Elements Definition and 1000 Threads

1. Homework Statement Remember, the set of groups (Gn, *), the group of multiplicatively-invertible elements of Z/n under multiplication. For p a prime, the elements of Gp are all elements of Z/p except 0; for n not a prime, the elements of Gn are all the elements of Z/n except 0 and those...

Hi All! This is my first time putting up my own thread on MF. I can usually find what I'm looking for, but this time: no go. As the title says, I'm trying to find the normalization constant of this 4x4 matrix (g and f are functions): (1-g^2) 0 0 0 0 (1+f^2)...

Homework Statement The current after t=0 in a single circuit element is as shown in Fig. 2-37. Find the voltage across the element at t=6.5\mu s, if the element is (a) 10 k\Omega, (b) 15 mH, (c) 0.3 nF with Q(0)=0. Ans. (a) 25 V; (b) -75 V; (c) 81.3 V...

Hi everyone, :smile: I was wondering why they only use 5th and 3rd groups elements to create n-type and p-type semiconductors respectively. Couldn't we mix 6th or 2nd groups' elements instead to make the semiconductors? What would happen if we do this? Perhaps elements of those groups will...

Hi All, does anyone know of a mathematica function that efficiently circularly shifts all array elements? e.g. {1,2,3,4,5} -> {4,5,1,2,3} without iterating? The reason I ask is because I have a huge data set I'm working with and right now iterating through is very processing intensive...

I have run into a problem where I have a frieze pattern F, the frieze pattern has horizontal refelctive symmetry, glide reflective symmetry, but does not have 180 degree rotation and does not have vertical reflective symmetry. G represents the symmetry group for F. G={reflection symmetry...

Hi, I have been using both ANSYS APDL and ANSYS Workbench (Mechanical) to run analysis on a structure. After loading the structure, in Mechanical i was able to scope my results for deformation and EQUIV stress to just the adhesive layer as this is what I am interested in. However, I can't...

Hello all: I'm new to the world of finite elements/finite differences. I'd like to understand the advantages of the finite element method. I read that the finite difference method cannot handle complex (e.g., curved domains, fractures) geometries. I have had no luck in understanding why...

If I have a list say li = {18, 22, 4, 10} and I want to add for example 7 to this list Join[li, {7}] to get {18, 22, 4, 10, 7}, can I insert the 7 after the 4, to get {18, 22, 4, 7, 10}, I can't just use Sort[ {18, 22, 5, 10, 7}] as I don' t want to change the order of the whole list?

Homework Statement Let G be a group and let a be an element in G. Show that a and a-1 generate the same cyclic subgroup <a> = <a-1> and have the same order o(a) = o(a-1). Homework Equations This is in the second section of the book I'm using, so there aren't really any theorems that...

hey everyone i hope to find the answer to my troubles here :) basically i have written a gravity simulator, it loads bodies from a file containing information on each body. using the orbital elements on each body taken from nasa's HORIZON system, i calculate the position and velocity of...

Homework Statement The voltages across two circuit elements in series is zero. Is it possible that the voltages across the individual elements are nevertheless not zero? Give an example. Homework Equations NA The Attempt at a Solution I am not really sure where to start with this problem...

I saw this question in an abstract algebra text that I was reading. "Is it true that (w − x) − (y − z) = (w − y) − (x − z) is an identity for real numbers? Can you say why or why not?" I know that an identity element does not change the value of a real number. So 0 is the identity element...

Like, maybe transmutate certain elements into rare metals that we have a very limited supply of? By "all of the Sun's" energy, I mean an amount of energy similar to the amount we could collect from solar panels if we covered the Earth with solar panels (obviously that isn't feasible, but we...

Hi: In the case of a finite-dimensional normed space V, it is relatively-straightforward to show that the kernel of any element of V* has 1 . ( Assume DimV=n): We take a linear map L:V-->F ; F the base field. We choose a basis to represent L, then we consider F as a vector...

