5 m wide x 2 m long and 2 m high. What characteristic length should I...

Hello all, Homework Statement $$x{u_{xy}} - y{u_{yy}} = 0$$ Assume $$x,y \in {\rm{Reals}}$$ Homework Equations I have been able to solve this using different methods, but my classmates and I are trying to figure out if there is a way to do this using the methods from the course's text. The...

I have come across this inequality:$$ g≤ log\ n <g + 1$$ We assume that the base of the log is b >1 and n is all the natural numbers. I would like to know if anyone could provide a proof regarding this and mention for what g ? Is it for all the g which are integers ?

what is the difference between property and characteristic of a material?

Homework Statement If I have the characteristic equation: -λ3 + 3λ2 + 9λ + 5 And I'm told that one of its eigenvalues is -1. How do I find the rest of the eigenvalues? Homework Equations -λ3 + 3λ2 + 9λ + 5 The Attempt at a Solution The furthest I can get is: -λ3 + 3λ2 + 9λ + 5 = (λ + 1) x...

THIS IS NOT A HW/COURSEWORK QUESTION! I am simply revising for an exam and am trying to better understand the behavior of the stripline as shown in the file attached. What would be the effect on the characteristic impedance, as W/b/epsilon_r/t increases (each separately)?

Homework Statement Using the diagram for the I-V characteristic of a semi-conductor (attached). Answer the following questions: 1. Why is the resistance of an I-V characteristic not determined by the gradient of the graph 2. Explain why the temperature of semiconductor increases 3. Explain why...

Homework Statement Given an NxN symetric tri-diagonal matrix, derive the recursion relation for the characteristic polynomial Pn(λ) Homework Equations Pn(λ) = |A -λI | Pn(λ) = (An,n - λ)Pn-1(λ) - A2n,n-1Pn-2(λ) The Attempt at a Solution This was easy to do by induction, but I am always...

I have a question about body inertness. Is moment of inertia is unambiguous inertness characteristic?

Homework Statement I'm looking to find the characteristic function of p(x)=\frac{1}{\pi}\frac{1}{1+x^2}[/B] Homework Equations The characteristic function is defined as \int_{-\infty}^{\infty} e^{ikx}p(x)dx 3. The Attempt at a Solution I attempted to solve this using integration by...

Homework Statement What are the energies of the characteristic Kα line and Kβ lines? Homework Equations K-shell ( n =1):-69.5 keV L-shell ( n =2 ): -11.3 keV M-shell ( n =3 ): -2.30 keV Z = 74 E = (energy level) (Z-1)2/n2 The Attempt at a Solution for alpha i have (-11.3keV) (74-1)2/22 for n...

Firstly, apologies if this is in the wrong thread. I'm currently writing a presentation on the physics of getting a spacecraft from Earth to Mars in the near future. In my research I've come up against Porkchop plots which seem to plot contours of equal characteristic energy so you can find...

Dear all! I have a question about the impedance characteristics in the distance relay used for transmission line protection. I understand that in the first quadrant we have a inductive load and in the fourth quadrant we have a capacitive load. I, however, do not understand what we measure in...

We can find differential of alloy and composite. MMC is came from 2 differential of metal, one from it aren't melting same as producing alloy. but there are might produce new reaction. ex: C with Fe, the name is carbon steel. the nano-composite just too, but the particle aren't big, and the size...

I am looking for a local field of positive characteristic, like Q22 was used in this article: http://8pic.ir/images/s9oiiuqqkq989w3posu9.png in fact, i need an another Example of a local field of positive characteristic like Q22 .

Homework Statement Hi guys, I am not sure what the characteristic time of something is. I've been looking online but am getting confused with the definitions. Say, for example, the characteristic time for some particles suspended it water to descend to the bottom. Homework EquationsThe...

