Composition Definition and 374 Threads

The question “how do we know the composition of the sun” falls shorts everywhere I look. 1. There is the spectral absorption lines. Explanations given how that works, indicate how we know the elements, but fails to tell us how we know about the preponderance of Hydrogen and Helium...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 4.2: Noetherian and Artinian Modules and need some help to fully understand the proof of part of Proposition 4.2.14 ... ... Proposition 4.2.14 reads as follows...

In binary phase diagram, We draw a tie line to know the composition of the liquid phase or the solid phase. Where the tie line is just a horizontal line. The question is why doesn't the liquid or solid phase composition change as you change the general composition of the alloy? Why does the...

Helo, given ##f:R^n\rightarrow R^m## and ##g:R^m\rightarrow R^e## both class ##C^m##. Is the composition ##g\circ f## of class ##C^m## ?.

The question wants (f•g)(x). I understand this to be f(g(x)). This means to plug the value of g(x) into every x I see in f(x) and simplify. f(3x^2) = 4(3x^2) + 7 f(3x^2) = 12x^2 + 7 So, f(g(x)) = 12x^2 + 7. This is not the book's answer.

Hi everyone, I have a few questions about the composition of light: First, what is it? Is white light the result of all color wavelengths present in an area? Second, if so, then why is there no interference in waves of light (or is there)? Third, if photons all travel at the same speed, then...

How can I derive mathematically law of composition of velocities from time dilation and length contraction But please use only algebra .Don't use four vectors and space time diagrams.

Hey! :o For which real constants $a,b,c$ is the following function $f$ continuous on $\mathbb{R}$ ? $$f(x)=\begin{cases}1+x^2 & \text{ for } x\leq 1, \\ ax-x^3 & \text{ for } 1<x< 2 \\ b & \text{ for } x=2\\ cx^2 & \text{ for } x>2\end{cases}$$ For $a=1, b=-6, c=-\frac{3}{2}$ the function...

Hi, I'm struggling to understand something. Does domain restriction work the same way for composition of inverse functions as it does for other composite functions? I would assume it does, but the end result seems counter-intuitive. For example: If I have the function f(x) = 1/(1+x), with...

Homework Statement Suppose that ##f## and ##g## are real-valued functions defined on all of ##\Bbb{R}##,##f## is measurable, and ##g## is continuous. Is the composition ##f \circ g## necessarily measurable? Homework EquationsThe Attempt at a Solution Let ##c \in \Bbb{R}## be arbitrary. Then...

So are there photons "flowing" from one end of a permanent magnet to the other? If so what determines the frequency?

Homework Statement given:-fuel and air mass flow, measured mole ratios of exhaust composition y_i. Let's assume stoichiometric combustion so we have only CO2, H20 and N2 as products. Homework Equations Can EGR ratio be calculated from available data? The Attempt at a Solution I get result...

Homework Statement Suppose g is a function with the property that g(x) =/= g(y) if x=/=y. Prove that there is a function f such that f( g(x) ) = x. (The composition) Homework Equations Definition of a function, collection of ordered pairs; g(x) =/= g(y) if x=/=y; x → g(x) → x (The composition...

Hey! :o Let $S_i$, $i=1,2$ the scaling with scaling factor $r_i$ and center $Z_i$. Let $r_1r_2\neq 1$. I want to show that $S_2\circ S_1$ is a scaling and to calculate the center and the scaling factor. When $Z_1\neq Z_2$ I want to show that $Z\in Z_1Z_2$. I don't really have an idea. Could...

Hello, I work in a apparel manufacturing warehouse and I'm planning to upgrade the Jacket Hanger Racks to a rotatable conveyor. So I want to insert new Steel Pipes for hanging the Jackets which will rotate. So, the length of the pipe is 370 cms / 12' 2", and the weight it will be holding is...

I've learned that composition of continuous functions is continuous. ##\log x## and ##|x|## are continuous functions, but it seems that ##\log |x|## is not continuous. Is this the case?

Hello. I couldn't sum my entire question in the title, so here it goes: I have a friend that needs information about the content of Iodine and Molybdenum in stars (from as much stars as he can). There are references to the content of many stars in books and papers, but most of them don't give...

