Composition Definition and 374 Threads

New to Western music theory.... About this concept of chord progressions -- is it that there is a large set of "officially approved" chord progressions for a given key (eg C major), and someone composing a melody will typically select a progression first, and make the melody conform to it? Or...

I was intrigued by a comment in Brilliant.org: Besides the proof provided by Brilliant, I also found a couple of other websites. But none of these proofs were entirely clear to me. So I tried to come up with my own proof. Since I am not a group theorist, I wanted to ask if the proof makes...

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Butane 0.75mol of C4H10 0.75 x C4 = 3mol of CO2 0.75 x H5 = 3.75mol of H2O 0.75 x 6.5O2 = 4.875mol of O2 Propane 0.10mol of C3H8 0.10 x C3 = 0.3mol of CO2 0.10 x H4 = 0.4mol of H2O 0.10 x 5O2 = 0.5mol of O2 Butene 0.15mol of C4H8 0.15 x C4 = 0.6mol of CO2 0.15 x H4 = 0.6mol of H2O 0.15 x...

I know how to solve each of those problems. For the set one, I look at the output of the S and try to match it with the input of T and then take the pair (input_of_S, output_of_T), and I do that for each pair. As for the formula one, I just plug in x = g(y). My confusion lies in trying to...

I'm trying to understand this paper (equation 2.16 specifically): Bini, D., Carini, P., & Jantzen, R. T. (1995). Relative observer kinematics in general relativity. Classical and Quantum Gravity. Am I correct in reading there is no way to express the relativistic relative velocity composition...

The LT can be derived from the first postulate of SR, assuming linearity an that velocity composition is commutative, and that GT can be excluded: ##t' \neq t##. Definition of the constant velocity ##v##: ##x' = 0 \Rightarrow x-vt=0\ \ \ \ \ \ ##(1) With assumed linearity follows for the...

https://cds.cern.ch/record/539311/files/ext-2002-016.pdf What was the composition of ether according to the ancients? [Non-English reference deleted by the Mentors]

I am learning some complex analysis as it is a prerequisite for the masters program that I was accepted into and I didn't take it yet during my bachelors. I am using some lecture notes in Slovene and I have run into a problem that has proven troublesome for me : If ##g: D \rightarrow \mathbb{C}...

I found the density of carbon and iron: ρ_fe=7.87 g/〖cm〗^3 ρ_c=2.26 g/〖cm〗^3 Using equation 2: atom density of iron and carbon N_fe = 8.48e22 cm^-3 N_c = 1.13e23 cm^-3 Using equation 1: macroscopic scatter and absorption cross sections of iron and carbon Σ_a,fe = .217 cm^-1...

As this page says: "A burnt-out star is basically a gas of electrons and ions. " In white dwarf, further collapse of the star is stopped by electron degeneracy pressure. But, if the star material is just a soup of ions and almost free electrons, why don't the electrons and ions separate into...

Thought experiment for discussion: You have a sealed transparent container with a "perfect vacuum" inside of it. 1) List what is inside of the "empty" container. 2) Explain how you might go about expelling EVERYTHING from the container.

> A Ti02 film of index 2.5 is placed on glass of index 1.5 to increase the reflection in the visible. Choosing a suitable value for wavelength, how thick a layer in microns would you want, and what reflectivity would this give you? My question is about the last question presented above...

Hello PF, I am teaching a general education college-level introduction to "Planet Earth" class that covers a bit of astronomy. This question is in regards to our unit on the formation of the Solar System. Specifically I am confused about the composition of Jupiter and Saturn. This is a figure...

g(f(x))=\( g(f(x))=2/(1/x-4)+4 \)

I have a pencil of Iron of length ##L## rotating about its center in a plane at constant angular velocity ##\omega##. The tip of the pencil in Newtonian mechanics has linear velocity ##\frac{\omega L}{2}##. It can exceed ##c##, of course. Now let us complicate this. Assume the center of the...

First, I calculated the velocity of the object with regards to earth, which is: $$v'=\frac{V-v}{1-\frac{vV}{c^2}}=0.34c$$ Now, the problem is solved if I consider the length ##l=45m##(so by calculating the ##\gamma## factor with ##v'##) to be the proper one... but since it's measured by the...

