Closed Definition and 1000 Threads

Say we have two charges in a closed spherical universe, of radius R, a distance r apart. If the charges are close, r<<R, we might guess that the force would go as 1/r^2? Let the two charges move away from each other till they are as far apart as possible. At this point the force between...

Let X be a normed space, F be a closed linear subspace of X, Let z be in X, z is not in F. Let S={x+az:a is in the field Phi}=Span of F and z We show S is closed. I would define a function f : S--> Phi by f(x+az)=a and show that |f|< or equal to 1/d where d= distance(z,F) hence f is in...

Homework Statement Let S={A (element) M2(R) : det(A) = 0} (b) Give an explicit example illustrating that S is not closed under matrix addition.Homework Equations The Attempt at a Solution 1) I think that the problem is saying S is a set of 2x2 matrices, whose determinant is zero? 2) I'm...

Could you consider the gamma function to be a closed form representation? If I could express a numerical series in terms of the gamma function, would it be considered a closed form representation?

Taking from Euler's offering that: \Sigma1/n= ln(n) + \gamma could you say that there is a closed form of the harmonic series? Does Euler's offering qualify?

My question is one of vocabulary. What does it mean to evaluate an infinite series in closed form? If I have a Series: \Sigma 1/ (N2), as N goes from 1 to infinity. This is similar to a test question I'm working on so, I DO NOT want to know how to solve it, I just want to know exactly...

Homework Statement Hi :) This question is from a test i had today. For some stupid reason we get to finish it off tomorrow. I figured i do what everyone else will, and sort out the what i didn't understand. Luckily this was it. Anyway, the question is typed from memory so it may seem a bit odd...

So, it goes in the first loop, no problem. In the second loop, no problem either, it could just change the spin. So, what about the third, will the electron interfere with its own past? Will it be destroyed? Will it mysteriously scatter and not interfere with its past. This is the same for all...

Identifying three identical metal bars (with your eyes closed!) Homework Statement How would you determine, non-destructively, and with eyes closed, which is which amongst three identically-shaped metal bars known to consist of a permanent magnet, a piece of soft iron and a piece of copper...

I wonder if Universe with a positive curvature everywhere can be infinite. As an example I see a spring: you make a full rotation, but you don't get into the same place, but another place. Spring is 1-dimensional object (line) so curvature is not defined for it. But is it possible for the...

Homework Statement How can a metrix space be open and closed?

By definition, D(irichle)-branes are branes on which open strings end. Then how closed string theories IIA and IIB may contain D-branes? Or more precisely, why the branes appearing in closed string theories are still called D-branes?

Homework Statement Let A be a subset of Rn and let \vec{w} be a point in Rn. Show that A is open if and only if A + \vec{w} is open. Show that A is closed if and only if A + \vec{w} is closed. Homework Equations The translate of A by \vec{w} is defined by A + \vec{w} := {\vec{w} +...

Homework Statement Let I C R be an interval which is open and closed at the same time. Prove that I=R or I is the empty set. Homework Equations The Attempt at a Solution I'm looking more for a outline structure for the solution. I have made assumptions that I is not equal to R...

Homework Statement A closed, rigid tank contains 2kg of water initially at 80 degrees C and a quality of .6. Heat transfer occurs until the tank contains only saturated vapor at a higher pressure. Kinetic and potential energy effects are negligible. For the water as the system, determine...

Homework Statement Find the closed form of the following power series 1+3x+6x^2+10x^3+15x^4+21x^5+... Homework Equations 1+x+x^2+.. = 1/(1-x) The Attempt at a Solution I tried differentiating but couldn't get it to any expression that I know the sum for.. I was playing around...

Let LG be the base point preserving loops (it's a Hilbert manifold). So LG = { f : S^1 -> G s.t. f(0)=1 } where G is a connected, simply connected Lie group. LG is embedded into the (vector space) Hilbert space L^2[0, 2pi] given by f |--> g(t) = f '(t)f(t)^-1 Is LG a closed subset of...