Hi everyone! I'm an italian undergraduate in physics and one of my course is called "Basics of Energy Physics". For the exam you have to write a brief composition based on one of the topic of the course. I've chosen the nuclear energy, because this will probably be my main interest in my post...

I am a little bit confused on how commutative diagrams show equality of two morphisms. For example, one can imagine the diagram for hf = kg, where composing f and g is the same morphism as composing h and k: https://upload.wikimedia.org/wikipedia/commons/9/91/Commutative_square.svg Why does the...

Is it mathematically correct to call any group operation in ##(G,\cdot)## composition?

So at 5:20 it is explained that many of the quarks are converted to strange quarks and this is a away of going around the pauli exlusion principle inside of a quark star. So does this mean it's like a Bose Einstien Condensate? The Bose Einstein Condensate is very cold though.

when any exoplanet passes through any star we can see the intensity dip from which we can detect the planet when an exoplanet passes through any star by spectroscopy we can find planet composition. So my question is did star glare effect light which is passes through planey atmosphere?

When a planet passes through any star, it absorb and transmit certain amount of light by which we can determine planet composition. My question is that did stars glare hide or inturupt the wavelength transmitted of reflected by planet?

I was wondering how they managed to know the internal structure of Earth and it's composition while there is lava and it's very hot such that no any instruments can get there...seriously I am confused

Homework Statement Let ##f(t)=\int_{t}^{t^2} \frac{1}{s+\sin{s}}ds,t>1.##Express ##f## as a composition of two differentiable functions ##g:ℝ→ℝ^2## and ##h:ℝ^2→ℝ##. In addition, find the derivative of ##f## (using the composition). Homework EquationsThe Attempt at a Solution Honestly, I have...

what is the chemical composition of common processed paper and what does the molecule's structure look like?

I have tried looking for papers on the composition of earth, but none of them seem to list the abundance of compounds. They just list the elements. So, what are the abundances of the most common compounds, by mass and/or percent of Earth?

Homework Statement A 15% by mass solution has a density of 1.2 g/mL. What is the mass per liter concentration of this solution? → (a) 180 g/L (this is the answer, pretend you don't know) (b) 150 g/L (c) 125 g/L (d) cannot be determined from this information Homework Equations Density...

Am I on the right path here? 1. Homework Statement i. Prove that ##T_{a}## and ##T_{b}## are linear transformations. ii. Compose the two linear transformations and show the matrix that represents that composition. 2. The attempt at a solution i. Prove that ##T_{a}## and ##T_{b}## are linear...

Hey! :o I want to find a normal series of $D_4$ and all the composition series for $D_4$. I have done the following: $D_4=\langle a , s\mid s^4=1=a^2, asa=s^{-1}\rangle$ A subgroup of $D_4$ is $\langle s\rangle=\{s, s^2, s^3, s^4=1\}$, that is normal in $D_4$, since $[D_4:\langle...

Hey! :o I want to find all the composition series for $A_4$ and $S_3\times\mathbb{Z}_2$. A composition series for $G$ is $$1=S_0\leq S_1\leq S_2\leq \cdots \leq S_k=G$$ with $S_i\trianglelefteq S_{i+1}$ and $S_{i+1}/S_i$ is a simple group, right? (Wondering) Could you give me some hints how...

It states "a pure chemical compound is always made up of the same elements combined together in the same fixed ratio by mass." But how can a compound have the same elements ? For example,let's take ethanol,it is composed of hydrogen,carbon and oxygen.So three elements and not the same element.

I read in my textbook that Scuba kit has mixture of air such as nitrogen hydrogen and oxygen sometimes even helium is used instead of nitrogen. As pressure increases going deep in oceans, solubility of gas in liquid increases. So oxygen starts to dissolve quickly. But I don't understand why...

My question is that can we use properties of quantum mechanics and thermodynamics to alter size of a non biological object such that properties like its density,optical activity, conductance etc remains same... For instance we know that cooling down a substance considerably reduces its size and...

