What is Constraints: Definition and 216 Discussions

The theory of constraints (TOC) is a management paradigm that views any manageable system as being limited in achieving more of its goals by a very small number of constraints. There is always at least one constraint, and TOC uses a focusing process to identify the constraint and restructure the rest of the organization around it. TOC adopts the common idiom "a chain is no stronger than its weakest link". This means that processes, organizations, etc., are vulnerable because the weakest person or part can always damage or break them or at least adversely affect the outcome.

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  1. R

    I Numeric impact of constraints on sets (passwords)

    Hi folks, I've got everything I need to write a paper on the effect of constraints on passwords... except the math. I actually could write it, but the math would make it much meatier. Here is what I know about math. If the answer to a math problem is obvious, it is probably wrong. If the...
  2. W

    I What is the lower bound constraint for G in terms of anthropic principles?

    Martin Rees talks about the strength of G in his book Just Six Numbers and how it couldn't be much stronger than it is for life to evolve. However he seems to hint that it could be weaker without much problem. I am wondering if anyone knowns any papers on the lower bound constraint for G in...
  3. binbagsss

    A String theory - no-ghost state - virasoro constraints

    1. Homework Statement Question (with the following definitions here): - Consider ##L_0|x>=0## to show that ##m^2=\frac{1}{\alpha'}## - Consider ##L_1|x>=0 ## to conclude that ## 1+A-2B=0## - where ##d## is the dimension of the space ##d=\eta^{uv}\eta_{uv}## For the L1 operator I am able...
  4. binbagsss

    Strings, Virasoro Operators & constraints, mass of state

    Homework Statement Question: (With the following definitions here: - Consider ##L_0|x>=0## to show that ##m^2=\frac{1}{\alpha'}## - Consider ##L_1|x>=0 ## to conclude that ## 1+A-2B=0##- where ##d## is the dimension of the space ##d=\eta^{uv}\eta_{uv}## For the L1 operator I am able to get...
  5. S

    Ultraviolet Laser Beam Shaping With Constraints

    Homework Statement Homework Equations Lens equation 1/f = 1/d_o + 1/d_i Minimum Gaussian beam spot 2*w_0 = ((4 * lamda * F)/(pi * D)) Where: w_0 = beam waist (half beam diameter) lambda = wavelength F = focal length of lens D = diameter of incoming spot Don't forget to match units. Let...
  6. G

    I Constraints on potential for normalizable wavefunction

    We know that in one dimension if ##E>V(\infty)## or ##E>V(-\infty)## then the resulting wave function will not be normalizable. The basic argument is that if ##E>V(\infty)##, then a stationary solution to the Schrodinger equation will necessarily have a concavity with the same sign as the...
  7. M

    MHB Finding Extrema under Constraints

    Hey! :o I want to find the critical points of the function $f(x_1, x_2)=x_1x_2$ under the constraint $2x_1+x_2=b$. Using the method of Lagrange multipliers I got the following: \begin{equation*}L(x_1,x_2,\lambda )=x_1x_2-\lambda \cdot \left (2x_1+x_2-b\right )\end{equation*}...
  8. Kaura

    Unbounded Feasible Region for Lagrange with Two Constraints

    Homework Statement Homework Equations Partials for main equation equal the respective partials of the constraints with their multipliers The Attempt at a Solution Basically I am checking to see if this is correct I am pretty sure that 25/3 is the minimum but I am not sure how to find...
  9. Buzz Bloom

    I Constraints on Dark Matter in the Solar System

    I wonder if someone can tell me if I have interpreted the cited article correctly. https://arxiv.org/abs/1306.5534 The article seems to have calculated upper bounds on the density of DM for different parts of our solar system. We have found that ρdm is less than 1.1⋅10−20 g cm−3 at the orbital...
  10. TheDemx27

    I Using determinant to find constraints on equation

    Basically I don't know how to get to the constraints from the system of equations. In class we used det to find constraints for homogenous equations, but we didn't go over this situation. Someone spell it out for me?
  11. Elvis 123456789

    Lagrangian of falling disk connected to another disk

    Homework Statement String is wrapped around two identical disks of mass m and radius R. One disk is fixed to the ceiling but is free to rotate. The other is free to fall, unwinding the string as it falls. Find the acceleration of the falling disk by finding the lagrangian and lagrange's...
  12. Nipuna Weerasekara

    Can a triangle be formed with these length constraints?

