Apply Definition and 508 Threads

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. XLAYZ

    Do the Fresnel equations of reflection apply to monochromatic light?

    Hello, I have a monochromatic light source (wavelength ~ 420 nm), which will be incident on the interface of two different media. Could someone please explain if the Fresnel equations applies with monochromatic light when estimating the reflectance and transmitance? Thank you in advance...
  2. J

    I Does the postulate of equal a priori probability apply only to equilibrium?

    In deducing the zeroth law of thermodynamics in micro-canonical ensemble, there is a frequently-mentioned example. Suppose we put two isolated system, system 1 and 2, in contact and allowing them to exchange heat. The total energy of the combined system is $$E = {E_1} + {E_2}$$ The total...
  3. D

    B Heisenberg's uncertainty principle - does it always apply?

    I am not too knowledgeable about QM, so please forgive me if this is a dumb question. I have outlined below an experiment setup for which Heisenberg's uncertainty principle seems not to apply: Imagine a particle for which we wish to collect the exact position and velocity. We have a detector d1...
  4. astroman707

    Studying What's the best way to apply the concepts learned in physics 2?

    I'm finishing up physics 2(intro E&M) at my college, and I'd like to apply the concepts I learned in it over the summer. I was considering working through an electronics book, or building a radio, etc. What kind of projects or books do you recommend to cement some of the topics I learned in a...
  5. Safder Aree

    How to apply the Fourier transform to this problem?

    I am struggling to figure out how to approach this problem. I've only solved a homogenous heat equation $$u_t = u_{xx}$$ using a Fourier transform, where I can take the Fourier transform of both sides then solve the general solution in Fourier terms then inverse transform. However, since this...
  6. gibberingmouther

    Trouble Understanding How to Apply Kirchhoff's Laws

    I'm taking a break from music for a few days because I do that sometimes, and it's like a rule for me, and I usually listen to music when doing my physics homework. I'm realizing I have a little more trouble without that boost I get. But it could also be that what I'm trying to do is hard. I...
  7. Haorong Wu

    Other Is it difficult to apply for a PhD in physics without experience?

    Hi. I’m currently self-learning physics and hopefully will apply for a PhD in physics, but there are some problems troubling me. I received my BS. and MS. degrees in EE in China. I’ve been working for five years since then. From high school, my two major interests are physics and computer...
  8. Callista

    Why doesn't Newtons third law also apply to the frame?

    Homework Statement A locomotive has broken through the wall of a train station. During the collision, what can be said about the force exerted by the locomotive on the wall? a)The force exerted by the locomotive on the wall was less than the force exerted by the wall on the locomotive. b) The...
  9. S

    I How to apply the disk/washer and shell methods

    In Calculus II, we're learning about solids of revolutions and computing their volumes. I'm unsure when to apply the appropriate methods and how to make the correct partitions. Please tell me if my reasoning is correct: The disk/washer method is applied when your partitions are perpendicular...
  10. TachyonLord

    Programs Where Should I Apply for Physics Internships and Workshops?

    So I'm an undergrad student from India pursuing physics, I'm currently in my first year and I'm really confused as to what I should do. I mean, I like physics, especially the computational aspect of it, but I don't know if I'll continue physics after three years. Summer's going to start soon and...
  11. PhysicS FAN

    What's the least force we should apply?

    Homework Statement 2 objects of the same mass are on a non-frictional level and are connected with a thread which has a resistibility limit T=20N. What is the least froce we should apply so that the thread breaks? Homework EquationsThe Attempt at a Solution I don't know how to proceed with...
  12. S

    MHB Does PEMDAS Apply to All Math Equations?

