What is Bound: Definition and 501 Discussions

Outward Bound (OB) is an international network of outdoor education organizations that was founded in the United Kingdom by Lawrence Holt and Kurt Hahn in 1941. Today there are organizations, called schools, in over 35 countries which are attended by more than 150,000 people each year. Outward Bound International is a non-profit membership and licensing organisation for the international network of Outward Bound schools. The Outward Bound Trust is an educational charity established in 1946 to operate the schools in the United Kingdom. Separate organizations operate the schools in each of the other countries in which Outward Bound operates.Outward Bound helped to shape the U.S. Peace Corps and numerous other outdoor adventure programs. Its aim is to foster the personal growth and social skills of participants by using challenging expeditions in the outdoors.

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  1. S

    How Does Subset Relation Affect Least Upper Bounds in Partial Orders?

    Homework Statement Suppose that R is a partial order on A, B1 ⊆ A, B2 ⊆ A, x1 is the least upper bound of B1, and x2 is the least upper bound of B2. Prove that if B1 ⊆ B2, then (x1,x2) ∈ R.Homework Equations The Attempt at a Solution This problem has been stumping me. After assuming B1 ⊆ B2...
  2. S

    Least upper bound proof (again)

    Homework Statement Okay, this is essentially the same question I had in an earlier thread, but i am trying to make my questions and uncertainties more clear for more accurate assistance: Suppose R is a partial order on A and B ⊆ A. Let U be the set of all upper bounds for B. a) Prove...
  3. S

    Least upper bound/ greatest lower bound proof

    Homework Statement Suppose R is a partial order on A and B ⊆ A. Let U be the set of all upper bounds for B. a) Prove that every element of B is a lower bound for U. b) Prove that if x is the greatest lower bound of U, then x is the least upper bound of B. Homework Equations The...
  4. P

    Proving no upper bound in A, where A = {x in Q | x^2 < 2}

    Homework Statement Prove that there is no upper bound in A, where A = {x in Q | x2 < 2} The Attempt at a Solution My attempt has been to assume that there is an upper bound p in A and then I have been trying to find a way to show that there is a number that is larger than p but still in A...
  5. M

    Optimization Solver - BFGS method with bound constraints

    Hello, I am working on a research project that requires me to write a solver for solving a particular problem. I could really use some math advice if anyone is willing to assist. I need to minimize a non-linear objective functions of 5 variables. It is a pretty complex function. Each of the...
  6. E

    In one dimension there are no degenerate bound states?

    Hi. In the book I'm reading I've come to a question regarding degenerate states in one dimension. It says that in one dimension there are no degenerate bound states. But say I have a stationary state with some energy E, and assume that it is normalizable. You can easily show that the complex...
  7. S

    Can everybody suggest a better upper bound?

    Hi, I have sent this question a couple of days ago, but it seems that its latex form had problem. So, I decide to send it again. I will thank If somebody help me solving this problem. Consider a random variable k_1 with the given pmf as: Pr[k_1=l]=\sum_{l_1+2l_2=l}...
  8. S

    Finding an upper bound for a probability

    Hi, I will thank If somebody help me solving this problem. Consider a random variable k_1 with the given pmf as: Pr[k_1=l]=\sum_{l_1+2l_2=l} \frac{N!}{(N-l_1-l_2)!l_1!l_2!}p_1^{l_1} p_2^{l_2} (1-(p_1+p_2))^{N-l_1-l_2}where l_1,l_2 \in [0,1,...,l] . but we don't have p_1 and p_2 separately...
  9. 5

    Quantum Mechanics: Choose an acceptable bound state function

    1. Which of the following is an allowed wave function for a particle in a bound state? N is a constant and α, β>0. 1) Ψ=N e-α r 2) Ψ=N(1-e-α r) 3) Ψ=Ne-α x e-β(x2+y2+z2) 4) Ψ=Non-zero constant if r<R , Ψ=0 if r>R Only one is correct. 2. What are the criteria for...
  10. S

    Dictionary order and least upper bound property

    Homework Statement Does [0,1] \times [0,1] in the dictionary order have the least upper bound property?Homework Equations Dictionary Order. (on \mathbb{R}^2) Let x , y \in \mathbb{R}^2 such that x=(x_1 , x_2) and y = (y_1 , y_2). We say that x < y if x_1 < y_1, or if x_1 = y_1 and x_2 < y_2...
  11. S

