Properties Definition and 1000 Threads

I'm having some trouble showing that a Mobius transformation $F$ maps $0$ to $\infty$ and $\infty$ to $0$ iff $F(z)=dz^{-1}$ for some $d \in \mathbb{C}.$ Mainly with the "only if" part. Do I need to use pictures? This is Exercise $23$ in Section $3.3$ of Conway's *Functions of One Complex...

Hi all, I've joined this forum as a last resort seeing no one else here knows (well, before maybe joining other forums?). I've been handed an old model of the iron ore plant I work at which was made in the 90s in excel (the model was made then, not the plant!). The metallurgist at the time was...

I am not clear on the below, so any additional information would also be good. Let's say a pair of photons is entangled on 2 properties. When we measure on property A -- the values for property A (for both the entangled photons) becomes determinate/locked/fixed when we measure on property B...

Is there something said about \lim_{||v||\to 0} \frac{v_i}{||v||} ? Is it correct to assume if the length of a vector approaches 0, then any component of that vector has to approach 0, aswell?

I have been studying quantum field theory and I am currently in the Lagrangian field theory chapter in my book. Now it says that the energy momentum tensor is as follows: Tμν= [∂L/∂(∂μφ) * ∂νφ] - δμνL Note: I am using L to symbolize Lagrangian density and not just Lagrangian since the latex...

Hi! I am modelling heat transfer through the oxide scales on the surface of steel but I cannot find the accurate properties of oxide scales. I need thermal conductivity, density and specific heat capacity. They shloud be dependent on temperature. I have found only one book in which are some...

Hi PF, i have several questions about univariate statistics that doesn't seem to be covered in my notes or online, i hope the question is not redundant on the forums, but i ran a search and saw nothing. In univariate statistics, you can have a PMF which is a discrete random variable (RV) and a...

Textbook says, Fourier transform expresses a function in time domain as a function in frequency domain. Basically, Fourier transform gives two different expressions in terms of t domain and f domain but they represent the same signal. It also says Hilbert transform is a different type of...

hello is there a reference, wikipedia article, other article, book, or something that will outline consisely and simply, without the maths (not necessary at this point) the thermal properties of materials what I mean thermal properties? how materials interact with heat for example, how do we...

I noticed a funny thing. The Cholesky decomposition can be defined as X=AB, where A is lower triangular. Generally Y=BA is not X, but Y seems to be a positive definite matrix. I wonder if there is any special properties to the pair (X,Y). I know that a positive definite matrix can be interpreted...

Warning: This is going to be a bit long. (Apparently my post was too long so it wouldn't render at all. I've split this into two threads.) I worked out some basic Algebraic properties of a Lie Algebra. This is similar to my previous thread about SU(2) but as I don't know this example I'm...

If antimatter moves in the direction it was pushed from, is this because it has its own sort of properties such as inertia in regular matter?

Homework Statement The Attempt at a Solution I thought that an ellipse shares vertices on the y-axis and the x-axis. Making it neither vertical major axis. I am unsure about the question.[/B]

I am reading an article by Vernon Chi on quaternions and rotations in 3-space. The title of the article is as follows: I am concerned that I do not follow the proof of one of the properties of unit quaternions in Section 3.1.3 of the article. Section 3.1.3 reads as follows: In the above text...

I'm studying for my prelim and am trying to understand inductance better based on some questions I have done I've come up with these statements can anyone confirm they are true the back emf in an inductive circuit at any given time equal to the voltage across the inductor I initially thought...

Homework Statement I need to figure out the energy, rest mass, speed, wavelength and momentum of a 2.2 eV electron. Thats all it says. Homework Equations Ek = 1/2mv^2The Attempt at a Solution I don't understand what 2.2 eV is. The kinetic energy? This converts to 3.52x10^-19 J Rest mass...

So we know that [Hodge duality](http://en.wikipedia.org/wiki/Hodge_dual) works this way $$⋆(dx^i_1 \wedge ... \wedge dx^i_p)= \frac{1}{(n-p)!} \epsilon^{i_1..i_p}_{i_{p+1}..i_n} dx^{i_{p+1} } \wedge dx^{i_n}$$ where p represents the p in p-form and n is the dimensional number. My question is...