    I was told PEMDAS isn't always followed, particularly in higher level math. Is this true? Because I recall the purpose of PEMDAS is to prevent ambiguity, and without it, at any level, would result in ambiguity, even though it's just a convention and not something we can really prove. Also...
  13. grandpa2390

    Job Skills Got my BS in Physics but I don't know what to apply for

    I'm not really sure what I am a qualified for, and when I look on job boards like zip recruiter, the only jobs i seem to find are truck driving and sales jobs. the sales jobs are mostly for places like retail and those guys who stand at walmart and push communication and television services on...
  14. Eclair_de_XII

    Math I need references to apply for a summer internship but....

    ...I feel very uncomfortable asking any of the teachers who have taught the classes I have taken so far. There was one teacher who I was considering asking to be one of my two references. I have already tried e-mailing him even though he has left the university, but he did not reply; whether it...
  15. navneet9431

    Is it possible to apply energy conservation here?

    Homework Statement Homework Equations Kinetic Energy =1/2*m*v^2 Spring Potential Energy = 1/2*k*x^2 Gravitational Potential Energy = m*g*h The Attempt at a Solution I am thinking to solve this problem using energy conservation but I feel that it is not possible to apply energy conservation...
  16. Krushnaraj Pandya

    Rules to apply L'Hospital on a limit

    Homework Statement ## \lim x-0 \frac {xcosx-log(1+x)}{x^2}## Homework Equations ##\frac{log(1+x)}{x}=1## ...(i) The Attempt at a Solution Using (i) we can write numerator as xcosx-x, cancelling x from denominator we have cosx-1/x, this is 0/0 form so we can use LHR which gives us -sinx/1 but...
  17. O

    What Torque Is Required to Raise a Water Bucket from a Well?

    Homework Statement Water is drawn from a well in a bucket tied to the end of a rope whose other end wraps around a cylinder of mass 50 kg and diameter 25 cm. As you turn this cylinder with a crank, the rope raises the bucket. If the mass of a bucket of water is 20 kg, what torque must you apply...
  18. M

    I How does the inverse square law apply to a focused detector?

    I am interested in evaluating light intensity variation in a digital image. A colleague wants to apply an inverse square law correction to account for distance variation. I am trying to justify that in this case, the inverse square law does not apply. Treating each pixel as a detector, it has...
  19. Machine1701

    I Why doesn't decoherence apply to unobserved experiments?

    This is based on the Hugh Everetts interpretation of quantum mechanics, where the waveform never collapses but the observer becomes a part of it, thus experiencing decoherence of the wave form from their point of view. So, let's say someone is doing the two-slit experiment. The particles going...
  20. K

    I What formulas would apply during a Big Crunch

    During a hypothesized big crunch, how quickly will a universe collapse? As the velocity approaches the speed of light, its mass will increase greatly. What equations will apply in such a collapse? Kurt Ludwig
  21. B

    How does Newton's 3rd law apply in this case?

    Homework Statement It is clear that SOMETHING exerts a force on the conducting wire in a downwards direction. By Newton's 3rd law, the (field of) this conducting wire also exerts a force on something. Homework Equations Could the magnet be said to move upwards (and hence reading decrease)...
  22. Nyang

    Admissions Can I Apply to ETH Zurich Master in Physics without Math Courses?

    I have a normal GPA grade(3.5/4.0), many research experience with professor at Max Planck Institute and many publication including PRB paper and 1st author paper(sci). I would like to apply to ETH Zurich master in Physics course, but i did not take math courses except mathematical physics1...
  23. S

    I Can Schrodinger's cat apply to things other than alive/dead?

    We know of Schrodinger's cat analogy, where a cat in a box that has a gas tube with deadly gas (or whatever it is) is both alive and dead at the same time until observed. Does it work on anything else? Like something is big or small, near or far, tall or short, red or blue, etc. at the same time...
  24. Nabin kalauni

    Schools Which college should I ED (apply) to?

    I am a Nepalese 12th grade student and I will be applying to a few US colleges for the Class of 2023. I am seeking to pursue a PhD in some field of physics that will pique my interest by the end of grads. I won the national physics olympiad and would be participating in IPhO now had it not been...
  25. Boltzman Oscillation

    Other Can I apply what I learn in quantum mechanics to electrical engineering?

