In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set. In a topological space, a closed set can be defined as a set which contains all its limit points. In a complete metric space, a closed set is a set which is closed under the limit operation.
This should not be confused with a closed manifold.
When a thread is closed for moderation, it would be nice if the moderation occured in a moderate amount of time (not days) so that the impact to the thread is minimized in the event that the thread is reopened, and so that participants can “move on” in the event that it remains closed...
A lot of 'hot threads' come up yet when I go there the discussion is already closed. Very frustrating. If you pour cold water on the discussion it's no longer a hot thread.
For a shape to qualify as a polygon does it have to be closed. I was just introduced to frequency polygons and was surprised to see each one was a shape that wasn't closed. The definitions of polygon that I've come across go something like, a closed shape consisting of three or more lines.
For part(a) of this problem,
The solution is, a. 160 J
In part (a), are they referring to the simi-circular path from R to S instead of the path from R back to R? I though the closed path would be the path from R to R, or the path from S to S, where both give W = 0 since ##W = P(V_f - V_i) =...
Looking at the given values, I thought the specific heat formula could be used to calculate the final temperature of the air: c = Q/mΔT. Since the final temperature is the sum of the initial temperature and the change in temperature, the formula can be rearranged to ΔT = Q/m*c.
Q = 30 W * 10 s...
Example: 3/4 pvc in closed circuit with pump. Linear distance of pipe=30ft / head 8ft .... so not counting friction, what general description of force can describe what's required to make the liquid circulate?
Hello,
What I have
I have a NEMA17 stepper motor driven by a DRV8825 driver module, an arduino uno, a multiturn potentiometer.
What I want to do
I want to control the stepper motors in a PID closed loop. The motor shaft will be connected to the potentiometer and I will be sure that the motor...
Following from Wikipedia, the covariant formulation of electromagnetic field involves postulating an electromagnetic field tensor(Faraday 2-form) F such that
F=dA
where A is a 1-form, which makes F an exact differential form. However, is there any specific reason for expecting F to be exact...
How can we control the pressure of the water inside a closed loop system (chiller system for example)?
Let´s say, we have a pump curve and an system resistance curve that can be modified (through opening or closing some valves)
In everywhere, what I see is that the intersection of the system...
Hello,
I am working on a theory for a Great Pyramid power plant and I need some help understanding if my current hypothesis is even possible and how to calculate how much water will fill the upper structure. I believe the water system to work as follows: An aqueduct delivers a steady flow of...
Greetings,
I've come across lots of exercises regarding Bernoulli's equation. However, never seen one where the top of the vessel is closed, and fluid flow exists via gas (air) going in. Has this problem been studied in the past?
Assume a cylindrical vessel filled to the maximum with a D-sized...
Hello everyone,
I am struggling to get insight into a certain set in 4D space. Given is a closed path in 4D-space with constant Euclidean norm
$$\vec{\gamma} (\theta):[0,2\pi]\to\mathbb{R}^4, \ \ \vec{\gamma}(0)=\vec{\gamma}(2\pi), \ \ ||\vec{\gamma}(\theta)||_2 = \mathrm{const.}$$
I am looking...
Hey all,
I was wondering if there was an equivalent closed form expression for ##\Gamma(\frac{1}{2}+ib)## where ##b## is a real number.
I came across the following answer...
Hello everyone,
I would need help to model a motorized system controlled in a closed loop. It is a personal project.
At first, I am looking to obtain the transfer function and simulate the system on computer. In a second step (not the aim of this thread), I would like to use this simulation to...
Hello!
(I am not asking for someone to do this for me. I am only asking a qualitative question.)
Suppose one knows the lengths of all six links that are involved in the Stewart platform.
Is that enough to define the position and orientation of the top (assuming the base is fixed)
I would...
Hello,
At my work I came up with the following question:
Say we have a vacuum chamber. Inside the vacuum chamber we have at the bottom a water bath. The rest of the chamber is filled with a air and water vapor mixture. The whole system is placed in a room, is at room temperature and is in...
just hypothetical question,
First off I am not very knowledgeable in pumps. Let's say you have a pump to pump fluid, i don't think the type matters, self priming as I understand it creates a vacuum with the air in the system to pull the fluid towards the gear pumps.