    Homework Statement There is a triangle with sides $$ 3,3r,3r^2 $$ such that 'r' is a real number strictly greater than the Golden Ratio. Is this statement true or false...? Homework Equations $$Golden \space Ratio = \phi = 1.618... $$ The Attempt at a Solution Actually I have no clue at all...
  13. M

    A Tree-level unitarity constraints in Two-Higgs Doublet Model

    Hi, I'm looking at the unitarity constraints for the Two-Higgs Doublet Model and I'm trying to follow what they do in the attached article, which can also be found here: https://arxiv.org/pdf/hep-ph/0312374v1.pdf. However I do not know how to get the scattering matrices in eq. (7). They say...
  14. S

    Forces of Constraints: Solved Example in Gregory's Book

    hello :) my question is about a solved example in gregory's book first of all , assuming that that a cylinder with radius "a" is rolling without slipping towrad the y direction in an incline plane with angle θ with the horizon and the cylinder him self is rotating with angle Φ about him self...
  15. petrushkagoogol

    I Imposition of relativistic constraints on Bell's theorem

    Bell's theorem states that super-luminal communication exists between particles that are separated by space-like separation viz. faster than light transmission of information. There is spontaneity in this. Relativistically this would amount to going back in time. The state of creation of...
  16. L

    Mechanical question -- Mechanical arm with special constraints

    Here in this case an arm in special constrain. The arm is capable to rotate around the main center if force is applied to the center. The torque practically generated by the force that is pushing Tarm. Tamr rotates and pulls with more or less the same force at the top that horizontal force then...
  17. J

    B Exploring Space: Unveiling the Constraints on Moon Exploration

    Following scenario: 1) Send a few rockets with large payloads to the moon, carrying various parts of a nuclear reactor to be assembled on the moon 2) Use the nuclear reactor to extract oxygen from various materials found on the moon 3) Use the power of the reactor to harvest resources for...
  18. S

    I Calculus of Variations Dependent variables and constraints

    If we have a function: \begin{equation} f(x,x',y,y',t) \end{equation} and we are trying to minimise this subject to a constraint of \begin{equation} g(x,x',y,y',t) \end{equation} Would we simply have a set of two euler lagrange equations for each dependent variable, here we have x and y...
  19. H

    Prove forces of semiholonomic constraints do no virtual work

    I do not see how (2.34) shows that forces of semi-holonomic constraints do no work in the displacements ##\delta q_k## between the varied path and the actual path. Starting from (2.31), I seem to be able to prove that such forces do do work, in contrary to what is claimed in the paragraph...
  20. mr.tea

    Quadratic forms under constraints

    Homework Statement Find the minimum value of ## x_1^2+x_2^2+x_3^2## subject to the constraint: ## q(x_1,x_2,x_3)=7x_1^2+3x_2^2+7x_3^2+2x_1x_2+4x_2x_3=1 ## Homework EquationsThe Attempt at a Solution I am not really sure how to think about it. I have seen the opposite way but have not seen this...
  21. Ornella

    Converting kW/h to kWh for Optimizing Fuel Cell Ramp-Up

    Hi everyone, I am working on a mathematical optimization model for a fuel cell. Currently I am facing a problem with the ramp-up of the cell. I have a modulation ramp of 4% of the nominal power (58.3 kW) per minute. My constraint in the model has to be in kWh (I have to precise that my...
  22. D

    Goldstein Derivation 1.6: Nonholonomic Constraints in Particle Motion

    1. The problem statement A particle moves in the ##xy## plane under the constraint that its velocity vector is always directed towards a point on the ##x## axis whose abscissa is some given function of time ##f(t)##. Show that for ##f(t)## differentiable but otherwise arbitrary, the constraint...
  23. noowutah

    Specify function given certain constraints

    Let F:V\rightarrow{}\mathbb{R}^{+}_{0} be a differentiable function. V is the set of all positive real-valued 2\times{}2 matrices, so V=\left\{\left[ \begin{array}{cc} a & b \\ c & d \\ \end{array}\right]\mbox{ with }a,b,c,d\in\mathbb{R}^{+}\right\} Here are the two constraints for F...
  24. Chrono G. Xay

    Finding Optimal Axis of Rotation with Constraints

    I really don't have much experience with calculus ( :sarcasm: Hooray! ), but earlier I was reading an introductory article explaining the usefulness of the Lagrange multiplier in dimensional optimization, http://www.slimy.com/~steuard/teaching/tutorials/Lagrange.html and it reminded me that...
  25. Chronos

    Is the Universe Flatter Than We Thought?

