Closed Definition and 1000 Threads

The problem: Appreciate help on the following Hot water flows in an insulated copper pipe L long starting at temperature, T0 Need the temperature history, T(t,x). T(0.x)=0 T(t,0)=T0 Heat transfer coefficient(conductance) water to pipe is U. Pipe heat capacity per unit length is C I...

Homework Statement Determine VC for the network in Fig. 7.24 (left-hand image). Homework Equations Kirchhoff's Voltage Law: The algebraic sum of the potential rises and drops around a closed path (or closed loop) is zero. The Attempt at a Solution This is an example problem...

[EDITED] Why is the electric flux through a closed surface zero? My book based the reasoning from a uniform electric field. I understand that for a uniform electric field, the electric field doesn't diminish in magnitude as we move away from the source, and if we construct a box-shaped closed...

Give an example of: a) a closed set S\subsetℝ and a continuous function f: ℝ-->ℝ such that f(S) is not closed; b) an open set U\subsetℝ and a continuous function f: ℝ-->ℝ such that f(U) is not open Solution: a) e^x b) x^2 here's my problem, this is what was given in the...

Homework Statement I'm doing a project right now which deals with designing a closed loop recirculating system using water to cool multiple components. However, this post will only deal with the fluids portion. Below is the diagram of a very simplified system. Note that the areas marked red...

Suppose that 1<p<inf and a=(a_k) a complex sequence such that, for all x in l_p, the series (which runs from k=1 to inf) Sigma(a_k x_k) is convergent. Define T:l_p--->s by Tx=y, where y_j=Sigma(a_k x_k) (where j runs from 1 to j). I need to prove that 1) T has a closed graph (as a linear...

My book says that the total vector displacement around a closed loop is zero. Is this a general thing for every type of closed loop? If so, should this be obvious?

Hi Guys, Attached is a problem from an old exam for a Process Control and Instrumentation unit. I have tried everything I know (which isn't much, it's not the main assessable portion of the unit). Other questions similar involve giving us either the characteristic closed loop equation...

I have a pressure flow problem where I'm trying to understand the velocity profile of a fluid in an annular space between a stationary exterior cylinder and a rotating, longitudinally advancing cylinder at its center. So the boundary conditions a zero velocity at the exterior surface and a...

Homework Statement Prove: If ##X## is a (possibly infinite dimensional) locally convex space, ##L \leq X##, ##dimL < \infty ##, and ##M \leq X ## then ##L + M## is closed. Homework Equations The Attempt at a Solution ##dimL < \infty \implies L## is closed in ##X## ##L+M = \{ x+y : x\in L, y...

In general, how do you prove that a given trajectory in phase space is closed? For example, suppose the energy E of a one-dimensional system is given by E=\frac{1}{2}\dot{x}^2 +\frac{1}{2}x^2 + \frac{\epsilon}{4}x^4, where ε is a positive constant. Now, I can easily show that all phase...

]Homework Statement A closed loop of wire 7.2 x10^{}-3 m^{}2 is placed so that it is at an angle of 60degrees to a uniform magnetic field. The flux density is changing at 0.1 T/s. The emf, in V, induced in the loop of wire is A) 3.6x10^{}-4 b)3.6x10^{}-2 6.9 Homework Equations emf...

Homework Statement This question comes out of "Introduction to Topology" by Mendelson, from the section on Identification Topologies. Let D be the closed unit disc in R^2, so that the boundary, S, is the unit circle. Let C=S\times [0,1], and A=S \times \{1\} \subset C. Prove that...

I'm looking for some study materials regarding Closed time-like curves (CTCs). Be it a book, paper or anything other. It is highly accepted, but I'm particularly looking for a book that includes it and similar topics.

Purpose of the "closed box" It's often stated that GR follows from the observation that an experimenter inside a closed box in freefall could not distinguish between the box being in that circumstance, and the box being in open space away from any gravitational field. In each case, objects...

If my understanding is correct, they use shapes of things great distances apart and they compare certain properties measured to what is calculated for a closed, curved or flat universe. But my questions is if a 2-manifold is topologically homeomorphic to any 2-sphere and the same is true of...

