Composition Definition and 388 Threads

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...

Suppose you have a mixture of 30 mol% pentane and 70 mol% hexane at 1 atm and 60oC. If the Tbubble-point = 55.1oC, calculate the composition of vapor of the first bubble as the mixture is heated. I found p*pentane = 1392.95 and p*hexane = 484.96 using Antoine's equation with T = 55.1. Now I...

Composition > Illustrative Essay On "Radio" Goal: 2-3 page essay on a topic of your choice. Must provide relevant photo's. My topic of choice is electromagnetism. I chose this topic because we live in a wireless age. I thought it'd be neat to provide some back round info on how it all...

Lets say there is an exoplanet 50 light years away. The radius of this planet is 2x Earths with 8x Earths mass and a density of 5.52 g cm/3. What is the composition of this planet?

I apologize in advance if the answer to this is really simple; I often overlook simple solutions when something trips me up. For example, if f(x)=x2 and g(x)=x3/2, and g(f(x)) is therefore, after simplification, x3, why is that still an even function if x3 graphed under other circumstances is...

Please watch from 0:00 to 1:23 Goal: Complete a short essay on my greatest accomplishment achieved. I have not achieved it yet, but my greatest accomplishment will be the language of mathematics. I thought about this last night, "The difference between arithmetic in algebra &...

Homework Statement So we are given an insulating container with two compartments between which, heat can flow. In the left one, there exists m_1 of water at temp T_1 and on the right there exists m_2 of ice at temp T_2. What is the final composition and temperature? Homework Equations...

Here are the questions: I have posted a link there to this topic so the OP can see my work.

Hi, Let f be a linear transformation over some finite field, and denote f^{n} := f \circ f \circ \cdots \circ f, n times. What do we know about the linear maps f such that there exist an integer n for which f^{N} = f^n for all N \geq n? Also, how about linear maps g satisfying g = g \circ f^i...

I am doing linear algebra and want to fully understand it, not just pass the class. I was recently taught matrix multiplication and decided to look up how it works. The good part is that I understand the concept. Matrices are a way of representing linear transformations. So matrix multiplication...

Homework Statement Reference the Cu-Zr phase diagram. If you make the alloy CuZr and heat it to 300°C, what percentage of the material will be Cu10Zr7 and what percentage of the material will be CuZr2? Homework Equations Phase diagram attached. The Attempt at a Solution I used the lever...

Here is the question: Here is a link to the question: HELP WITH THIS FUNCTIONS QUESTION!? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

This question is killing me. I'm finding it difficult to do and it's a problem with my homework. Given that f(x)=2x^2-x+1,\,g(x)=2\sin(x)\text{ and }h(x)=3^x, determine the following. You need not simplify the expressions. f(g(-\pi))=? \left(h^{-1}\circ f \right)(x)=? g(f(h(x)))=? I am...

Homework Statement I\!f~ f(x+1)=\sqrt{x^2-2x}~~~and~~~g(x)=f(\!\sqrt{x}) Find: g'(x-1) Homework Equations In order to find g'(x-1) I know the following steps have to be taken: f(x+1) \rightarrow f(x) \rightarrow f(\sqrt{x}) = g(x) \rightarrow g'(x) \rightarrow g'(x-1) The Attempt at a...

I was just reading about how the redshift-relation for angular diameter distance is calculated, and the example in my textbook used a matter-dominated universe to calculate the formula. It seems to rely heavily on the relationships between t, a(t) and H(t), which are different in radiation...

Did The Dark Matter Really exist ? did we have an evidence ? and What is the compositions Of The Dark Matter ?

Here is the question: Here is a link to the question: Denote by A the 3x3 matrix which rotates by 90 degrees around the z-axis? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement Let ψ(x) = x sin 1/x for 0 < x ≤ 1 and ψ(0) = 0. (a) If f : [-1,1] → ℝ is Riemann integrable, prove that f \circ ψ is Riemann integrable. (b) What happens for ψ*(x) = √x sin 1/x? Homework Equations I've proven that if ψ : [c,d] → [a,b] is continuous and for every set...

Hey, just trying to get my head around the logic of this. I can see that if composition factors are cyclic then clearly the group is soluble, since there exists a subnormal series with abelian factors, but I am struggling to see how the converse holds. If a group is soluble, then it has a...

