Composition Definition and 388 Threads

Hi, I'd like to find easily-accessible composition series of an interesting lengths say 10 or so (to study some theorems about subgroup series experimentally). I'm thinking the integer mod unit groups, that is ##\mathbb{Z}_n^*=Z_0\rhd Z_1\rhd Z_2\rhd \cdots \rhd Z_9\rhd Z_{10}=\{1\}##. Would...

Homework Statement This is a homework problem for my Honors Calculus I class. The problem I'm having is that though I can solve a traditional function composition problem, I'm stumped as to how to do this for multivariate functions. I read that it requires an extension of the notion of...

1. In a gas UF6 (uranium hexafluoride) are uranium atoms of both the fissionable uranium isotope 235U , and 238U. To enrich the fissile isotope can let a gas UF6 with natural isotopic composition (0.7% 235U, 99.3% 238U) undergo effusion process. The process is then repeated in many steps in the...

Hello, I am kindly asking for some help with following theoretical problem. Imagine at least two lasers emitting light at certain wavelength, each from different angle. Imagine that the rays cross at some point. Is is possible to observe at the crossing point light of different wavelength...

I was wondering if I was holding a handful of ordinary dirt would there likely be some amount of every naturally occurring element in it?

Chemical Composition (%) C 0.472 Si 0.216 Mn 0.67 P 0.0014 S <0.0011 Cr 0.077 Ni 0.015 Mo <0.0020 Al 0.026 Cu 0.021 Co 0.0034 Ti <0.0010 Nb 0.011 V 0.0030 W 0.016 Pb 0.014 Mg 0.0011 B <0.0005 Sn 0.0024 Zn 0.0038 As 0.0093 Bi >0.025 Ca...

Is possible to study the composition of a function f with itself when the number of compositions goes to infinity? I am interessed in the functions that can be written as a complex exponential of the function itself. Where i can study this kind of things?

Hi. I'm trying to write some anatomical systems for a game I'm coding, and i need some good data to work from. Our game is about dogs, not humans, but i figure a human will be close enough What I'd really like is a case study of a specific organism, and i'd like to know the compositions, by...

Doing a bit of revision at the moment and I've been looking at the baryon spin-1/2 octet and the spin 3/2 decuplet. I've noticed that a lot of particles have the same quark composition. For instance the Δ0 particle from the 3/2 ducuplet has the same quark composition as a proton. Now I know that...

Hi ! This is Mustafa. I recently did my bachelor's and started working with Honda Motors. So my manager asked me to do a little research regarding the Gear type (SCM415H) used. I have to check how varying the chemical composition of each element will result in the properties of the gear...

Suppose frame ##S^\prime## moves in the positive ##x## direction at ##v## with respect to frame ##S##, and frame ##S^"## moves in the positive ##y## direction at ##v^\prime## with respect to frame ##S^\prime##. Then, ##E^\prime_x=E_x## ##E^\prime_y=\gamma(E_y - vB_z)## ##E^\prime_z=\gamma(E_z...

Homework Statement If ## f(x) = sin^2x + sin^2(x+ π/3) + cosxcos(x+ π/3) ## and $$g(5/4)=1$$, then ##(gof)(x)## is equal to? Options are 0 1 sinx None of these Homework Equations I know gof(x) is g(f(x)) but here g(x) is not given. The Attempt at a Solution Basically I think we have to put...

When can I do the following where ##h_{i}## is a function of ##(x_{1},...,x_{n})##? \frac{\partial}{\partial x_{k}}\frac{\partial f(h_{1},...,h_{n})}{\partial h_{m}}\overset{?}{=}\frac{\partial}{\partial h_{m}}\frac{\partial f(h_{1},...,h_{n})}{\partial x_{m}}\overset{\underbrace{chain\...

I am solving a nonlinear ODE in the form of Newton's Second Law. In the equation, there is a Heaviside Theta Function of the function which I am solving (##\theta (x(t)##). Since it is quite troublesome to have both the left side of the ODE and the imput of the ODE to contain function of unknown...

I've looked around on the internet a bunch, for a standard way to write an arbitrary number of nested functions (eg. ##{f_1}\circ{f_2}\circ\cdots\circ{f_n}##) without ellipses and with a second input variable (eg. the i in ##f_i##), but never found anything. If anyone does this, what is the...

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown. Initial work is shown in the attachment. > Hello, l need to find the acceleration in the D point but i don't know how. the 2 circles turn in the same speed ( pi rad/s). I use a simulation...

