What is Weak: Definition and 503 Discussions

In mathematics, weak topology is an alternative term for certain initial topologies, often on topological vector spaces or spaces of linear operators, for instance on a Hilbert space. The term is most commonly used for the initial topology of a topological vector space (such as a normed vector space) with respect to its continuous dual. The remainder of this article will deal with this case, which is one of the concepts of functional analysis.
One may call subsets of a topological vector space weakly closed (respectively, weakly compact, etc.) if they are closed (respectively, compact, etc.) with respect to the weak topology. Likewise, functions are sometimes called weakly continuous (respectively, weakly differentiable, weakly analytic, etc.) if they are continuous (respectively, differentiable, analytic, etc.) with respect to the weak topology.

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  1. Math Amateur

    The Weak Nullstellensatz .... aspects of proof by Cox et al

    Homework Statement I am reading the undergraduate introduction to algebraic geometry entitled "Ideals, Varieties and Algorithms: An introduction to Computational Algebraic Geometry and Commutative Algebra (Third Edition) by David Cox, John Little and Donal O'Shea ... ... I am currently...
  2. Math Amateur

    MHB Understand Theorem 1: Weak Nullstellensatz Proof by Cox et al - Exercise 3(a)

    I am reading the undergraduate introduction to algebraic geometry entitled "Ideals, Varieties and Algorithms: An introduction to Computational Algebraic Geometry and Commutative Algebra (Third Edition) by David Cox, John Little and Donal O'Shea ... ... I am currently focused on Chapter 4...
  3. Samia qureshi

    B Understanding the Weakness of Gravity and its Role in the Universe

    If gravity is a weak force , then How it holds planets , stars and galaxies together ? let me know if i am right..? Gravity only attracts there is no negative version of the force to push things apart and while gravity is powerful enough to hold galaxies together, it is so weak that you...
  4. P

    Weak Decay of Nucleus: 3-Momentum Analysis

    Homework Statement An example of a weak decay of a nucleus is (Z, A) → (Z +1, A) + τ- + ντ-bar where (Z,A) represents a nucleus with Z protons and A−Z neutrons. (d) Suppose the gauge boson in the above process is produced at rest. Assuming the neutrino is massless, what must the 3-momenta of...
  5. tzukishiro

    I Why is the weak force 10^-7 times the electromagnetic force?

    In the case of two protons in the nucleus. I've seen charts with that info, but I don't know how... How can I calculate that ratio? I've looked everywhere, and I can't find anything... Thanks
  6. G

    Weak form of Navier-Stokes and heat transfer coupling(COMSOL)

    I am asked to simulate a 2-D coupled problem in COMSOL(Navier stokes with Heat transfer) of a simple room. I'm not sure if COMSOL already has preexisting physics for navier stokes and heat tranfer that I could use directly but I am provided with two differential equations and boundary...
  7. A

    What is a very weak shock wave? (Gas Dynamics)

    I stumbled upon this concept when studying gas dynamics. What I get from my readings it must occur when Mach number is really close to 1. But I didn't understand how the property relations across a shock wave is affected by it.
  8. UMath1

    Ka vs Kb Weak Acids: Acetic Acid Low Ka, Lower Kb?

    Since Acetic Acid is a weak acid, it has a low Ka which means that the forward reaction is not favored as much as the reverse reaction. However, the Kb is even lower than the Ka...how is this possible? Shouldn't the Kb be higher to indicate that the reverse reaction is favored?
  9. hideelo

    I Equivalent statements of the weak energy condition

    Im reading Carroll's Spacetime and Geometry section 4.2 where he claims the following as the weak energy condition: Given a energy momentum tensor T and a timelike vector t then Tμν tμ tν ≥ 0. He claims that for a perfect fluid this is equivalent to the statement that ρ ≥ 0 and (ρ+P) ≥ 0...
  10. S

    A Exploring Chiral Symmetry in Weak Interaction

    Dear all Do we have chiral symmetry for weak interaction? I know that weak interaction is chiral. thank you
  11. strangerep

    I Weak-* topology & Neighborhoods

    I'm trying to understand a paper which uses weak-* topology. (Unfortunately, the paper was given to me confidentially, so I can't provide a link.) My specific question concerns a use of weak-* topology, and interpretation/use of neighborhoods in that topology. First, I'll summarize the context...
  12. H

    Need help with generating a uniform weak magnetic field

    Hi, I'm developing a new bio reactor, which in this instance you can think of as just a perspex fish tank. But have come across an unusual requirement to apply a roughly 0.01T magnetic field across the volume of the tank with mainly water in it. No position in the tank can be less than 0.08T and...
  13. S

    Weak Ductile Materials: Easily Broken by Traction?