Solution attempt: $$F(F(x,y))=(z,w)$$ is the map given by $$x=z$$ $$y=w$$

Hey! :giggle: Question 1: Let $C$ be a $\mathbb{R}$-vector space, $1\leq n\in \mathbb{N}$ and let $\phi_1, \ldots , \phi_n:V\rightarrow V$ be linear maps. I have shown by induction that $\phi_1\circ \ldots \circ \phi_n$ is then also a linear map. I want to show now by induction that if $V$ is...

Hi can someone give an hand on understanding how to handle such kind of problems ? can't come up with a valid solution. if i do ##\frac {0,56}{2*14.00}## do i get the molar fraction of nitrogen?

Under the topic of simple harmonic motion comes the composition of two SHM's with the same angular frequency, different phase constants, and amplitudes in the same directions and in perpendicular directions. composition of SHM's in same direction: say a particle undergoes two SHM's described by...

I am quite unsure where to post this, as I am a chemical engineer and that I am working with phase equilibrium. My issue however is regarding statistical mechanics, thus me posting my problem here. I keep on encountering that the second virial coefficient of a mixture must be quadratically...

Which of the following implies that S∘S=S? There are 5 options, select all that are right. S is reflexive S is symmetric S is transitive S is reflexive and symmetric S is reflexive and transitive I assume that S acts on a set A. So let a,b,c be elements of A. For S to be reflexive, for all a...

I have seen that interstellar dust contains the detritus of supernova explosions. But whet else does it contain? How uniform is it? Does its compositions vary significantly from place to place? This question started with wondering whether one could back out the origins of the Earth from it's...

Let the empirical formula be ##Na_x S_y O_z## then we can concude $$\frac {29.11}{100} = \frac{xM_{Na}}{xM_{Na} + yM_S + z M_O}$$ $$\frac {40.51}{100} = \frac{yM_S}{xM_{Na} + yM_S + z M_O}$$ $$\frac {30.38}{100} = \frac{zM_O}{xM_{Na} + yM_S + z M_O}$$ where ##M_{Na} = 23, M_S = 32,M_O = 16##...

Attempt: Consider an arbitrary normal series ##G = G_0 \ge G_1 \ge G_2 \ge \dots \ge G_n = 1##. We will refine this series into a composition series. We start by adding maximal normal subgroups in between ##G_0## and ##G_1##. If ##G_0/G_1## is simple, then we don't have to do anything. Choose...

Attempt so far: We're given that ##G## and ##H## have equivalent normal series $$G = G_0 \ge G_1 \ge \dots \ge G_n = 1$$ and $$H = H_0 \ge H_1 \ge \dots \ge H_n = 1$$ We can assume they have the same length because they are equivalent. I think from here I need to construct two composition...

Hi, I'm hoping this will be a fairly easy question for someone on here to answer. If I wanted to make a (small?) vacuum tank (basically a hollow cylinder capped with two similarly hollow hemispheres - like so: (===)), how thick would the walls of the tank need to be for it to withstand the...

I ask the foundry to cast nickel alloys and I took a piece metal to do a chemical test. The element composition of the nickel alloy is Ni 70% Cr 12% Fe 1.2% Mo 2.5%...so far they all are in the allowable range. But I found the alloy also contains W 0.004% ! Is this the normal condition ? ? I...

Hey! 😊 Let $\delta_a:\mathbb{R}^2\rightarrow \mathbb{R}^2$ be the rotation around the origin with angle $\alpha$ and let $\sigma_{\alpha}:\mathbb{R}^2\rightarrow \mathbb{R}^2$ be the reflection about a line through the origin that has angle $\frac{\alpha}{2}$ with the $x$-axis. Let $v\in V$...

why isn't Surface tension reliant on the composion of the atm? For an instance; If you place a glass of water in a room with regular atmosphere or you place it in a room filled with other gasses. The coefficient of surface tension of the fluid will change? Maybe? why isn't viscoty of a fluid...

Hi guys, suppose we have a function ##C(x, y)## into the real numbers. Suppose also that ##y=y(x)##, i.e. ##y## is a function of ##x##. Now in my script, I have a term ##\nabla_x C(x_0, y(x_0)) ##. From my point of view, this means that you take the partial derivative of ##C(x,y)## with...

I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 3: Continuous Functions on Intervals and am currently focused on Section 3.1 Limits and Continuity ... ... I need some help in understanding the proof of Proposition 3.12...

I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 3: Continuous Functions on Intervals and am currently focused on Section 3.1 Limits and Continuity ... ... I need some help in understanding the proof of Proposition 3.12...