Homework Statement An alloy of copper and silver weighing 0.5000 grams is dissolved in HNO3 and treated with H2S to precipitate both CuS and Ag2S. It is found that the solid sulphides weigh 0.7300 grams. Calculate the percentage of Ag in the alloy. (12.9 %) 2Ag+(aq) + H2S(aq)→ Ag2S(s) +...

I am trying to figure out how to make a world where flight is a lot easier. How much easier could it be on a human (or near human) habitable world? Lower gravitational force might help although too low would presumably be untenable due to loss of the atmosphere? A higher pressure atmosphere...

How to find the composition series of a group of order 30

Please answer for this question with detailed working. Let f and g be function from the positive integer defined by the following pairs f: N find the composition. a) f(n) = n + 60 g (n) = 100n b) f (n) = g(n) = c) F(n) = log(n+3)...

Let f and g be function from the positive integer defined by the following pairs f : N →R,g∶N →R. Find the composition f ° g and g ° f.A) F(n) = log(n+3) g(n) = log log(n + 10) .................... B) F(n) = n log(n+2) g(n) = n^(1.1) .................... Could you...

Homework Statement The problem states that we have L as the linear transformation as: \begin{align*} A= \left( \begin{array}{ccc} 2 & 0 & 1 \\ -2 & 3 & 2 \\ 4 & 1 & 5 \end{array} \right) \end{align*} And when given another linear transformation T as: \begin{align*} B= \left( \begin{array}{ccc}...

Homework Statement Hello everyone, I have completed a lab and I’m working on my report. I’m not sure if my work is correct but I would most definitely appreciate it if anyone could check it for me? I’m particularly having trouble finishing question #3. It’s worth a lot of my grade so I want...

I'm currently completing a project about gas giants. Could anyone point me in the right direction to find out about the density change as one approaches the centre of a giant? I can kind of do it if I assume it's incompressible, but does anyone know the current theories for it in practice...

I need some help with the proof of Lemma 21.2.4 in Eie & Chang's book: A Course on Abstract Algebra: Lemma 21.2.4 reads as follows: My questions regarding the proof are as follows: Question 1 Eie & Chang write: "... ... It is possible to insert a normal subgroup H of H_{i+1} with H_i...

This is a problem that has been bugging me for ages. I just can't wrap my head around this weird result. I know I went wrong somewhere [as a matter of fact, that was the answer I was hoping for], but most sources, (including, but not limited to, wikipedia), suggest otherwise. I will cut to the...

The Lorentz's transform: ##x' = k(x - vt), t' = k(t - vx)\ k = \gamma,\ and\ c = 1## I. The speed composition derivation: ##w' = dx'/dt' = \frac{dx - vdt}{dt - vdx}## and we divide everything by dt, and: ##w' = \frac{dx/dt - v}{1 - vdx/dt}## now we assume the dx/dt is some speed u, and the...

I am reading "Introduction to Ring Theory" by P. M. Cohn (Springer Undergraduate Mathematics Series)[/COLOR] In Chapter 2: Linear Algebras and Artinian Rings, on Page 61 we find a definition of a refinement of a chain and a definition of a composition series. The relevant text on page 61 is as...

A thread on this forum Plans for Asteroid Mining has more than 9000 views. From that I conclude that belief that asteroid composition must be highly varied mu thast be wide spread. I'm having a hard time understanding why that should be. So unless the planitesimals formed at approximately...

I'm learning maths myself, but I'm going to university in 2 months. This is my first try at proving anything. Homework Statement Prove that the composition of surjective functions is also a surjection. Homework Equations A definition of surjective function: If f:S_1\rightarrow S_2...

Hello, first post here. I'm trying to wrap my head around something here and I'm wondering if anyone can help. I've read that all terrestrial planets have basically the same chemical components - Iron, Silicon, Oxygen, etc - in roughly the same percentages. I also read that the composition of...

Homework Statement Find conformal function that maps ##D_1=\left \{ z;Re(z)>0,0<Im(z)<2\pi \right \}## on to ##D_2## where ##D_2## is unit disc.Homework Equations The Attempt at a Solution Ok, I haven't got any problems with conformal mapping but I have huge problems with function composition...

Recently, my lab has bought a BioRad Turbo Blot Transfer system. It allows for you to do an efficient 7 minute transfer from a minigel to nitrocellulose. The transfer buffer, however is very expensive because you can only purchase it in conjunction with precut nitrocellulose membranes and thick...

Homework Statement Let f: A→B and g: B→C both be bijections. Prove that the composed function fog is also a bijection. Write (fog)-1 in terms of f-1 and g-1.Homework Equations fog = f(g(x)) The Attempt at a Solution I know what the composed function means and what bijective means...

