Zero Definition and 1000 Threads

Hi, I am reading a paper, and at some point the authors claim that: \sum_{m=1}^{L+1}\frac{\prod_{\substack{l=1\\l\neq m}}^{L+1}\frac{\lambda(m)}{\lambda(m)-\lambda(l)}}{\lambda^r(m)}=0 the question is HOW? Any tiny hint will be highly appreciated. Thanks

Homework Statement A point charge q = -8 µC is surrounded by two thick, conducting spherical shells of inner and outer radii a1 = 0.2 m, a2 = 0.3 m, a3 = 0.8 m, and a4 = 0.9 m respectively. The inner shell is uncharged; the outer shell has a net charge Q = -8 µC. At this point in the...

Homework Statement Prove that a set consisting of a single point is measurable and has zero area. Homework Equations Area Axioms: M is a class of measurable sets. (a) Every rectangle R \in M . If the edges of R have lengths h and k, then the area a(R) = hk . Additionally, a...

Homework Statement Why is the electric field, in static equilibrium, equal to zero. The Attempt at a Solution The only way I can see why is to picture that there was an electric field inside a conductor. The field would cause the electrons to move freely inside the conductor. This...

I was reading in George Gamow's book and he talks about drawing a one-to-one correspondence between the natural numbers and their squares and how these sets have the same size. But could I take each natural number to \aleph_{0} like 1^{\aleph_0}, 2^{\aleph_0} and draw a one-to-one...

According to Gauss, a closed conducting body will distribute the charge to the surface. Since the human body is a conductor does that mean the electric field in our body is zero? :cool:

Homework Statement Two tiny objects with equal charges of 65.0 µC are placed at two corners of a square with sides of 0.335 m, as shown. How far above and to the left of the corner of the square labeled A would you place a third small object with the same charge so that the electric field is...

Please teach me this: Why in general speaking the mass of gauge boson particle is zero(except W,Z bosons)?Because if we consider the self-energy of the bosons,we might think of the mass of gauge bosons. Thank you very much for your kind helping.

Let f(z) be analytic with a zero of order k ... Homework Statement Let f(z) be analytic with a zero of order k at z0. Show that f '(z) has a zero of order k-1 at z0. Homework Equations f(z) has a zero of order k at z0 if Ʃcn(z-z0)n (here n goes from k to ∞, and k ≠ 0) The...

Speed of light becomes Infinity and Zero! Hi Guys, I am just new to SR & GR. I learned about Lorentz contraction and time dilation, but they don't make sense when i consider the following situation... Your(Moving non inertial frame) Time runs slow relative to a stationary observer when your...

Hello, Given the hamiltonian : H = -( aS_z^2 + b(S_+^2 +S_-^2) ) with S=1 and a,b>0 are constants. working with the base: { |m=1> , |m=-1> , |m=0> } The matrix form of H is: H = \left( \begin{array}{ccc} -ah^2 & -bh^2 & 0 \\ -bh^2 & -ah^2 & 0 \\ 0 & 0 & 0 \end{array}...

This question seems to befall everyone at one point or another. So much so I begin to get deliberately silly when it is asked http://www.wolframalpha.com/input/?i=Abs%5B1%2F0%5D Anyway, I'm wondering if there is a sticky present on these forums that addresses it specifically. Something...

I'm a novice at MATLAB so I apologize if this is a dumb question: I need to find the sum of A, B and C given X, Y and Z, where ln(A)=X, ln(B)=Y etc. However, the values A, B and C are so small that when I try to use 'exp' the result is rounded to zero. This is a problem because later in my code...

Please explain -- total electic field Ec + En within the coils must be zero Hi This is from the text University Physics. In pg. 1035, chap 10, in order to justify the use of Kirchoff's rule to analyze circuits containing inductors it is written : Let's assume we are dealing with an inductor...

Homework Statement When a body is weighed on an ordinary balance we demand that arm should be horizontal if the weights on two pans are equal. Suppose equal weights are put on two pans, the arm is kept at an angle with the horizontal and released. Is the torque of the two weights about the...

