Partition Definition and 307 Threads

Homework Statement Suppose f is increasing and continuous on [a,b]. Show for any partition P, \int^b_a f(x)dx - L_f(P) \leq [f(b) - f(a)] \Delta xHomework Equations Not sure if there are any . but for people unfamiliar with this notation: L_f(P) = Lower sum for f with the partition P...

write a function called int partition(int arr[], int size) which input an array of integers and decides whether it is possible to divide the array into two groups so the sums of both the groups will be equal. for example arr = {1,2,2,3,5,6,1} its could be divided into {2,2,6} and...

Homework Statement a) Suppose particles can be absorbed onto a surface such that each absorption site can be occupied by up to 6 atoms each in single-particle quantum state \psi_{\it i} with an absorption energy \varepsilon_{i}. Write down the grand partition function for one site. b) If...

Homework Statement This is the integration i have to solve I=\int x^{2}In(1-exp(-ax))dx integration is from zero to infinity The Attempt at a Solution I know that it should be solved with integration by parts so u=In(1-exp(-ax)) du=[a exp(-ax)] / [1-exp(-ax)] dv=x^{2}dx...

Homework Statement a) Suppose particles can be adsorbed onto a surface such that each adsorption site can be occupied by up to 6 atoms each in single-particle quantum state \psi_i with an adsorption energy \epsilon_i. Write down the grand partition function for one site. b) If...

Homework Statement Hi all. The partition function for fermions is (according to Wikipedia: http://en.wikipedia.org/wiki/Partition_function_(statistical_mechanics)#Relation_to_thermodynamic_variables_2) given by: Z = \prod\limits_i {\left( {1 + \exp \left[ { - \beta \left( {\varepsilon _i -...

Hello! I've got a problem. If you scroll down to page 118 on the following link http://books.google.com/books?id=ntrPDA6zE1wC&dq=Quarks+bound+by+chiral+fields&pg=PP1&ots=_29vGOurGs&source=bn&sig=h4vGPNBbKX14DpoOyt4tuRZHkRc&hl=de&sa=X&oi=book_result&resnum=4&ct=result#PPA118,M1 there you...

I am aware that there are several generator functions for the Partition Function p(n), but does anyone know if a closed form formula exists for this function?

Homework Statement Prove that the nonempty fibers of a map form a partition of the domain. The Attempt at a Solution Ok so we have some map phi: S -->T And we want to show that its pre-image phi-1(t) = {s in S | phi(s)=t} forms a partition of the domain. Im really confused here. I assume...

Homework Statement For a magnetic particle with an angular momentum "quantum number", j, the allowed values of the z component of a particles magnetic moment are: µ = -jδ, (-j + 1)δ, ..., (j-1)δ, jδ δ is a constant, and j is a multiple of 1/2 Show that the partition function of a...

For the set A = {1,2,3,4,5,6,7}, determine whether script A is a partition of A. script A = {{1,3,},{5,6}, {2,4},{7}} Describe the partition for the equivalence relation T defined for x,y \in \mathbbc{R} by X T y iff \left[ \left[x \right] \right] = \left[ \left[y \right] \right] where...

The question: A system consists of N sites and N particles with magnetic moment m. each site can be in one of the three situations: 1. empty with energy zero. 2. occupied with one particle and zero energy (when there isn't magnetic field around). 3. occupied with two particles with anti...

Hi, I am trying to work through some of the problems in Reif, not for homework, but to prepare for a final. I was hoping someone could show me how to work through the first problem of chapter seven in Reif. 7.1 - Consider a homogeneous mixture of intert monatomic ideal gases at absolute...

given a partition function of the form Z[u]= \prod Z_{i} [u] Z_{i} [u] = \sum_{n=-\infty}^{\infty}e^{iuE_{n}^{i}} what is the meaning of zeros ? i mean the values that make Z[u]=0 and how could we calculate these zeros ??

Homework Statement Does anyone know the mathematical definition of the microcanonical partition function? I've seen \Omega = {E_0\over{N!h^{3n}}}\int d^{3N}q d^{3N}p \delta(H - E) where H=H(p,q) is the Hamiltonian. This looks like a useful definition. Only thing is I don't know what E_0...