Hello, I have a general understanding of how we are aware of the presence of dark matter in the universe and the fact that we still don't know exactly what is that dark matter is made of. I would like to know which instruments are used to try and find an answer. For instance, from what I...

I've been thinking about this from time to time, I'll try to make this short and understandable. So we go back to the early universe within our current best model of extrapolation called the Big bang theory. In the early universe as it was expanding we have a very dense and energetic matter...

Hello! My name is Fabrizio, I'm a high school student doing some research on the atmosphere. Right now, I'm trying to figure out how much matter escapes into space via Jean's Escape. I've found several formulas, all of which require me to know what the amount of particles per m3 of a certain...

The thing is that, I don't know how to approach this question and the particular steps for relevant value findings. Please show me the path, and I will go in it friends. I couldn't attempt as I have no clue how to approach this. Thank you very much in advance.

Wet basis 0.75mol C4H10 Requires 4.875 mols O2 Produces 3 mols of CO2 and 3.75 mols of H2O 0.1mol C3H8 Requires 0.5 mols O2 Produces 0.3 mols of CO2 and 0.4 mols of H2O 0.15mol C4H8 Requires 0.9 mols O2 Produces 0.6 mols of CO2 and 0.6 mols of H2O Theoretical oxygen= 6.3mol +10% excess...

Hello! I am reading Modern Particle Physics by Mark Thomson and in chapter 9.6.2 he writes the composition of certain mesons. However for some of them he uses an equality sign: $$|\rho^0> = \frac{1}{\sqrt{2}}(u\bar{u}-d\bar{d})$$ while for others he writes: $$|\omega> \approx...

It's a beginner's question : if I consider compositions of Givens' rotations, how many should I combine to obtain the whole group, since those don't commute and hence their order is important ? Is it 6 ?

Homework Statement If ##f\left(x\right) = x^2 + 2x + 2##, find two functions ##g## for which ##\left(f \circ g\right)\left(x\right) = x^2 - 4x + 5##. Homework Equations If ##f\left(x\right) = x^2 + 2x + 2##, then ##\left(f \circ g\right)\left(x\right) = g\left(x\right)^2 + 2g\left(x\right) +...

Hi guys, Merry Christmas to you all! I wanted to know whether a neutral pion can be made up of a strange quark and an anti-strange quark. I know that the kaon is the only strange meson and all variations contain an s quark but wouldn't the strangeness be zero in an s quark/anti-s quark pair as...

Hi All, Is it possible to know the concentration of a solute when you have only its composition? I.e : the solute contains 1 molecule of water for each k+

Homework Statement "If ##f:\mathbb{R}^n \rightarrow \mathbb{R}^m## and ##g:\mathbb{R}^m\rightarrow \mathbb{R}^p##, show that ##(g\circ f)_*=g_*\circ f_*## and ##(g\circ f)^* = f^* \circ g^*##." Homework Equations Pushforward: ##f_*(v_a)=(Df(a)(v))_{f(a)}## Pullback...

Homework Statement Prove that for any finite group ##G## there exists a sequence of nested subgroups of ##G##, ##\{e\}=N_0\leq N_1\leq \cdots \leq N_n=G## such that for each integer ##i## with ##1\leq i\leq n## we have ##N_{i-1}\trianglelefteq N_i## and the quotient group ##N_i/N_{i-1}## is...

Homework Statement f(x)= x/(1+x) What is f(f(x)) and what is its domain. 2. The attempt at a solution I found f(f(x))= x/(1+2x) and the domain: (-∞,-1/2)∪(-1/2,∞) , but it is saying that I have the wrong domain. What mistake have I made? My process for finding domain: 1. Find the domain...

Homework Statement Silver has two naturally occurring isotopes: Ag−107 with a mass of 106.905 amu and a natural abundance of 51.84 %, and Ag−109. Use the atomic mass of silver listed in the periodic table to determine the mass of Ag−109. express answer to 4 sig-figs and use appropriate units...

Homework Statement Let A, B, C be finite sets such that A and B have the same number of elements, that is, |A| = |B|. Let f : A → B and g : B → C be functions. (a) Suppose f is one-to-one. Show that f is onto. (b) Suppose g ◦ f is one-to-one. Show that g is one-to-one.Homework EquationsThe...

Hello, I am looking for a resource on the composition of transuranics in a typical commercial PWR after the fuel is cycled and put into dry cask storage. Anyone have material on this? Thanks!