    An upper bound for a conditional probability

    Hi everyone, The problem: Is this relation true? If so, how (or maybe where) it could be proved?P(A│B∪C)≤P(A│B)+P(A│C)-P(A|BC) and what about its possible generalization? thanks a lot in advance.
  12. U

    Volume bound by rho=2+2cos phi

    Homework Statement Find the volume bounded rho=5+2cosphi Homework Equations dV=rho squared drho d phi d theta The Attempt at a Solution I am guessing this is some cylindrical shape. Theta should be 0-2pi and phi=0 pi/2
  13. U

    CLYINDRICAL coordinates of volume bound by z=r and z^2+y^2+x^2=4

    Homework Statement Find the smaller volume bound by cone z=r and sphere z^2+y^2+x^2=4 using cylindrcal coordinates Homework Equations dV=r-dr d-theta dz The Attempt at a Solution Limits on r: z to sqrt (4-z^2) limits on theta: 2pi to 0 limits on z: 2-0 Did this and got 8...
  14. U

    Spherical coordinates: volume bound by z=r andz^2+y^2+x^2=4

    Homework Statement Using spherical coordinares, find the smaller volume bounded by the cone z=r and the sphere z^2+y^2+x^2=4 Homework Equations x^2+y^2+z^2=4 ; rho=2, z=rhocosphi The Attempt at a Solution Shot in the dark: Tried function integrating (rho squared - rhocosphi)...
  15. G

    Transition from bound states to continuous states

    Transition from bound states to "continuous" states If I have the Hamiltonian for the Hydrogen atom and a perturbation given by a classical electric field (the kind of problems you get in an ordinary course about QM, no QFT involved), can I have a transition from a bound state (I intend a...
  16. N

    Distinction free and bound current (or charge) [very confused]

    Hello, I'm reading Griffiths' Introduction to Electrodynamics and I got quite confused in 9.4.1 page 392 (but the question is general, for anyone who does not have that book): It's about EM-waves in conductors. I will quote a paragraph: What is the definition of bound (or free)...
  17. A

    Using Lagrange Error Bound

    Homework Statement Im supposed to use the lagrange error bound to find a bound for the error when approximating ln(1.5) with a third degree taylor polynomial about x=0, where f(x)=ln(1+x) Homework Equations Lagrange error bound m/(n+1)! abs(x-a)^n+1, m=f(n+1)(c) The...
  18. M

    Traffic Flow - Junction, Delay, Webster, Greatest Upper Bound

    [PLAIN]http://img96.imageshack.us/img96/7816/12530747.jpg Hopefully this will post successfully... Erm its the first part I'm not sure on, after that it's easy. I'm just not understanding the wording. I need to work out the effective green time during the cycle
  19. K

    Rotate the area bound by the following lines around the x-axis.

    Homework Statement Rotate the area bound by the following lines around the x-axis. y = x^2+1, y = -x^2+2x+5, x = 0, x = 3 Homework Equations None that are uniform enough to put here considering I'm fairly sure it's not washer... The Attempt at a Solution
  20. I

    Greatest lower bound of Vector Space

    Homework Statement Prove: The set S(V) of all subspaces of a vector space V is a complete lattice under set inclusion, with smallest element {0}, largest element V, meet glb(S_{i} | i \in K) = \cap_{i \in K} S_{i} and join lub(S_{i} | i \in K) = \sum_{i \in K} S_{i} (Btw, how can I write...
  21. F

    Bounding the Error in Taylor Series Approximations for ln(1+x)

    Had a recent homework questions: Find a bound for the error |f(x)-P3(x)| in using P3(x) to approximated f(x) on the interval [-1/2,1/2] where f(x)=ln(1+x) abd P3(x) refers to the third-order Taylor polynomial. I found the Taylor series of f(x) seen below: x- x^2/2!+(2x^3)/3! I know...
  22. A. Neumaier

    Effective theory of bound states from QCD?

    Effective theory of bound states from QCD?? Do you know any work that actually succeeds in producing the action of an effective field theory for nucleons and mesons, starting from the QCD action?
  23. A

    Can you integrate with respect to y to find the area bound between two curves?

    Find the area bound between y2 = x + 5, and y2= 3 - x.I can't figure out how to put limits of integration, the integrand, or really anything besides just the integral sign to work with Latex, so bear with me (or better yet, direct me to a tutorial! I will search for one after this post, if there...
  24. C

    Is light bound to travel at C?