Hiya, I've been mucking around with a 2n7000 MOSFET and I can successfully turn it on and off, but to turn it off I either have to put the gate at 0v and wait a few seconds and it turns off itself or apply negative voltage to the gate and it'll stay off when I return it to 0v. Is this normal for...

Title basically says it all. I'm a physics undergrad trying to wrap my head around quantum physics, and I was hoping people here could help. My question comes from something in one of my textbooks. It tries to explain particle-wave duality through a piece of string, which I'll quickly go over as...

Homework Statement Light with wavelengths of 520 nm and 630 nm passes through a diffraction grating that contains 6000lines/cm. a) Sketch a diagram of the image produced from m = 0 to m = 2. Label the order of each fringe. b) Calculate the angles for the first and second order maxima that would...

Hi, just curious: I saw a result that for the multiplicative group G:= {1,-1, i, -i } , "every homomorphism ## h: G \rightarrow G ## is of the form ## z \rightarrow z^k ## for some ##k \in \mathbb Z ##. I can show this is true by considering the image of a generator, but I was wondering if...

Hi all - in the question below I could do with some help on the "..explanation for the relative strengths..." bit, as I can't think of anything to say. 1. Homework Statement Compare and contrast the properties of the strong and weak interactions. Include in your account an explanation for the...

I am doing some self study of groups and can solve problem #3 but not Problem #4. Problem 3. Let A be a finite set, and B a subset of A. Let G be the subset of S_A consisting of all of the permutations f of A such that f(x) is in B for every x in B. Prove that G is a subgroup of S_A. Problem...

I'd trouble remembering decision properties of languages like Regular, CFL, RE, etc. So I made a table of it. Are all the entries of table correct or has some errors http://postimg.org/image/bdb5tqkfl/][/PLAIN] http://s24.postimg.org/bdb5tqkfl/Decision_Property.jpg

Hello! (Wave) For each pair of natural numbers $m \in \omega, n \in \omega$ we define the multiplication between $m,n$ (as a function $\cdot: \omega \times \omega \to \omega $) like that: $$m \cdot 0=0$$ $$m \cdot n'=m \cdot n+m$$ I want to show that for each $m \in \omega, n \in \omega, k...

Hello! (Wave) For each pair of natural numbers $m \in \omega, n \in \omega$ we define: $$m+0=m\\m+n'=(m+n)'$$ We fix a $m$ and recursively the operation $m+n$ is defined for any $n \in \omega$. Knowing for example that $m+0=m$ we can conclude what $m+1$ means. $$m+1=m+0'=(m+0)'=m'$$ and...

I had a couple of questions. 1. Why does the integral ∫exf(t) dt transform to ex∫f(t) dt? Shouldn't ex be a part of the integrand too? 2. Why is the difference dy - dy1 = d(y - y1)?

Hi all, I have a few questions regarding electron shells and seeing if they should be intuitively connected to de Broglie's description of electrons as waves. I teach high school level and occasionally get wild questions...if I can ever help a student in the slightest I am inclined to try. So...

Homework Statement Dear Mentors/PF helpers, Please help me with part (ii), I couldn't find a way through this part. Homework Equations The Attempt at a Solution My solutions: (i) angle RPS = 65 deg (angles in the same segment are equal) (iii) angle PRS = 110 - 65 = 45 ( exterior...

Hi all, I have a general question about material properties. We know that the material property value depends on the input level. For example, the permittivity in a dielectric material changes depending on the applied electric field. That being said, when we apply an alternating electric...

O is the centre of the circle and XTY is a tangent to the circle. The chord TC intersects the diameter BOD at Z. If angle TÂB = 124° and angle CBD = 28° calculate 1) angle YTB 2) angle CTD 3) angle BOT 4)angle DZC 5) angle OTD 6) angle CTY

What would be the reducing reaction for these in water?

Homework Statement If the shear stress in steel exceeds about 4.0 x 10^8 N/m^2, the steel ruptures. Determine the shear force necessary to punch a 1-cm diameter hole in a steel plate that is 0.5 cm thick. Homework Equations The Attempt at a Solution The way I tried to solve this problem...

What I'm asking for is if there is a guide for the properties of processes like isochoric, isobaric, isothermal and adiabatic. For instance, a comprehensive guide that tells me that the pressure in an isobaric expansion is the same before and after, etc. If there isn't, does anybody have any...