New data from NASA's Cosmic Background Explorer (COBE), the Wilkinson Microwave Anisotropy Probe (WMAP), and Planck have found evidence that the composition of the universe: Matter - 4.9 % Dark Matter - 26.8 % Dark Energy - 68.3 % These numbers seem almost too coincidental to numbers...

Homework Statement If f is meromorphic at a in ℂ^ (extended complex plane), and g is meromorphic at b = f(a) in ℂ^, show that h := g ° f is meromophic at a, with an exception. If f takes on the value b in ℂ^ with multiplicity m at a and g assumes the value c = g(b) in ℂ^ with multiplicity n...

I work at an Aluminum sheet casting plant, we use AlTiB as the grain refiner for our cast products.Ti:B ratio as indicated on certificates is 5:1 .We recently received a new consignment of AlTiB from another supplier in India.The certificates from our new supplier show that the The AlTiB we...

Suppose that $U$ is open in $\mathbb{R}^{m}$, that $L\in U$ and that $h:U\setminus \left \{ L \right \}\rightarrow \mathbb{R}^{p}$ for some $p\in N$. If $L=\lim_{x\rightarrow a}g(x)$ and $M=\lim_{y\rightarrow L}h(y)$. Then $\lim_{x\rightarrow a}(h\circ g)(x)=M$. (Someone told me that this...

Hey, I have a question on determing the composition of a state of a system of composed of only two eigenvectors, the question is displayed below: I initially assumed that the ket v was given by: |v>=a|\omega_{1}>+b|\omega_{2}> Where 'a' and 'b' are constants which will determine...

Hello guys, I wonder and would like to know what kind of metal to made a motorcycle chassis such as Yamaha YZF-R1 and Yamaha Raptor 700R? Is it solid or hollow? Is it cast or extrude? Thank you MyMachine

Homework Statement Let A, B be subsets of ℝ and f : A → ℝ and g : B → ℝ and f(x)\inB for every x \in A. Prove: If f(x)→L as x → a, for x\in I and g is continuous at L \in B then lim x->a g(f(x)) = g(lim x->a f(x)). Homework Equations f is said to be continuous at a point a iff given ε>0 there...

Homework Statement The question is let E1 and E2 be equivalence relations on set X. A new relation R is defined as the E1 o E2, the composition of the two relations. We must prove or disprove that R is an equivalence relation.Homework Equations The Attempt at a Solution I know that we must...

Hello, let's suppose I have two functions \phi:U\rightarrow V, and T:V\rightarrow V that are both diffeomorphisms having inverse. Furthermore T is linear. I consider the function f(u) = (\phi^{-1}\circ T \circ \phi)(u), where \circ is the composition of functions. Since T is linear, we...

My sum total of knowledge of composition series is: the definition, the jordan holder theorem and the fact that the product of the indices must equal the order of the group. With this in mind, can someone help with me with finding a composition series for the following:(1) Z60 (2) D12...

Homework Statement http://sphotos-h.ak.fbcdn.net/hphotos-ak-snc6/282312_368248176595083_1229435302_n.jpg Homework Equations To subtitute x into U, but that did not work. The Attempt at a Solution I have tried subtituting x into U like this ...

Prove that if S: U-->V and T: V-->W are isomorphisms, then TS (composition) is also an isomorphism. Idea: So my idea was since both S, T are both isomorphic that means they both have inverses S-1 and T-1. Now this is where I'm a little grey, in order to show that TS is isomorphic, is it...

Homework Statement Can't believe I forgot how to do this... Prove if fog = x and goh = x then f=h for all x. Homework Equations Obviously the associativity of composition here. The Attempt at a Solution So we know : fog = goh fogoh = gohoh fo(goh) = (goh)oh I've...

Showing the sum of functions are uniformly continuous Homework Statement Suppose f and g are uniformly continuous on an interval I. Prove f + g are uniformly continuous on I. Homework Equations The Attempt at a Solution Let ε >0 By definition, since f and g are uniformly...

Homework Statement Suppose that f has the intermediate value property on an interval J, that g has the intermediate value property on an interval I and that g(I) is a subset of J. Prove that f°g has intermediate value property on I. Homework Equations The Attempt at a Solution I...