    This paper;http://arxiv.org/abs/1508.02469 ,Geometrical Constraint on Curvature with BAO experiments, suggests an improvement of curvature constraints on the geometry of the universe. On a purely geometric basis the authors' measurements suggest σ(ΩK) \simeq0.006 The GR+Λ case yields a value...
  26. Garth

    Primordial gravitational wave constraints from Planck 2015

    In today's Physics ArXiv: New constraints on primordial gravitational waves from Planck 2015. Authors Luca Pagano, Laura Salvati, and Alessandro Melchiorri of the Physics Department and INFN, Universita di Roma. Primordial gravitational waves from the universe exiting Inflation get more and...
  27. Titan97

    Finding Normal Reaction between Wedge and Block

    Homework Statement A block of mass m is kept on a smooth wedge of angle α and mass M which is in turn kept on a smooth floor. When the system is released from rest, calculate the force exerted by block on the wedge. Homework Equations None. The Attempt at a Solution Let the block a have a...
  28. freutel

    What are kinetic and geometric constraints?

    Homework Statement The question is to specify all forces and constraints that are applied in a system of a two-seat merry go round model in terms of the generalised coordinates - and their type (e.g. geometric, kinetic). http://i.imgur.com/FQ7PJyg.png The system is modeled as central...
  29. Coffee_

    When do time dependent constraints mean energy conservation?

    Define energy as E=T+U. For anyone using different terminology, by rheonomic (time dependent constraints) I mean that if a system has N degrees of freedom, the position vectors of each particle of the system are given by ##\vec{r}_i(q_1,q_2,...,q_n,t)##. Where ##q_i## are generalized...
  30. L

    MHB Very dificult: The minimum perimeter and maximum height of a triangle under constraints

    Obtain -The maximum height corresponding to the side b of any triangle (abc) once known the value of its perimeter and height corresponding to the a side a. -The minimum perimeter of any triangle (abc) once known the heights corresponding to the a and b sides. Aux: Geogebra construction...
  31. milkman_78

    Size constraints of generators

    Based on what I have gathered so far, I don't see why a micro-scale generator wouldn't work, but then again I am a geographer with modest calculus skills. My biggest problem is not knowing how much I don't know, and I am hoping some kind and wise soul on PF can cure my ignorance. Let's say I...
  32. M

    Optimal Control of Linear-Affine System w/ Constraints

    Although this could fall under engineering, I thought the Diff Eq forum was the most relevant. Let me know if I should post elsewhere. I have a fairly basic system for which I'm trying to find a minimum-time optimal control policy. I know there are many ways to do this numerically, but since...
  33. O

    Are Constraints Necessary in Hamiltonian Dynamics?

    Hi there, I'm reading on the hamiltonian method and it says we can ignore constraints? Is this true, or am I missing something here, so if we have a constraint in the system we do not have to include it in the final calculation for the equation of motion? Hope someone could clear this up, thanks!
  34. M

    Are there closed curve solutions for these ODE constraints?

    Are there closed curve solutions for ##\mathbf{v}(t) \in \mathbb{R}^3## satisfying this constraint? $$\mathbf{v}(t) \cdot \frac{d^2}{dt^2}\mathbf{v} = 0 $$
  35. marcus

    Constraints on Inflation (Planck 2015 results XX)

    An interesting dimension of the Planck results that can use a thread on its own. http://www.cosmos.esa.int/documents/387566/522789/Planck_2015_Results_XX_Constraints_Inflation.pdf/ Planck 2015 results. XX. Constraints on inflation Preprint online version: February 7, 2015 ABSTRACT We present...
  36. anemone

    MHB Solving for $3x+y+2z$ Given Integer Constraints

    If $x,\,y,\,z \in Z$ and that $z\ge y \ge x$ and also, $x+y+z=-3$ $x^3+y^3+z^3-20(x+3)(y+3)(z+3)=2013$ evaluate the value for $3x+y+2z$.
  37. Feeble Wonk

    How Do Quantum Probability Waves Differ from Classical Waves?

