Sigma Definition and 229 Threads

Can anybody please suggest some references (preferably review articles or lecture notes etc, freely available online) for learning linear and nonlinear sigma models and their applications in particle physics?

Meaning of "countable" in definitions of sigma algebra In the third axiom defining a \sigma-algebra, (X,\Sigma), does countable mean (a) "finite or countably infinite", or does it mean (b) "countably infinite".

Ryder, QFT, 1985, pg. 40, Eq. (2.69) K = sigma?? For the similar page in the 2nd edition, turn page 37 at this...

Say we have sp2 hybridization of nitrogen, can the unhybridized p orbital form sigma bonds too or can it only form pi bonds? So in the case of nitrogen, it would be able to form molecules with 2 sigma bonds and one pi bond, correct? Thanks

The problem posed is: Evaluate \sum_{i=1}^{n} (2i + 2^i) I know that I can break the summation down to this: 2\sum_{i=1}^{n} i\, +\, 2\sum_{i=1}^{n}1^i and then after using some Fundamental Theorems... =2\Bigg(\frac{n(n+1)}{2}\Bigg) + 2^n I can't seem to get it to look like my answer...

In Zee's quantum theory text, introducing the Dirac equation, he states the gamma matrices as direct products of Pauli matrices. The statements involve the identity matrix, sigma matrices, and tau matrices. It took me a bit to realize that the latter were identical. I hadn't seen the tau...

how would i plug this into the calculator? to find the sum? step by step process? thankss! 4 ∑ 2 cos (π/k) k = 1 i tried this site http://mathbits.com/mathbits/tisection/Algebra2/summation.htm and i got a different answer...so i just need help with the set up on a T.I calc.

I've been clawing at my mind for a while regarding this, I pray somebody can help me. I was implementing a method from a computer science paper when I came across this: [PLAIN]http://www.mattkent.eu/challenge.png Bearing in mind that x is a vector, epsilon is a vector of integers (and...

4 ∑ 2cos (π/k) k = 1 i have the answer..but all i need it the steps on how to figure it out! thanks!

Write the sum in expanded form. I don't know where to start with...

Hi this isn't actually a homework question more my own curiosity/confusion. They have the same quark constituents and http://en.wikipedia.org/wiki/File:Baryon_octet.png" for both but mass and decay rate are different, please explain. (if the lambda is an excited state of the sigma why isn't it...

A vector A, can be expressed in sigma notation as \sum Ai where i runs from 1 to 3, i.e. A1 for x coordinate, A2 for y coordinate and A3 for z coordinate. I wonder how to express vector A in polar form using sigma notation. Could anyone share their knowledge to me?

1. Write each series using sigma notation. 2. The series is: 2 + 5 + 10 + 17 + 26 + 37 3. I know that above the sigma, the number is 6 because there are only six terms in the series. The trouble I seem to have with this is the fact that the series is neither arithmetic or geometric. It...

Hi everybody, I'm reading about sigma delta adc, the base theory. I've read about the first order modulator and now the second order, but I have a problem (maybe stupid) with a phrase of my book (Data Converters by F.Maloberti), when he describe the 'passage' from first order to second order...

Homework Statement Consider the power series. sigma (n=1 to infinity) x^n / [n(n+1)] if f(x) = sigma x^n / [n(n+1)], then compute a closed-form expression for f(x). It says: "Hint: let g(x) = x * f(x) and compute g''(x). Integrate this twice to get back to g(x) and hence derive...

Homework Statement I have estimated the standard deviation of the population of my samples from the standard deviations from each of the samples with the equation found below. And I am to construct a confidence interval for a contrast, thus I will need the number of degrees of freedom for which...

I just need a quick clarification on how to read this function f(x) = sigma of X^2, starting at j=1, and n so does that mean that f(3) would equal to 36, if n=4?

Homework Statement Hi. For the question given (attachment) where does the factor of 2PI in the function for sigma come from in the first step because I don't get it in my working for the first step. Homework Equations see attachmentThe Attempt at a Solution I got sigma (without the 2PI) by...

how can I understand the difference between algebra, sigma algebra and topology If I take the set A that contains a,b,c,d,e,f the set C that contains A,phi,{a},{b,c,d,e,f} then C is algebra on A and C is sigma algebra on A and (A,C) is topological space is that true? what is the...

