# What is Smooth: Definition and 227 Discussions

Smooth muscle is an involuntary non-striated muscle, so-called because it has no sarcomeres and therefore no striations. It is divided into two subgroups, single-unit and multiunit smooth muscle. Within single-unit muscle, the whole bundle or sheet of smooth muscle cells contracts as a syncytium.
Smooth muscle is found in the walls of hollow organs, including the stomach, intestines, bladder and uterus; in the walls of passageways, such as blood, and lymph vessels, and in the tracts of the respiratory, urinary, and reproductive systems. In the eyes, the ciliary muscle, a type of smooth muscle, dilate and contract the iris and alter the shape of the lens. In the skin, smooth muscle cells such as those of the arrector pili cause hair to stand erect in response to cold temperature or fear.

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1. ### I Mobius strip smooth section

As discussed in a recent thread, I'd ask whether any smooth section over a Mobius strip must necessarily take value zero on some point over the base space ##\mathbb S^1##. Edit: my doubt is that any closed curve going in circle two times around the strip is not actually a section at all. Thanks.
2. ### I Grassmannian as smooth manifold

Hello! There is a proof that Grassmannian is indeed a smooth manifold provided in Nicolaescu textbook on differential geometry. Screenshots are below There are some troubles with signs in the formulas please ignore them they are not relevant. My questions are the following: 1. After (1.2.5)...
3. ### I Smooth coordinate chart on spacetime manifold

Hi, I'm puzzled about the definition of smooth coordinate chart for a manifold (e.g. spacetime). From my point of view there is no invariant way to define a smooth coordinate chart since a coordinate system is smooth only w.r.t. another coordinate system already defined on the given manifold...
4. ### A Regarding fibrations between smooth manifolds

Definitions: 1. A map ##p : X → Y## of smooth manifolds is called a trivial fibration with fiber ##Z## which is also a smooth manifold, if there is a diffeomorphism ##θ : X → Y ×Z## such that ##p## is the composition of ##θ## with the natural projection ##pr_1:Y × Z → Y##. 2. A map ##p: X →Y##...
5. ### A A claim about smooth maps between smooth manifolds

Given the definition of a smooth map as follows: A continuous map ##f : X → Y## is smooth if for any pair of charts ##\phi : U →R^m, \psi:V →R^n## with ##U ⊂ X, V ⊂Y##, the map ##\phi(U ∩f^{-1}(V)) → R^n## given by the composition $$\psi ◦ f ◦ \phi^{-1}$$ is smooth. Claim: A map ##f : X → Y##...
6. ### POTW Smooth proper self-maps on Rn

Let ##f : \mathbb{R}^n \to \mathbb{R}^n## be a smooth proper map that is not surjective. If ##\omega## is a generator of ##H^n_c(\mathbb{R}^n)## (the ##n##th de Rham cohomology of ##\mathbb{R}^n## with compact supports), show that $$\int_{\mathbb{R}^n} f^*\omega = 0$$
7. ### Force to smooth a 1 mm surface bump out of a steel of sheet

Roughly, how much force does it take to make 1 mm surface bump of diameter 16 mm circle area out of 1 mm thick steel plate of far larger area (e.g. a muscled hand pounding it laid over the base with 16 mm dia. hole by M16 bolt medium is viable enough) ?
8. ### I Several Questions About Smooth Infinitesimal Analysis

Hello. I read about smooth infinitesimal analysis and I have several questions: 1.What does "ε.1" and "ε.0" mean in this proof? (photo1) (https://publish.uwo.ca/~jbell/basic.pdf , page 5-6) 2. For what purpose do we use Kock-Lawvere axiom when we deal with law of excluded middle? (photo2)...
9. ### I Proving Continuous Functions in Smooth Infinitesimal Analysis

Hello. How to prove that in smooth infinitesimal analysis every function on R is continuous? (Every function whose domain is R, the real numbers, is continuous and infinitely differentiable.) Thanks.

49. ### Is Acceleration/Decceleration smooth?

Firstly I must say if this is in a wrong sub-forum I apologise. This is my first post and I'm new to the website so please bare with me. Also I was unsure of the Prefix so I again apologise if that to, was incorrect. But my Question is that is the acceleration (or deceleration) of an object...
50. ### B Is the smooth dark matter deBroglie's subquantic medium?

https://www.inverse.com/article/24863-dark-matter-might-be-smoother-than-we-thought Scientists have yet to actually observe dark matter in the flesh, but most research up to now posits it’s the kind of stuff that clumps up and aggregates into unwieldy masses around the universe. New research...