Closed Definition and 1000 Threads

Homework Statement Use, using the result that for a simple closed curve C in the plane the area enclosed is: A = (1/2)∫(x dy - y dx) to find the area inside the curve x^(2/3) + y^(2/3) = 4 Homework Equations Green's Theorem: ∫P dx + Q dy = ∫∫ dQ/dx - dP/dy The Attempt at a Solution I...

Homework Statement Show that the set S of all (x,y) ∈ ℝ2such that 2x2+xy+y2 is closed but not compact. Homework Equations set S of all (x,y) ∈ ℝ2such that 2x2+xy+y2 The Attempt at a Solution I set x = 0 and then y = 0 giving me [0,±√3] and [±√3,0] which means it is closed However, for it to...

Homework Statement Ok I created this question to check my thinking. Are the following Sets: Open, Closed, Compact, Connected Note: Apologies for bad notation. S: [0,1)∪(1,2] V: [0,1)∩(1,2] Homework Equations S: [0,1)∪(1,2] V: [0,1)∩(1,2] The Attempt at a Solution S: [0,1)∪(1,2] Closed -...

In practice, is a closed or isolated system possible? My friends keep saying No, but isn't a system inside say, a vacuum isolated? There is no outer atmosphere for transfer of energy to take place.

Homework Statement D1 = {(x,y) : x^2 + y^2 < 3, x+2y = 2} D2={(x,y) : x^2 + y^2 > 2} D3={(x,y) : x + 2y = 2} Homework EquationsThe Attempt at a Solution D1 is neither, D2 is open and D3 is closed, am I right or wrong?

According to both Wikipedia and Wolfram MathWorld, a binary operation must be closed. Wiki does leave room for a so-called external binary operation, i.e. a function from (K X S) to S, but not from (S X S) to K. (This would make the operators in physics actually "external operators", no? Do we...

Hi! It is stated in V. Mukhanov's book "Physical foundations of Cosmology" the following (page 44, after equation 2.25): "In contrast, for the dust dominated universe, where ηmax=2π, the event horizon exists only during the contraction phase when η>π." could someone please explain why is this...

Is there an f(x) which is differentiable n times in a closed interval and (n+1) times in an open interval? I think I saw this in a paper related to Taylor's theorem (could be something else though). It didn't make sense to me, how can something be differentiable more in an interval that contains...

Homework Statement I am supposed to determine the potential differences between the points. However, I thought circuits had to be closed...

I read everywhere about the formulas for calculating B at a point from a length of straight wire, or at a point from the centre of a closed loop. But what about at a point over a closed loop that wasn't the centre? Is there a simple calculation for that? Thanks

Let X be a real Banach Space, C be a closed convex subset of X. Define Lc = {f: f - a ∈ X* for some real number a and f(x) ≥ 0 for all x ∈ C} (X* is the dual space of X) Using a version of the Hahn - Banach Theorem to show that C = ∩ {x ∈ X: f(x) ≥ 0} with the index f ∈ Lc under the...

In theory, is time travel to the past possible by traveling completely around the loop of the CTC (where it would seem future links with its own past) or is a wormhole the only way to time travel by way of short cutting the CTC.

Homework Statement The question is as follows, there is a cylinder with length L and radius R, there is a sound wave with a phase velocity v, they ask for the normal modes and the 5 lowest frequencies when L=R Homework Equations Wave equation for 3D, (d^2/dt^2)ψ=v^2*(∇^2)ψ The Attempt at a...

Homework Statement Before I write the question you should know that my maths is all correct in my solution but I must have used the formulas incorrectly (or used the wrong formulas). I can't pinpoint where I've gone wrong or if I have left a formula out (I'm a teacher solving this question for...

Hi, I'm stuck on a problem in functional analysis. Let x be a sequence on the Natural nummers such that for any square summable sequence y, the product sequence xy is absolutely summable. Then x is square summable. Hint : Use the Closed graph theorem. If I can prove the map Tx : y -> xy had a...

Homework Statement I got questions a) and b), but I'm stuck at c) and d). Homework Equations Kirchhoff's Loop and Junction rules. Equivalent resistance in series: Req = R1 + R2 Equivalent resistance in parallel: Req = ((R1)-1 + (R2)-1)-1 The Attempt at a Solution I really haven't gotten...