Hi. If a metal is very pure but still has other elements in it like this: -1 or 2 at 500ppm, 1 at 150ppm, 2 or 3 at 20-30ppm, 1 or 2 at 3-5ppm. Which are manufacturing impurities and which are deliberate doping? Are the 500ppm doping?

Homework Statement Suppose that A = { 1, 2, 3} , B = { 4, 5, 6} , R = { (1, 4), (1, 5), (2, 5), (3, 6)} , and S = { (4, 5), (4, 6), (5, 4), (6, 6)}. Note that R is a relation from A to B and S is a relation from B to B . Find the following relations: (a) S ◦ R . (b) S ◦ S−1...

I am reading John M. Lee's book: Introduction to Smooth Manifolds ... I am focused on Chapter 3: Tangent Vectors ... I need some help in fully understanding Lee's definition and conversation on pushforwards of $$F$$ at $$p$$ ... ... (see Lee's conversation/discussion posted below ... ... )...

Homework Statement A 16.00g sample of a mixture of KClO3 and KCl is heated until all the oxgen has been removed from the sample. The product entirely KCl (no O), has a total mass of 9.00g. What is the percentage of KClO3 present in the original mixture? 16.00g mixture 9.00g mixture without...

Is there any good information about the chemical composition of relativistic jets from neutron stars? If the chemical composition of the jets was different from the accretion material it could shed light on the process that forms the jets.

Homework Statement An ##\mathrm{8~g}## sample of ##{Fe_3O_4}## and ##{Fe_2O_3}## containing some inert impurity was treated with excess of ##\mathrm{aq}## ##{KI}## in acidic medium. which converted all iron to ##Fe^{2+}##. The resulting solution was then diluted to ##\mathrm{50~ml}##...

Guys I have a doubt or rather a misconception It is as follows: Consider a container with a partition having a gas A occupying 2/3rd of the volume and gas B occupying 1/3 rd of the volume Now suppose we remove the partition .As a result,gas A will occupy the whole volume of the container and gas...

Homework Statement If ##f(2x-1)= 6x + 15## and ##g(3x+1)=\frac{2x-1}{3x-5}##, then what is ##f^{-1}\circ g^{-1}(3)## ? a) -2 b) -3 c) -4 d) -5 e) -6 The Attempt at a Solution I think the f inverse and g inverse is ##f^{-1}(6x+15)= 2x-1## ##g^{-1}(\frac{2x-1}{3x-5})=3x+1## and,##f^{-1}\circ...

I am reading "Introduction to Ring Theory" by P. M. Cohn (Springer Undergraduate Mathematics Series ... ) 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...

I have made two posts recently concerning the composition series of groups and have received considerable help from Euge and Deveno regarding this topic ... in particular, Euge and Deveno have pointed out the role of the Correspondence Theorem for Groups (Lattice Isomorphism Theorem for Groups)...

I am reading Paolo Aluffi's book, Algebra: Chapter 0 ... I am currently focused on Chapter 4, Section 3: Composition Series and Solvability ... I need help with Exercise 3.3 on page 213, which reads as follows: I hope someone can help ... and in so doing use Aluffi's notation ... So that MHB...

I was wondering if anyone knew the standard notation for the following. Suppose I have functions ##f_1,f_2 \ldots,f_n##, is there a compact way of writing ##f_1 \circ f_2 \circ \ldots \circ f_n## ? I am debating whether ##\bigcirc^n_{i=1} f_i## is proper or good notation. Have anyone encountered...

Here is the question: Provide a logical argument that demonstrates that when applying any two reflections, the outcome will always either be equivalent to a rotation or a translation. This is what I came up with: •Translation A reflection is defined as, “a transformation in which a...

f(x)=log(1+x)/(1-x) and g(x)=(3x+x2)/(3x2+1) prove that (fοg)(x)=3f(x)

IF f(X)={x2, X>3 ; 3X+4, 0<X<3 ; X3+2 , X<0 } find (f°f°f)(-1) p.s the answer is 49! i don't know how this f(x) includes three terms x2 , 3x+4 and x3+2 And which term i need to use for the (f°f°f)(-1)

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...