Notation Definition and 1000 Threads

ive noticed some problems have the quark composition of Λ as uds, but in the Baryon Octuplet that is the same composition as ∑. I always thought Λ was another way of writing Δ, so the quark composition would be ddu, am I wrong?

The Fourier integrals and series can be written of 3 forms (possibly of 4): the "real cartesian": a(ω)cos(ωt) + b(ω)sin(ωt) the "real polar": A(ω)cos(ωt - φ(ω)) where: A² = a² + b² sin(φ) = b/A cos(φ) = a/A tan(φ) = b/a the "complex polar" A(ω)exp(iφ(ω))exp(iωt) And my...

How do you define a set without using set builder notation? For example, let's say that I want to define set S as: S={x ∈ ℕ ∣ 0<x<5} Then S={1,2,3,4} However, suppose that I wanted to define S without set-builder notation, as below? ∀x(x ∈ ℕ ^ 0<x<5 ⟺ x∈S ) Would these two...

I must become good at this ASAP. Homework Statement prove \vec{\nabla}\cdot (\vec{a}\times\vec{b} ) = \vec{b} \cdot(\vec\nabla\times\vec{a}) - \vec{a}\cdot(\vec\nabla\times\vec{b}) Homework Equations \vec a \times \vec b = \epsilon_{ijk}\vec a_j \vec b_k \vec\nabla\cdot =...

I apologize if this is the wrong section This is an integral written with the first 7 digits of pi, reversed, I think... Can somebody write this out with traditional notation ? I am still learning the basics of integrals, so I am completely unsure of how to write it out...

I'm having some confusion with index notation and how it works with contravariance/covariance. (v_{new})^i=\frac{\partial (x_{new})^i}{\partial (x_{old})^j}(v_{old})^j (v_{new})^i=J^i_{\ j}(v_{old})^j (v_{new})_i=\frac{\partial (x_{old})^j}{\partial (x_{new})^i}(v_{old})_j...

I've been trying to think of the grammatically correct way to translate A\cupB and A\capB. So, let's say A is the set of all animals and B is the set of all boats. Then, A\cupB is the set of all entities which are either animals or boats (or both). And A\capB is the set of entities...

I'm hoping that you can help me settle an argument. For a matrix \textbf{M} with elements m_{ij}, is there any sitaution where the notation (M_{ij})^{-1} could be correctly interpreted as a matrix with elements 1/m_{ij}? Personally I interpret (M_{ij})^{-1} in the usual sense of an inverse...

I asked this in the logic&probability subforum, but I thought I'd try my luck here. ... Let (A,\mathcal A), (B,\mathcal B) be measurable spaces. Let p be a probability measure on (A,\mathcal A), and let q:A\to\mathcal P(B,\mathcal B) be a measurable function which takes each a\in A to...

Let (A,\mathcal A), (B,\mathcal B) be measurable spaces. Let p be a probability measure on (A,\mathcal A), and let q:A\to\mathcal P(B,\mathcal B) be a measurable function which takes each a\in A to some probability measure q(\cdot|a) on (B,\mathcal B). Then there is a unique probability...

Homework Statement Form negation and then either prove statement or negation: \forally \in { x | x \in Z, x>=1}, 5y^2+5y+1 is a prime number. The Attempt at a Solution Answer given: \existsy \in { x | x \in Z, x>=1} such that 5y^2+5y+1 is not prime. The negation is true...

I understand how contravariant 4-vectors transform under a Lorentz transformation, that is: ##x'^μ= \Lambda^\mu~_\nu x^\nu## [1] and how covariant 4-vectors transform: ##x'_\mu=(\lambda^{-1})^\nu~_\mu x_\nu##. [2] Now, I have come across the following relations...

Homework Statement This makes intuitive sense to me, but I am getting stuck when trying to read the Dirac notation proof. Anyway, the author (Shankar) is just demonstrating that the product of two operators is equal to the product of the matrices representing the factors. Homework Equations...

Homework Statement So I solved this problem ∑ (-1)^n (x+5)^n by finding the sum of the series to be 1/(x+6), which was correct. I am stuck on the second part of the problem asking for interval notation. It says: Determine, in interval notation, the values of x for which the series converges...

I would like members views on right notation for maps/functions. I am thinking of studying some material in some of the chapters of the book: Introduction to Ring Theory by P. M. Cohn Cohn claims his book is suitable for 2nd and 3rd year undergraduates and the book seems to have some really...

Homework Statement Show that the equation \nabla \times \vec{p} = -\frac{\vec{B}}{r^3} + 3\frac{\vec{B} \bullet \vec{r}}{r^5}\vec{r} Where ; \vec{p} = \frac{\vec{B} \times \vec{r}}{r^3} \vec{r}=(x_1 ,x_2 ,x_3) and \vec{B} is a constant vector. and r is the magnitude of \vec{r}...