Homework Statement For the following set, state and justify whether or not it is open or closed. Homework Equations A={z| I am z >1} The Attempt at a Solution I know the definition of an open set, but I am not sure how to use it to solve this question.

If the Universe stopped expansion 10 million years ago and started to collapse Whould it their be such a thing as cosmological blueshift? Would the scalefactor-redshift be R=1/(z - 1) or R=1/(1+z)? I think since universe is collapsing then spectra will be blueshifted! The scale...

I'll try to make this as concise as possible. I'm trying to get my head around how signals behave in coaxial cables. If you set up a circuit like this: Then the earthed end will force a node at that end, right? So you'll end up with your reflections having a phase shift of pi and looking...

Homework Statement For the following set state and justify: i) whether or not it is open? ii) whether or not it is closed? {z||z|<2} Homework Equations The Attempt at a Solution I really don't know where to start on this question, i don't understand this topic at...

Imagine processing the gas clockwise through Cycle 1 and then counterclockwise through Cycle 1. Compare these two processes on the basis of the heat energy transferred to the gas in the entire cycle. Choose the correct comparison symbol. Q_clockwise for Cycle 1 <,=,> Q_counterclockwise for...

What does it means by closed under addition For eg : As S is closed under addition S = {gn : n is a member of integers} could anyone elaborate more on this and gimme some example ? Does it mean that when something is closed under addition , we only consider addition and nothing else ?

I was reading about the Nested sphere theorem and a thought occurred. if you have a sequence of decreasing closed sets whose diameter goes to zero in the limit, we can show that the intersection of all these sets is a single point. my idea was to show this using nested sphere theorem if we...

Hi All, I need some basic info of He closed cycle cryos..(like working principle, etc).. I have a compressor, which compress He gas and passed into a cryo's coldhead. So He gas expands in side the coldhead and cools the coldhead..then it again passes into compressor..so the cycle repeats.. I...

Homework Statement which of the following has closed neutron shells? (the number in front should be a superscript) 36S, 50V, 50Ca, and there are more but i just want to understand why. Homework Equations The Attempt at a Solution i know the answers, i just don't know how to get...

1. A hydroponic garden uses the 10 m long perforated pipe system to deliver water at 20ºC. The pipe is 5cm in diameter and contains a circular hole every 20 cm. A pump delivers water at 75 kPa (gage) at the entrance, while the other end of the pipe is closed. pressure near the closed end of the...

Homework Statement The Lowest note on an organ is 16.4 Hz. a. What is the shortest pen organ that will resonate at this frequency b. What is the pitch of the same organ pipe is closed Homework Equations f=V(n)/2L, n=1,2,3.. f=V(n)/4L, n-1,3,5... The Attempt at a Solution I understand...

I'm not very good at topology but am reviewing it for the GRE Subject Test. Here's a question that I think I know, but would like to check with you guys. We define: Ek = B(0, k) - B(0, k-1), where B(0,k) is an open ball around the origin with diameter k. Now suppose that Tk is a subset of Ek...

It is said that every magnetic induction line is closed.but recently I happended to find one which isn't. Consider the magnetic field generated by a ring form circuit, the magnetic induction line which I have found is not closed is the one that go through the center of the circuit,which is...

I am trying to compare the fluid velocity given by the closed form solution and FEA analysis for fluid flowing through a channel that is 800u long and 100u wide. I am using the equation vmax= (gradP)*(radius)^2/(4*viscosity) I got 8.4cm/s in the former compared to ~10cm/s in the latter...

Homework Statement I want to show that if C and D and closed sets, then C \bigcup D is a closed set. Homework Equations A set is called closed iff the set contains all of its accumulation points. The Attempt at a Solution In order for me to prove this statement, I will be able...