I'm trying to understand the difference between these two algebraic structures. An algebra is a collection of subsets of a set X that is closed under pairwise unions and complements of individual subsets with respect to X. A sigma algebra is a collection of subsets of a set X that is closed...

What's the point of defining \sigma algebras, i.e., why must we assign measures only to elements of a \sigma algebra? Second, can you give an example of a set contained in the Lebesgue \sigma algebra, but not the Borel \sigma algebra? Also, is there a set not contained even in the...

I am working on the last step of a proof to show that \sigma(O) = \sigma(C2). C2 = {(-\infty, a): a \epsilon R and O = all the open sets in R1. I have already showed that \sigma(C2) C \sigma(O). I am now trying to show the converse, that \sigma(O) C \sigma(C2). To do this, I know I just...

In my lab I measure some chemical data. Output from the software I use contain also some stats, like the mean value, standard deviation and some number called SIGMA MEAN. My typical dataset looks like this: sample MgO Al2O3 a 5,307872109 7,45113642 b 8,496074587 9,182072932 c...

I have a question about sigma notation and parentheses. Does \sum x[k] + x[n] mean \sum( x[k] + x[n]) or \left(\sum x[k] \right)+ x[n] I find it a personal annoyance for things to be written with parentheses even if there are rules about it. Including parentheses would just reduce...

Homework Statement Hello, I am trying to draw a Feynman Diagram at quark level for the decay sigma+ -> neutron + pi+.Homework Equations sigma+ -> neutron + pi+ uus -> udd + udbarThe Attempt at a Solution Well, the attachment is what I came up with. I have no idea if it's right to be honest...

1. The problem statement, all variables and given/nknown data Find a formula for the expression. Use sigma notation. (x + 1/y)n The Attempt at a Solution Not sure how to do this we have only dealt with sigma notation involving only n as a variable

Homework Statement t1, t2, t3, t4 , ... , tn is a sequence t2 - t1 = t3 - t2 = t4 - t3 ..... = t(n-1) - tn show that: 1/t1t2 + 1/t2t3 + 1/t3t4 ... + 1/tn-1tn = n-1/t1tn Homework Equations The Attempt at a Solution I tried to use sigma but I couldn't solve it ...

I understand how to solve sigma notation problems where the index variable is equal to 1, but how would I solve a problem like this?? n \Sigma (i2-3) i=3 If i was equal to 1 I would be able to solve this, but I'm not sure what to do since it is equal to 3. Thanks!

Hello, I've got some questions for the hardcore analytical mathematicians and electronic engineers. The context: A gain relation in a circuit of RCL and dependent sources ends up in an H(s) which is a quotient of polynomials in s. Number of poles is the number of energy storing...

hi are all answer are correct ? help please http://img73.imageshack.us/img73/2421/10267725rs8.png

Homework Statement Evaluate the telescoping sum. a) Sigma i=1 to n [i^4 - (i - 1)^4] Homework Equations sigma i=1 to n [f(1) - f(i+1)] The Attempt at a Solution so i plug in for the eqns. and get 1^4 - n^4 the correct answer should be n^4 but don't know how to get that.

Homework Statement If \sum_{n=1}^{4}log_{2}x^{n}=80, determine the value of x.Homework Equations S_{n} = \frac{a(r^{n}-1)}{r-1} S_{n} = \frac{rt_{n}-a}{r-1}The Attempt at a Solution log_{2}1+log_{2}x^{2}+log_{2}x^{6}+log_{2}x^{12}=80? log_{2}x^{20} = 80 2^{80}=x^{20} x=16 Is this right...

Homework Statement I am trying to write a paper describing my undergraduate research and its progress to a committee. I am having trouble making my sigmas boldface using LaTeX. I am using the correct coding, because it is working when I wish to type other vectors, but the sigmas look the...

