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. E

    Ranking Lewis Acids: Weak to Strong - Resources & Tables

    Hello, Just wondering if anyone could post some resources on lewis acids: ie weak to strong lewis acid ranking or maybe some table or chart of lewis acids and their reactivity I haven't been able to find any resources thus far regarding lewis acids and their reactivity rankings... ...
  2. radou

    What is the Definition of a Weak Direct Product in Group Theory?

    Well, I have trouble understanding the definition of the weak product of a family of groups, which states that it is the set of all f \in \prod_{i \in I} G_{i} such that f(i) = e_{i} \in G_{i}, for all but a finite number of i from I (Gi is a family of groups indexed by the set I). The bolded...
  3. O

    RICE Tables for Weak Acid/Base Reactions: When to Neglect X?

    when you're doing RICE tables for weak acid/base reactions, when do you neglect x? thanks for ANY input :biggrin:
  4. T

    Question about the weak field approximation

    How come in the weak field approximation, where the metric is equal to, ds^2=-(1+2phi)dt^2 + dr^2(1-2phi). where of course dr is the three distance. why is phi multiplied by 2? I have two more stupid question regarding a different approach. please just explain it to me as i want to to see...
  5. H

    Calculating Kb: Ph 0.3mol/l Weak Base, 10.66

    The Ph of 0.3mol/l of a weak base is 10.66, calculate kb. I was thinking of using ph and calculate the concentration of H ions and then calculate poh and OH, but don't know what to do next. Any ideas?
  6. S

    Cubic equation for weak acid hydronium

    If one would make no assumtions to try to simplify, except for just assuming OH- were negligible in a solution of weak diprotic acid, H2A, we can create four equations to represent concentrations for : H2A == H + HA- HA- == H + A- Each of those has a K value for equilibrium constant...
  7. S

    Weak Interaction: e+e- to Mu+Mu- | Probability & Exceptions

    e^+ e^- \rightarrow \mu^+ \mu^- The reaction above can take place in two different ways: 1) The electromagnetic interaction by exchanging a \gamma 2) The weak interaction by exchanging a Z^0 Can somebody explain which way is more probable and why. I'm not sure but I guess that the...
  8. E

    Why Use a Weak Base to Neutralize a Strong Acid?

    Question: TRIS is a weak base. Compute pH of a solution containing .050 moles of TRIS and .020 moles of HCl in a total volume of 2L. pKb for TRIS is 5.92. Use RNH2 to represent TRIS. Equation: pH = pKa+ log ([conjugate base]/[acid]) Work: change equation for pOH: pH = 14-pOH pOH =...
  9. R

    Titrating weak acid buffer with strong acid after the base is used up

    Homework Statement I'm making a table on excel with the calculated pH of the solution vs the actual measured pH from the lab. My problem is finding the pH of a acetic acid-acetate buffer that has been titrated with HCl, once the moles of HCl are greater than the initial quantity of mols of...
  10. L

    Titriation Calculation for Weak Acid, Strong Base

    Homework Statement Sketch curve of pH vs volume of base added for the titration of 50.0ml of 1.00M acetic acid with 1.00M sodium hydroxide. Homework Equations none, i think. The Attempt at a Solution Okay, first off, this is a weak acid, the first point on the curve would be the initial...
  11. O

    Weak interaction cross-section

    Homework Statement Cross-sections for weak interactions at an energy E increase with E as E^2. Show that the rate of weak interactions in the early universe depends on the temperature T as \sigma_{wk} \propto T^52. The attempt at a solution The only formula I can find is \sigma_{wk} = g_{wk}^2...
  12. S

    Weak interaction - half-lifetime of a decay

    Hello! I need help with an exercise about the weak interaction: How do the mass, the q-value and the vertices depend on the half-lifetime of a decay? The myon decay has a half-lifetime of 0.0000015 seconds, the neutron decay has a half-lifetime of 607 seconds. Why is there such a big...
  13. H

    Understanding 'var' Type in C#: Strong or Weak Type?

