Sigma Definition and 229 Threads

I am think what is the structure of generated ##\sigma##-algebra. Let me make it specific. How to represent ##\sigma(\mathscr{A})##, where ##\mathscr{A}## is an algebra. Can I use the elements of ##\mathscr{A}## to represent the element in ##\sigma(\mathscr{A})##?

I'm working on a project where I have about 120,000 sources and my supervisor has told me to work out what significance to use for taking results. I had set it at 3 sigma. But there's roughly 1 in 500 chance that we will get a 3 sigma result by chance. I've been looking for a table to compare...

Homework Statement I've been given the series 3,4,6,10,18... and asked to express as the ∑ar, between r=0 and r = infinity. Homework EquationsThe Attempt at a Solution Well, I can see a pattern! The difference between terms doubles every time. I'm having difficulty expressing this...

1. Are uncountable unions of sigma algebras on a set X still a sigma algebra on X? 2. Are uncountable intersections of sigma algebras on a set X still a sigma algebra on X? (I think this statement is required to show the existence of sigma algebra generated by a set) 3. If 2 is true, can we...

I'm doing a little project which came to a stop. I calculated expected material stress to be ~10 MPa. (bending) I know that my material (AlMgSi0,5) should carry well that stress, however I'm interested in max allowable stress for this material...

I would like to know in the following equation (attached) how can I incorporate BER for BPSK? is BER the same as Rc? The equation is relation between SNR and sigma square.

Homework Statement Hello, I found this problem in the book I borrowed from the library, but this book does not have solutions in the back...I tried to lent the solution book but the library does not have it...so could someone help me out? The question is: It is possible to decompose the...

For the non-linear sigma action, S_G=\frac{1}{4\pi\alpha^\prime}\int d^2\sigma\sqrt{-\gamma(\sigma)}\gamma^{\mu\nu}(\sigma)G_{ij}(X)\partial_\mu(\sigma) X^i\partial_\nu X^j(\sigma), Let us consider an infinitesimal target space transformation X^\mu\to X^{\prime\mu}(X)=X+\epsilon\xi^\mu(X). The...

I have an experiment in which I want to extract the distribution function of a process. I expect it to be Gaussian. Each data point measured is an entire distribution, f(x), but I am forced to average over many points such that the result of the experiment is the sum of many measurements of...

Hey, I've begun going through a book called "An introduction to geophysical exploration" by Phillip Kearey and Michael Brooks and I've come across a problem I can't for the life of me see how they got their answer. Essentially, given an input function gi (i = 1,2... m), and a convolution...

Hi every one, I am examining a prototype device that is designed to analyse current from an electrochemical O2 sensor (current source), The sensor will output 1.124 uV per PPM (cross 47 ohms @0.023 uA), and has acuracy of +- 2 PPM, with max 1000 PPM. it ueses 16 bit Sigma Delta ADC with...

Homework Statement how many is total number of C-C sigma bond in phenylethene? Homework Equations The Attempt at a Solution i have drawn the the strucutre as in the photo. i ended up getting 8 C-C sigma bond. but the ans from my book is 12. How to get 12?

hi! i have a doubt, how can i know the total number of bonding and antibonding electrons given a diatomic molecule's electronic configuration in therms of sigma and pi orbitals? I have to add these σ and π orbitals are of the type gerade and ungerade. does anyone can help me?

According to the Molecular orbital theory, diatomic oxygen should have σ2px (internuclear axis) and \pi2py and \pi2pz orbitals filled with two unpaired electrons, one at antibonding \pi2py and the other at antibonding \pi2pz. And of course, the 2s bonding and antibonding orbitals as well...

What value of sigma guarantees the integral converges? \[ \int_0^{\infty}e^{-5t}e^{-(\sigma + i\omega)t}dt = \frac{1}{5 + \sigma + i\omega} \] I don't see a problem as long as \(\omega\neq 0\) and \(\sigma\neq -5\), but by the way the question is worded, it sounds like it is after something else...

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 $z$ is...

Homework Statement Find a set X such that \mathcal{A}_1 \text{ and } \mathcal{A}_2 are \sigma-algebras where both \mathcal{A}_1 \text{ and } \mathcal{A}_2 consists of subsets of X. We want to show that there exists such a collection such that \mathcal{A}_1 \cup \mathcal{A}_2 is not a...

