Closed Definition and 1000 Threads

I have a set of questions concerning the perennial sum \large \sum_{k=1}^{n}k^p and its properties. 1. For p \ge 0, the closed form of this is known (via Faulhaber's formula). I know little about divergent series, but I've read that in some sense there exists a value associated with these sums...

Homework Statement In class a 3 m long aluminum bar was made to resonate by clamping it at a node in the centre of the bar. The frequency heard was 1200Hz. Homework Equations L = \frac{n}{4}\lambda v = f\lambda The Attempt at a Solution Knowing that L is 3, we can...

The Laguerre polynomials, L_n^{(\alpha)} = \frac{x^{-\alpha}e^x}{n!}\frac{d^n}{dx^n}\left(e^{-x}x^{n+\alpha} \right) have n real, strictly positive roots in the interval \left( 0, n+\alpha+(n-1)\sqrt{n+\alpha} \right] I am interested in a closed form expression of these roots...

Let L^2 be the usual vector space of complex sequences. Let F be the subspace of sequences whose first term is zero. Show that F is closed. Let $((V_{nk}):k=1,2,...)$ be a convergent sequence in F. I need to show it converges to a sequence whose first term is 0. Well, for all positive...

This is not really a homework question. Just a question regarding the normally open (NO) and normally closed switches. For an NO switch, if the button is pressed (not open anymore) and then the button is released, is the switch still in the "not open" state or does it go back to the open state?

I have read about CTCs from some books and find the explanations confusing. -Are they simply natural trajectories in the given spacetimes? -How is energy-momentum conserved if a particle can simply travel back in time? i.e. Observers will observe particles traveling in a CTC to simply...

Hi, I'm trying to teach myself electricity and magnetism (and it's not easy!) and I'm not sure I understand flux... For one thing, why is the flux through a closed surface zero if there is no charge inside of the surface (but there IS one outside)? Another thing I'm not really sure about this...

Hi I've got a recurrence relation: x_n = a*x_(n-1) + b; I think I'm going mad trying to figure out a closed form, eg. x(n) = ? the nth iteration Is there a trick or something I'm missing? Thanks

Homework Statement Hi, This is my first post. I had a question regarding open/closed sets and subspace topology. Let A be a subset of a topological space X and give A the subspace topology. Prove that if a set C is closed then C= A intersect K for some closed subset K of X. Homework...

Homework Statement When the switch is closed, Potential drops to 40v across C1 & C2(Parallel series). Find the Capacitance of C2 Homework Equations Before switch is closed C1=300uF and holds a charge of Q1=3e4 uC V=100vAfter switch is closed V'=40vThe Attempt at a Solution V1=V2 So...

Theorem: Let S be a compact subset of ℝ^n. Then S is closed. Before looking at the book I wanted to come up with my own solution so here is what I've thought so far: Fix a point x in S. Let Un V_n (union of V_n's...) be an open covering of S, where V_n=B(x;n). We know that there is a...

From control systems: I am asked to find the value of K that gives the closed loop damping ratio of 1/sqrt2. The value for the complimentary sensitivity is T(S)=(2KS +4K)/(s^3 +162S^2 +(320+2K)S +4K) so how do I find the value for K? I tried putting it in the general equation, but it...

$\displaystyle \int^{\infty}_0 \, \frac{\log (1+e^{ax})}{1+e^{bx}}\, dx $ I am not sure whether it can be solved :confused:

Does water speed in the pipes having the same diameter is strictly the same in any point of a closed (heating) system (with pump working) ? On the contrary, although liquids are "incompressible" in practice, however, does the piping still allows it to be so : the more far the water from the...

Hi everyone, I posted this a couple days ago and didn't get a response, so I thought I'd try again. Let me know if something about this is confusing. Thanks! Homework Statement Let X be a metric space and let x\in{X} be any point. Prove that the set \left\{x\right\} is closed in X...

I'm seeing the term "measurable sets" used in the definition of some concepts. But when comparing with other concepts that rely on "closed sets", I can't seem to easily find whether measureable sets are open or closed. Does anyone have any insight into that? Thanks.

It's said that it is not possible to tell the difference between acceleration of objects within a closed box and acceleration due to gravity. Is this allways the case.Does the acceleration of objects within a closed box act uniformly or does this depend on the gradual acceleration of the...