Homework Statement Open and closed pipe, give 5 beats per second. Open pipe is 30 cm long and gives a tone of frequency f0. Speed of sound is 330 m/s. How long do we need to extend closed pipe so both pipes give equal frequencies? Homework Equations Open pipe, fn=n*f1, f1=v/(2L) Closed...

Homework Statement (C2H4NO6, EGDN) is an explosive with perfect attributes. We fill 20% of a sealed container with an EGDN. Assume that EGDN explodes and the created gas bahaves according to ideal gas law. What is the excess pressure in the sealed container? My problem: I don't know where to...

Hi everyone, I'm doing a simulation and need some help. A capillary which is closed on both ends with the length l (x=0 to x=l), with a radius R and the volume pi*R^2*l is dropped on a parachut at the time t=0 from a hight h above ground. At t=0 the pressure inside the capillary is p_i0 (this...

Is a coffee cup usually considered to be a closed system? Why or why not? Does it matter that steam or hot coffee may be evaporating? (I think the steam is usually considered to be an insignificant amount of matter, allowing classification to be a closed system, but am unsure.) Is a bomb...

what is definition of closed packing?a close packing plane is a plane that the atoms cannot be packed any closer?

Homework Statement A pipe resonates at successive frequencies of 540 Hz, 450 Hz, and 350Hz. Is this an open or a closed pipe? Homework Equations -- The Attempt at a Solution My assumption is that because the harmonics of an open pipe are odd number multiples of the fundamental frequency (1f...

Vapor pressure possible only in closed system? b.p is when vapor pressure become equal to atmospheric pressure in which system closed or open ?

Homework Statement does it mean only one side of the pipe is open or both sides are closed. Homework EquationsThe Attempt at a Solution i think it means only one side is open, but i just need to make sure

Homework Statement Now consider a 2-torus ## S_1 × S_1## and a coordinate patch with coordinates ## (\alpha_1, \alpha_2)## such that ## 0 < \alpha_i < 2 \pi##. Let us introduce in this patch a 1-form of the type: $$\omega = (A + B\alpha_2 + C sin(\alpha_2 ) + D cos(2\alpha_1 + \alpha_2...

Why Mobius strip closed?Mobius strip is compact because it is confined and closed. But I can't understand closed of Mobius strip. Help please.

Homework Statement Find a closed form expression for the function f(x) which the power series Σn=0..∞ n(-1)nxn+1 converges to and determine the values of x for which f(x) equals the given power series. Homework Equations N/A The Attempt at a Solution I'm actually not sure how to start. First...

Is there a way to determine the profile of the field around a charged closed loop - particularly on the direction normal to the plane of the loop, both front and back? For generic values of V, I, B, H, etc., and any dimensions of the loop, any particular formulae possible to obtain? Thank you...

Does the forum have built in LaTeX for multiple closed integrals? I know that ##\oint## is for a single contour integral. I would've expected things like \oiint and \oiiint to work for surface and volume integrals.

Hi all, I'm new here, and I hope I'm doing this right. I mean posting where I should. Feel free to let me know. ;-) First, I'm a biologist but I'm a scientist and I'm interested in magnets recently. I read that magnetic field attract oxygen liquid (all over you tube) and also gaseous since...

I have a multivariable function, z = f(x, y, w), represented by a surface plot in 3D (z versus xy) for each value of w. As w varies, the function z varies (goes up and down and changes shape) over a given rectangular xy region. As z varies with w, contour lines with given constant values of z...

Hi all, I'm wondering if anyone knows of a way to obtain elasticity properties (Ex, Ey, Ez, Gxy, Gxz, Gyz, vxy, vxz, vyz) from the terms of a 6x6 anisotropic stiffness or compliance matrix. I'm looking for a closed form solution, preferably. I would think that there should be a closed form...

Okay, I have a simple plant which is 1/s*(s+1) Two poles on 0 and -1 and no zeros. This is the case for open loop. But when I close the loop with unity feedback and add a K gain, I end up with following transfer function; K/s^2 + s + K So, clearly the poles are now at somewhere else. However...

What is a closed chain (or circuit) that is used in solving a transportation problem (a special type of linear programming problem)? I'm having some problems with it. Please clarify it. I read its definition in a book, but it was not clear. I searched the net, but I failed in finding a...

