Closed Definition and 1000 Threads

Hello again I have another question regarding absolute min-max over a region. This is a weird one. My function is: \[f(x,y)=x^{2}+y^{2}-xy\] and the region is: \[\left | x \right |+\left | y \right |\leq 1\] Now, I have plotted the region using Maple: The answer in the book where it...

Can anyone tell me if Control bandwidth and closed loop bandwidth means the same thing? If not what does control bandwidth mean? Please & Thank you!

In this paper; http://arxiv.org/abs/1405.7860, What is the distance to the CMB? How relativistic corrections remove the tension with local H0 measurements, it is suggested cosmological distance may be miscalculated due to failure to take into account systematic accumulation of lensing effects...

Homework Statement Let ##X## be a topological space. Let ##A_1 \supseteq A_2 \supseteq A_3...## be a sequence of closed subsets of ##X##. Suppose that ##a_i \in Ai## for all ##i## and that ##a_i \rightarrow b##. Prove that ##b \in \cap A_i##. Homework Equations The Attempt at a Solution...

I have a problem with this excercise. Ironically I think I can manage the part that is supposed to be hardest, here is the problem: Let (V,||\cdot||), be a normed vector-space. a), Show that if A is a closed subset of V, and C is a compact subset of V, then A+C=\{a+c| a \in A, c \in C\} is...

Let $a$, $b$ be reals and $f: (a,b) \rightarrow \mathbb{R}$ be twice continuously differentiable. Assume that there exists $c \in (a,b)$ such that $f(c) = 0$ and that for any $x \in (a,b)$, $f'(x) \neq 0$. Define $g: (a,b) \rightarrow \mathbb{R}$ by $\displaystyle g(x) = x -\frac{f(x)}{f'(x)}$...

If a pump pumps water to a heat exchanger at a certain height, say, 20 m is the head required indeed lower for a closed loop system than an open loop system? The link below says so, but I wanted to verify. Assume pipe friction losses are the same in both cases. Can one really take credit for...

Within the scope of classical mechanics, what exactly is the definition of a closed system, and of an isolated system? Also, do these definitions differ in thermodynamics? And does the law of conservation of linear momentum apply to a closed system or an isolated system?

Suppose I have a smooth curve \gamma:[0,1] \to M, where M is a smooth m-dimensional manifold such that \gamma(0) = \gamma(1), and \hat{\gamma}:=\gamma|_{[0,1)} is an injection. Suppose further that \gamma is an immersion; i.e., the pushforward \gamma_* is injective at every t\in [0,1]. Claim...

If I am understand correctly a moving mass has more energy than a stationary mass. Mass and energy are two forms of the same thing so more mass is more energy and more energy is more mass. Suppose we decided to take our (almost) light speed rocket ship and reach the edge of this apparently...

f^-1 (E^c) = (f^-1(E))^c where f is map from X to Y and E is in Y. Prove equality is true.

What exactly does it mean for something to be closed under addition. most of the examples and questions i have gone past, are answered with u + v = u1+v1, ... , u_n + v_n and hence this is closed under addition. So i tried looking for examples where something was not closed under addition...

Homework Statement Using the divergence theorem, evaluate the total flux of a magnetic field B(r) across the surface S enclosing a finite, connected volume of space V, and discuss its possible dependence on the presence of an electric field E(r). Homework Equations ∇.B=0 The...

I am doing a project on string theory and my first task is to work out fundamental string solution from the I(10) string action in NS sector.I am following A.Dahbolkar, G.Gibbons, J.A.Harvey & F.Ruiz Ruiz, Nuclear Physics B340 (1990) 33—55. Why is it called fundamental string? I have not taken...

According to Faraday's Law a changing magnetic field induces an electric field, an example of this is if you have a wire close enough to another wire with current flowing through it the first wire will also have current run through it because of the induced electric field by the second wire...

I have this assignment (First problem - exercise 2 - dias 7) http://site.iugaza.edu.ps/bhamed/files/2010/02/L4-Root-Locus.ppt Which i am having some problems solving. I am stuck at B) So far i tried to solve the problem, by calculating the distance from origin to the breakaway point, by...