Hi pf, I thought that current will flow in closed loops only , but the figure attached shows working of antenna with current in open circuit, but how? :confused: -Devanand T

Hi I'm currently studying Electromagnetism, and we keep coming across this symbol: \oint A closed line integral, something I have never really been able to understand. If a normal integral works like this: http://imageshack.us/a/img109/3732/standardintegral.png where f(x) is the "height"...

Homework Statement I'm studying small oscillations. When can I say that an orbit is closed? The Attempt at a Solution I remember that there is a ratio that must be a rational number but I don't remember other thing... Thank you!

Homework Statement Let H= C[-1,1] with L^2 norm and consider G={f belongs to H| f(1) = 0}. Show that G is a closed subspace of H. Homework Equations L^2 inner product: <f,g>\to \int_{-1}^{1}f(t)\overline{g(t)} dt The Attempt at a Solution I've been trying to prove this for a...

Here's my circuit The question at hand is what happens when the trigger switch is closed during the timing cycle (after being closed once already to initiate said cycle) here's the waveform I'm getting, but I'm not sure what to make of it. could someone please help me understand...

For any integral where the integrand is of the form f(θ)^z, with z a complex number, and f(θ) = sin(θ), cos(θ), tan(θ), ... etc., θ being either real or complex. Is it possible to explicitly solve for an antiderivative? I'm not aware of any such way I could use residues/series representations...

Show that the system has no closed orbits by finding a Lyapunov ... Homework Statement I'm at the point in the problem where I need constants a and b satisfying ax2(y-x3) + by2(-x-y3) < 0 and ax2+bx2 > 0 for all (x,y)≠(0,0). Homework Equations Just in case you're wondering...

1. The air in a closed pipe with an adjustable plunger in is made to vibrate at a frequency 256 Hz over its open end. As the length of the pipe is increased, loud notes are heard as the standing wave in the pipe resonates with the tuning fork. (a) What is the shortest length that will cause a...

If I have a series of pipes and containers (containing liquid) soldered together to create a circular path, and then heated at a particular point or multiple points, is it possible to somehow have the gas move in a particular direction without the gas every leaving the system? I'd prefer not to...

Hello. I wish to prove this: $$\text{A function } f: X \to Y \text{ is continuous if and only if the inverse image of any closed set is closed.}$$ Proof: $(\implies)$ Let $V \subset Y$ be a closed se. By definition, $Y-V$ is an open set, and by the continuity of $f$ it follows that...

http://imgur.com/PQ4XCEo 2.V=IR 3. I know the capacitor has a voltage of 5.5 because it is charged to the supply voltage, I don't understand what happens to current when the switch is opened.

Homework Statement So this question arose out of a question about showing that a set χ is dense in γ a B* space with norm ||.||, but I think I can safely jump to where my question arises. I think I was able to solve the problem in another way, but one approach I tried came to this crux and I...

(a) Suppose \kappa is a clockwise circle of radius R centered at a complex number \mathcal{z}0. Evaluate: K_m := \oint_{\kappa}{dz(z-z_0)^m} for any integer m = 0, \pm{1},\pm{2}, ,... Show that K_m = -2\pi i if m = -2; else : K_m = 0 if m = 0, \pm{1}, \pm{2}, \pm{3},... Note...

Homework Statement I am considering the space \tilde{W}^{1,2}(\Omega) to be the class of functions in W^{1,2}(\Omega) satisfying the property that its average value on \Omega is 0. I would like to show that \tilde{W}^{1,2}(\Omega) is a closed subspace of W^{1,2}(\Omega). Homework...

Can someone please give me a list of examples of closed loop functions, the only one I know is the equation for a circle y^2 + x^2 = r^2 Also are there any closed loop functions that aren't multi variable, i.e in the form y=f(x) and not z=f(x,y) Is there a way to tell that a function is...

Homework Statement Let X be an infinite set. For p\in X and q\in X, d(p,q)=1 for p\neq q and d(p,q)=0 for p=q Prove that this is a metric. Find all open subsets of X with this metric. Find all closed subsets of X with this metric. Homework Equations NA The Attempt at a...

