Elements Definition and 1000 Threads

Homework Statement I wanted to ask why the symbols of capacitor , resistor and inductor is such which they have..?? Why are we denoting capacitor by 2 parallel plates why not 2 zig-zag plates..and same for inductor??Homework EquationsThe Attempt at a Solution As much I got , resistor has such...

Hey! :o Let $p$ an odd prime and $F=F_{p^n}$ the finite field with $p^n$ elements. 1. Show that the set $F^2=\{a^2, a \in F\}$ has $\frac{p^n+1}{2}$ elements. Conclude that , if $t \in F$ the set $t-F^2=\{t-a^2, a \in F\}$ has $\frac{p^n+1}{2}$ elements. 2. For $t \in F$ show taht the set...

Hello! (Wave) I want to describe an algorithm with time complexity $O(m)$ that, given a set $M$ with $m$ numbers and a positive integer $p \leq m$, returns the $p$ closest numbers to the median element of the set $M$. How could we do this? (Thinking)

Hi, I'm trying to understand the process of finding the elements of a given group, such as SE(2). What I do understand is limited to finding elements of very simple symmetry groups, such as those corresponding to rotations/reflections of shapes. My overall knowledge of groups is also pretty...

My interest leans more towards space opera than hard science fiction, but I'm aware that I can't completely ignore the universe as we know it. A question that has intrigued me lately is: "Are there really new elements and materials to be found in the galaxy, or are we going to find the same...

What I am asking is not a math "problem" but something about presenting the problem in math language. Assume $0<a_{i}<1, i=1,2,3,...,N$ and $a_{i} \neq a_{j}$, I want to have a set $A$ which contains the $M$ indices with the top $M$ values of $a_{i}$. For example, we have $a_{1}=0.2...

Write a for loop to print all NUM_VALS elements of vector courseGrades, following each with a space (including the last). Print forwards, then backwards. End with newline. Ex: If courseGrades = {7, 9, 11, 10}, print: 7 9 11 10 10 11 9 7 Hint: Use two for loops. Second loop starts with i =...

Hi! (Smile) Given two sorted lists $M_1, M_2$, I want to write an algorithm, that creates a new list $M_3$, that contains the elements of $M_1$, that do not exist in $M_2$. That's what I have tried: Algorithm(M1,M2){ pointer q=M1, p=M2, M3; int same=0; if (M1==NULL) return error...

I need to know how to relate this to physics. I've already said that gravity is used when you slide the cups down to stack them. What else can I say? Thanks.

This one is for people working with electromagnets (more specific, DC) etc. I have a few questions that I am struggling with: I am quite comfortable with the concept of the response time (time constant) of a coil in free space, μ0 =4π x 10-7 . The thing I am struggling with is the response time...

Homework Statement Let A=RxR=the set of all ordered pairs (x,y), where x and y are real numbers. Define relation P on A as follows: For all (x,y) and (z,w) in A, (x,y)P(z,w) iff x-y=z-w Homework Equations R is reflexive if, and only if, for all x ∈ A,x R x. R is symmetric if, and only if, for...

Greetings, I am interested in creating a thread dedicated to the discussion of the uses of currently discovered and used and theorized/dreamed of types of matter in our universe. This includes R.E.E's (Rare Earth elements, like Neodymium or Yttrium...

In the same way one can show that \nabla^{2}\theta=0 has only one smooth solution, namely \theta=0, I would like to show that \gamma^{i}\partial_{i}\epsilon=0 has only one smooth solution, where \gamma^{i} is a Dirac gamma matrix (or an element of the Clifford algebra), and \epsilon is a...

Hi! (Smirk) $$x \in \mathcal{P}A \cup \mathcal{P} B \rightarrow x \in \mathcal{P}A \lor x \in \mathcal{P}B \rightarrow x \subset A \lor x \subset B \rightarrow x \subset A \cup B \rightarrow x \in \mathcal{P} (A \cup B)$$ So, $\mathcal{P}A \cup \mathcal{P}B \subset P(A \cup B) $. The equality...

Homework Statement Suppose that ##G## is a cyclic group with generator ##g##, that ##H## is some arbitrary group, and that ##\phi : G \rightarrow H## is a homomorphism. Show that knowing ##\phi (g)### let's you compute ##\phi(g_1)## ##\forall g_1 \in G## Homework Equations ##\phi(g^n) =...