Homework Statement a) Let U be a closed subset of the reals with an upper bound. You know that U has a supremum, say z. Prove that z is an element of U. b) Suppose U is a closed subset of the real numbers with an upper and lower bound. Prove that U has a maximum and minimum.The Attempt at a...

Consider a scenario of a sound wave inside a closed end and opened end tube. We always learn that the displacement amplitude at the closed end is always zero but at the opened end is always maximum. My friend can see it quite intuitively. For the closed end, we expect there is no...

Homework Statement Suppose f: [a,b] -> R and g: [a,b] -> R are both continuous. Let T = {x: f(x)=g(x)}. Prove that T is closed. Homework Equations If a function f: D -> R is continuous, then for each E > 0 there exists a delta >0 such that if |x-x0| < delta (for x, x0 in D) then...

Is the restriction that a field is divergence-free enough to ensure the field lines will be closed? How can one (dis-) prove such a statement?

Homework Statement An example of a function that is open but not closed, and an example of a function that is closed but not open. Homework Equations The function f is open (closed) if f[A] is open (closed) for each open (closed) set A in X. The Attempt at a Solution This is a...

Homework Statement http://img527.imageshack.us/img527/6049/48193240ao5.png I don't understand this proof. The first two lines are clear to me: the sequence xn is in F and F is closed so its complement is open so there is a ball with radius r around x in Fc. But I don't understand the last...

I recently was having a discussion about entropy and the concept of the universe being an open or closed system came up. Assuming that the universe is infinite, would it be considered to be an open or a closed system? A closed system being a system in the state of being isolated from the...

Homework Statement A well-insulated closed tank is of volume 70 m^3. Initially, it contains 25000 kg of water distributed between liquid and vapor phases at 30 deg C. Saturated steam at 11 bar is admitted to the tank until pressure reaches 7 bar. What mass of steam is added? Homework...

Hi this is my first post so please be nice :) 1. Homework Statement The problem has been set up that a circuit containing a resistor and switch is being driven by a power source of unkown potential. The switch is flick to short the power source leaving only the resistor in a closed loop...

A set S of (necessarily square) matrices is said to be closed under multiplication if AB∈ S whenever A, B ∈ S. Which of these matrices are closed under multiplication? Circulant matrices Upper triangular matrices Hessenberg matrices My trouble: How do I go about figuring this one out?

i was going over some relativity search online and came across what is called a closed timelike curve and that i actually allows time travel, am i right?

In classical mechanics (also in QM I guess), the fundamental laws of conservation (energy, momentum and angular momentum. tell me if I forget something) are valid only if the system is closed and the net external force is zero. WE define what the system is. We can include or exclude things...

Homework Statement Beaker A contains a volatile solvent and beaker B contains 10% solution of a non-volatile solute in the same solvent. Both beakers are placed in a closed environment as shown. The question asks what will happen when the system has reached equilibrium. The answer is given...

1. The problem: The function f is continuous for -3\leqc\leq5 and differentiable for -3<x<5. If f(-3)=6 and f(5)=-2, which of the following could be false? (a) there exists c, where -3\leqc\leq5, such that f(c)\geqf(x) for all on the closed interval -3\leqx\leq5. (b) There exists c, where...

im doing my project for school on this a need help.

Hi, I can't think / remeber how to write the following expresion in a closed form, the function is a summation of natural numbers between 1 and an upper limit "K", written as Sigma x with limits K and 1 effectivly, straightforward etc... what i want is the summation of all the...

Homework Statement a pipe in air at 20 degrees celsius ia to be designed to produce two succesive harmonics at 240Hz & 280Hz. how long must the pipe be, and is it open or closed? Homework Equations v=\lambdaf The Attempt at a Solution sorry, i could not do it. i totally can't...

I am new to this forum. I am an applications engineer. I design, build and program industrial automated control systems. I am currently working on a project for a lime calcining kiln. Our project involves an upgrade of the coal-fired kiln's fuel delivery system. This involves a coal grinding...