Homework Statement Let G be a smooth Lie group with Lie algebra \mathfrak g . Consider a curve X: [t_0,t_1] \to G whose dynamics are given by \frac{dX}{dt}(t) = H X(t) for some H \in \mathfrak g . Show that this equation is well defined for all time. The Attempt at a Solution Okay, so...

Hey, So I'm trying to figure out how the matrix representatives of Lie-algebras can act as derivations. In particular, let N \in \mathbb N and consider the Lie group of special unitary matrices \mathfrak{SU}(N). Now we know that the Lie-algebra is the set of skew-Hermitian matrices...

I believe this is the correct place to post this as I believe I'm going to need to solve this as a linear system, however I suppose it might be solvable using trig as well. However, I've been at it for a while and I'm out of ideas and I think I'm missing something silly. Consider the...

What are the main contributions to the matrix elements (intensity asymmetries with respect to normal emission) in ARPES? Is there a theoretical paper on that?

• Can we create any of the periodic table elements? • Can we make it cost efficient in the future? • Can we synthesis H20 in the laboratory?

Homework Statement Hi, i need to show how many elements there are in the group u={B in B : det(B)=1} where B is the group of invertible matrices - B = b(ij) in GLn(Fp) where Fp is a field with p elements. Homework Equations The Attempt at a Solution I know Fp^n has p^n elements...

Homework Statement The last 2 parts of the attached photo. (4 and 6 marks) Im really not sure how to go about them in a (clever) way that won't take 2 hours. Homework Equations Possibly the fact that the product of the raising/lowering operators, J-J+ = J2x + J2y Answers to previous...

First off I am nothing of a scientist or chemist. can you add a oxygen molecule to say marijuana without screwing it up? or if i add one of the inert gases to it? haha, I'm just thinking out loud what you scientists say?

Hi to everyone, I have a problem with sizing pipe threaded elements. I am looking for guide rules that with a simple external meassurement I'll be able to determine the element size such as safety valves,threaded pipes,pressure gages,caps etc. To clarify my question, hereby an example, when...

Homework Statement Let R = Q[x]/(x^2-4x+4). Show that R has infinitely many nilpotent elements. Homework Equations The Attempt at a Solution I see that x^2-4x+4 = (x-2)(x-2) and that a nilpotent means a^2 = 0. Other than that, I'm not sure where to start.

Hello, I have this problem that I am struggling with. I have a heating element that is submerged in a water tank. The temperature of the water in the tank starts at say 5C. The temperature of the water flowing through the heating element is at 90C. I can also assume that the metal of the...

Many physicists claim that decoherence determines the emergence of the worlds in the Many World Interpretation (MWI). I have always found such a claim elusively proved and actually wrong. Recently I wrote a paper: http://arxiv.org/abs/1008.3708 addressing such a subject, and I sent it to...

Homework Statement Let G be a group, and a an element of G of order m. What is the order of a^k? The Attempt at a Solution Well, first of all, if (a^k)^p = e, for some p, we have kp = mq, for some q. Now, for some k, the order of a^k is the least such p. Hence, it would make to sense...

Homework Statement Consider the elements marked with letters from a to h. Give the answer using these letters Homework Equations a) Give all of them which do not form compounds? b) Give all of them which form cations with charge 2+? c) Give all of them which form a gaseous molecule...

Prove that any two elements of order 3 in GL(2,Z) are conjugates. A paper on "the group of units of the integral group ring ZS3" by Hughes and Pearson refers to this result and says that it has been picked up from "Representation Theory of finite groups and associated algebras" by Curtis and...

So, the rule for finding the matrix elements of an operator is: \langle b_i|O|b_j\rangle Where the "b's" are vector of the basis set. Does this rule work if the basis is not orthonormal? Because I was checking this with regular linear algebra (in R3) (finding matrix elements of linear...

can anyone give me a first-order sentence that says there exist exactly three elements. Please explain it to me. Thanks

Homework Statement For any integer n>2, show that there are at least two elements in U(n) that satisfy x^2 = 1. Homework Equations None The Attempt at a Solution If the definition of the group U(n) is "the set of all positive integers less than n and relatively prime to n" then the...