    I teach soil mechanics and I introduce to my students brittle and ductile materials. Failure of brittle materials is obvious for them but not for ductile materials. Do you know any ductile material that can be easily broken by traction? Unfortunately I do not have any tensile testing machine so...
  14. A

    Poisson, Einstein, Weak Energy Condition

    Hello In Newtonian theory Poisson's equation holds: ## \nabla ^{2} U = 4 \pi G \rho ##. So: given a density ##\rho ##, it is possible to find a potential U. On the other hand, I can choose a random function U and give it a gravitational significance if it gives, by Poisson's eq., a density...
  15. K

    Commutator of Charges of the charged Weak Currents

    Homework Statement I'm having a bit of trouble evaluating the following commutator $$ \left[T^{+},T^{-}\right] $$ where T^{+}=\int_{M}d^{3}x\:\bar{\nu}_{L}\gamma^{0}e_{L}=\int_{M}d^{3}x\:\nu_{L}^{\dagger}e_{L} and...
  16. Jimmy D

    Electro Weak Unification Theory

    Hello all, I'm curious about Electro Weak relationship. I differentiate between mechanism and mathematics, with the equilibrium falling heavily to the left. Good with the former, weaker with the latter. Anybody aware of relevant philosophy/findings? Thanks much. Jim
  17. yango_17

    Monoprotic weak acid in water

    Homework Statement If enough of a monoprotic acid is dissolved in water to produce a 0.0153 M solution with a pH of 6.31, what is the equilibrium constant, Ka, for the reaction? Homework EquationsThe Attempt at a Solution I have attempted to solve this problem using ICE tables, but keep getting...
  18. Ryan Reed

    Why does the Weak Force only interact with certain handedness?

    Why does the weak force only interact with left-handed particles or right-handed antiparticles? And does this mean that the particles that don't have those properties won't decay?
  19. Einstein's Cat

    Particles with neutral charges but not affected by the weak or strong force

    Are there any particles which have a neutral electrical charge and are not affected by the weak or strong nuclear force? Thank you for your time and please excuse me if I'm being very ignorant!
  20. J

    What Causes Beta Decay and the Role of the Weak Nuclear Force?

    I am familiar with the proton:neutron ratio and stability but what about this instability actually causes a quark to emit a boson and change flavour? And what does this have to do with the weak nuclear force? Thanks
  21. F

    Is Gravity Really the Weakest Force in the Universe?

    All physicists I've heard discussing gravity to the public always mentions that it's a very weak force compared to the other forces and that no one knows why. One possible reason could be that the gravitational force is propagating in other dimensions. As far as I know gravity works in a...
  22. Titan97

    Why equilibrium favours weak acid or weak base

    Homework Statement Which side does the equilibrium favour? Homework Equations Equilibrium favours weak acid or weak base (I don't know why :frown:) The Attempt at a Solution Using the given pka values, since the reactant is the weaker acid, reactants are favoured. (Backward reaction is...
  23. M

    Why Radioactivity is caused by weak nuclear force?

    There is confusion in my mind regarding Weak forces
  24. N

    Running Coupling for Weak Interaction

    How can I derive the running coupling for the weak interaction. I have found derivations for QED and QCD that involve the β function http://www.physics.umd.edu/courses/Phys741/xji/chapter1.pdf but I can't find anything specific for the WI. Thanks.
  25. N

    B Weak measurement in double slit experiment gives which path

    In 2012, experimenters showed that when two entangled photons separate and when one goes through the double slit, we can tell which slit it went through and see that they still created an interference pattern because the photon that it was entangled to tells us which slit it went through. What...
  26. T

    Gauge bosons and the weak mixing angle

    <<Mentor note: Moved from other thread.>> I have 4 questions: 1. Why Weinberg angle affects neutral boson mixing, while W+ and W- are unaffected? 2. Is there any relation between Weinberg angle and CP violation angle? Are they absolutely independent? 3. How our world would be different if...
  27. T

    Why is Gravity Weak? Understanding the Fundamental Forces and Magnetism

    Why am I able to repel two liked poles magnet despite the presence of Earth gravity? The Earth gravity is able to hold skyscrapers together but yet unable to prevent two magnets from repelling? I know there is an explanation that says that unlike graviton, all the other fundamental forces are...
  28. Jamie Harper

    Why do we believe gravity to be a weak force....?

