What is Apply: Definition and 508 Discussions

In mathematics and computer science, apply is a function that applies a function to arguments. It is central to programming languages derived from lambda calculus, such as LISP and Scheme, and also in functional languages. It has a role in the study of the denotational semantics of computer programs, because it is a continuous function on complete partial orders. Apply is also a continuous function in homotopy theory, and, indeed underpins the entire theory: it allows a homotopy deformation to be viewed as a continuous path in the space of functions. Likewise, valid mutations (refactorings) of computer programs can be seen as those that are "continuous" in the Scott topology.
The most general setting for apply is in category theory, where it is right adjoint to currying in closed monoidal categories. A special case of this are the Cartesian closed categories, whose internal language is simply typed lambda calculus.

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  1. Logan Rudd

    When can you apply Ehrenfest's theorem?

    I know when the initial state (##\Psi(x,0)##) is given, ##\frac{d<x>}{dt} \not=<p>##. I thought you can only apply Ehrenfest's theorem when ##\Psi## is a function of x and t, however it seems like you can also apply it to the time-independent part (##\psi(x)##) by itself as well. Can someone...
  2. petormojer

    Is there a way to apply mathematics to this?

    What I mean by this is the following: -know what the inside of a closed shape (defined by an equation) is -recognize objects in a picture (2d plane?) using parameters -know the relations of a certain variable in a group -a system in which the input changes the output but at the same time changes...
  3. T

    What statements can you apply to infinity

    For example; Please tell me which are false and true. If false explain why, don't just say because so and so said so, please EXPLAIN the concept otherwise I will never learn or explain the true answer! Can infinity odd or even? If not what state is it in? Or the fact that it is never...
  4. B

    Does Associative Property Apply to Subtraction and Division Too?

    I show that the assoc. property applies to addition and multiplication in my book: (a+b)+c = a+(b+c) (ab)c = a(bc) But what about subtraction and division?
  5. DivergentSpectrum

    How do I apply rk4 to a second order pde?

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  6. C

    Schools Which universities I should apply to without a Physics GRE?

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  7. H

    Schools Generally, when do you have to apply to University?

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  8. R

    Does the uncertainty principle apply at all to photons?

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  9. evinda

    MHB How to Use Euclidean Division in $\mathbb{Z}_7$?

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  10. A

    Boundary conditions don't apply in the equation's region of validity

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  11. M

    How to apply boundary condition in generalized eigenvalue problem?

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  12. D

    Schools Suggestions for grad schools to apply to

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  13. T

    What Direction is C? Apply the Right Hand Rule

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  14. M

    MHB Apply the divergence theorem to calculate the flux of the vector field

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  15. M

    Why can't we apply trig ratios to any angle of a right triangle?

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  16. M

    MHB Apply the divergence theorem for the vector field F

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  17. evinda

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  18. T

    Does Heisenberg apply to a collapsed wavefunction?

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  19. D

    Schools What Are Good Alternative Engineering Schools for a Transfer Student?

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  20. N

    Applying to SCIT: What You Need to Know

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  21. mrspeedybob

    How do intelectual property rights apply to scientific discoveries?

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  22. A

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  23. C

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  24. T

    Does gravity apply to ionised objects?

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  25. N

    Schools Should I apply for Purdue University?

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  26. A

    Got a call from a company I did not apply too

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  27. J

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  28. N

    Why can we apply the symmetries of S-Matrix to part of Feynman diagram

    How can we demonstrate that the symmetries of S-Matrix can be applyed to parts of Feynman diagrams?The S-Matrix is the sum of infinite diagrams,why we know each or part of each diagram has the same symmetries as the symmetries of S-Matrix?
  29. S

    Can undocumented students apply for private student loans?

    Can undocumented students get private student loans? I'm a senior and I want to apply to colleges but don't know what college is best for me. I'm applying to MIT, Boston University, MSOE, Worcester Polytechnic Institute. But can someone recommend me a few other no loan colleges that have strong...
  30. S

    How to apply Thevenin and Norton Model

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  31. J

    Can I apply L'Hopital's rule to this integral expression?

    Hi, Suppose I have \lim_{r\to 0} \left\{\int_0^{\pi} \frac{f(r,t)}{r^2}dt - \int_0^{\pi} \frac{g(r,t)}{r} dt\right\} and both integrals tend to infinity. So I combine them: \lim_{r\to 0} \int_0^{\pi} \frac{f(r,t)-r g(r,t)}{r^2} dt now at this point, the numerator in the...
  32. F

    Does E=mc^2 apply to the proton

    Most of the proton REST mass is energy anyway. So how does that work?
  33. S

    Schools MSEE Programs for Low GPA - Schools & Atlanta Area Options

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  34. B

    Schools Which German Universities Should I Apply to for a Master's in Applied Physics?