Hello! (Wave) In my notes, there is the following theorem: Theorem: Let $Q(X_1, X_2, \dots, X_n)=\sum_{i,j=1}^n a_{ij} X_i X_j$ $$a_{ij}=a_{ji}, \ \ \ \ ch K \neq 2 ( \text{ Characteristic of polynomial })$$ symmetric quadratic form of $n$ variables. There is a linear transformation of the...

In physics one often invokes arguments about a characteristic scale. For example at distances much larger than the Compton wavelength (a characteristic length scale) one might ignore quantum phenomena and calculate classically. I would like to read up some more on the thinking behind such...

I have just finished a junior-level lab assignment in which we used X-ray diffraction to determine the lattice constants of unknown materials. In the theory section of the lab write-up, it briefly explains the K-alpha doublet of the characteristic spectrum. I understand that it is the result...

Find the characteristic function for the PMF \(p_X[k] = \frac{1}{5}\) for \(k = -2, -1,\ldots, 2\). The characteristic function can be found with \begin{align*} \phi_X(\omega) &= E[\exp(i\omega X)]\\...

I am integrating the characteristic equation in order to recover the PMF, but I am going to get the answer to be zero so something went wrong. \begin{align*} p_X[k]...

Hello, All Outstanding electrical engineering student, I have a some question. As posted, 1. At low frequency, the inversion electrons will be able to respond to the ac voltage => CG (ω= 0) = Cox (Why?). 2. At high frequency, inversion electrons are not able to respond to ac voltage...

Hello Everyone, I am currently reading about when the Quantum Mechanical Theory becomes relevant. A term that continually emerges is "characteristic length." Could someone provide me with a thorough definition of this concept? Thank you!

I am working on impedance measurements of close-wound electromagnetic coils. I am using an Agilent LCR meter to measure the impedance of these coils over a frequency range of 20Hz-2MHz. When I perform the measurements, I get impedance magnitude and phase angle in degrees. I would like to...

Hello everyone! In the following speed-torque characteristic of a DC shunt motor, we see that if the speed exceeds a certain value, then the machine becomes a generator. I don't understand something. How is it possible for the machine to have a negative torque and a positive speed...

Homework Statement Find the output signal for an amplifier with transfer characteristic: vO = 10-10-11e40*vi output bias of 5V input bias of 0.673 V and an input signal of 1 mV superimposed on the bias Homework Equations vO = bias out + signal out vI = bias in + signal in The...

Hello guys, I posted this question in the classical mechanics forum (thinking stochastic mechanics falls into the classical mechanics category) but I haven't gotten an answer there. I was told I'd be better off posting the question here. I don't know how to move a thread, so I'll just copy and...

Hello I confused about the equation for the biot number Bi = hLc/k For a slab, sphere, and cylinder, what are the characteristic lengths?

Homework Statement suppose u(x,y) satisfies the partial differential equation: -4y\frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}=0 Find the characteristic curves for this equation and name the shape they form The Attempt at a Solution \frac{dy}{dt}=1 \Longrightarrow y=t+y_0...

Now w/ Attachment: Telephone Wire w/ Load and Characteristic Impedance Homework Statement Please see attachment. Homework Equations I(z)=I+(exp(-γz)) + I-(exp(γz)) V(z)=V+(exp(-γz)) + V-(exp(γz)) The Attempt at a Solution I solved easily for the characteristic impedance and gamma...

Homework Statement A:B→B a linear operator Show r is multiple root for minimal polynomial u(x) iff >$$\{0\}\subset \ker(A - rI) \subset \ker(A - rI)^2$$ note: it is proper subsetHomework Equations The Attempt at a Solution Homework Statement My thought: I know ker(A−rI) is basically {{0}...

Dear all, Greetings! I was given a problem from Reichl's Statistical Physics book. Thank you very much for taking time to read my post. Homework Statement The stochastic variables X and Y are independent and Gaussian distributed with first moment <x> = <y> = 0 and standard deviation...