    So - this may sound like an easily answered question - but with push-back on my part I hope I can get to the real crux of what I'm asking, in any replies you might be kind enough to provide. I hope the answer is not, eventually, simple. The crux of my issue is this: Why do we believe gravity...
  29. olgerm

    Potential energy in strong- and weak- nuclear interaction

    Schrödinger equation for N-particles is: U_{System Potential Energy}(r_1,r_2,r_3,...,r_n,t)-\sum_{n=1}^{n_{max}}(\sum_{d=0}^{d_{max}}(\frac{d^2Ψ(r_1,r_2,r_3,...,r_n,t)}{dx_n^2})*\frac{ħ^2}{m_n})=i*ħ \frac{dΨ(r_1,r_2,r_3,...,r_n,t)}{dt} Where \sum_{d=0}^{d_{max}} is summation over dimensions...
  30. Andre' Quanta

    Hamiltonian Weak Gravitational Field - Learn Free Particle Theory

    In weak field regime i know that it is possible to quantize the gravitational field obtaining a quantum theory of free particles, called gravitons, which is very similar to the one for the electtromagnetic field. Do you know some book in wiich i can study this theory? In anycase what is the...
  31. Anchovy

    Weak interaction SU(2) gauge fields W^{1,2,3} and charge?

    When we start by postulating local SU(2) gauge invariance for our weak isospin doublets \begin{align} \psi &= \begin{pmatrix} \nu_{e} \\ e^{-} \end{pmatrix}_{L} \end{align} etc., we have to introduce massless gauge fields to preserve the Lagrangian's invariance. For SU(2) this demands 3...
  32. Sagar Singh

    Strong nuclear force and weak nuclear force

    Hi There! i am little bit confused in between existence of strong and weak nuclear force, can someone please explain about these forces and about their existence
  33. Yohanes Nuwara

    What is the entropy of weak and strong force?

    What is the entropy of weak and strong force? Can we determine their entropy? If so, I would like to know the formula of determining this. Thanks:wink:
  34. AnkurGarg

    What does molarity mean in case of weak electrolytes?

    I am really confused about it.Suppose we add 5 moles of acetic acid in 1 litre of water..The molarity of solution will be -(5 moles)/volume of solution?Or it will be -(the number of moles of acetic acid dissociated/dissolved)/volume of solution
  35. AlanKirby

    Why can only the weak interaction change quark flavour?

    Hi there, so my question is as follows. I understand that only the weak interaction can change the flavour of a quark, but why? Idea 1: It's due to the change in flavour also meaning a change in mass, thus a massive exchange particle is needed (gravity is negligible so forget the massive...
  36. S

    Solution of salt of a weak base and salt of a weak acid

    I am trying to get a better understaning of the pH of a solution containing a salt of a weak base and a salt of a weak acid. I know it depends on which equlibrium constant is greater but I am thinking more of what it is that actually happens. For example let say we have a solution containing...
  37. I

    QCD & Weak Theory: Furry's Theorem & Beyond

    Hello, everyone! I have a short question. I think everybody knows the Furry theorem for QED, which tells, in particular, that fermion loops with odd number of fermions always give 0. Does the same true for QCD of weak theory? Can one have non-zero contribution to 3-gluon vertex (or 3-boson...
  38. agent009

    Weak Isospin, Chirality and Helicity

    Could someone please help me to understand the difference between the concepts of Weak Isospin, Chirality and Helicity. In particular, I have the following questions to which I was unable to find answers so far: 1. Since both spin direction and momentum are vectors, would not their apparent...
  39. Saffat Rafsan

    Uncovering the Truth About Gravity: Exploring the Role of Atomic Space

    Today i was just randomly browsing the internet. Then i found this image: What if gravity is not the weakest fundamental force at all? Like the picture above if we remove the space among all atoms the Earth will occupy relatively a very small space. Then we know the gravity of that tiny...
  40. haael

    V - A weak interaction theory?