I'm wondering what happens...
Hello,
I would like to know, if there's a closed form solution to the following problem:
Given a sum of say, 3 sines, with the form y = sin(a.2.PI.t) + sin(b.2.PI.t) + sin(c.2.PI.t) where a,b,c are constants and PI = 3.141592654 and the periods in the expression are multiplication signs, what...
The Korean textbook standard defines the convexity of the function as an open section. Many textbooks and university calculus textbooks define the convexity of the curve as an open section. However, some textbooks define convexity as closed sections.
Do you think it is right to define the...
If C is the simple closed curve in the xy plane not enclosing the origin, how to prove that $\displaystyle\int_C \vec{F}\cdot d\vec{r} =0 $ where $$ F= \frac{yi +xj}{x^2+y^2}$$
How to answer this question? Any math help will be accepted. I am working on this question. If any member of Math...
Whicle has 4 wheels, inside is oval closed room with fan that blow inside air to the wing. Wing produce difference in static pressure in direction of travel.
Will vehicle move forward or not?
If I look just at pressure difference at wing, vehicle will move forward but I know from Newton 3 law...
Problem: Let ## (X,d) ## be a metric space, denote as ## B(c,r) = \{ x \in X : d(c,x) < r \} ## the open ball at radius ## r>0 ## around ## c \in X ##, denote as ## \bar{B}(c, r) = \{ x \in X : d(c,x) \leq r \} ## the closed ball and for all ## A \subset X ## we'll denote as ## cl(A) ## the...
Greetings All!
I have hard time to make the difference between the equation of a closed solid and a cartesian surface.
For example in the exercice n of the exam I thought that the equation was describing a closed solid " a paraboloid locked by an inclined plane (so I thought I could use...
During our classes, we haven't discussed the situation of a tube closed at both ends. But, assuming the position of the nodes and antinodes, I think it's a case similar to the one where the tube is open at both ends, so I think that f = v/λ = nv/(2L). Using the numeric data, my frequency would...
I'm just looking at a Bode plot of log(gain) vs log(frequency) for a an amplifier circuit. I'm trying to figure out whether I'm expecting to see a resonance in the gain at the frequency where I measured one. How could I, in principle, work out theoretically where the peak gain should occur - is...
In a closed system consisting of a set of particles not at rest relative to each other and acting on each other only by classical mechanical collision (i.e. billiard balls model, not including gravity or other long-range interactions), does conservation of momentum imply that the system will...
Problem statement : As a part of the problem, the diagram shows the contour ##C##above on the left. The contour ##C## is divided into three parts, ##C_1, C_2, C_3## which make up the sides of the right triangle.
Required to prove : ##\boxed{\oint_C x^2 y \mathrm{d} s = -\frac{\sqrt{2}}{12}}##...
For an opamp in open look configuration,
Here Ad should be equal to open loop gain of opamp and
Now consider the closed loop config of opamp (negative feedback used):
However, Ad is closed loop gain here (according to Sedra Smith) and
In terms of open loop gain,
A is open loop gain...
Bertrand's Theorem says : the only forces whose bounded orbits imply closed orbits are the Hooke's law and the attractive inverse square force.
I'm looking at the hookes law ##f=-k r## and try to see explicitly that the orbit is indeed closed.
I use the orbit equation ##\frac{d^{2} u}{d...
Floating inside a closed spaceship, no windows, not knowing if I'm free falling near a gravity source or far away from any gravity source, are there any experiments that can be made, to determine if there is a gravity source near and if there is such an experiment, to determine the gravity...
Given that one of the ##S_i## (let's name it ##S_{compact}##), is compact. Assume there is an open cover ##\mathcal V## of ##S_{compact}##. By definition of a compact subspace, there is a subcover ##\mathcal U## with ##n<\infty## open sets. Notice that ##\forall x\in (\bigcap_i S_i)##, ##x\in...
Hi Guys - I have very simple question but I cannot get my head around.