Homework Statement Let f:S→T and let A\subseteqT. Define the preimage of A as f-1(A)={x in S: f(x) is in A}. Demonstrate that for any such map f and B\subseteqran(f), f(f-1(B)) = B. I am going to use set inclusion to prove this, but can I use function composition in the portion in red? I...

Given three functions $F,G,H$ what restrictions must be placed on their domains so that the following four composite functions can be defined? $$ G\circ F,\quad H\circ G,\quad H\circ (G\circ F),\quad (H\circ G)\circ F. $$ I need a hint or something.

I want to define something like: A\left(\begin{matrix} x \\ y\end{matrix}\right) = \left(\begin{matrix} 1 & -1 \\ -1 & 1 \end{matrix}\right)\left(\begin{matrix} x \\ y\end{matrix}\right) B\left(\begin{matrix} x \\ y\end{matrix}\right) = \left(\begin{matrix} 0 & 1 \\ 2 & -1...

I'm trying to give an answer to the following problem, I hope someone could come in help! Consider a smooth n-dimensional manifold M with smooth (nonempty) boundary \partial M, and suppose given a function f: M\setminus \partial M \to \mathbb{R} (which one can assume to be differentiable)...

Ive read that elementary particles can decay. I am trying to understand how this can be with a particle that has no composition. So i have two questions: If elementary particle A decays into particles B and C, then why can't we say that A is composed of B and C? If an elementary particle can...

Why does the genetic composition of sex cells of an individual vary since the genome of an individual is same throughout his/her body.

Homework Statement R = { (1,2), (3,5), (2,2), (2,5) } S = { (2,1), (5,3), (5,1), (5,5) } Explicitly find the relation R^-1 o S^-1 Homework Equations The Attempt at a Solution This was on my test. First I just wrote down the inverses: R^-1 = { (2,1), (5,3), (2,2), (5,2)...

When mixing special grades of alloys, or even in commercial production of common alloys, furnaces are often used where metals or additives are added and mixed, then samples taken at the core and characterized, then adjustments are made by adding additives until the desired composition is...

Does a Beta(?) Particle as a whole, comprise electrons and anti-neutrino?? or just a electron??

Homework Statement Give a genuinely new (i.e. not discussed in class or in the book or in tutorial) example of: two sets X and Y , and two functions f : X →Y and g : Y → X, such that the composition g ◦ f is the identity function 1X : X → X, but neither f nor g are bijective. (Reminders: if...

Homework Statement Find g(x) if f(x) = (3x-1)/(2x+5) and f(g(x)) = (x+9)/(12x-11) Homework Equations N/A, as far as I know The Attempt at a Solution I tried doing it as though g(x) = y and it turned out like this: (3y-1)/(2y+5)=(x+9)/(12x-11) I very quickly saw that that wouldn't...

Homework Statement Let f:R->R, differentiable, f(1)=1 and f'(1)=2. Homework Equations Prove that g:R->R such that g(x)=f(x)Arctg(f(x)) is differentiable in x=1 and calculate g'(1)The Attempt at a Solution I would prove it saying that if a function is differentiable then the product and...

Homework Statement For each m >= 2, find a group with a composition series of length 1 with a subgroup of length m. Homework Equations Simple groups iff length 1. If G is abelian of order p1^k1...pr^kr, then length G = k1 + ... + kr If G has a composition series and K is normal...

Homework Statement R is a rotation around the origin by ∏/4, G is a glide reflection; the reflection is across y=x and the glide is by (2,2). Find the compositions R°G and G°R and characterize them. If you find a glide reflection, specify both the mirror line and the "glide" vector...

Homework Statement Define Function f: [0,1]x[0,2∏)→ℝ2 by f(r,θ)= (r(2+cos5θ)cosθ) (r(2+cos5θ)sinθ) Let g: [0,2∏)→[0,1]x[0,2∏) be defined by g(t)= (1) (t) Compute the function δ=f°g, what are the domain and codomain of δ? Homework Equations The Attempt at a Solution Replacing r with 1...

Homework Statement Prove that the composition of one-to-one functions is also a one-to-one function. Homework Equations A function is one-to-one if f(x1)=f(x2) implies x1=x2. Composition is (f*g)(x)=f(g(x)). Proof-based question. The Attempt at a Solution A...