''..Cauchy stress tensor in every material point in the body satisfy the equilibrium equations.'' \sigma_{ij,j}+F_i=0 I would appreciate if you could write out what it means. Also there is this notation which I don't understand: \frac{\partial}{\partial y_j}\sigma_{ij}(x,y)

I'm trying to write a contracted general equation for an expandable equation. Just like there's the summation symbol for sums, is there something for multiplying terms? for example.. how do i contract the following? $$C_{i}C_{ii}C_{iii}C_{iv}C_{v}...$$?

Question and symbols: Consider a state|ε> that is in a quantum superposition of two particle-in-a-box energy eigenstates corresponding to n=2,3, i.e.: |ε> = ,[1/(2^.5)][|2> + |3>], or equivalently: ε(x) = [1/(2^.5)][ψ2(x) + ψ3. Compute the expectation value of momentum: <p> = <ε|\widehat{}p|ε>...

I cannot for the life of me remember what to do with the diode: It is a DC Current hooked up to one resistor in series with a pair of resistors in parallel drawn vertically, but then the diode is hooked up to (on paper) the top two ends of the parallel resistors? It's aligned horizontally...

Homework Statement Hi I have a vector v. According to my book, the following is valid: \frac{1}{2}\nabla v^2-v\cdot \nabla v = v\times \nabla \times v I disagree with this, because the first term on the LHS I can write as (partial differentiation) \frac{1}{2}\partial_i v_jv_j =...

Homework Statement At one instant, force F: 4.0j N acts on a 0.25 kg object that has position^vector^V : (2.0t - 2.0k) m and velocity vector /: (-5.0i + 5.0k) m/s. About the origin and in unit- vector notation, what are (a) the object's angular momentum and (b)the torque acting on the object...

I'm working on some MIT OCW for probability theory, and I've come across some confusing notation in the assignmnet. Look at exercise 3 here: http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-436j-fundamentals-of-probability-fall-2008/assignments/MIT6_436JF08_hw01.pdf...

Is there a standard algorithm or procedure that defines addition, multiplication of big O terms. I want definitions for problems like:- 1) (x-1) * O(x) 2) O((x-a)2) where a is some positive number etc. Since I want to implement this on a computer I would prefer some algorithm or paper...

I have the following question for anyone who can help: Suppose in Dirak notation i have the following state: /ψ> = 2 /u1> + /u2> where /u1>,/u2> are the two first eigen kets of energy of the infinite square well. That means <x/u1>= Asin(π x /L) and <x/u1>= Asin(2 π x /L) which gives ...

Hello everyone! I have this polynomial: $p(x) =$ $$1 + \sum_{k=1}^{13}\frac{(-1)^k}{k^2}x^k$$ - I'm supposed to show that this polynomial must have at least one positive real root. - I'm supposed to show that this polynomial has no negative real roots. - And I'm supposed to show that if $z$...

Homework Statement Say for example, a particles velocity was given by the following equation: \vec{V}[SIZE="3"](t) =[SIZE="3"] (2t2-4t3)\hat{i} - (6t +3)\hat{j} + 6\hat{k} If I wanted to find the displacement of the particle between t=1s and t=3s, could I just integrate like this...

Homework Statement Show that the dot product in two-dimensional space is linear: <u|(|v> + |w>) = <u|v> + <u|w> The Attempt at a Solution I feel like I'm missing some grasp of the concept here ... I would think to just distribute the <u| and be done in that one step, but I'm being...

I'm brand new to this website, and couldn't figure out how to start a new thread, but I also have a question about Big Theta notation. Is big-theta(x/y) = big-theta(x)/big-theta(y)? I know big-o(x/y) = big-o(x)/big-o(y), but I don't know if big-omega(x/y) = big-omega(x)/big-omega(y). I can...

Franke's "condensed notation for structural synthesis" in this pic I don't understand how we can labelled some lines as 0s and others as 1s.

Hello, I'm reading "Complex Made Simple" by David Ullrich. He has these notation for disks D(z_0,r) = \left\{ z \in \mathbb{C}: |z-z_0|< r \right\} \bar{D}(z_0,r) = \left\{ z \in \mathbb{C} : |z - z_0| \leq r \right\} I understand that these sets are to be the open and closed disks with...

Homework Statement What is meant by A^c notation in matrix, where A is any arbitrary matrix?The Attempt at a Solution I've searched all over the internet and reference books that I have but none of them gives information about this thing. Please help me.