    Are there any projects I can build? What are the applications of QM in electrical engineering?
  26. r0ss

    I Why can't we apply Gauss's law to a circular disk?

    We apply Gauss's law to find electric field at a point due to chaged plane or plate. But what's wrong when applying to circular disk which can also be considered as a plane?
  27. Felipe Lincoln

    Stokes' Theorem, how to apply for this surface?

    Homework Statement With the stokes' theorem transform the integral ## \iint_\sigma \vec{\nabla}\times\vec{F}\cdot\vec{\mathrm{d}S} ## into a line integral and calculate. ## \vec{F}(x,y,z) = y\hat{i} -x^2\hat{j} +5\hat{k}## ##\sigma(u,v) = (u, v, 1-u^2)## ## v\geq0##, ##u\geq0##...
  28. Lukejohn

    How to state the laws of refraction and apply them to....

    How do i apply the laws of refraction to plane and curved surfaces. I have absolutely no idea how to even start on this one, its got nothing to do with the course, i am going to study. i need to understand this to move on but i genuinely have absolutely no interest in optics. I really can not...
  29. Y

    Why does Fleming's right hand rule apply for induced current

    I know that the right hand rule applies for induced currents, and the left hand rule is for motors, but why? It doesn't seem to connect with any other physics laws and is very counter-intuitive that the current will flow in one direction rather than the opposite direction if both are...
  30. Barath Kr

    How to apply moments in ANSYS Explicit Dynamic Analysis?

    Hello All, I want to apply moments to Revolute Joints in Explicit Dynamic Analysis. But i could not find any option to apply moments. I saw an youtube video, from which it is cleary know that it is possible to apply moments to revolute joints under initial conditions. But i don't know how they...
  31. S

    Schools Where to apply for PhD physics in Europe

    I am planning to do a PhD degree in physics since I have recently completed my masters degree, my research field was mainly on cosmology but I am getting interested in some fundamental aspects of physics, like GR and QG. I have tried to apply to some universities in Germany and failed to be...
  32. SmamMir

    System of equilibrium, why won't the normal force apply?

    Homework Statement Homework EquationsThe Attempt at a Solution I've resolved all the relevant forces (tension, weight, normal force), but upon looking at the mark scheme, there is no normal force to be resolved. Forgive me if I'm missing out on something obvious, but shouldn't there be a...
  33. Sorcerer

    I GR: Does Clock Hypothesis Apply?

    *This question is beyond my education, but if you need to post graduate level math, feel free to, and if it requires changing this to A level, be my guest* So in SR, we assume that time dilation does not depend on acceleration, but only instantaneous speed. But in first learning about the...
  34. R

    When to apply Pascal's Law vs Bernoulli's equation

    Hello, I was solving a problem regarding pressure at different elevations. The question regarded water flowing through a pipe which travels up 5 meters. I used Pascal's Law (p = p(initial) + rho*g*h : rho is density of fluid, g is gravity and h is the height) and came up with an answer...
  35. EnigmaticField

    Programs Apply for a PhD in theoretical condensed matter physics?

    I did research on theoretical formulations in general relativity during my MSc studies. I look forward to pursuing PhD and have searched many universities and some research institutes for suitable research themes, but haven't found many research groups undertaking research consistent with my...
  36. T

    I Does Hyugen's principle apply in three dimensions?

    Does Hyugens principle apply in three dimensions ? If a surface wave (for simplicity an ocean wave) is propagating along the x-axis we know that this wave ray is a point source for wavelets on the y-axis but what about the z axis? If this diagram was 3d would we see a spherical wave front...
  37. P

    Does Bernoulli's equation apply to a fountain?

