Decomposition Definition and 414 Threads

Referring to first figure attached, if we put a system of a certain composition at a T and P corresponding to a point inside the spinodal, will it (with very small fluctuations) just jump to the corresponding binodal compositions at that temperature and pressure? As per this figure, the system...

If C NOT Hermitian, show we can decompose C into $\frac{1}{2}\left( C + {C}^{\dagger} \right) +\frac{1}{2i}i\left( C- {C}^{\dagger} \right) $ I've managed to prove C = C a couple of times, EG taking Hermitian or conjugate of both sides, probably there is a bit of info I am not thinking of or...

I have a matrix for which I know its QR decomposition: A = QR. I want to estimate the largest and smallest singular values of A (\sigma_1 and \sigma_n) however in my application it is too expensive to compute the full SVD of A. Is it possible to estimate the largest/smallest singular values...

Homework Statement Consider the reaction of pyruvic acid (CH3COCOOH) into gaseous acetaldehyde (CH3CHO) and gaseous CO2, which is catalyzed an aqueous solution by the enzyme pyruvate decarboxylase. Assume ideal gas behavior only for the CO2. (a) Calculate ∆298 0 for this reaction. (b) Calculate...

< Mentor Note -- thread moved to HH from the technical forums, so no HH Template is shown > experiment for testing type of catalyst on reaction rate? I need an experiment (just the method) Where I can test the reaction rate of changing the catalyst type I need about 3 differnet catalysts e.g...

Homework Statement SO3 decomposes on heating: 2SO2(g) 2SO2(g) + O2(g) A sample of pure SO3 was heated to a high temperature T. At equilibrium, the mole ratio of SO2 to SO3 was 0.152 and the total pressure was 2.73 atm. If the piston was pushed into cut the volume in half what is the new...

I synthesized 5 grams of nitrocellulose from cotton balls. I stored it for a couple weeks with no problem. I feel as if I didn't neutralize it very well, but I did wash it with water very thouroughly and dried it. It was safe to touch and dried fine. I stored it in a plastic ziploc bag for two...

Ok so I took partial fraction decomposition in Calc II, and now I'm taking it again in Differential Equations course. The problem is that I don't really understand what I'm doing. I understand the procedure when having simple real roots, for example 2x+1/(x+1)(x+2), it becomes A/(x+1) + B/(x+2)...

Hi, I'm reading Schwartz's book "Quantum field theory and the standard model", section 7.3.2., page 95 (https://books.google.com/books?id=HbdEAgAAQBAJ&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false) where he's talking about disconnected diagrams, the ones that have subsets...

Homework Statement Hello! Please, take a look at the picture attached. I would be grateful for the step by step explanation of the math equation; how it has been derived from f/s (1 + libor eur) - (1 + libor dol) to the one with logs? Homework EquationsThe Attempt at a Solution Thank you very...

Hi. In Georgi's book page 143, eqn. (10.29) he gives an example of decomposing a tensor product into irreps: u^iv_k^j=\frac{1}{2} \left( u^iv_k^j+u^jv_k^i-\frac{1}{4}\delta_k^iu^\ell v_\ell^j-\frac{1}{4}\delta_k^ju^\ell v_\ell^i \right)\\ +\frac{1}{4} \varepsilon^{ij\ell} \left(...

Hello, I was just introduced to this concept and I have solved a few problems, but I haven't come across any with denominators to a raised power yet. ∫ 1 / [(x+7)(x^2+4)] dx I would appreciate any directed help. 1. from the initial state I have broken the fraction into two assuming that...

The decomposition potential is always higher than the theoretically determined potential by thermodynamics. E=η+Eeq where E is the decomposition potential, η is the overpotential and Eeq is the theoretically determined potential. And ΔG=-nFE and if we were to substitute the decomposition...

Homework Statement I want to express the following expression in its Taylor expansion about x = 0: $$ F(x) = \frac{x^{15}}{(1-x)(1-x^2)(1-x^3)(1-x^4)(1-x^5)} $$ The Attempt at a Solution First I tried to rewrite the function in partial fractions (its been quite a while since I've last...

The decomposition potential is always higher than the theoretically determined potential by thermodynamics. E=η+Eeq where E is the decomposition potential, η is the overpotential and Eeq is the theoretically determined potential. However since the decomposition potential is higher doesn't it...