Homework Statement If we have a system of N independent particles and the partition function for one particle is Z_1, then is the partition function for the N particle system Z=(Z_1)^N? Homework Equations The Attempt at a Solution I'm pretty sure that this is true for a classical...

Homework Statement Partition Function: Z = 1/N! [8 pi V (kT/hc)^3]^N There are several parts to this but here are the parts I'm struggling with: a) Compute the entropy of the system S. b) Computer the energy density u and compare the result with the corresponding results for a...

Homework Statement Find the partition function for a two-dimensional nonrelativistic classical gas. Find the equation of state. Calculate the specific heat at constant volume cv and the entropy S. Homework Equations The partition function is Z = (A^N / N!) [(2 pi m k T / h^2)^N]...

I have been messing up the partition function for thermo all semester, and now it's really starting to bite me with the carry-down error (i.e. mess up Z for (a) which in turn will mess up S in (b) and so on). I was looking at Reif Problem 9.1 and was wondering if someone could please explain...

Homework Statement Suppose that we partition R^3 into horizontal planes. What equivalence relation is associated with this partition? Suppose that we partition R^3 into concentric spheres, centered at (0,0,0). What equivalence relation is associated with this partition? Homework Equations...

Homework Statement a. Let A={1,2,...10}. Describe a partition of A that gives rise to five distinct paritioning sets. b.Describe a partition of Z that gives rise to five distinct partitioning sets c. Describe a partition of R that gives rise to five distint partitioning sets Homework...

Homework Statement Describe the partition associated with the following: On Z, we define x~y if and only if x-y is divisible by 3 Homework Equations The Attempt at a Solution Could someone please give me a hint? I don't understand what I'm supposed to do. Thank you

Homework Statement A certain magnetic system has N independent molecules per unit volume, each of which as 4 distinct energy levels: 0, \Delta - \mu_BB, \Delta, \Delta + \mu_BB. i) Write down the partition function, and hence find an expression for the Hemholtz function ii) Use this...

given a partition function Tr[e^{-BH}] or Z(B)= \int_{P}dx dp e^{-BH(p,q)} is there any meaning for its zeros ? , i mean what happens in case the partition function Z(B)=0 for some 'B' or temperature B=1/kT do these zeros have a meaning ?? thanks

In an Excel group someone connected with the Texas caucus gave this math problem> how to subdivide the following set of precincts into subsets so that there are a maximum number of subsets from this set with each subset of precincts totaling at least 180 votes. Since the caucus is this month it...

Homework Statement Use a graphing utility to approximate the partition numbers of the function f(x) to two decimal places. Then solve the following inequalities. (a) f(x)>0 (b) f(x)<0 Express all answers in interval notation Homework Equations The Attempt at a Solution...

Is it possible to obtain the relation S = \log Z + \langle U \rangle /T directly from the Boltzmann distribution? Edit: It seems that we can if we use the VN entropy: S = -\Sigma p_i \log p_i This suggests that the entropy of a single microstate should be s = -\log( \frac{e^{-\epsilon...

Partition function for a gas in a cylinder -- urgent! Hi, Here's the problem -- it's supposed to be a specimen of what I can expect in my exam, but it isn't much like the tutorial questions I've been doing. I'd really appreciate some help -- fast! Homework Statement An ideal gas consisting...

Is the energy given by the first or the second? I have seen both relationships in different websites, and I am confused. E = kT^2 \frac{\partial Z}{\partial T} or E = - \frac{\partial ln Z}{\partial \beta}

The partition function in the classical theory is an integral over phase space. Thus, the partition function is often not dimensionless. Then the formula F = -T \log Z can no longer be valid, as you can only take the logarithm of a dimensionless number. In the quantum theory, this...

What is the relation between the partition function and the Boltzman, Maxwell distribution? Differences and similarities? Both have exponentials to the power of the negative total energy of the microstate. Although the word microstate dosen't occur in the Boltzman, Maxwell case. Is the BM...

Homework Statement When modeling ideal gas molecules using a grand partition ensemble, is heat flow = 0? So if U=Q-W then in a grand canonical ensemble, U=-W?The Attempt at a Solution I think so as the system is in thermal equilibrium with the surroundings. So in this system the total energy is...

Is ther any form by bisection or simiar to obtain a partition for an infinite-dimensional interval (aka functional space)?? i believe you could obtain a partition for every interval 'centered' at a certain function as: X(t), X(t)+\delta (t-t`), X(t)+2\delta (t-t`), X(t)+\delta (t-t`), ...