"closed electron configuration" equivalent to "closed shell" Hi, is the term "closed electron configuration" equivalent to "closed shell"? derivator

2. A closed, adiabatic device claims to derive useful work by expanding 1 kg of steam from 500 C and 20 bar to 100 C and 1 bar. Do you believe this claim? Assume steam is a real fluid following the steam tables in Appendix A.III.

This is elementary but surely this set is closed | c – i | ≥ | c | with c being in ℂ I am trying to picture the set. Is it outside the disc centered at (0,1) with radius equal to modulus c (whatever that is) ? Thanks

I am completely lost with this problem. How would I go about breaking it up into manageable components that so I won't get lost in the problem? Homework Statement A 2 m3 rigid storage tank containing 10 kg of steam is heated from 300 to 400 C by transferring heat from a hot reservoir at...

I'm not sure if this belongs here or in Cosmology - possibly either would do, I think. I was reading the thread about open/closed/flat universes that's currently ongoing in Cosmology, and a related question occurred to me. According to post #7 you can have geometrically flat universes that...

Homework Statement Let Ʃ 1\(n^2-1) from n=2 to k. It says find a closed for it and prove it using sum notation. Homework Equations The Attempt at a Solution I can easily prove it by induction but I don't know what a closed form means. I tried looking it up online but there really...

Meaning of a "Flat," "Open," and "Closed" Universe Hello all, I'm reading up on cosmology and the potential shapes of the universe based on its density in relation to the critical density. When one says that a universe is "flat," what precisely does this mean? Does this mean that the...

Why is the interval ##(-√2,√2)## closed in ##\mathbb{Q}## I know why it is open, but do we consider it closed because it has no limit points in ##\mathbb{Q}##, thus vacuously it is closed.

If you consider a bounded linear operator between two Hausdorff topological vector spaces, isn't the kernel *always* closed? I mean, if you assume singleton sets are closed, then the set \{0\} in the image is closed, so that means T^{-1}(\{0\}) is closed, right (since T is assumed continuous)? I...

Find the net electrical flux through a closed sphere of radius R in a uniform electric field I know that the flux is going to be 0 since there is no charge enclosed, but how would I show this mathematically? The next half of the question asks about a cylinder with sides parallel to the electric...

Hi, Thank you in advance if anyone can answer this question. How any stationary distributions exists in below matrix and what are the value [ .5 0 0 .5 .25 .5 .25 0 0 0 1 0 1/6 0 0 5/6 ] Any information regarding how to compute stationary distribution in a martrix with more...

Let \{ [a_j, b_j]\}_{j\in J} be a set of (possibly infinitely many closed intervals in R whose intersection cannot be expressed as a disjoint union of subsets of R. Prove that \bigcup\limits_{j \in J} {\{ [{a_j},{b_j}]\} } is a closed interval in R. I don't understand how to attack this...

\int_{\gamma (t) }\, f(z) dz \int_{\alpha}^{\beta} \, f(\gamma (t))\, \gamma '(t) \, dt \text{Use the substitution : } \gamma (t) = \xi \int_{\gamma (\alpha) }^{\gamma (\beta)} \, f(\xi )\, d \xi \text{If we integrate around a closed loope : }\gamma (\alpha) = \gamma(\beta)...

Dear Physics Forums denizens, I have a tricky problem that I hope one of you can help me with. (It's for a personal project, nothing to do with school.) I'm looking for a closed-form expression for the sum of the first through m-th terms of a combinatorial number. For those of you...

Homework Statement (i) Let U and V be open subsets of C with a function f defined on U \cup V suppose that both restrictions, f_u \mathrm{and} f_v are continuous. Show that f is continuous. (ii) Illustrate by a specific example that this may not hold if one of the sets U, V is not open...

We are just looking for an example of a quotient map that is not open nor closed. Let π: ℝxℝ -> ℝ be a projection onto the first coordinate. Let A be the subspace of ℝxℝ consisting of all points (x,y) such that x≥0 or y=0 or both. Let q:A -> ℝ be a restriction of π. ( Note: assume that q was...

The Universe is expanding at an increasing rate, and from what I've read there is still much debate around its fate. Will it continue to expand forever, slow to a constant rate of expansion, or slow and fall back in on itself? Why can we not yet prove that the Universe will eventually fall...