    As far as I understand type systems in strongly typed system such as the one found in Java you must specify the exact type of the variable. Like e.g. int x = 5; // strongly typed also this would fail Object x = 5; Object y = "Not soo strong are we?"; Object z = x + y; // would throw a...
  14. O

    What can weak lensing be used for?

    Gravitational lensing (GL), first mooted in 1924, is now a technique being used by astronomers to detect dark matter. Lensing depends on the bending of light by the gravity of a mass concentration, such as a galaxy or galaxy cluster. In glass, it is the spatial gradient of the optical path...
  15. I

    Question: photon analogs for strong and weak forces

    I was wondering if someone could answer these questions? It is obvious that the forces due to electromagnetics are due to the transfer of photons. What particles are responsible for the strong and weak forces in the nuclei? Are they massless like photons (which would imply that they travel...
  16. B

    Dissolving Weak Acids: What to Expect with 0.5g Sodium Acetate in Water

    "If 0.5g of sodium acetate is dissolved in water, what would you expect to find in the resulting solution"? Is it acetic acid, acetate, or hydroxide? I don't know how to set this one up
  17. P

    Continuous spectrum and weak solution of eigenvalue equation

    Hi All! Preliminaries: Let H denote the Hilbert-space, and let A be a densely defined closed operator on it, with domain $D(A) \subset H$. On D(A) one defines a finer topology than that of H such way that f_n->f in the topology on D(A) iff both f_n->f and Af_n->Af in the H-topology. Let...
  18. A

    Are All Solid Ionic Compounds Truly Strong Electrolytes?

    I am slightly confused about the following statement from my chemistry book: "Note that essentially all solid ionic compounds are strong electrolytes in solution, because, no matter to what extent they dissolve, they give only ions" (https://www.amazon.com/dp/0030312914/?tag=pfamazon01-20)...
  19. M

    Higher-order weak interaction decays

    Considering the decay of certain exotic mesons, such as the following: B^{+} --> D^{0} \pi^{+} Apparently the decay proceeds via a weak interaction where multiple W boson exchanges occur. I was trying to nut out how this actually occurs, and draw up a sensible Feynman diagram...
  20. S

    Explaining Resistance in pH of Buffer: Strong vs Weak Acids

    could the equation - pH=pKa+log([A]/[HA]) - be applied for the case of strong acid? Although the percentage of dissociation of strong acid/base is very high, there still exists a equilibrium, right? secondly, if i tried to explain the resistance in pH of buffer *in terms of* the above...
  21. D

    Solar wind + Weak magnetic field = No water?

    Is it possible that one day, the Earth magnetic field get so weaken that solar wind could strip off water from earth? I ask this because of this article which leads me to draw the parallel. http://www.geotimes.org/sept04/NN_solarstorms.html
  22. L

    Weak and strong equivalence principles

    Hello, I would like to see more clearly the differences between the various forms of the equivalence principle. When reading about it on http://en.wikipedia.org/wiki/Equivalence_principle" I have the strange feeling that the difference is too small and too easily accepted to justify the...
  23. D

    Is the Conjugate Base of a Weak Acid Always a Weak Base?

    If the conjugate base of a weak acid ends up being determined as a weak base by dividing the acid dissociation constant by the ion product of water, how can this be? My book had an example, but goes on to generalize that if a salt's anion is the conjugate base of a weak acid, then the salt...
  24. T

    What is the significance of the weak field approximation in general relativity?

    Looks like I really don't have a feel for it. So I was working on this the other day. (arranged in order) http://img218.imageshack.us/img218/9613/1gx9.jpg http://img68.imageshack.us/img68/4677/2te4.jpg http://img68.imageshack.us/img68/7853/3jg9.jpg...
  25. Q_Goest

    Weak and Strong Emergence, what is it?

    The idea of weak and strong emergence seems to be one that is easily confused. I've seen numerous mentions of "emergence" in the literature without classifying which they are talking about. Many times it seems the author wants to imply strong but is really only looking at a weakly emergent...
  26. A

    Continuity in weak field approx.