Homework Statement Mercury is a silvery liquid at room temperature. The freezing point is -38.9 degrees celcius at atmospheric pressure and the enthalpy change when the mercury metls is 2.29 kJ/mol. Wat is the entropy change of the mercury if 50.0 g of mercury freezes at these conditions? The...

Homework Statement -- Homework Equations -- The Attempt at a Solution This isn't really a proper homework question so I'll just write my problem here: I'm trying to compute a closed line integral over a triangular region. I have calculated two of the sides, but am now left...

Given the domain ℂ\[-1,1] and the function, f(z)=\frac{z}{(z-1)(z+1)}, defined on this domain, the Residue Theorem shows that for \alpha a positive parametrization of the circle of radius two centered at the origin, that: \int_{\alpha}f(z)=\int_{\alpha}\frac{z}{(z-1)(z+1)} = 2\pi i Can I...

The Friedmann–Lemaître–Robertson–Walker metric is a solution of the field equations of GR. It tells us the local behavior of spacetime, that is, g(x) at a given spacetime point x If the matter density is high enough, the curvature is positive. It is said then that the universe is closed...

Homework Statement The closed cylinder of the figure has a tight-fitting but frictionless piston of mass M. the piston is in equilibrium when the left chamber has pressure p0 and length L0 while the spring on the right is compressed by ΔL. a. What is ΔL in terms of p0, L0, A, M, and k...

Hey guy's, trying to figure out another closed form formula but this time for the sum of 1/squares of the first n consecutive integers. Or in other words: 1/(1^2) + 1/(2^2) + 1/(3^2) + 1/(4^2) +1/(...= I tried using the same technique as last time by setting up the formula based on...

So we recently began electrostatics and here you encounter Gauss' law saying that the flux integral of an electric field E over a closed surface is only dependent on the charge confined within the surface. Now for a sphere that's pretty obvious why. Because since the field gets weaker...

y(4C) ≈ 7.3 + C + \frac{C}{3^{10C}} + \frac{C}{3^{20C}} + \frac{C}{3^{30C}} Would: y(nC) ≈ 7.3 + C\sum_{n = 0}^{\infty}{\frac{1}{3^{10Cn}}} Be an acceptable answer? If not, what am I doing wrong here?

Homework Statement Let T: \ell^{2} \rightarrow \ell be defined by T(x)=x_{1},\frac{1}{2}x_{2},\frac{1}{3}x_{3},\frac{1}{4}x_{4},...} Show that the range of T is not closed The Attempt at a Solution I figure that I need to find some sequence of x_{n} \rightarrow x such that...

Homework Statement Is C^{k}[a,b] closed in C^{0}[a,b]? The Attempt at a Solution C^{k}[a,b] is obviously a subset of C^{0}[a,b]. My gut feeling says no. I thought the best way would be to construct a function f_{n}(x) which converges to f(x) and where f_{n}(x) is in C^{k}[a,b] but f(x) is...

Say we have NA blue balls and NB red balls mixed together in an urn. When we pick a ball it leaves the urn. I want to find the probability of picking n red balls in a row. The probability of picking a red ball is: NA/(NA+NB) But each time a red ball leaves the urn the probability of picking...

determine a closed expression for b(n), given b(0) = 3 b(n+1) = 2+\prod (k=0 to n) * b(k) , n >= 0 , without using recursion og or the product given by \prod. I want to start out by b(n+1) -1 = (b(n)-1)^2 for n >= 0 , but I am not sure. kind regards Maxmilian

Homework Statement When is the magnetic flux on a section of a closed surface equal to zero? A. When the magnetic field is in the direction opposite that of the section’s area vector. B. When the magnetic field is in the direction of the section’s area vector. C. When the magnetic field...

Suppose that E is a field extension of F, and every polynomial f(x) in F[x] has a root in E. Then E is algebraically closed, i.e. every polynomial f(x) in E[x] has a root in E. I've been told that this result is really difficult to prove, but it seems really intuitive so I find that...

If u is harmonic function defined on (say) the open unit disc, then it can be continuously extended to the closed unit disc in such a way that it matches any continuous function f(θ) on unit circle, i.e. the boundary of the disc. But my understanding is the same cannot be said of holomorphic...