∫f(x).dx from a(lower limit) to a(upper limit) =0 Is this always true

Lets say if we have an induction motor or any motor whose rotating shaft acts as a source of alternating emf to another motor and rotating shaft of this motor again acts as a source of alternating emf to third motor and so on... We connect such a finite number of motors and we call it as a...

Hi, I'd like to know the solutions for these equations, and how to arrive at them. Is it possible to derive the general form of F(x,y,z) analytically? I'm still studying linear differential equations so I have no clue on what to do with partial differential equations... div F = 0 curl F = 0...

How would you analytically prove that: \displaystyle{\lim_{m\rightarrow ∞}} (\frac{1}{m}\sum^{n=1}_{m}\frac{1}{n})= 0 ? The way I did it, I just proved that the greatest lower bound of \frac{1}{m} is 0, and so since the function is monotonically decreasing I proved that the limit of...

Why is the inner product of two orthogonal vectors always zero? For example, in the real vector space R^n, the inner product is defined as ||a|| * ||b|| * cos(theta), and if they are orthogonal, cos(theta) is zero. I can understand that, but how does this extend to any euclidean space?

Hello~ I’m sorry. I can’t English well. 1. Assuming that total energy of universe is zero. It looks more natural when an initial energy value of universe is 0. Therefore, negative energy is needed to offset positive energy of matters. E_T = 0 = ( + E) + ( - E) = 0 2. Mass-energy...

Homework Statement Two charges, q1 and q2, are separated by a distance r. Find the position at which a third charge, q3, can be placed so that the net electrostatic force on it is zero. Homework Equations Coulomb's Law: F = (kq1q2)/r122 * (r12hat) The Attempt at a Solution I was...

I've heard of something called Absolute Hot...the opposite of Absolute Zero (Absolute Cold). What happens at Absolute Hot?

I'm writing a paper for a philosophy elective on the Cosmological argument. One of my counter arguments is that a causal loop (treated as a paradox in the Cosmological argument in favor of a creator) is not a paradox if time is cyclic in nature rather than linear. I treat the fact that the...

I remember reading an old article about ZPE. Physicists claim that the ZPE found within a common light bulb has the potential to boil away the Earth's oceans. This got me to thinking of Star Wars and the super laser of the Death Star. It destroyed a whole planet! I know it was only a sci-fi...

Take for instance putting the large hadron collider in space at a near absolute zero where you never have to put energy into cool down the system. The LHC takes 10 GJ to run and the total energy of the two beams is 724 MJ. [1] Since the power to run the system never experiances resistence, would...

Homework Statement How long would a day have to be on Earth if there was zero net acceleration at the equator? Homework Equations Ac=v^2/r Vrotational=Ac / Radius of earth g = 9.8m/ss T = Earth's circumference / rotational velocity V= SQRT(Ac*R) Earth's Radius = 6.37x10^6 Earth's...

Homework Statement Show that the expectation value of angular momentum <Lx> is zero Homework Equations L±|l,m⟩ = SQRT(l(l+1)−m(m±1)h|l,m±1⟩ L± = Lx ± iLy The Attempt at a Solution I'm supposed to use ladder operators here to show <Lx> is zero. I start with...

Hi, not sure if this is the right forum.. pls move if not. Almost 30 years ago, I was studying engineering and my math tutor spoke about 0 (zero) being special. We talked about how nothing can be divided by zero, and sure enough, enter 1/0 into a calculator produces an error. (I vaguely recall...

Zero to infinity...can we assume same for universe ?? Hi, I am new to this forum, Basically I am not a scientist(not at all), like others in the forum, I belong to computer and Network field, However the science fantasies and attracts me very much just like others, ever since I was a kid , I...

We were presented with a task of calculating the temperature of absolute zero experimentally. To do this, we were given a capillary tube with one end sealed. Then we heated the tube up in a bunsen burner and quickly put the open end in some cooking oil. The oil was sucked up as the gas within...

Can someone help me intuitively understand why if a field has zero curl then it must be the gradient of a scalar potential? Thanks!