Homework Statement What is the partial fraction decomposition in ##\mathbb{R}[X]## of ##F = \frac{1}{X^{2n} - 1 } ##, ##n\ge 1##. Homework EquationsThe Attempt at a Solution Is this correct ? ## F = \frac{1}{2n}(\frac{1}{X-1} - \frac{1}{X+1} + 2 \sum_{k = 1}^{n-1} \frac{ \cos...

(x-3)/(x^2+4x+3) After i factor the denominator what do i do next to find A and B? =(x-3)/(x+3)(x+1) =A/(x+3)+B/(x+1)

Hi All, Can someone tell me why gravitational waves are always decomposed in spin weighted spherical harmonics with spin weight -2 ? I'm assuming you can hand wave the answer with something to do with the 'graviton' being a spin 2 particle but this isn't very satisfying to me. Are there any...

Hello everyone have a look at this video of Fourier Decomposition of an image.also we know that Fourier series is given in the image as...

Hi, just curious: I was able to simulate rotation motion in Alice software , as a combination of two motions: 1)Moving forward 2)Turning left (I can choose the rate at which each of these happens , in terms of meters and revolutions respectively.) Done simultaneously, at just the right rate...

Why does the thermal decomposition of group 1 metals, except for lithium, yield a nitrite while that of group 2 metals yield oxides?

Homework Statement Decompose x5 - 1 into the product of 3 polynomials with real coefficients, using roots of unity. Homework Equations As far as I know, for xn = 1 for all n ∈ ℤ, there exist n distinct roots. The Attempt at a Solution [/B] So, let ω = e2πi/5. I can therefore find all the 5th...

Hi Guys, I'm solving this for almost a week, this is a part of our probset in chemical kinetics: The thermal decomposition of dimethyl ether: CH3OCH3 ---K1--> CH3' + OCH3' CH3' + CH3OCH3 ---K2--> CH4 + CH2OCH3' CH2OCH3' + --k3---> CH3' + HCHO CH3' + CH2OCH3' ---k4--> C2H5OCH3 using steady-state...

Homework Statement http://i.imgur.com/Ypqcw19.png Homework Equations N/A The Attempt at a Solution Since the reaction involves the breaking of bonds in MCO3, I assume we are looking at coulomb interactions. I'd think the answer is D) BaCO3 because all the options have a 2+ charge, but barium...

Homework Statement Internal Energy Change Homework Equations N/A The Attempt at a Solution If internal energy change equals enthalpy change, then I am looking for the reaction which has the enthalpy change closest to zero. I know it cannot be A, as the formation of water is highly exothermic...

Homework Statement We performed a lab experiment where we heated (NH4)2CO3 in a test tube and observed the results. The solid compound turned into a gas and evaporated, leaving condensation of a clear liquid on the inside of the test tube. The lab report asks: What is the chemical equation...

Suppose we have a general timelike congruence of curves with tangent vector field ##V##, then the standard decomposition of the covariant derivative in index form (see e.g. Hawking and Ellis' "Large scale structure of space and time" equation 4.17) is given by $$V_{a;b} = \omega_{ab} +...

Homework Statement Let α = (α1α2...αs) be a cycle, for positive integers α1α2...αs. Let π be any permutation that παπ-1 is the cycle (π(α1)πα2...π(αs)). Homework EquationsThe Attempt at a Solution I started by choosing a specific α and π, and tried finding παπ-1 to give myself some idea of...

Could anybody link me to some good examples on how to go about doing them? I honestly have no idea how to go about doing these two types of problems.

I noticed a funny thing. The Cholesky decomposition can be defined as X=AB, where A is lower triangular. Generally Y=BA is not X, but Y seems to be a positive definite matrix. I wonder if there is any special properties to the pair (X,Y). I know that a positive definite matrix can be interpreted...

I have no idea what it is, and I really don't know how to go about using SVD on a matrix. All I know is that it could be useful for image compression (okay...?). Are there any resources or videos I can look at that will simplify the problem solving process for this? I've found a few that pertain...

Hello, I feel very uncomfortable with some aspects of the theory of valuations, places, and valuation rings. Here is one of my problems : Assume that L/K is a finite Galois extension of fields, and that F is a place from K to its residual field k, whose associated valuation ring is discrete. F...

In the proof of the Hahn Decomposition Thm located here, there is the following sentence at the top of page 4. "However, we shall prove that there is a positive subset of E carrying a positive charge, thereby obtaining the contradiction." but, if ##G## is the positive subset of ##E## mentioned...