Homework Statement I have problem with properties of compatible observable Homework Equations [AB,CD]=AB CD – CD AB ………. (1) ABCD+ACBD-ACBD-ACDB+ACDB+CADB-CADB-CDAB ………. (2) A{C,B}D-AC{D,B}+{C,A}DB-C{D,A}B ... (3) The Attempt at a Solution How can the equation (1) become (2), and eq (2)...

Homework Statement Let ##O## be a proper open subset of ##\mathbb{R}^d## (i.e.## O## is open, nonempty, and is not equal to ##\mathbb{R}^d##). For each ##n\in \mathbb{N}## let ##O_n=\big\{x\in O : d(x,O^c)>1/n\big\}## Prove that: (a) ##O_n## is open and ##O_n\subset O## for all ##n\in...

Hello! (Nerd) I want to write an algorithm that checks if a binary tree has the properties of a $\text{ 2-3 tree }$. The properties of the $\text{ 2-3 trees }$ are the following : All the leaves have the same depth and hold one or two elements. Each internal node: either holds one...

Hi! (Wave) We have an $\text{AVL tree}$ and we are given a key $r$. I want to write an algorithm that finds the depth and height of the node, of which the key is $r$. So, do we have to compare the key of the root with the key $r$ and if it is greater we will have to continue at the left...

Are there any particles on the Standard Model of Particle Physics with all the properties of a WIMP particle(Weakly Interacting Massive Particles)?

I was wondering, how does a photon look like? What does it look like? I'm taking modern physics at the moment and I'm able to calculate lots of things quite well. Like DeBroglie wavelengths, I'm able to utilize the Schrodinger equation and the Heisenberg uncertainty principle and what not but I...

Say a person was descending at constant rate of 1m/s while holding a ball. Then, without stopping, the person dropped the ball which assumed a free fall. Would the ball assume an initial velocity of 0m/s, or would it start at the one 1m/s that the person is traveling? If anyone can, please...

Hi All, Please let me set things up before the actual question: I have a Lefschetz fibration ## f: W^4 \rightarrow S^2 ## , where ## W^4## is a closed, oriented manifold, and ## S^2## is the 2-disk. This f is a smooth map with finitely-many singularities {## x_1, x_2,..,x_n ##}, so that we have...

How exactly does light move through space in terms of EM radiation and photons. What I'm confused about is the electromagnetic field. How does it oscillate, and in which directions? Also do photons have Electromagnetic fields associated with them?

If you had to a create a super element to be added to the periodic table, what would it be? I'm talking about it's properties.. give me some good techno babble.

hi guys I am trying to understand the properties of waves, does a wave oscillate on a 2 dimensional or 3 dimensional plane? if a wave need a hole the size of its double its amplitude to pass through un-effected can it pass though a thin slot with a length that is double the waves amplitude...

Hi. I'm looking for a recommendation for a book (or website) that has detailed information on properties of materials. Specifically on mechanical properties. A book that covers all grades of materials, not just a general guide. I'm forever to-ing and fro-ing between websites, datasheets and my...

Hi All, AFAIK, the key property that separates/differentiates a Hilbert Space H from your generic normed inner-product vector space is that , in H, the norm is generated by an inner-product, i.e., for every vector ##v##, we have## ||v||_H= <v,v>_H^{1/2} ##, and a generalized version of the...

How did he figure out the many properties of the Universe such as time dilation/relativity and energy matter equivalence and his numerous other contributions. This might be a dumb question but was this all just done on paper? I don't recall reading that Einstein ever conducted experiments...

Hi all, I'm wondering if anyone knows of a way to obtain elasticity properties (Ex, Ey, Ez, Gxy, Gxz, Gyz, vxy, vxz, vyz) from the terms of a 6x6 anisotropic stiffness or compliance matrix. I'm looking for a closed form solution, preferably. I would think that there should be a closed form...

I just studied about the QM of singlet spin pairs. I have additional questions. Neither Wikipedia, nor past threads on this forum seem to address the questions. 1) A pair of electrons forming a singlet pair A. Can the pair be split again into non-entangled electrons? If yes how; just hit...