I understand that an inductor acts as a closed circuit to DC because it's just a coiled wire but why doesn't it act the same way for AC? What does it act as in AC?

How the charge is conserved in a closed loop circuit?

Hey! :o I am lokking at the proof of the following sentence. An infinite orthonormal system $\{e_1, e_2, ... \} \subset H$, where $H$ an euclidean space, is closed at $H$ iff $ \forall x \in H$ $$||x||^2=\sum_{i=1}^n{|(x,e_i)|^2}$$ We suppose a subspace of $H$, that is produced by the basis...

I've been trying to prove that the closed unit ball is a manifold with boudnary, using the stereographic projection but I cannot seem to be able to get any progress. Can anyone give me a hint on how to prove it? Thanks in advance :)

How to solve this question. Please explain step by step.

Around the 4 minute mark the lecturer makes this statement, but I am not convinced this is true. I accept that (1) if a set is closed, its complement is open. but consider the converse. Consider an open ball S of some arbitrary radius centered at the origin (in whatever dimension d...

How much oxygen would make it's way down to the water if no mixing happens when put into container? I always hear of blanket of CO2 over a liquid. I'm trying to relearn some thermodynamics principles. Would the partial pressure between the CO2 never allow the oxygen diffuse into the water if...

Hi, I'm an automotive technician. I have trouble understanding a couple basic electrical concepts. The problem is that I am more or less taught that current flows through CIRCUITs. When analyzing electrical problems, I think current will only flow if there is a voltage (potential...

Closed, collapsing universe+only photons at first --> matter when hot? Suppose we had closed, collapsing universe with a uniform thermal distribution of low energy photons like that of the CMB and no other matter (I suppose we must pick the initial conditions right for collapse to occur) . As...

Could someone explain to me about what closed under addition and closed under scalar multiplication means? I have a patchy idea of what it is but how does it relates to A = {(x,y) | x^2 + y^2 <= 1}? What does A stands for? What does the language implies? Edit: My interpretation: Let's...

1. Homework Statement [/b] http://snag.gy/m9Iq0.jpg Homework Equations The Attempt at a Solution I know that the sensistivity of a closed for at small change is given by the formula S = ∂ Ln T/∂ Ln G And T(s) = G_c(s)G(s)/1 + G_c(s)G(s) But since i don't have any G_c(s), i...

If I push a book horizontally across a table I do work. But is energy conserved?

[FONT=Helvetica Neue]A closed organ pipe has a length of 2.40 m. [FONT=Helvetica Neue]a.) What is the frequency of the note played by the pipe? Use [FONT=Helvetica Neue]343 m/s as the speed of sound. [FONT=Helvetica Neue]b.) When a second pipe is played at the same time, a 1.40 Hz beat note...

Homework Statement Homework Equations A set is closed if it contains alll of its boundary points. A boundary point is a point where an open ball around that point has one point inside the ball that's in the set, and one point in the ball that's not in the set.The Attempt at a Solution As seen...

In this note (http://sgovindarajan.wdfiles.com/local--files/serc2009/greenfunction.pdf) the Klein-Gordon retarded green function is derived on the form $$G_{ret}(x − x′) = \theta(t − t') \int \frac{d^3 \vec k}{(2\pi)^3 \omega_k} \sin \omega_k (t − t′) e^{i \vec{k}\cdot (\vec x - \vec x')}$$...

For a system I am studying the following sequence (which I would assume is quite common) came up: n1=1, n2=2, n3=4, n4=7, n5=11, n6=16, n7=22 ... i.e. the difference betweens two successive numbers grows with 1 as we move from (n_N-1, n_N) to (n_N,n_N+1). Is there a closed form expression f(k)...

Let H be a hilbert space. Let T be a bounded normal operator on H. Consider the closure of the set of polynomials in $T$ and $T^{*}$. Show that if T has an inverse in B(H), then the inverse is in this generated algebra. Notes: This is pre-gelfand naimark so can't invoke that My thoughts: If...