Homework Statement I have 2 simple harmonic motions and I want to compose them on the same axis. So: x1 = A1*sin(ω1*t+θ1) x2 = A2*sin(ω2*t+θ2) The goal is to find the resultant motion of these 2 in the form: X = A*sin(ω*t+Θ), so to find A,ω and Θ as functions of A1,A2,ω1,ω2,θ1 and...

What is the funda behind the Elemental Composition Calculation of Cathode Material for Sodium / Lithium Ion Battery (Na2/3 Ni0.4 Mn0.4 Co0.2 O2)/ AMO2? Apart from the Oxidation state calculation, Phase Diagram Elimination of mixtures and Random Compistion, is there any Principle behind it?

Homework Statement An alloy of gold, aluminum, and copper has a density of 10,000 kg/m3. The alloy contains at least 10% aluminum and 5% copper by mass. The densities for the three metals are respectively ρAu = 19320 kg/m3, ρAl = 2712 kg/m3, ρCu = 8940 kg/m3. Find the maximum and minimum...

Homework Statement Given that f is continuous and strictly increasing, f:[0, ∞)->[0, ∞), f(0)=0, and d(x,y) is the standard metric on the real number line, Is there a function f such that d'(x,y)=f(d(x,y)) is not a metric on the real number line? The Attempt at a Solution The standard...

Homework Statement a) Find the inverse of the matrix: \begin{pmatrix}1 & 2 & 0\\ 2 & 0 & 1\\ 1 & 1 & 2\end{pmatrix} (sorry I don't know how to show a matrix more clearly on this) b) Write A and A-1 as a composition of matrices of the form Rij(k), Tij and D22(k) Homework...

Homework Statement Let S : U →V and T : V →W be linear maps. Given that dim(U) = 2, dim(V ) = 1, and dim(W) = 2, could T composed of S be an isomorphism? Homework Equations If Dim(v) > dim(W), then T is 1-1 If Dimv < dim(w), then T is not onto. The Attempt at a Solution So...

A body is orbiting the sun and rotates about its axis (z). My coordinate system is co-rotating with the body. I need to determine how does a vector that points to the sun change after a certain period of time. Initially the sun vector lies in the xz plane. Basically I need to find the rotation...

Homework Statement Find the domain and range of (f+g)(x) Given that F(x)= 1/(x-1) and g(x) = sqrt(x) Homework Equations The Attempt at a Solution I added the two functions to get 1/(x-1) + sqrt(x) To get domain, i look at the restrictive x values for both to get x greater than 0 and not...

So... Theoretically, planets (that are not gas giants, or water planets) could be composed of silicon, iron, or carbon. Are there any other elements that could make up most of a planet?

My teacher discussed an in and out method that could be used however I don't understand how that works. Can someone explain it to me? The teacher said this method would allow us to determine the domain and range without knowing what the graph looked like. How I have been doing it is looking at...

Homework Statement If F(x)= 1/(1+x) G(x)= 1/(2+x) determine f(g(x)) Homework Equations No equations for composition functions The Attempt at a Solution F(g(x)) = 1/1+ 1/(2+x) Then do you try to eliminate the fraction in the denominator by multiplying it by (2+x)? They said...

Homework Statement Be z=F(u,v,w), u=f(x,y), v=e-αx, w=ln y, get the expression \partialz/\partialx, \partialz/\partialy. Homework Equations Chain rule. The Attempt at a Solution \partialz/\partialx=\partialz/\partialv*dv/dx=-α e-αx \partialz/\partialy=\partialz/\partialw*dw/dy=1/y

I have not met differential equations involving the composition functions (also not much literature on it). Assume we know the form of g=g(x), and need to solve the following differential equation, finding f=f(x): (g∘f)f'=g Where g∘f=g(f(x)). Does anybody have a strategy for solving...

Homework Statement It's such a gory problem, I'm going to have to attach a small image. http://i.minus.com/j9XQTP6pIlh1a.png Homework Equations PV=nRT Molarity (M) = moles/liter The Attempt at a Solution Okie dokie. 1) Let's find how much iodide reacted with the sulfur dioxide...

What was the primordial composition of U isotopes in solar system? Solar system contained isotopes less than a million year halflife, because meteors have clear traces of having crystallized with abundant aluminium 26. So, what was the actinide composition? We know the exact amount of...

I am reading Dummit and Foote (D&F) Section 15.1 on Affine Algebraic Sets. On page 662 (see attached) D&F define a morphism or polynomial map of algebraic sets as follows: ----------------------------------------------------------------------------------------------------- Definition. A map...