Let \text{ } H \text{ }be \text{ }a \text{ } Hilbert \text{ } space, \text{ }K \text{ }be \text{ }a \text{ }closed\text{ }convex\text{ }subset \text{ } of \text{ }H \text{ }and \text{ }x_{0}\in K. \text{ }Then \\N_{K}(x_{0}) =\{y\in K:\langle y,x-x_{0}\rangle \leq 0,\forall x\in K\} .\text{...

Hey! :o I am looking at the proof of the theorem that for any rectangle the outer measure is equal to the volume. At the beginning of the proof there is the following sentence: It is enough to look at the case where the rectangle R is closed and bounded. Why does it stand?? (Wondering) Is...

Hi, let ## \alpha, \gamma ## be non-isotopic curves in a compact, oriented surface S. There is a result to the effect that ## S-\alpha## is homeo. to ## S- \gamma ## . This is not true as stated; we can , e.g., remove a disk (trivial class) in a copy of S and then remove a meridian ( a...

I'm relearning basic electricity concepts and I can't find an answer to a situation I've thought up. Imagine a cube with no enclosed charge and an electric field through it parallel to two of its faces. Guass's law says that the flux should be zero because there is no enclosed charge. Every...

I'm relearning basic electricity concepts and I can't find an answer to a situation I've thought up. Imagine a cube with no enclosed charge and an electric field through it parallel to two of its faces. Guass's law says that the flux should be zero because there is no enclosed charge. Every...

This isn't quite a calculus question, but it didn't seem right for any of the other mathematics forums, either. Does anybody if there is a closed form for the following infinite series: \sum_n x^{n^2} for 0 < x < 1

Hi, I am a bit confused about the terminology used for the boundary conditions describing open and closed strings. For the open string, Ramond case: \psi^+(\sigma = \pi, t) = \psi^-(\sigma = \pi, t) Neveu-Schwarz case: \psi^+(\sigma = \pi, t) = -\psi^-(\sigma = \pi, t) Question 1: Is it...

Hi All, One gets homological/topological information (DeRham cohomology ) from a manifold by forming the algebraic quotients H^Dr (n):= (Closed n-Forms)/(Exact n- Forms) Why do we care only about closed forms ? I imagine we can use DeRham's theorem that gives us a specific...

Homework Statement A 60 kg person is exercising in the gym, doing external work at a rate of 200W. If they have an efficiency of 20%, calculate the rate of temperature increase of their body if none of this heat was able to be transferred to their surrounds. (a) 828 ◦C per hour. (b) 13.8 ◦C...

I've been starting to look at the Hilbert action derivation of Einstein's equations, and have an introductory question. When the Lagrangian is excpanded into three integrals (for variation of metric determinant, metric and Ricci Tensor), the Ricci term is always dropped after a discussion of...

Hi, I am a little confused with the phase change that occurs in closed end wind instruments. According to http://newt.phys.unsw.edu.au/jw/flutes.v.clarinets.html, the phase does not change when the sound wave reflects off the closed end of the instrument. I thought that the phase changes by 180...

My question relates to entropy generation in a closed system ΔS=dQrev/T for a reversible process ΔS=dQ/T + Sgen for an irreversible process This seems to suggest that Sgen arises because of the irreversibility of the heat transfer process (eg across a finite temperature difference). If...

I was going through "Engineering Thermodynamics" by Cengel & Boles studying exergy analysis of a closed(non flow) system.Referring to the attachment as you can see the equation, δWHE=δQ(1-T0/T)=δQ-T0/T.δQ should give δQ=δWHE+T0dS (using dS=δQ/T) but in the textbook...

If you take two arbitrary numbers from a set N - let's say N stands for the natural numbers - and add them together, the sum will always be an element of N. In my language, there is a word for this, but i don't know what it is in english? If i translate it from norwegian, it would be something...

Hello, i'm working through Lang's 'Introduction To Linear Algebra' and am on page 18 (in case any of you are familiar with it). He says that the set of points X, such that ||X - P|| < a where P is a point in the plane and a is a number > 0 is an open disc. He then goes on to say that ||X -...

Definition/Summary In mathematical physics, a closed timelike curve (CTC) is a worldline in a Lorentzian manifold, of a material particle in spacetime that is "closed," returning to its starting point. 'Inside the inner horizon (of a charged/rotating black hole) there is a toroidal region...