I just got invited to Sigma Pi Sigma and I'm wondering if it's worth paying the fees to join. It does not seem to be very selective (it says GPA > 3.0), so I'm not really sure if it means much being in it. The way I see it, I am paying $45 for something to fill one of the "Honors and...

Hi everyone, When people present their data in plots, they always talk about 1-sigma errors, which I totally don't understand. Don't we use the standard deviation to tell us how far the a data point is from the "mean"? Why would I care about the mean when discussing errors? Shouldn't one care...

Homework Statement x^2 = sigma. The permutation sigma = (1 2 6 7 5 3 4), a cycle of length seven. Determine x! The Attempt at a Solution I have tried a few times but my attempts are totally wrong. I don't know where to start! :S I found a similar problem in the textbook. They...

Homework Statement The question is to draw possible Feynman diagrams of the following decay. Sigma(plus) ----> proton + photon Homework Equations Quark content of sigma(plus) is uus Quark content of proton is uud The Attempt at a Solution I know that the decay has to proceed by...

Homework Statement Prove the magnitude R of the position vector \vec{R} for the center of mass from an arbitrary point of origin is given by the equation M^{2}R^{2} = M\sum{m_{i}r^{2}_{i} - \frac{1}{2}\sum{m_{i}m_{j}r_{ij}^{2} Homework Equations \vec{R} = \frac{1}{M}...

I am struggleing in an identity, i.e. \nabla_m R_{ikjl}(\overline{\epsilon}\psi^m)(\overline{\psi^i}\psi^j)(\overline{\psi^k}\psi^l)=0 , where i,j,k,l,m are dummy indices, \nabla_m is covariant derivative, R_{ikjl} is Riemann-Christoffel curvature tensor, and it is known that, for any two...

Perturbative Super-Yang-Mills from the Topological AdS_5xS^5 Sigma Model A proof of the AdS/CFT correspondence Is this serious ?

Homework Statement Show: \sum_{i=1}^n (x_i - \overline{x}) = 0 Homework Equations Sigma notation The Attempt at a Solution \sum_{i=1}^n x_i - \sum_{i=1}^n \overline{x} = \sum_{i=1}^n x_i - \frac{1}{n}\sum_{i=1}^n \sum_{i=1}^n x_i = 0 \sum_{i=1}^n x_i = \frac{1}{n}\sum_{i=1}^n...

A parody of Crank that Soulja boy... about math =). There was very little choreographing done, so bear with it. I hope you like it. The lyrics are in the "about this video".

[SOLVED] Sigma Notation Question/Trig Identity I posted this elsewhere but I think I put it in the wrong place so I'm going to post my question again here. Basically I have to deduce the second formula from the first. Both equations are the same except for the top of the right side...

I have no idea how to use the forum equation code so I just attached the question as a word document. I have no idea how to start this one. Any help is appreciated. Edit: Ok I just took a screenshot and uploaded it as an image.

[SOLVED] Electric Potential Homework Statement 20. [1pt] A 30.6- cm-diameter conducting sphere is charged to 538 V relative to V = 0 at r =infinity. What is the surface charge density sigma? Correct, computer gets: 3.11E-08 C/m^2 = Sigma, r=.153 21. [1pt] At what distance will the potential...

[SOLVED] Sigma notation of a series. I have the formula 1+2+3+...+n = (n^2+n+1)/2, and I thinkthat this is the formula for the sum of a series. I need to write this thing in sigma notation, and then prove it by induction. I'm usually good and proving things by induction, but I can't...

If N is of null Lebesgue measure. Can we find a Borel set B of null measure such that N is entirely contained in B?

[a]1. Homework Statement [/b] Evaluate: 12 \sum (6n + 1) n=5 2. The attempt at the solution So, how do i go about doing this? I tried finding the first three numbers of the series to find the difference by substituting n = 5,6,7 and then use the Sum formula S = n/2[2a +...

sigma Fx= Sigma F-x is an equilibrium, how do i distinguish when i have an equilibrium?

Homework Statement Sigma = { ~S V R, R -> P, S } Give a deduction with the last component P. The Attempt at a Solution I came up with what I think is an answer, but I was a little unsure on what can go in a deduction so I would really like someone to re-check and tell me if I'm right...