Homework Statement Decomposition potential can be affected by the concentration of sulphuric acid electrolyte and whether there is stirring. Explain how they affects. Homework Equations ED = Ecathode - Eanode + ɳ where ɳ is the overpotential The Attempt at a Solution I'm thinking that the...

I have been reading Georgi "Lie Algebras in Particle Physics" and on page 183 he mentions how that the SU(3) defining representation decomposes into an SU(2) doublet with hyperchage (1/3) and singlet with hypercharge (-2/3). I am confused on how he knows this. I apologize if this is not the...

Homework Statement the problem is to find the inverse of a 3x3 matrix using LU Decomposition with C++ command, with the numbers designated. in my case, my numbers for the matrix are '306 410 780' #include <stdio.h> #include <iostream> #include <stdlib.h> #include <math.h> using namespace std...

I have drawn such a graph, but the two different methods of decomposition under a negative price change of commodity X have revealed two different natures of commodity X - the Slutsky decomposition concludes that X is normal, while the Hicksian decomposition yields the opposite conclusion. Is...

Homework Statement An #a*b*c box is given in x,y,z (so it's length #a along the x axis, etc.). Every face is kept at #V=0 except for the face at #x=a , which is kept at #V(a,y,z)=V_o*sin(pi*y/b)*sin(pi*z/c). We are to, "solve for all possible configurations of the box's potential" Homework...

please help decompose$\frac{4x^2y}{(x^2-2xy+2y^2)(x^2+2xy+2y^2)}$ I've used the cases I know for this problem but to no avail. please help me.

Homework Statement To find the decomposition of a polynomial with a repeated factor in the denominator, you should separate them into (x+a)^1 + ... + (x+a)^n. But, my question is why? For example, why should you decompose it in the following way: \frac{x+2}{(x+1)(x+3)^2} = \frac{A}{x+1}...

Hello again PF! I had a question on singular value decomposition. My question relates to a pepper I have been reading, and I'm wondering if any of you would be able to glance over the paper and let me know your thoughts? The link is here...

Alright, I am here again with another question... When I have a rational function, let's say (x+4)/(x-2)(x-3) I rewrite it like A/(x-2) + B(x-3) and then solve it for A & B. But when we have for e.g (x^2 + 3x + 2)/(x(x^2 +1 )) the book tells me to rewrite it like: A/x + (Bx + C)/(x^2 + 1)...

Just as the title says, what is a POD? I've tried reading papers but I feel I am missing something. Does anyone have a good, intuitive understanding of this? Let me know if I've accidentally posted in the wrong section. Thanks!

Long time reader, first time poster. Originally, it was my contention that all Lie groups could be written as the semidirect product of a connected Lie group and a discrete Lie group. However, I no longer believe this is true. The next best thing I could think of was to say that a Lie group is...

Find the partial fraction decomposition for the rational function. \frac{-4x^2 - 8x - 19}{(x^2 + 2)(x-9)} I'm not sure what to do.

Using the conventions of http://www.damtp.cam.ac.uk/user/db275/Cosmology/Chapter4.pdf (not mine). For a flat FRW perturbed universe, the metric is can be written in general as: ds^2=a^2(\tau)[(1+2A)dt^2-B_idtdx^i-(\delta_{ij}+h_{ij})dx^idx^j] I understand intuitively that we can decompose Bi...

Let $m$ be an integer ${\geq}3$ and $f(x,y,z)=y^m(x+y^3)-z^3$ be in $k[x,y,z]$. Find the singular points of $f$ and find a minimal primary decomposition of the jacobian of $f$. I find the set of singular points of $f$ to be {$(x,0,0): {x\in k} $} and the jacobian to be $\langle...

Homework Statement \int \frac{-2x + 4}{(x-1)^{(2)}(x^{(2)}+1)}Homework Equations The Attempt at a Solution I've done the problem a couple times but the answers keep coming out differently so I'm assuming I am messing up the setup. This is what I have for the first part of the setup: -2x +...

Homework Statement Evaluate ∫((secx)^2)/[((tanx)^2)+(3tanx)+2] Homework Equations Partial fraction decomposition The Attempt at a Solution So here's what I did: But this is incorrect. It says the correct answer is -2lnabs(\frac{1}{2tanx+3}+\sqrt{4(tanx+3/2)^{2}-1}), which was...

Please see attached picture. I need verification of my answers. I unfortunately found these problems on an old book with no answer. I would really appreciate it. (a) Ok. For this one, I am really not sure. PLEASE help. I get a very complicated formula. (1+x)(x^4)/(1-x)^2=Kp. Now, this...