"Find the most economical dimensions of a closed rectangular box [. . .]" Homework Statement Find the most economical dimensions of a closed rectangular box of volume 8 cubic units if the cost of the material per square unit for (i) the top and bottom is 5, (ii) the front and back is 2 and...

I tried very long time to show that For closed subset A,B of R^d, A+B is measurable. A little bit of hint says that it's better to show that A+B is F-simga set... It seems also difficult for me as well... Could you give some ideas for problems?

Homework Statement Prove that the closed interval [0,1] is not a homogeneous topology by showing that there's no bijective, open and continuous (bi-continuous) mapping h: [0,1]→[0,1] such that h(1/2)=0.Homework Equations The closed interval is equipped with the usually metric. If the mapping...

if the universe is not infinite in size is that mean a closed universe ?

i have got a solution of my differential equation - consists of Bessel function and hyper-geometric function....should i call it as a closed form solution? and i would also like to know about the importance of closed form analytical solution of any problem...what is the greatness of...

This is not a homework problem, just something I was thinking about. In a general metric space, is it true that every closed set can be expressed as the intersection of an infinite collection of open sets? I don't really know where to begin. Since the finite intersection of open sets is open...

Homework Statement Suppose S is a nonempty closed subset of \mathbb{R}^n, and let x \in \mathbb{R}^n be fixed. Show that A = \{d(x, y) : y \in S\} is closed. Homework Equations A set is closed if its complement is open, or if it contains all of its limit points. The Attempt at a Solution I...

Hi all! My question is the following. Suppose we have two normal topological spaces X and Y and we have a continuous map from a closed subset A of X to Y. Then we can construct another topological space by "glueing together" X and Y at A and f(A). By taking the quotient space of the disjoint...

Homework Statement Find (X,d) a metric space, and a countable collection of open sets U\subsetX for i \in Z^{+} for which \bigcap^{∞}_{i=1} U_i is not open Homework Equations A set is U subset of X is closed w.r.t X if its complement X\U ={ x\inX, x\notinU} The Attempt at a Solution Well...

Electric Field inside a closed gauss box. Homework Statement there are +2uC and -2uC charges inside a close "Gauss" box. Which of the following statement is true? Homework Equations given option are: 1) the net electric flux through the box is zero 2) the electric field is zero...

I'm trying to prove the following and all I've got is like one line worth of proof. If we had that sigma-rings were closed under complementation, this would be easier, but we only know that if A in R and B in R, then A \ B in R and B \ A in R (symmetric difference). Is there a way to...

Homework Statement Hello, This expression was derived from a polygon word problem and I need to find a closed form for it with repeated substitution (I think). T(k, n) = T(k, n-1) + (k-2)(n-1) + 1 Homework Equations The Attempt at a Solution Get a pattern like: = T(k, n-2) + (k - 2)(2n -...

Hello all. I have a platform that is controlled by two electric motors (one for elevation, one for rotation). During the application, I would like to have the platform maintain it's current position. I'm imagining a system where you set the position manually, and then press a button that...

Homework Statement Let [a,b] be a closed, bounded interval of real numbers and consider L^{\infty}[a,b]. Let X be the subspace of L^{\infty}[a,b] comprising those equivalence classes that contain a continuous function. Show that such an equivalence class contains exactly one continuous...

Is the imaginary axis considered a closed curve on the Riemann Sphere?

Hi, I know that the mean curvature at an extremum point where the function vanishes must be nonpositive.can this say something about the sign of the mean curvature at the farthest point on a close surface from the origin? Thank's Hedi

Recently I read about Saab's experiments at closed loop spark advance, and it got me wondering. If you are controlling spark advance to maintain a constant peak pressure position of 20 deg after TDC is it possible to get into a situation where detonation or pre-ignition is possible. It seems to...

Homework Statement Let K be the closed interval [0,1] and consider the function f(x)=x^2. Is f convex? Is f linear? help please :/ i don't even know how to set this up to check, our teacher didn't even get to this in class yet! Homework Equations The Attempt at a Solution

Homework Statement W is a subset of C[-Pi,Pi] consisting of all finite linear combinations: 1,cos(nx),sin(nx) i) Show that W is a subspace of C[-Pi,Pi] ii) Is W closed in C[-Pi,Pi]. Hint from Fourier analysis: For x in [-Pi,Pi]...