Homework Statement I've been given the line element given below in the relevant equations section and I need to prove that the space it represents is just the same as the 2-D Euclidean plane. Homework Equations ds^2 = a^2 \frac{d\eta ^2 }{cosh^4(\eta)} + a^2 tanh^2(\eta) d\theta ^2 Where...

Hey guys, I'd love to get the formula to answer the following question: I have 50 colorless balls and 100 different paints. All balls have to be painted. Note that the balls' order is not important and repetition is allowed (means I can paint up to 50 balls in any single color if I want). With...

Hi, I would like to establish a advancing/learning way to learn and understand machine elements. Today I tried to search for hydrodynamic radial sliding bearings on search engines but I have find only two results. Is something wrong for it? it should have another names...

In Alaca and Williams' (A&W) book: Introductory Algebraic Number Theory , Theorem 1.2.1 reads as follows:Without any earlier definition or clarification, A&W refer to a/p and b/p (see text above) ... BUT ... how should we regard such elements? What exactly do they mean and how do we know they...

I recently watched a documentary presented by Professor Brian Cox called Human Universe. In it he was wondering how much leeway he would have, if he was "the creator of our universe", to alter the physical constants. He then went on to say that if he altered the speed of light one way then...

Hello! (Wave) I have to write a recursive algorithm, that, given a list in descending order with $M$ elements, creates a new list, that contains the element of the list in ascending order. The list is singly linked and we are given a pointer that shows to the first element of the list. That's...

Homework Statement I am trying to follow Sakurai's use of perturbation theory on a harmonic oscillator, Homework Equations Perturbation: v=\epsilon x^2 , \epsilon << 1 Matrix elements: V_{km}=<k|v|m> The Attempt at a Solution The book says that all other matrix elements besides V_{00}...

ok I am a little confused. can both [i] and .at(i) be used to same way to access an array element?

Some people may remember awhile back when I made a thread showing how when I derived the Einstein tensor and the stress energy momentum tensor for a certain traversable wormhole metric, that the units of the energy momentum tensor were not the same for each element and how a couple of the...

What are the most reactive elements in the periodic table?

I'm asked to figure out how the so-called "coordinate space matrix elements" relate to "momentum space matrix elements <p|H|p'> but I don't understand what they are. any idea on how <x|H|x'> is defined? thanks in advance.

Let F ={0 , 1 , a , b} be a field with four elements. What is a + b^2 and a^2 + b^2. Apparently, the answers are b and 1, respectively. How do we come to that conclusion?

Hello! (Wave) I want to find the powerset $\mathcal{P} \mathcal{P} \{ \varnothing, \{ \varnothing \} \}$, which has $16$ elements. I found that $\mathcal{P} \{ \varnothing, \{ \varnothing \} \}=\{ \varnothing, \{ \{ \varnothing \} \}, \{ \varnothing \}, \{ \varnothing, \{ \varnothing \} \}...

Homework Statement A) If ab+ba = 1 and a^3 = a in a ring, show that a^2 = 1 Homework Equations none The Attempt at a Solution Little confused. If we know that a^3 = a, can't we just multiply each on the right or left side by a^-1 to get a^2 = 1? Or could we only do that if the ring is said...

Homework Statement Show that 0 is the only in R if and only if a^2 = 0 implies a = 0. Homework Equations none The Attempt at a Solution So I'm not sure if I'm doing this right. a^2 = a*a = 0. Therefore, either a or a is zero. The reason I'm not sure about this is because I'm thinking...

Homework Statement For a quantum oscillator find all non-zero matrix elements of the operators ##\hat{x}^3## and ##\hat{x}^4## Homework Equations ##\hat{x} = \sqrt{\frac{\hbar}{2m\omega}}\left(a+a^\dagger\right)## ##a^\dagger |n\rangle = \sqrt{n+1}|n+1\rangle## ##a |n\rangle =...

Homework Statement The classification of the states of matter as we now know them is a relatively recent system evolved from more ancient and holistic views. These ancient systems, many of them still very prominent today were the guides to thinking about the natural world, they were the...

Hey! :o "Show that a group of even order contains an odd number of elements of order $2$." We know that the order of an element of a finite group divides the order of the group. Since, the order of the group is even, there are elements of order $2$. But how can I show that the number of...