    Does anyone know any good introduction to V-A weak interaction theory?
  41. binbagsss

    Deriving Schwarz Metric Weak Limit: Carroll's Lecture Notes 1997

    I'm looking at Carroll's lecture notes 1997, intro to GR. Equation 7.27 which is that he's argued the S metric up to the form ##ds^{2}=-(1+\frac{\mu}{r})dt^{2}+(1+\frac{\mu}{r})^{-1}dr^{2}+r^{2}d\Omega^{2}## And argues that we expect to recover the weak limit as ##r \to \infty##. So he then...
  42. U

    Weak Gravity & Newtonian Limit: Letting g^kmu = eta^kmu

    Assume we have a free-falling particle in gravity in a static metric. Its worldline is described by: g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu} where ##|h_{\mu \nu} << 1|##. Taken from Hobson's book: Why did they let ##g^{k\mu} = \eta^{k\mu}##?
  43. binbagsss

    Comparing Weak Field Approx, Sign Question, & Derivatives

    Comparing two sources one has ##\frac{d^{2}x^{i}}{dt^{2}}=-\frac{1}{2}\epsilon\bigtriangledown_{i}h_{00} ## and the other has ##\frac{d^{2}d^{i}}{dt^{2}}=\frac{1}{2}\epsilon\bigtriangledown^{i}h^{00}##, And the one using the lower index has the Newton-Poisson equation as ##...
  44. binbagsss

    Weak Field Approximation - Quick Sign Question

    http://www.mth.uct.ac.za/omei/gr/chap7/node3.html Shouldn't eq 45 have a minus sign, looking at eq 29. Although I'm confused because the positive sign makes sense when comparing with the Newton-Poisson equation. I can't see a sign error in eq 29. (I believe the metric signature here is...
  45. N

    Weak Field Approximation and Tidal Forces

    The weak field approximation in the Newtonian limit shows that the coordinate acceleration along a geodesic is related to the gravitational force. The geodesic deviation equation relates the coordinate acceleration between adjacent geodesics to tidal forces. If I drop 2 balls together from the...
  46. EddieP

    Repelling a very weak permanent magnet with an electromagnet

    I have a question about magnetic repulsion. Suppose I have a permanent magnet (axially magnetized) placed on top of the iron core of an electromagnet. I want to switch on the elctromagnet to repel the permanent magnet. (Please assume the permanent magnet is contained in some kind of tube that...
  47. binbagsss

    Raising Indices with Minkowski Metric: Solving Weak Field Approx

    I have the expression ##g_{ab}=\eta_{ab}+\epsilon h_{ab}##, The indices on ##h^{ab}## are raised with ##\eta^{ab}## to give ##g^{ab}=\eta^{ab}-\epsilon h^{ab}## I am not seeing where the minus sign comes from. So I know ##\eta^{ab}\eta_{bc}=\delta^{a}_{c}## and...
  48. binbagsss

    Weak decay, decay rate, colour-supressed and colour-allowed

    My textbook says: One of the decays occurs via a ## b \to c ## quark transition and is 'colour-allowed'.(Left of diagram). The other decay has a of ## b \to c ## and is 'colour-suppressed'.(Right of diagram) I'm unsure of what is meant by these terms, it doesn't really explain. I've...
  49. Euler2718

    Identifying a Weak Acid: Solving for pH in a 0.50 mol/L Solution - Homework Help

    Homework Statement What is the likely identity of a weak acid if a 0.50 mol/L solution of the acid has a pH of 3.18? Homework Equations HA + H2O <=> H3O + A K_{a} = \frac{[P]}{[R]} [H3O] = 10^{-pH} The Attempt at a Solution [/B] I set up an ICE table with the concentration given...
  50. A

    What were the clues that the weak and EM force are the same

    Hello, I've been reading a book on particle physics for the general audience, and as you might expect, I was left with a slew of nagging unanswered questions. There was a chapter on gauge symmetry where the author described that the weak and the EM forces are the same force at some energy...
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