Homework Statement Using Dirac Notation prove for the Hermitian operator B acting on a state vector |ψ>, which represents a bound particle in a 1-d potential well - that the expectation value is <C^2> = <Cψ|Cψ>. Include each step in your reasoning. Finally use the result to show the...

Homework Statement On Wikipedia there is an article about perturbation theory. To understand something I need to understand the following relation. They say: Homework Equations H |n> = E_n |n> So: <n| H = <n| E_n H is Hermitian. So: Why is this? The Attempt at a Solution...

http://i.imgur.com/ORtBJdT.jpg i don't understand why the old base is written in terms/as a linear combination of the new bases. wouldn't i want to map my coordinates from old to new not new to old?.. here's what my textbook says about it, can you guys interpret this for me, i still don't...

forgive the messiness; i take bad notes in class. http://i.imgur.com/VmW8Ubg.jpg towards the middle of the page where it says "this is equivalent to..." and then my professor wrote what follows but i thought the row vector should be complex conjugates? ie, the red writings are not actually...

[a;b[ I want to do a problem with this but i can't find anything about it, if anyone can help me it'd be very useful, thank you. :) The one i want to do exactly is [20;30[ , in case anyone is wondering.

Homework Statement Hi there! Here is a problem from our 1st year course. We have covered the basics on charges and Coulomb's Law. However our prof said he designed the following question to be "deliberately obscure"! Two charges of 4.00μC are fixed in space, Q1 at (0,0,0) and Q2 at...

Hi I have a textbook which uses the notation: \sum\limits_{i\neq j}^N a_i a_j I can't find anywhere what this actually means. Is it equivalent to: \sum\limits_{i}^N \sum\limits_{j}^N a_i a_j where j can't equal i? Thanks.

u and v are vector or whatever in that base, and A is an operator. What does <u|A|v> mean?

so I'm fine with the kets, e.g, |a>.. but i don't understand what the bras are. the kets are basically just a column vector right? ie the components (with the direction) of the vector being described. but what is the bra? this was given to us in class: <a|=a1<e1|+a2<e2|= (a1* a2*) (where e1...

I know how to solve linear systems but I came across this question where I've never seen the notation before. I searched all over the internet but still couldn't figure it out. The question asked to find all solutions in Z_{2}^{5} of a linear system. I'm guessing that Z^5 means all integers on...

I am not sure how to properly use the scientific notation in this problem. I have attempted to solve it several different ways to no avail. A house has a volume of 1.45 x 10(4)m(3). At 20.0° C and 740 mm Hg, the air fills the house. If the temperature and pressure increase to 35.0°C and...

Homework Statement I have the following rank-2 tensor T = \nabla \cdot \sum_{i}{c_ic_ic_i} I would like to write this using index notation. According to my book it becomes T_{ab} = \partial_y \sum_{i}{c_{ia}c_{ib}c_{iy}} Question: The change \nabla \rightarrow \partial_y and c_i...

Q) I am using index notation to show that ε^{0123}=-1 given that ε_{0123}=1. The soluton is: ε^{0123}=g^{00}g^{11}g^{22}g^{33}ε_{0123}=-ε_{0123} where g_{\alpha\beta} is the metric tensor. I am struggling to understand the last equality. Many thanks for any assistance.

Ok I have T_{ij}=μS_{ij} + λ δ_{ij}δS_{kk}. I am working in R^3. (I am after S in terms of T) . I multiply by δ_{ij} to attain: δ_{ij}T_{ij}=δ_{ij}μS_{ij} + δ_{ij} λ δ_{ij}δT_{kk} => T_{jj}=δ_{jj}λS_{kk}+μS_{jj} * My question is , for the LH term of * I choose T_{jj} rathen than T_{ii}. I...

Q) I am using index notation to show that ε^{0123}=-1 given that ε_{0123}=1. The soluton is: ε^{0123}=g^{00}g^{11}g^{22}g^{33}ε_{0123}=-ε_{0123} where g_{\alpha\beta} is the metric tensor. I am struggling to understand the last equality. Many thanks for any assistance.

Hi folks. Hope that you can help me. I have an equation, that has been rewritten, and i don't see how: has been rewritten to: Can someone explain me how? Or can someone just tell me if this is correct in tensor notation: σij,jζui = (σijζui),j really hope, that...

Can anyone please give a succinct and clear description on this? I'm a little confused...

I have an vector calculus identity to prove and I need to use vector notation to do it. The identity is $$\vec{\nabla}(fg)=f\vec{\nabla}{g}+g\vec{\nabla}{f}$$ I tried starting with the left side by writing $\vec{\nabla}(fg)=\nabla_j(fg)$. Now I look and that and it really looks like there is...