    I need help conceptually visualizing the mechanics of an EM wave, and especially a DeBroglie type of quantum "wave". I realize that it's a probability wave, but I'm trying to extrapolate a classical image to the general idea. "Normal" force waves result from modulations and/or imbalances between...
  38. marellasunny

    Superposition of loadcases in FEA software (with SPC+inrel)

    I am curious as to how finite element analysis software(like Hypermesh) go about superposition of loadcases(applied on the same model). I constrain my vehicle body for 1.loadcase (say bending) with the standard SPC's and constrain my 2.loadcase(say torsion) with Inertia relief constraints...
  39. O

    Constraints for Linkage system

    Hi guys! I have a question on applying constraint on Linkage systems. Assumed that there is a two dimensional one-bar linkage, one end can only rotate and one end is free (Such as the figure above, please neglect the damper-spring system if you want). This link can rotate only 180 degrees, not...
  40. C

    Explain geometric constraints solver for CAD to a newbie

    I have seen the following said on a forum: This makes good sense to me. To me, as a programmer, this sounds like he is asking for a better API to look up the coordinate at runtime; perhaps that would force the engine to evaluate expressions in a particular order, but then that's what functional...
  41. Vigardo

    Boundary conditions for a grid tube under combined loading

    Dear experts, I´m trying to model in ANSYS Mechanical (v14.5) the linear buckling behavior of a cylinder made of BEAM4 elements under combined loading (axial compression and bending moment) applied at the ends. How should I set up the boundary conditions of a cylinder to keep rigid the ends...
  42. Albert1

    MHB Finding $a_{50}$ with Coprime Constraints

    given : $a_1<a_2<a_3<--------<a_{50}$ $a_1,a_2,a_3,------,a_{50}\in N$ all $a_1,a_2,------,a_{50}$ are coprime with 987 that is $(a_n,987)=1 $ here $1\leq n\leq 50$ please find $a_{50}$
  43. J

    Constraints of an L-shaped feasible region

    I am writing the constraints for the feasible region within the L-shaped feasible region. The diagram is at this http://www.mathworks.com/help/optim/ug/writing-constraints.html Are these equations the right constraints: –1 ≤ x ≤ 1 and 0 ≤ y ≤ 1 Thanks for the help.
  44. S

    Moving Constraints: Virtual Work in Classical Mechanics

    the virtual work done in the case of moving constraints is obviously not zero(argument as shown in classical mechanics by r douglas gregory page 345 under the heading of Lagrange's equations with moving constraints.i just wanted to understand how come the virtual work done the constraint forces...
  45. E

    Lagrange multipliers for multiple constraints of multiple coordinates

    Homework Statement Sorry for the long derivation below. I want to check if what I derived is correct, I can't find it anywhere else, feel free to skip to the end. Thanks! I am confused by how to write the EL equations if I have multiple constraints of multiple coordinates. For example, let's...
  46. twoski

    Regex for given languages with constraints

    Homework Statement Make a regex for the following languages on Σ = {a, b}: (a) {w | each 'a' in w is immediately preceded and followed by 'b'}. (b) {w | w has both 'ab' and 'ba' as sub-strings } (c) {w ∈ {a, b} |(na(w) − nb(w)) mod 3 =/= 0}. For c, the number of a's minus the number of b's...
  47. Chronos

    Constraints on gravity and dark energy

    This paper; http://arxiv.org/abs/1408.6248, Constraints on gravity and dark energy from the pairwise kinematic Sunyaev-Zeldovich effect, proposes an ingenious way to constrain gravity and dark energy models based on ksz effects. They have carefully assessed the potential for errors and biases in...
  48. phosgene

    Maximise the volume of a rectangular prism with 2 constraints

    Homework Statement Maximise the volume of a rectangular prism with the following constraints: the surface area must equal 2m^2 and the total edge length must be 12m. Homework Equations Using Lagrange multipliers, we construct the function we want to optimise with h(x,y,z, λ_{1}...
  49. ELB27

    Constraints the elements of the 3D-rotation matrix must satisfy

    Homework Statement Taken from "Introduction to Electrodynamics" by David J. Griffiths p.12 problem 1.8 (b): What constraints must the elements R_{ij} of the three-dimensional rotation matrix satisfy, in order to preserve the length of vector A (for all vectors A)? Homework Equations The...
  50. C

    Constraints on a fourth rank tensor

    Homework Statement Consider a theory which is translation and rotation invariant. This implies the stress energy tensor arising from the symmetry is conserved and may be made symmetric. Define the (Schwinger) function by ##S_{\mu \nu \rho \sigma}(x) = \langle T_{\mu \nu}(x)T_{\rho...
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