    Given c=1, weak field approx for g: g(/mu,mu)=eta(/mu,mu)-2phi Derive eqn contiuity: d(rho)/dt+u(j)rho,j=-rho u(j/),j (all der. partial) Given T(mu,nu/)=(rho+p)u(mu/)cross u(nu/)+pg(mu,nu/) using divergenceT =0 i.e.T(mu,nu/;nu)=0: Step in the proof is Gamma(0/mu,j)u(mu)=-phi,j I get...
  27. T

    Exploring the Weakness of Gravity: Unifying the Four Fundamental Forces

    If all four fundamental forces were once unified and equal, why is gravity so much weaker than the other three forces?
  28. P

    Weak field general relativity

    I was asked to do a problem about the gauge freedom one has in the weak field limit in general relativity. I am given a coordinate transformation x^{\mu '} = x^{\mu} - \zeta^{\mu}. Now I have to show how the perturbation of the metric transforms under this coordinate transformation. The result...
  29. wolram

    Exploring the Weak Coupling Between Matter & Space Time

    I have read that, on the scale of clusters (million light years) the effect of the expansion of the universe is 10 million times smaller than the gravity binding the cluster. So space time, (flows) through the cluster (like a super fluid) or akin to a group of logs staying in a fixed...
  30. A

    About weak potential (solid state)

    In solid state physics, a proof of bearing energy gaps in one-dimesional dispersion relations is given by a quantum-mechanical perturbative approach applied to the level belonging to two bands at once, that is twice degenerate. For example for k=pi/a there's one of these levels between n=0 band...
  31. X

    Is Luzin Hypothesis Consistent with Set Theory?

    Regarding the weak continuum hypothesis (B.F. Jones): {\displaystyle 2^ {\aleph_{0}} < 2^ {\aleph_{1}}} and the Luzin Hypothesis: {\displaystyle 2^ {\aleph_{0}} = 2^ {\aleph_{1}}} Where can I find Bukovsky's paper that shows the Luzin Hypothesis is consistent with set theory? Or perhaps...
  32. T

    If you have a weak stomach don't click here

    I had dinner at the Mexican restaurant again. Got it to go. I got a burrito and a pop. After I had eaten and drank my pop I took the lid off the pop and was chewing on some ice. that's when I noticed something at the bottom of the cup. I reached in and pulled it out. I placed the object on my...
  33. homology

    Understanding Weak Convergence in Little l1 and Little l∞ Spaces

    hello folks, I've got a question about weak convergence. I'm sure I'm missing something but can't see what it is (<--standard "I'm dumb apology") The problem concerns little l 1 and little l infinity (which is dual to little l 1) To make notation easier I'm going to denote these...
  34. R

    Question on Weak Energy Condition

    Hi, I have just read that one of the restrictions on T^{\mu\nu} is that: T^{\mu\nu}u^au^b > 0 where u is a timelike vector. Can someone please tell me WHAT u actually is (other than saying it is a timelike vector). What sort of vector is it, what is the context? i.e Once...
  35. W

    Weak and strong anthropic principle

    Can somebody post the diferences. To me they seem to be the same
  36. P

    Identifying Weak Acids: HCNO, HBr, HF, HNO2, and HCN

    i had this question on atest recently, it said to identify whish of these is not a weak acid: HCNO : HBr : HF : HNO2 : HCN. Now the problem i am having with his, is in my book it gives that theyre common acids...ig deal, not if theyre strong or weak, and on the internet as far as i have found...
  37. H

    Understanding the Weak Nuclear Force: Effects on Quarks & Leptons

    Whenever i research the weak nuclear force i always get how it is the cause of beta decay and other ways it effects an atom, but i can never get a clear answer to what the force actually is, what does it do? i know that it effects quarks and leptons but i have no idea how it effects them, can...
  38. D