So I've set up my computer to dual boot into WinXP or Fedora Core 6. As recommended by some walkthroughs I found, I've created a FAT32 partition for passing data back and forth between WinXP and linux. Alas, it only has 8 character filename support. I would like to have a partition for...

Let us consider a collection of non-interacting hydrogen atoms at a certain temperature T. The energy levels of the hydrogen atom and their degeneracy are: En = -R/n² gn = n² The partition function in statistical physics is given by: Z = Sum(gn Exp(-En/kT), n=1 to Inf) This...

If I have a 2 state system with energy levels of the 2 states to be 0 and V. I find the partition function to be Z = 1 + e^(-V/kT). Am I correct? If so, does that not mean the average energy is V? and thus the entropy is 0? This doesn't make sense, how is the entropy of a 2 state system (when 1...

Hi, I just made some changes to my partition table in linux using fdisk that are very bad. For the moment everything is fine but when I reboot those changes will take effect. Is there any way to restore my partition table from the good version that the kernel is still using? Thanks

I want to partition a number n into k parts for example 9 into 3 parts x+y+z=9 and each element must be non zero , first look tells me it's combination with repetition. however C(n-1,n-k) doesn't give the same number of possibilities when trying all of them. x+y+z=9 C(8,6)=28 while trying...

Let be the continuous partition function: Z(\beta)=(N!)^{-1}\int_{V}dx_1 dx_2 dx_3 dx_4 ...dx_N exp(-\beta H(x_1, x_2 , x_3 , ... ,x_n,p_1 , p_2 , ..., p_N if the Hamiltonian is 'quadratic' in p's are q's do this mean that the particles in the gas solid or whatever follow a Normal...

bah nevermind the question is too complicated to even write down :cry: i hate this :(

hay everyone can u help me. how u delete or format ntfs partition? i need to get it out or format it if u want to Email me it is codename951@yahoo.com thank bye :cry:

Let be the Hamiltonian Energy equation: H\Psi= E_{n} \Psi then let be the partition function: Z=\sum_{n} g(n)e^{-\beta E_{n}} where the "Beta" parameter is 1/KT k= Boltzmann constant..the question is..let,s suppose we know the "shape" of the function Z...could we then "estimate"...

how to reformat & partition the HDD ?? hi, My computer has become very slow & sluggish & fully crammed up! So i want to reformat my HDD & make new partitions for proper management of data. Please tell me how to do it through dos ( ie without using any additional softwares like partition...

This is a question about thermal physics. There's this partition function Z = sum over all states s of the system ( exp(-E_s/T)). And its just used to calculate the probability of any state by taking the Boltzman factor exp(-E_s/T) of that state and dividing over the partition function. Theres...

I got a problem by finding an proper explanation. The Boltzmann factor is defined as P_j=\frac{1}{Z}e^{-\beta E_j} I know, this is a probability distribution. but what exactly does it mean? Wikipedia says: "The probability Pj that the system occupies microstate j" (link) But that doesen...

Let X be a set. A partition of X is a subset \pi \subseteq P(X) so that for every x \in X there is precisely one A \in \pi so that x\in A. If R is an equivalence relation on X, then \pi_R = {R(x): x \in X} is a partition. If \pi is partition of X then R_\pi= \bigcup A x A is an...

I have 160 gb hdd and i partitioned it 32 gb(fat32) chunks using extended partitions. I am now using windows xp. Can windows 98 detect this hdd?

Folks, I'm running Windows XP, but now I need to format my hard drive. The only potential difficulty that I foresee is having to deal with the NTFS partition. I'd like to get rid of it, install Windows ME and then upgrade it back to XP. I've read that the only way to delete any NTFS...

Hi, i'm having trouble with a thermal physics problem relating to the partition function and i was wondering if anyone could help me out. the problem is as follows: (a) Consider a molecule which has energy levels En=c|n| , where n is a vector with integer components. Compute the partition...

I partitioned my hard drive into two sectors (I installed windows on one).. it turns out to be too small (sp2 makes a backup of the whole system :rolleyes:).. I'm at a loss how to redistribute the size though :rolleyes: Anyone a clue? I'm running Windows XP (I guess I need to go into BIOS at...