Hello! I'm new to the forum so please don't mind any mishaps. I am very interested in the unstable radioactive elemts. I read that the thing that makes elements radioactive is ther different amounts of neutrons. Does this mean that all the radioactiive elements are radioactive just because...

Homework Statement Let v(t) = V_{max}\cos(\omega t ) be applied to (a) a pure resistor, (b) a pure capacitor (with zero initial capacitor voltage) and (c) a pure inductor (with zero initial inductor voltage). Find the average power absorbed by each element.Homework Equations P_{avg}(\tau) =...

I have several Questions. 1. What are the elements commonly used in a battery and why are they used? 2. What purpose does each chemichal in abattery serve 3. How does a battery truly work? thanks for answering, all postr will be helpful, BT

Hi, As part of my final year project I have to heat air within an exclosed environment (i.e. a 1m x 1m x 1m insulated box) to test the effectiveness of using phase change materials to regulate ambient air temperature. To do this I need to slowly heat the air inside the box at a rate that...

How did Dimitri Mendeleev know that some of the elements were missing/not discovered? How did he know that the missing elements existed? Did he find some sort of pattern when he created the Periodic Table?

Are there any simple elements out there that expose quadratic behavior? I. e. current to voltage or frequency to voltage or anything. I have done some google digging for multiplying circuits and found out that they are all very complex. But a simple circuit can be made using square function...

Homework Statement Show that the elements 3 and 2+\sqrt{-5} in \textbf{Z}[\sqrt{-5}] have a greatest common divisor of 1, but the ideal I = (3, 2+\sqrt{-5}) is not the total. Conclude that I is not principle. Homework Equations The Attempt at a Solution I have got as far as...

Assuming that super-heavy atoms were stable (at least up to 118), what would be some interesting chemical properties of some of them?

Can react with other atoms of their element and form diatomic molecules, while others cannot?

Because let's say we have Hydrogen and Chlorine, they with both react very well with each other due to the reason that Hydrogen wants to get rid of its only Valence electron, to have an empty shell, and Cl needs only one more to have a full shell. Right?

Homework Statement State the definitions of greatest and least elements in terms of strict orderings. Homework Equations Let \leq be an ordering of A and < be a strict ordering on A, and let B \subseteq A. b \in B is the greatest element of B in the ordering \leq if, for every x \in...

Is there a way to see that if \|x-y\| is "small", then so is \|x^{-1}-y^{-1}\|? For example, if \|x-y\|<r, is there a function f such that \|x^{-1}-y^{-1}\|<f(r) Edit: Nevermind. What I needed is just the operator version of (1/2-2/3)=(3-2)/6...

Homework Statement Let S(n,r) denote the number of elements of A_n of rank r. Then S(n,r) satisfies the recursion S(n,r)=(n-r)S(n-1,r-1) + S(n-1,r) Verify this formula for n=4 and r=0,1,2,3,4, using the values S(3,0) = 1 S(3,1)=3 S(3,2)=1 Homework Equations The Attempt at a...

Homework Statement Remember, the set of groups (Gn, *), the group of multiplicatively-invertible elements of Z/n under multiplication. For p a prime, the elements of Gp are all elements of Z/p except 0; for n not a prime, the elements of Gn are all the elements of Z/n except 0 and those...

Finding voltage across elements in phasor diagram, URGENT! Hi there, first time posting here, just caught up on a question with no worked solutions and it's driving me crazy! I've attached the question below,and the answer to b is v(t)= 5cos(2t-112). I can do part a but am struggling on...

Sorry if this question is too elementary (no pun intended) for this forum. If stellar fusion of iron takes more energy than it produces, how are heaver elements formed? Cheers, JP

Is there a website where you can enter the Compound's chemical formula and it's will give us the names of elements? like if i will enter to the website this chemical formula CH4 and it will give me the name Methane. thanks.