Homework Statement A rocket ejects exhaust with an velocity of u. The rate at which the exhaust mass is used (mass per unit time) is b. We assume that the rocket accelerates in a straight line starting initial mass (fuel plus the body and payload) be mi, and mf be its final mass, after all...

A harmonic function in a region is zero on an open portion of the boundary, and its normal derivative is also zero on the same part, and it is continuously differentiable on the boundary. I have to show that the function is zero everywhere, but I have no idea how. I have tried this for hours...

My memory on this is a bit foggy, but a couple of years ago one my math professors had a digression about a system of voting where no one would be able to know what anyone else voted. It involved the graph of a polynomial, and the kicker was that this system couldn't be implemented in society...

Homework Statement While studying a book "analysis on manifolds" by munkres, I see a definition of measure zero. That is, Let A be a subset of R^{n}. We say A has measure zero in R^{n} if for every ε>0, there is a covering Q_{1},Q_{2},... of A by countably many rectangles...

as we know that light consist packets of energy called photons And mass of a body when moving with the speed of light increases so, the mass of photon increases when it moves with light and when mass increases its energy is also increasing it means that when light travels it never stops and...

Individual Photons Are Zero Mass Particles. Is Zero Mass Defined By This? Is zero mass as we know declaired because photons are theorisized to be true "weightless" and massless, or could it be a case that we do not have sensitive enough instrements and limited in our detection? Or on the other...

does particles stop radiating or do particles have kinetic energy at absolute zero?

A = [0 0] [1 -3] (2 x 2 matrix, bad formatting) I need to find the eigenvector for lambda1 and lambda2. I figured out lambda1 = 0 and lambda2 = -3. For lambda1 the eigenvector works fine, but for lambda2 I get it as v = (0,0), which is not possible. Any ideas?

I made an animation to explain how cats can initiate rotation and turn around during free fall, without violating the conservation of angular momentum: https://www.youtube.com/watch?v=yGusK69XVlk Some footage of real cats: https://www.youtube.com/watch?v=Ua4Gh_4XdwQ...

The kinds of experiments involving animals in space have only answered simple questions of survivability in captivity where human assistance is at hand. The big problems of space colonization have yet to be answered. I thought up this question when someone on this forum posted a response to my...

Let δ(x)=∞ at x = 0, and zero elsewhere. Then δ(x)(1-exp(x)) = ? It seems the above expression is zero. But isn't it zero times infinity at x = 0?

Homework Statement Given F1= 36N[25degrees N of E] and F2= 42N [15 degrees E of S], determine the force F3 that must be added to the sum of F1+F2 to produce a net force of zero. Homework Equations Sine law, a/sina= b/sinb Cosine law: c^2= a^2 + b^2- 2(a)(b) Cos(theta) The Attempt...

how potential energy of electric dipole perpendicular to electric field is zero in this situation the torque is maximum so how P.E. can be zero please help

With the last year or so I came across a great discussion in these forums about the different types of infinity. It had never occurred to me there would necessarily be different types with different "values". How about zero? Are there different mathematical concepts regarding it or are all...

Hello! If you do a plot in Mathematica, for example Plot[Sin[x], {x, -, 2 Pi}] it won't put zero near origin of coordinates. So how can do it ? I tryed actually AxesOrigin or smth like that, but it didn't help me. Thanks!

Not a homework question - Just wondering. What is the real meaning of non-zero velocity compared to non-zero acceleration like i don't really understand the difference. Anyone care to explain?

why do we call a zero watts bulb as it so?? a zero watts bulb is common in houses,commonly called as 'night lamp'.., if v say it as zero watts lamp., then is it conducts zero current or zero voltage? what is the power consumption by modern led lamps and by other fluorescent lamps??

Homework Statement Prove that \Sigma^{n}_{k=1} wk = 0 and there has to be at least two phasors/exponentials Homework Equations complex analysis The Attempt at a Solution I tried writing out the sigma on the first line. Then I tried writing the same thing with n+1 on the...