Say if we cut pipeline into one section (12m) then close each cut end with temporary plugs
Water depth is 100m. Before the cut there is seawater inside the pipeline.
Now I understand there is no differentiated pressure...
This problem comes from fluid dynamics where Kelvin circulation theorem states, that if density "rho" is a function of only pressure "p", then closed line integral of grad(p) / rho(p) equals zero. It seems so trivial, so that no one ever gives reason for this claim.
When trying to solve it...
Hello,
We had a wind storm. We have a dumpster with a lid. On that lid we put a heavy brick to keep the lid closed during wind storms. It's worked great for years. But we had a very strong wind storm and it launched that brick quite a distance. I'm trying to figure out the wind speed that would...
I am confused with some basic definitions in general topology.
Topological space is defined as a set ##X## and a collection ##T## of its subsets that satisfies some general properties (which I will not list here, but I will assume that the reader knows them). But such a very general definition...
In a globally hyperbolic spacetime you have a global time ##t: M \longrightarrow \mathbf{R}## which foliates it into Cauchy surfaces ##\Sigma_t## and the metric can be written ##\mathrm{d}s^2 = -N^2 \mathrm{d}t^2 + h_{ij}(\mathrm{d}x^i + N^i \mathrm{d}t)(\mathrm{d}x^j + N^j \mathrm{d}t)##. By...
If I knew how much of the gasoline evaporated, then I could use p = nRT/V to fine the partial pressure of the gasoline and add it to the pressure of the atmosphere. So my question is, How do I find how much of the gasoline will evaporate. I would think that the gasoline would evaporate until it...
When using the voltmeter and ammeter to investigate the circuit, it was found that the batter had a current of 0.67 A, the two 30 Ω bulbs had a current of 0.17 A, and the two 10 Ω bulbs had a current of 0.50 A. In terms of voltage, each bulb had a voltage of 5 V. When the switch was closed, the...
https://www.physicsforums.com/threads/is-the-universe-a-closed-system.620503/
Hello.
I was looking back at this thread from 2012 and, to be honest, I'm a bit confused.
Quoting Drakkith...
To our knowledge it is. At minimum you could count the observable universe as a closed system because...
Kepler's equation is M = E - e*sinE
According to wiki - Kepler's equation - "Kepler's equation is a transcendental equation because sine is a transcendental function, meaning it cannot be solved for E algebraically. Numerical analysis and series expansions are generally required to evaluate...
Hello all,
Is this statement true ? Is every increasing monotonic function in a closed interval also continuous ?
How do you prove such a thing ?
Thank you !
In thinking about temperature stratification of air: I assume that in a truly closed system with no heat inputs, air would NOT stratify by temperature.
On the other hand, a heat source introduced in a closed container would generate stratification while it was generating heat (and following for...
Hi everyone, I have a question about Maxwell's laws. According to Maxwell the magnetic flux of a magnetic field through a close surface is 0.
But his third law says the circuitation of an electric field depends from magnetic flux variation. I can't understand how this can be possible since...
Hi all Physics Forum User, I am again coming to you to ask for help.
For the above question I can't make sense of how a larger G will cause Vo/Vi to approach 1. For this I'll call Vo=V and Vi=I
As can be seen from the control loop
B = A*H and V = B*K hence V = A*H*K
Also A = I - C and...
So, my dad (non-scientist) was debating with his cousin over whether he needed to spend $$$ on a crawlspace dehumidifier and get closed vents.
It was both a heated/fierce debate and interesting. Mostly, I just listened to two old dudes arguing in partial amusement, but some intrigue as well...
Hi,
I was just working through a closed loop stability problem in Control Theory and I don't really understand how the answer has arrived at the solution so quickly.
Problem: We are working with the closed loop transfer function:
$$ P(s) = \frac{K(s) G(s)}{1+K(s)G(s)} $$, where $$ G(s) =...
What would happen if the water pump output or outlet is closed and pump continues running. Will the rotor or impeller inside just rotate and rotate slowly just raising temperature of stuck water in the impeller or would there be sudden increase in pressure immediately damaging the seal. This is...