    Hi all, May be this topic has been discussed many times in forums. I am a design engineer(experience of 2+ years in control systems, embedded) from India wishing to pursue my masters in applied physics(optics or solid state physics or photonics). I took the ielts exam and got overall...
  35. P

    Admissions Cornell physics PhD admissions? Is it pointless for me to even apply?

    I graduated 4 years ago from a small university and received a dual BS in EE and physics. I went into a decently ranked EE PhD program but dropped out after a year. I attempted to go back a couple times but just didn't care too much for the courses and dropped my classes both times. I have...
  36. K

    How to apply force to individual rigid bodies based on impact?

    Hello, SCENARIO : I am a game developer and I am playing around with rigidbodies. I have a piece of wall which might get impact by an external force. The wall has in turn several other broken pieces (hidden for the moment) put up together to resemble this huge wall. Upon impact I switch...
  37. N

    Determine the total charge needed to apply to the electroscope.

    Homework Statement A large electroscope is made with "leaves" that are 78-cm-long wires with tiny 24-g spheres at the ends. When charged, nearly all the charge resides on the spheres. If the wires each make a 26^{\circ} angle with the vertical, what total charge Q must have been applied to...
  38. N

    Physics Can physicists apply their own research?

    If I was a physicist and did research on superconductors can I apply it and make a product or a prototype on my own?
  39. C

    How to apply ladder operators?

    The total energy of a particle in a harmonic oscillator is found to be 5/2 ~!. To change the energy, if i applied the lowering operator 4 times and then the raising operator 1 times successively. What will be the new total energy? i want the calculation please
  40. P

    Are Liberal Arts Colleges a Good Choice for Undergraduate Physics Programs?

    Hi, this fall I'll be a senior in high school and with the Common Application nearly out, I need to finish my final college list. The reason I'm posting on this forum is because my goal is to ultimately attend grad school for a PhD in physics. This is my current list that I've come up with after...
  41. V

    Is there an error in the Feynman rules for QFT in the Mandl & Shaw book?

    I have found an error in the QFT book by Mandl & Shaw, 2nd ed. In eqn (8.53), there is a minus sign in front of e^4. However, this cannot be justified on the basis of how the equation is derived. In the unnumbered eqn below eqn (8.52) there is a minus sign, and the trace in this eqn is to be...
  42. L

    Why does Ampere's law only apply to enclosed currents?

    In my textbook it tells us ∫B ds = I μ (line integral and I = current enclosed) It also states that the current not enclosed does not affect the magnetic field along the line. I don't see a reason for other currents outside the loop not to affect the magnetic field thanks for any help
  43. P

    When we apply AC to an inductor

    "when we apply AC to an inductor (pure inductance), the current will lag the applied voltage by 90 degrees. " how this happens? why current lags applied voltage by 90 degrees? :confused:
  44. M

    Schools Dual Major, Crappy Cum. GPA, can I apply to top schools

    Stats after the fall semester (the time I will be applying for graduate school for Physics) Best case scenario I will have a 3.4 cumulative GPA, 3.85 Physics GPA, and a 3.0 Math GPA Dual Mathematics and Physics major, took 5 years to complete. 1st - 3rd year grade were par or less...
  45. V

    Where can I apply as an international student?

    I want to apply for b.s. Physics as an international student to get quality education, can someone please name such universities all over the world(except MIT,caltech and others biggies) which can provide scholarships. I'm from india, 18yo
  46. A

    How do I Apply for Post Graduate Course in USA for Physics

    I am under graduate (Bachelor of Science) in Physics from Gujarat University. I have passed following papers during my study in 3 years. (I did not found 2 papers from Gujarat University website so I have given reference for rest of papers) Second Year Bsc Syllabus...
  47. K

    Why L' Hospital's rule cannot apply directly for sequence

    Homework Statement Well, this thread is purposely to clarify my question on the use of L'Hospital's rule for sequence. As I have read from the calculus book, the sequence can be defined such that f:N → ℝ with function f(n)= an where n inside natural numbers,N. So, we cannot apply L'...
  48. K

    Where can we apply the first law of thermodynamics?

    Hi people, I have a question. Where can we apply the first law of thermodynamics? I mean is it applicable between 2 equilibrium points? Or between a reversible process? When we consider free expansion of a gas into vacuum, we apply the first law. But since the process isn't reversible (or even...
  49. T

    How to Use Comparison Test for Convergence?

    Homework Statement Is the series convergent or divergent? \sum_{n=0}^{\infty}{\frac{1}{\sqrt{n+1}}} Homework Equations I can use any test but wolfram alpha says that it is divergent by comparison test. The Attempt at a Solution How do I apply comparison test? I can compare it to: \sum _{...
  50. A

    Looking to Apply to Medical Physics PhD Program

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