    Can I use Bernoulli's equation to calculate certain measures of a fountain, or does it only apply to fluids in pipes? Also if so, how could I calculate the pressure inside a tube used in a fountain?
  38. S

    Can I apply a voltage higher than a capacitor's rated voltage

    I have a 5.5v .22F capacitor and I plan on using a 6v led on it for a project. Since I am not going to need to use it much and I am willing to do minor damage to the capacitor could I do that. By the way its for a school project so I will likely use it once or twice then keep it but never use it...
  39. axer

    Why can't we apply the speed equation in a free fall?

    Hello, so i know in a free fall the acceleration is constant (9.8 m/s2) therefore speed/velocity is increasing.. But I am wondering why we can't use Speed=D/T
  40. A

    Studying How to apply for a research internship for undergraduate students?

    I am an undergraduate physics student studying in UK. I hope I can continue study to PhD in the future, and I heard that I have to or better to apply a research internship in summer in order to go further study. But I have no idea how to apply and what I need to do in the internship. Since I am...
  41. mertcan

    Magnetic flux is the same if we apply the Biot Savart?

    Hi, initially I am aware that magnetic flux is conserved due to divergence of magnetic field is zero and for long solenoid, magnetic field inside is uniform. So magnetic field intensity (B) at point P,Q,S, T,R,U(in the attachment) must be same. But my question is : can we obtain the same...
  42. Hawksteinman

    Programs Apply for a PhD in Astrophysics | Physics & Astrophysics

    I'm currently studying Physics & Astrophysics with Foundation Year, and I want a PhD in Astrophysics. How would I apply for one, when the time comes? :smile:
  43. J

    A Do the equations of motion simply tell us which degrees of freedom apply?

    A massless spin 1 particle has 2 degrees of freedom. However, we usually describe it using four-vectors, which have four components. Hence, somehow we must get rid of the superfluous degrees of freedom. This job is done by the Maxwell equations. To quote from Gilmore's "Lie Groups, Physics, and...
  44. S

    Schools Suitable list of schools for an MS to apply for a PhD program in Optics

    Fifth Year BS-MS Student from one of the premier institutes in India CGPA: 8.1/10 GRE : 310/340 168Q 142V 4AWA TOEFL: 104/120 22R 27L 26S 29W I am applying for graduate schools in the following universities. Is the list sufficient? Any suggestion is most welcome. The list is not priority-wise...
  45. S

    How exactly does torque apply to gymnastics?

    Well, if I have this down correctly, torque is equal to force times distance of the lever arm. The more force or the longer the lever arm, the more torque something has. If that is true, how can you apply that to gymnastics, mainly somersaults, cartwheels, flips, spins and the like?
  46. M

    MHB What is the correct way to apply Green's Theorem in this scenario?

    Hey! :o I want to compute the integral $\oint_C \cos \left (x^{2017}\right )dx+\left (\frac{x^2}{2}+\sin y^{2018}\right )dy$, where $C$ is the boundary of the bounded field that is defined by the curves $y=2-x^2$ and $y=x$, with positive orientation. We have to apply Green's Theorem, or not...
  47. F

    Exploring the Relationship Between Heat and Force in Molecular Breakage

    When we heat something then it breaks and it is due to the transfer of energy . But what if we ignore the energy and thought it as Force I.e. the object molecules break due to Force applied on each other ( molecules) . So is it right to say heat apply Force.?
  48. T

    Can electric motors possibly apply continuous upward force?

    Is it possible for an electric motor to exist (based on our current understanding) which is capable of applying continuous upward force upon an object, enabling that object to fly or lift above the air?
  49. C

    I Relativistic Field Transformations and EM Waves

    If we move towards a source of EM waves, in our reference frame the frequency appears (and it is) higher than what a stationary observer will see due to Doppler effect. The field transformations show that these two observers will se static fields differently so I would also expect that the peak...
  50. I

    B How can the Big Bang model apply to the entire universe?

    The ubiquity of the big bang holds no matter how big the universe is or even whether it is finite or infinite in size. How are we so confident that the part of the universe that is unobservable also falls under the Big Bang model?
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