    So I'm kind of new to the whole physics thing so be nice please :P If i guess "nature" keeps objects from being able to go the speed of light then does "nature" keep light from going slower/faster than that speed? I first thought of this when i read a thread asking if gravity actually...
  25. H

    Can a Bound be Found for the Error in Higher Order Taylor Series?

    Hello, I am trying to come up with an expression for a bound on the sum of higher order terms, above second order. Consider the following Taylor expansion of a function f(x) around a point a, f(x) = f(a) + \frac{f^{(1)}(a)}{1!}(x-a) + \frac{f^{(2)}(a)}{2!}(x-a)^2+...
  26. D

    Magnetization in Classical EM: Bound Electric vs. Magnetic Charges

    I have been trying to remember if in classical EM it is equivalent to describe magnetization through bound electric currents A. \vec{j_b} = \nabla \times \vec M \vec{k_b} = \vec M \times \vec{\hat{n}} OR bound magnetic charges B. \rho_b = -\nabla \cdot \vec M \sigma_b = \vec M \cdot...
  27. N

    Upper bound turning into supremum

    i proved that sin (1/x)<1/x prove that sup{xsin (1/x)|x>0}=1 if we say that A={xsin (1/x)|x>0} xsin (1/x)<x(1/x)=1 so one is upper bound now i need to prove that there is no smaller upper bound so that 1 is the supremum suppose that "t" is our smaller upper bound t<1 and...
  28. A

    Simplifying a geometric series with an infinity summation bound

    Homework Statement I am solving some convolutions, and i have come to these solutions. a)\sum2k, summing from -\infty to -1 b)\sum2k, summing from -\infty to n , where n <=-1Homework Equations the geometric series summation formula, from 0 to N \sumak = 1-aN+1 / 1-a , summing from 0 to N The...
  29. D

    What does it mean to have an integral with a lower bound of infinity?

    I am working on a proof in which I have an integral with bounds negative infinity to zero, with an even function, i.e., f(y) = f(-y). I took the limit to infinity rather than negative infinity since y is negative (which is OK I think) but now I have an integral that goes from infinity to 0. What...
  30. M

    Least upper bound property of an ordered field

    I am trying to understand the following theorem: An ordered field has the least upper bound property iff it has the greatest lower bound property. Before I try going through the proof, I have to understand the porblem. The problem is, I don't see why this would be true in the first...
  31. L

    You're welcome. I'm glad I could help.

    Homework Statement Find an upper bound M for f(x) = abs ( x+2 / x-8 ) if abs(x-7) < 1/2Homework Equations The Attempt at a Solution i first found set of x values using abs(x-7) < 1/2 which is 13/2 < x < 15/2. Now, i believe i have to find other set of x values to compare to find upper...
  32. J

    Electrons bound to the nucleus/ Bohr hypothosis

    Question: If we assume that an electron is bound to the nucleus (assume a H atom) in a circular orbit, then the Coulomb force is equal to the centripetal force: mv^2/r= ke^2/r^2 In the Bohr hypothesis, angular momentum, L = mvr is...
  33. A

    Lower bound for the norm of the resolvent

    Hi all! I hope this is the right section to post such a question... I'm studying the theory of resolvent from the QM books by A. Messiah and I read in a footnote (page 713) that the norm of the resolvent satisfies \|R_A(z)\| = \lVert \frac{1}{A-zI} \rVert \ge \text{dist}(z,\sigma(A))^{-1}...
  34. F

    Proof of the least upper bound

    Homework Statement LEt S is supset of real numbers and suppose that there is X0 is member of S such that x0>=x for all x which is member of S(i.e. x0 is the maximum of S). show that x0=supS Homework Equations The Attempt at a Solution Not: this seems too easy question but i...
  35. Simfish

    Upper bound to 2-norm of a matrix

    Homework Statement Using the fact that ||A||_2 = \sqrt { \rho ( A^* A )}, prove that ||A||_2 \leq \sqrt { ||A||_1 ||A||_\infty }. This is an easy estimate to find in practice for an upper bound on ||A||_2. Homework Equations The Attempt at a Solution Or, in other words, the...
  36. R

    Basic Analysis - Proof Bolzano Wierestrass by Least Upper Bound

    Homework Statement Let (an) be a boundedd sequence, and define the set S= {x\in R : x < a_n for infinitely many terms a_n\} Show that there exists a subsequence (a_n_k)converging to s = sup S Homework Equations This is supposed to be a direct proof of BW using the LUB property, so no...
  37. D

    Solving ODE with Neumann Boundary: Finite Differences Method

    I am new to differential equations, any help would be great. I have a ODE of the second order u''x = e^x over the domain [1, 1] where u'(0) = 0 is a Neumann boundary on the ODE. I am trying to approximate the solution using the finite differences method, I can do Dirichlet boundaries with...
  38. L

    Norganic cofactors such as metal ions permanently bound

    Homework Statement I have a small question, are inorganic cofactors such as metal ions permanently bound or temporarily bound to enzymes...? i can't find any info concerning this..and if anyone could tell me if i understand this concept properly: Cofactors are separated into either organic...
  39. J

    What is the influence of time dilation on bound electrons?