I have a finite sum of the form: ∑n=1Nexp(an+b√(n)) Is there any trick to evalute this sum to a closed form expression? e.g. like when a finite geometric series is evaluated in closed form.

Homework Statement Hello everybody I was hoping some of you could give me some some examples of some closed feedback loop mechanical systems. This is for my controls class where we have to design our own control system. I'm having trouble trying figure out some systems. I know one would...

http://www.bbc.co.uk/news/uk-england-cumbria-25975785 They have/had "above normal levels" at a perimeter detector. As far as I know this would detect airborne radiation. And presumably at far lower levels than the source. "A spokesman stressed there was no risk to the public or...

Homework Statement We place a speaker near the top of a drinking glass. The speaker emits sound waves with a frequency of 3.75 kHz. The glass is 14.1 cm deep. As I pour water into the glass, I find that at certain levels the sound is enhanced due to the excitation of standing sound waves in...

Homework Statement A steel cylinder filled with water contains 3000psi of pressure, completely sealed, walls ≈ infinite thick. No gas is present inside of the cylinder, and no heat exchange. To the problem; if a solid rod/piston enters on top of the cylinder with no possibilities to bleeding...

I remember reading something, long ago, to the effect that any attempt at creating a CTC would be doomed by energy from vacuum fluctuations piling up through it and leading to explosive behavior (I think the idea originated in work done by Misner and Taub in 1969?). Does anyone know what is...

I find it sometimes confusing dealing with integrals of multi-valued functions in distinguishing a closed integration path, and an integration path which forms a closed loop over the function. They can of course be quite different. For example: $$\oint f(z)dz.$$ Now, is the integration to...

1. Homework Statement [/b] Hey Guys Firstly thanks for looking, I really appreciate any help or interest with my problem. The problem is a closed loop feedback system it's unlike any I have come across before. I have been given the definition which is as follows:- G(t)^-1 = 2.5...

A recent post of chisigma rings me the bell of an old problem I thought of posting in a forum (either here or MMF). Is there any particular approach to computing a closed form for derivatives of certain smooth and continuous functions of $\mathbb{R}$? For example, it is easy to find the $n$-th...

Please help me to understand what happens to an electron when its used in a closed circuit. Main Question: How can electrons within a circuit perform work i.e. illuminate a light bulb or heat a stove and not be lost or changed from one state to another? How could it just stay the same and...

The set of the real numbers is closed. For me this is nearly trivial (*) but perhaps I miss something; a colleagues insists that there are some deeper considerations why this is far from trivial - but I don't get his point (*) A) A set is closed if its complement is open; the complement...

If exist a formula for calculate the area of a closed curve: http://en.wikipedia.org/wiki/Green%27s_theorem#Area_Calculation, so, there is a analogous for calculate the volume of a closed surface? I search but I not found...

A small container is filled with water (30ml). Next it is heated at 140°C. I need to determine the internal pressure caused by the heating process. The containers dimensions: height : 100mm Diameter: 39 mm Volume= circa 0,0203 m³ First thing I did was to look it up at steamtables. For...

Hi, (not homework/academic) Is a closed form of the following expression possible? Either way, some pointers in the right direction would be really helpful. H(s)=\sum_{n=-\infty}^\infty \frac{k^n}{k^n+a/s} Thanks, D

Hi! My question is: Find maximum and minimum values of the function: f(x,y) = 2x-y+x^2+y^2 when x^2+y^2 ≤ 4 I would like to solve this without using Lagrange method. I get x=-1 and y=1/2 when using partial derivative and set it equql to 0. I can see that the maximum value...

Closed form for "geometricish" series (index squared in the exponent)? Hi all, Is there a nice closed form for the following series? \sum_{k=0}^n x^{k^2} Even a decently tight upper bound and lower bound would be nice (obviously it is bounded by the corresponding geometric series \sum...

Homework Statement Hey guys, So the title pretty much says it. I have to find the total charge density produced by all the electrons in a closed subshell where n = 3 and l = 2. The charge density produced by a single electron is (-e)|R_{32}(r)Y_{2,m}(\theta , \phi)|^{2}Homework Equations So he...