    PH of weak acid/weak base salts

    I'm trying to show my students that CaCO_3 is basic. Ca^2^+ comes from Ca(OH)_2, which is a weak base due to it's low solubility. CO_3^2^- comes from the weak acid HCO_3^-. To compare the two we compare: 1) Ca^2^+ + H_2O --> Ca(OH)_2 + H_3O^+ and 2) CO_3^2^- + H_2O --> HCO_3^- +...
  39. A

    Solve Ka for Weak Acid HCN - 0.18mol KCN in 1.00L, pH 9.70, 298K

    hi forum, would nebody be able to help me solve this problem? 0.18mol of potassium cyanide (KCN) was dissolved in 1.00L of a solution in which the pH was held constant at 9.70 at a temperature of 298K. the equilibrium concentration of CN- was 0.13M. Calculate Ka for the weak acid HCN...
  40. Clausius2

    What causes the condensation trails behind airplanes?

    Everybody has seen the weak of condensed water which is left behind an aircraft when it flies in air. To say the truth I am not an specialist in Aeronautical stuff, so I am searching a brave who tells me from where this weak comes from: -does it come from the products of combustion (H2O...
  41. JamesU

    What are the strongest and weakest substances in my house?

    Strongest substances in my house 1) Xacto knife-I fell back in my chair. before I fell all the way, I wedged the Xacto knife in my hand under the desk. It bent, but pulled me back up. :biggrin: 2) The Jelly jar lid- Can't Get It open! :mad: 3)My cat- after multiple times of throwing...
  42. S

    Weak Nuclear Force: Get Basic Explanation & Characteristics

    I'm looking for some sort of basic explanation on the characteristics of the weak nuclear force. All of the physics books I've checked up in have only minimal references to the weak force, and the only information I've been able to get on it is a) that it plays some role in radioactivity, and b)...
  43. S

    Question about weak convergence in Hilbert space

    The Question is as follows: let A be a bounded domain in R^n and Xm a series of real functions in L^2 (A). if Xm converge weakly to X in L^2(A) and (Xm)^2 converge weakly to Y in L^2(A) then Y=X^2. i don't know if the above theorem is true and could sure use any help i can get. if...
  44. tandoorichicken

    Weak Monoprotic Acid Ratio: 1?

    for a weak monoprotic acid is the ratio \frac{[A^-]}{[HA]} always equal to 1? edit: never mind. answered my own dumb question. :bugeye:
  45. A

    What is the Best Method for Titration of a Weak Acid with a Strong Base?

    Hiya, Im trying to determine the initial molarity of an unknown acid, sooo I am trying to titrate it with standardized sodium hydroxide solution (0.1M). But I am having a load of problems figuring out what the heck I am supposed to do since i am told the acid is a weak acid. If I am...
  46. J

    Nuetralization Reaction involving a weak acid and weak base

    CH3OOH (aq) + NH3 (aq) ‹———› NH4+ (aq) + CH3COO- (aq) Would the above reaction, involving acetic acid and ammonia qualify as a proper neurtalization reaction involving a weak acid and weak base? Or, would a reaction involving acetic acid and sodium bicarbonate be better? Regards
  47. R

    Pion decay via the weak interaction

    Hi, i have a particle physics exam in 2 days and am confused on pion decay via the weak interaction, namely: pi[-] ->muon + anti-muno neutrino Thankyou Ray Veldkamp
  48. M

    The weak interaction and fusion?

    I've heard that the weak interaction actually governs fusion between hydrogen especially in the sun, how does this actually works?
  49. turin

    What determines the behavior of weak interactions in fundamental particles?

    Can the cross-section of the weak interaction be extended? Are there things that can be done to fundamental particles in order to either increase their likely-hood or range of interacting weakly with a neutrino? What causes a fundamental particle to emit a weak boson anyway?
  50. N

    Isn't this a weak basis for time paradoxes ?

    Your wide spaceship has inside a light and a receiver, widely separated, sideways to direction of travel. As pilot, you notice the blinking light always takes the same time to hit the receiver, whether you are approaching speed of light or not. But an outside observer notices that the path the...
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