Homework Statement The stochastic variables X and Y are independent and Gaussian distributed with first moment <x> = <y> = 0 and standard deviation σx = σy = 1. Find the characteristic function for the random variable Z = X2+Y2, and compute the moments <z>, <z2> and <z3>. Find the first 3...

[FONT=arial]Find characteristic functions of [FONT=arial]1. The random variable X uniformly distributed on[-1..1] [FONT=arial]2. The random variable Y distributed exponentially (with exponent λ) [FONT=arial]3. The random variable Z=X+Y

Homework Statement See attached image Homework Equations The Attempt at a Solution For the first half of the question, ordered pairs would be (1, [1]), since 1 and [1] are the multiplicative identities in these rings. but no matter how many times we add (1, [1]) to itself...

This was something I noticed as I was trying to practice solving PDEs using the method of characteristics. The text has the following example: $$\frac{\partial u}{\partial x} + x \frac{\partial u}{\partial y} = 0$$ This should be easy enough. I let p(x,y) = x and solve for \frac{\partial...

[SIZE="5"]Homework Statement Calculate the Characteristic Impedance (Z0) of the two port network? Homework Equations When port 2 open-circuit, [SIZE="5"]I2 = 0 So, [SIZE="5"]Z11 = [SIZE="5"]V1 / [SIZE="5"]I1 = 40(60) / 100 = 24 Ω When [SIZE="5"]I2 = 0, thus [SIZE="5"]V2...

Similar matrices share certain properties, such as the determinant, trace, eigenvalues, and characteristic polynomial. In fact, all of these properties can be determined from the character polynomial alone. However, similar matrices also share the same rank. I was wondering if the rank is...

Hi there, I'm an instructor teaching a Physics course for Radiography students designed for students with little to no Physics background. In prepping the course, I've come up with a couple of questions that are bothering me and hope someone here can be of assistance. My questions pertain to...

I'm just starting to read up on RF circuits, and I'm a little confused about what the characteristic impedance of a system is (not the characteristic impedance of a transmission line, I understand that pretty well). For example, in Pozar's book he talks about a 3 dB attenuator with a 50 Ω...

I've been looking for proof of the fact that the characteristic polynomial of an n by n matrix has degree n with leading coefficient ## (-1)^{n} ##. I first tried proving it myself but my method is a bit strange (it does use induction though) and I am doubting the rigor, so could perhaps...

Homework Statement The given quantities are the shunt resistances across each of the 3 diode junctions,assume them to be Rsh1,Rsh2,Rsh3; Tunnel diode resistances as Rt1 and Rt2, Photocurrent for each of the junction be Ip1,Ip2,Ip3 and bandgap of each subcell be Eg1,Eg2,Eg3 are given.Let V & I...

Hi I am a little confused as to what length to use as the characteristic length of the Reynolds number for a body in and incompressible flow that has no boundary conditions(ie there all open). im going to try and draw a few examples to help me out..(i have no idea why..) from what i have read...

I have an x-ray tube. When I see the spectrum, I notice the characteristic lines of the anode. What do I have to do if I want to absorb a characteristic line? I have thought that I can add a filter. But.. which filter? Should it be an element such that the bound energy for the K-shell electrons...

Hi, this is not a homework. I need your help to understand basic concepts. I am learning by myself. In textbooks, I usually see the circuit used to make Ic -Vce characteristics. I see that there are no resistors at base and collector/emitter. What will happen if VBE is larger than 1V or...

We all know that the Euler characteristic is a topological invariant. But let's suppose that we don't know this or anything else about algebraic topology for that matter. We are given only the Gauss-Bonnet theorem, which expresses the Euler characteristic in geometrical terms. In his string...

Hi This is just a quick question, it should have a pretty simple answer however I can't find the information anywhere on the internet. When you are calculating/estimating the heat transfer coefficient for a prismatic fin using the reynolds, prandtl, grashof, and nusselt number, what length do...