I currently work in semiconductors (research) and I am interested in earning my Lean Six Sigma certification, possibly through a university online class. Has anyone gone through the process? If so, what is the level of difficulty to obtain a green belt? I have a solid background in statistics...

Homework Statement My apologies in advance for the messiness of the equations; the computers available to us do not correctly process the LaTex code. I am tasked with estimating the area under the curve f(x)=x2+1 on the interval [0,2] using 16 partitions. Online calculators and my...

Homework Statement Given 3 measure spaces (X,A,\mu), (Y,B,\zeta), (Z,C,\gamma), show that the product of the three sigma algebras A, B, and C is associative, meaning that: AxBxC=(AxB)xC=Ax(BxC) Homework Equations We can make use of the fact that XxYxZ=(XxY)xZ=Xx(YxZ) The Attempt at a...

Prove that a set $A\subset\mathbb{R}^n$ is (Lebesgue) measurable $\iff$ there exist a set $B$ which is an $F_{\sigma}$ and a set $C$ which is a $G_{\delta}$ such that $B\subset A\subset C$ and $C$~$B$ (C without B) is a null set. $F_{\sigma}$ is a countable union of closed sets, and...

Respected Members, Suppose Ω is the set of eight possible outcomes of three coin tosses i.e. Ω={{HHH, HHT, HTH, HTTT, THH, THT, TTH, TTT} So if we are not told the results then the sigma algebra ( denoted by F_α) at position α=0 is F_0 = {∅, Ω} Now if are told the first coin toss only...

How would you Integrate a Sigma Sum?

Dear friends, Over the past week, I tried to plot implicit function by mathematica but failed. I am very disappointed. Hopefully someone help me at this time. My equation is given by (see below figure): Where z0 := 6 d := 12 k := 11800 w0 := 0.025 w[z_] := sqrt[w0^2*(1 + (z/z0)^2)]...

Homework Statement Notice that ln [∏(k=1)^n a^k] = Ʃ_(k=1)^n * ln (a_k) I couldn't get the LaTeX right on this ^ But k=1 is below the product sign, and n is above. And (a^k) is the formula. From this, as well as some calculus, calculate that: lim as n->∞ ∏_(k=1)^n e^\frac{k^2}{n^3} For...

Homework Statement a_{1}r^{1} + a_{1}r^{2} + a_{1}r^{3} +... + a_{1}r^{n-3} + a_{1}r^{n-2} + a_{1}r^{n-1} = \sum_{n=1}^{?} a_{1}r^{n-1} What value would replace the "?" 2. The attempt at a solution EDIT: I edited this post after receiving your reply Cepheid. My gut would say...

Here are the questions: Here is a link to the questions: How do you write the summation notation for: 4 - 24 + 144 - 864 + ... ? - Yahoo! Answers I have posted a link there so the OP can find my response.

I'm putting together a lab report and my result is off from the known value by 1.43 σ. According to the error function tables provided by my prof, and using the error function in my error analysis textbook, that gives me a probability of ~85%. I don't understand what this means though. Will...

Hello, I am looking at the sigma and pi bonds and trying to understand them. I know that the bond is the overlap of the orbitals, in the case of sigma bonds two s-orbitals and the pi bonds is the p-orbitals. When you have the sp hybrid orbitals, how are there only the same number of hybrid...

I model arterial baroreflex data that I have collected in humans using the Kent equation which is: y=p1/(1+exp((x-p3)*p2))+p4; where Y=heart rate, X= estimated carotid sinus pressure, p1=range of Y, p2=slope coeff, p3=centerpoint on X, p4 = minimum Y. I use Sigma Plot to do a best fit line...

Homework Statement if f is integrable, then the set N(f) = {x : f(x)≠ 0} is \sigma-finite Homework Equations i am stucked in this proof , somebody help me pleaseThe Attempt at a Solution if f is simple the it seems the set is finite since otherwise the the integral won't exist but how can it...

In addition to my Faddeev-Popov Trick thread, I'm still tying up a few other loose ends before going into Part III of Peskin and Schroeder. I was able to show that the other Lagrangians introduced thus far are indeed invariant under the transformations given. But, I am hung up on what I think...

P(x=mean) of normal PDF with low sigma -- not allowed? About the normal probability distribution: with formula P(X=x) = (1/(σ*sqrt(2π))*exp(-(x-μ)2/2σ2), what happens when you look at P(X=μ) if σ<(1/sqrt(2π))? You get P(X=μ)>1, an absurdity. What is going on? Second question is one about...

