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JUNIORMARK 4TH DESTINY #DestinyClinicxJuniorMark ว่าด้วยเรื่องแคปชั่นในวันวาเลนไทน์ขอน้องมาร์ค ‘ It’s all do ’ 🐱: มันเป็นท่อนนึงของเพลงที่ผมใส่ในโพสนั้น คุณลองไปฟังดูแล้วคุณจะรู้ความหมาย ละเพลงความหมายประมาณว่า ‘ ครั้งนี้จะตกหลุมรักคุณ นั้นคือสิ่งที่ทำมาตลอด คือรักคุณ ’ ไอ่เจี้ย กุตาย y—y
24,025 просмотров • 7 месяцев назад •via X (Twitter)
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![Lecture 4 on Calculus of Variations You might wonder...If I’m optimizing a shape...a curve, a surface, a whole path, what does "take the derivative and set it to zero" even mean? Do I take the damn derivative with respect to a curve/surface? 🤔 In normal calculus the variable is a number x, so the reflex is clean...f′(x)=0. In calculus of variations the variable is a whole function...the geometry itself, like a curve y(x) (or a surface z(x,y)). So the derivative can’t be a single slope. It has to be a pointwise sensitivity, i.e. how the objective reacts to tiny local deformations. You’re holding a whole shape, like a curve y(x). Your objective isn’t f(x) anymore, it’s a functional J[y], and as we've seen with our first there examples, usually an integral that depends on the entire curve (often through y and y’). To talk about a “derivative”, you do the only thing that makes sense: you nudge the entire curve by a tiny amount and see how J changes. Pick a wiggle shape η(x). It’s not random...it’s any admissible deformation direction. Admissible just means it obeys the constraints. If the endpoints are fixed, you force η(0)=η(1)=0 so the wiggle doesn’t move the endpoints. Then scale that wiggle by a small number ε and define the perturbed curve yε(x)=y(x)+εη(x). Now treat ε like the usual scalar in a Taylor expansion. As ε→0, J[y+εη] expands as J[y+εη] = J[y] + ε · (first-order term depending linearly on η) + o(ε). So the difference is J[y+εη] - J[y] = ε · (linear functional of η) + o(ε). For the standard integral of a Lagrangian problems, that linear functional can be written as an inner product with some function of x: J[y+εη] - J[y] = ε ∫ (δJ/δy)(x) η(x) dx + o(ε). That’s the definition-level meaning of δJ/δy: it’s the unique pointwise sensitivity function that makes this identity true for every admissible η. If δJ/δy is positive at some x, then choosing η negative there decreases J; if δJ/δy is negative there, pushing y upward locally decreases J. It’s literally a map along the curve saying push this way to go downhill. Now translate “set the derivative to zero.” At a minimizer y*, the first-order change must vanish for every admissible wiggle: J[y*+εη] − J[y*] = o(ε) for all η. Plug in the expansion and the ε-term must be zero: ∫ (δJ/δy)(x) η(x) dx = 0 for all admissible η. Here’s the crucial logic step: the only way an integral against every test function η can be zero is if the integrand itself is zero (in the usual sense used in analysis). So you get δJ/δy = 0. For the common case J[y]=∫ L(x, y, y’) dx, you can compute δJ/δy explicitly and it becomes the Euler–Lagrange expression δJ/δy = ∂L/∂y − d/dx(∂L/∂y’). So if you name the Euler–Lagrange residual as “left-hand side” R(x) = ∂L/∂y − d/dx(∂L/∂y’), then “set the derivative to zero” is exactly R(x)=0. That’s why animation works so well. You don’t have to solve R=0 in one shot. You can evolve the curve in an artificial time τ by pushing it in the downhill direction: ∂y/∂τ = −R(y). Where the residual is large, the curve moves a lot; as the residual drains toward zero, the motion dies out and the curve settles into an extremal. In our animations, we start from an intentionally ugly curve/surface. Frame by frame the functional drops, the residual drains away, and the geometry relaxes into an extremal. #CalculusOfVariations #EulerLagrange #FunctionalDerivative #GradientFlow #Optimization #MathAnimation](https://image.24vids.com/tw-2005012934343467237/amplify_video_thumb/2005008764127076352/img/icWC3mGkeN2DfPJK.jpg)
![Alfonso Cuarón & the cast of "Y tu mamá también" (2001) explain the reasons for the movie's success: "CUARÓN: One part is obvious. Putting teenagers in situations that include s€x will always be attractive to a certain audience. But I hope “Y Tu Mamá También” transcended that, because we set out to not be “American Pie” (1999). We wanted the s€x scenes to get a point across about these characters and about the social elements we were playing with, like class and the conceptions of masculinity that these characters have. DIEGO LUNA: This is a great movie, of course, but not all great movies arrive in the correct moment. “Y Tu Mamá También” had such luck. It found an audience that needed a journey like the one the movie proposes. The movie speaks of fundamental relationships and it’s very easy to reflect yourself in it. It’s also a movie that portrays a Mexico that seemed to be hidden before. The way it depicts the economic inequality and class conflict was very painful for some to see back then. I remember a lot of people complained, “Why do you portray Mexico this way?” But at the same time it portrayed the beauty that the country has to offer. GAEL GARCÍA BERNAL: It caused a schism within the Mexican audience. Many people connected positively with the movie but it angered the pearl-clutchers. [Laughs] Some audiences projected a certain discomfort with the s€xual openness or with the fact that the movie touched on gay themes in an ambiguous way. All of that created a dialogue. Outside Mexico what transcended was the desire to live that this movie instills in you. When you come out of the theater, you want to head to the beach and go on a crazy adventure. MARIBEL VERDÚ: I believe it’s authenticity. It’s a movie that feels like a documentary. It looks like something improvised, but there’s so much work behind it. There [were] rehearsals to have it all very tight, but to make it seem like everything was just happening in front of us. That’s so magical and audiences felt that too." ("When ‘Y Tu Mamá También’ Changed Everything", Carlos Aguilar, The NY Times, 2021)](https://image.24vids.com/tw-2073845618657886524/amplify_video_thumb/2073829975439163392/img/FQVoOpia851Kj6aG.jpg)
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Akademiks speaks out after closely analyzing the leaked video of Daphne Joy, Diddy, and Sly Diggler for “research purposes” “These b——s are taking baseball bats in their p—y, straight fist, BANG! I’m sorry 50’s baby mama calls you over after she just had six rounds with the Punisher, Sly Diggler… N—a, you think you’ve seen a real UFO until that b—h opens her legs. It’s straight blackness; it’s a fucking portal, n—a… Call me small all y’all want. Listen, I’m going with a bag of tools, gang—a lot of tools. I’m having batteries, rechargeable batteries, power banks. I’m bringing everything… Brother, she took more than 100 inches of d—k in one night. What the f—k you think you gonna do, n—a? Guinness Book world record… I ain’t gon’ lie, I’m anti-paying for p—y. I wouldn’t pay a b—h a dollar, but yo, I ain’t gon’ lie, I’m making too much money. Yo, I got 10 grand for you too, f—k that shit. I got my 10 bands—10 a month easy… This is gon’ be a subscription.”
FearBuck
781,971 просмотров • 4 месяцев назад