Hey! :o Show that a cyclic group with only one generator can have at most two elements. I thought the following: When $a \neq e$ is in the group, then $a^{-1}$ is also in the group. So, when $a$ is a generator, then $a^{-1}$ is also a generator. Is this correct?? (Wondering) But I how can I...

Hey! :o Show that the elements $ab$ and $ba$, with $a,b \in G$ have the same order. The same stands also for the elements $a$ and $c^{-1}ac$. I have done the following: Let $m=ord(ab) \Rightarrow (ab)^m=1 \Rightarrow ababab \dots abab=1 $ Since $a \in G$, $a^{-1} \in G$: $\Rightarrow...

The reason I have that in quotes is because by definition, elements in a set must be unique, and there is no concept of repeated elements. I was just wondering if there is a word to describe such an object - namely, a collection of "items" (or whatever you'd like to call them), where you might...

Hi, So I understand this problem a little, I just can't understand the ending! So saying that we have n elements, we want all the subsets consisting of r elements where r goes from 0 to n. So we want (n choose 0) + (n choose 1) + ... + (n choose n) which is the summation of n choose r for...

We fix some N=1,2,3,\ldots, and define the factor group \mathbb{Z}_N as \mathbb{Z}/N\mathbb{Z}, and denote the elements x+N\mathbb{Z} as [x], where x\in\mathbb{Z}. My question is that how do you solve [x_1] and [x_2] out of \left(\begin{array}{c} \lbrack y_1\rbrack \\ \lbrack y_2\rbrack \\...

[The homework format does not appear on mobile] Problem: Show that a finite group of even order has elements of order 2 Attempt: The book gives a suggested approach that lead me to write the most round about, ugly proof I've ever written. Can't I just say: 1.) If G has even order, G/{1} has...

Hello, Is there a quantum mechanical reason why elements 119+ might not exist? i.e. would the crazy orbitals associated with these elements violate the laws of physics in any way?

Homework Statement Taken from "Introduction to Electrodynamics" by David J. Griffiths p.12 problem 1.8 (b): What constraints must the elements R_{ij} of the three-dimensional rotation matrix satisfy, in order to preserve the length of vector A (for all vectors A)? Homework Equations The...

How can scientists determine,calculate or understand that in the universe hydrogen is the most abundunt element as there are thousands of galaxy with their own planets. There might even an undiscovered element that could be most abundunt. Have a nice day.

I am reading Beachy and Blair's book: Abstract Algebra (3rd Edition) and am currently studying Theorem 6.5.7. I need help with the proof of the Theorem. Theorem 6.5.7 and its proof read as follows:In the above proof, Beachy and Blair write: By Lemma 6.5.4, the set of all roots of f(x) is a...

What exactly is all this 'matrix elements of vectors' stuff that Landau is talking about? I don't mean to ask people unfamiliar with this section to read it for me, so hopefully for someone who's read it - what's going on and where would I find a more modern discussion of this section (I'm...

I'm not sure where to post this so forgive me if the is the wrong place. Can any element be a plasma or only certain ones? Could you make iron plasma?

Homework Statement I need to know is how to figure out the ratio's in which the elements in period 2 combine with chlorine and oxygen i.e a method to solve the problem. I 'm currently in 10th grade. Thanks in advance I appreciate the help. Homework Equations None that I know of...

I have very large data sets: coins & amount i.e. {10 & 11, 9 & 7, 8 & 9, 4 & 5, 3 & 1} graphed would show greater volume to the left side while {1 & 0, 2 & 3, 2 & 1, 4 & 6, 9 & 10} would reflect greater volume on the right, and {1 & 4, 2 & 3, 12 & 10, 4 & 4, 3 & 2} would reflect a surge in the...

Homework Statement Find the eigenfunctions of a particle in a infinite well and express the position operator in the basis of said functions.Homework Equations The Attempt at a Solution Tell me if I'm right so far (the |E> are the eigenkets) X_{ij}= \langle E_i \vert \hat{X} \vert E_j \rangle...

can you write theae elements ...from more reactive to less reactive...side to side C Br N O I Cl S F P

I am reading Joseph Rotman's book Advanced Modern Algebra. I need help with Problem 2.34 on page 101. Problem 2.34 reads as follows: -------------------------------------------------------------------- Prove that any two fields having exactly four elements are isomorphic...