    An electron in an orbital of an atom has some energy and some momentum. In some ways it can be considered "orbiting" but it is not really moving in a classical sense. I've heard more than once the explanation that electrons in high orbits move close to the speed of light and that this...
  40. Q

    Exploring the Relationship Between Gravity and Bound States in Hydrogen Atom

    In hydrogen atom the electron and the proton come very close to each other statistically(their wavefunctions even merge), so why we do not see the effect of gravity which should be on the order of other forces at Planck distance. Otherwise, compton to compton wavelength distance is too high for QG.
  41. romsofia

    Quantum Mechanics- Albert Messiah (Two volumes bound as one)

    Any reviews of this book? Any would be helpful!
  42. ╔(σ_σ)╝

    Prove that the least upper bound of a set of a set of integers is

    Problem Statement: Prove that the least upper bound of a set of integers is an integer. Attempt: Using well ordered principle this is very trivial. However, is there another way? ANY comments or ideas relating to the topic would be highly appreciated. It is assumed that the set...
  43. Z

    Partial Order/Upper Bound Proof from How to Prove It

    Partial Order/Upper Bound Proof from "How to Prove It" Homework Statement Suppose R is a partial order on A and B is a subset of A. Let U be the set of all upper bounds for B. Prove that U is closed upward; that is, prove that if x E U and xRy then y E U. Homework Equations N/A The...
  44. A

    Is f(n) an Upper or Lower Bound of g(n)?

    Homework Statement 1. f(n) = n - 100 g(n) = n - 200 2. f(n) = log(2n) g(n) = log(3n) n >= 0 in all cases Find out if f(n) is an upperbound, lowerbound or both of g(n) Homework Equations The Attempt at a Solution in case of 1, f(n) has to be an upperbound of g(n) because...
  45. W

    Reason a Dineutron is not bound?

    Hello, I am learning very, very basic quantum from the internet, and I have a question about the reason why dineutrons cannot exist. I know that the standard answer is that they aren't bound, but I don't understand why they are not, whereas a proton-electron system is. Here is the context in...
  46. A

    Average electronic momentum in bound state: please see this

    Someone please tell me if I am thinking right: Let's consider an unperturbed electronic state of an atom/molecule. If we denote it by [a>, then the average electronic momentum in state [a> is, <p> = <a]p[a> = (<a]p<a])* (because p is hermitian) = (<a]*p*[a>*)...
  47. A

    How to prove that for any bound electronic state, < p > = 0

    Hey all. So, I understand that every bound electronic state will have zero average electronic momentum, because otherwise the electron will fly off the atom. But how do I show mathematically that < p > = 0 for any bound state. Any help or reference greatly appreciated. Thanks.
  48. maverick280857

    Delta well + infinite barrier -> bound state

    Hi, I'm trying to understand the quantum mechanical solution to this potential: V(x) = \left\{\begin{array}{cc}\infty & \mbox{ for } x < 0,\\-\lambda\delta(x-d) & \mbox { for } x > 0\end{array}\right. A particle of mass m is constrained to move on the half straight line \{x \in \mathbb{R}: x...
  49. K

    Correct Form of Likelihood Function for Data w/ Upper/Lower Bound

    So, I have this problem I am tackling where I am doing a Bayesian scan of a multi-dimensional model. Most of the quantities predicted by the model have likelihood functions which are normal distributions (as functions of the possible data values), however there are some pieces of experimental...
  50. A

    Sum or upped bound of geometrico-harmonic series

    Hi, I need help to determine the upper bound of this infinite series. \sum_{k=p+1}^{\infty} \frac{1}{k} a^k \ \ \ \ ; a \leq 1 The paper I am reading reports the upper bound to be, \sum_{k=p+1}^{\infty} \frac{1}{k} a^k \leq \frac{1}{p+1}\sum_{k=p+1}^{\infty} a^k = \frac{1}{p+1} \cdot...
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