Homework Statement My Calc II final is tomorrow, and although we never learned it, it's on the review. So I have a few examples. Some I can figure out, some I cant. Examples: f(x)=sinh(x), f(x)=ln(x+1) with x0=0, f(x)=sin(x) with x0=0, f(x)=1/(x-1) with x0=4 The only one of those that I was...

How do I evaluate the sum of this sigma notation problem? 20 ∑ k k=10 Normally, I would think to use the theorem for the sum of the first n integers: n ∑ k = n(n+1)/2 k=1 I don't know how to do this, however, since the lower limit is k=10, not k=1. My professor wrote this note on the board...

This topic came up while studying measures on sub-intervals of [0,1]. The collection of all intervals in [0,1] is a semi-algebra, say J. Now from finite disjoint union of members of J let's say we form a set A. I was able to prove that A is an algebra, since for any C,D ε A, C\capD and C^{c}...

Homework Statement I have read the following text in a textbook(look the attaxhement) ,and i have a simple question .WHY every 2x2 hermitian matrix would have to satisfy this Equation.It is not obvious to me why.Does anyone know the answer? The textbook stops there without giving any...

Hi all, I have spent a good half hour searching for the meaning of this, but have only found results for upper-case sigma Ʃ and lower-case sigma σ. Can anyone tell me the meaning of the "word-final" version of sigma, which looks like ζ ? I am trying to evaluate 3ζ(4) but I just need a...

Homework Statement A sigma plus,\sum+ particle is a baryon a)How many quarks does sigma plus contain? b)If one of these particles is an s quark, by what interaction will it decay? c)Which baryon will it eventually decay into? b]solution attempt [/b] Baryons contain 3 quarks don't know...

Is anyone familiar enough with excel to use it to find the sum in of sigma notation when "n" is large? \Sigma^{40}_{k=1} \sqrt\frac{3k-3}{4} Something like this?

Hi, I've been wondering this since I started learning integration. I get that ∫ is basically an elongated S for "sum", because that is what it is basically doing. But then Ʃ does the same thing as well. If I'm understanding the difference, it is that Ʃ increments by finite measures, whereas ∫...

Hello, I have read several different sources on this very topic, and the one thing that confused a little was defining it using sigma notation. Could some please explain to be what it means?

Homework Statement Prove that: \sum_{n=1}^{14} 10n = \sum_{n=1}^{7} (20n+70) Homework Equations properties of sigma notation The Attempt at a Solution I know several properties of sigma notation but none that I know can be used to prove this. I don't know how to change 10 n to 20...

Homework Statement find total sigma and pi bonds in c6h6 Homework Equations Benzene structure The Attempt at a Solution if i consider benzene structure, then total will be 12σ and 3∏ but according to the random structure that i managed to draw, it showed, 11σ and 4∏, was i wrong...

Homework Statement Suppose \Omega = \mathbb{R}. Let A_n = [0,\frac{1}{n}]. Let \mathcal{A}=\{A_n:n\in\mathbb{N}\}. Is \{0\} an element of \mathcal{F}=\sigma(\mathcal{A})?Homework Equations The Attempt at a Solution Clearly \lim_{n\rightarrow\infty} A_n = \{0\}. Not sure how to show that it...

Hi guys, when I was trying to post something in the H/W forum and tried to use the Latex reference I could press the tab, but nothing happened. Is this a bug? Thanks!

Is there only 1 σ-algebra generated for a set? Consider M={1,2}. Ʃ(M)={∅,M} satisfies the definition of a σ-algebra. However, Ʃ(M)={∅,{1},{2},{1,2}} also satisfies the definition of a σ-algebra. However, the way that my text presents these problems (Prove that the σ-algebra generated...)...

Just to be clear, I understand the difference between sigma summation and integration. Sigma summation is, put simply, the discrete version of integration. Rather than a continuous sum of a function for given values, sigma summation provides a sum of a function for given regions that is...

I am trying to better my understanding of \sigma-algebras, and I have a bit of an issue with one of the examples. This is from Cohn Measure Theory, and before I give the problem, here are two definitions: Let X be an arbitrary set. A collection \delta\Large of subsets of X is an algebra on X...

Please correct me where I am wrong but it seems to me that you could generate a very high value of sigma (e.g. 6 sigma accuracy) from a very small sample size. How then is sigma on its own reliable? Let me see if I understand sigma. To determine the standard deviation I first compute the mean...