Zero Definition and 1000 Threads

Quick question on eigenvectors; Are there any general properties of a matrix that guarantee that a zero will or will not appear as an element in an eigenvector? Thank you!

Homework Statement what is the limit of (4x^2-1)/(4x^2) when x→0 Homework Equations In order to find the Indicial Equation, do I need to take the limit of p(x) and q(x), the non-constant coefficients? If so, can the limit of this function be found using LH Rule? The Attempt at a...

Homework Statement Determine the point (other than infinity at which the electric field is zero. There is a diagram that has 2 charged particles along the x-axis separated by a distance of 1.00m. The charged particle on the right is -2.50μC and the charged particle on the left is...

Homework Statement A metal ball with pressure gauge at room temperature and standard pressure is immersed into three different liquids each with different temperatures in succession (the three liquids are alcohol in dry ice, boiling water, and freezing water), and then is immersed into these...

Homework Statement The question is: Let ##\pi=\left \{ x\in\mathbb{R}^n\;|\;x=(x_1,...,x_{n-1}, 0) \right \}##. Prove that if ##E\subset\pi## is a closed Jordan domain, and ##f:E\rightarrow\mathbb{R}## is Riemann integrable, then ##\int_{E}f(x)dV=0##. Homework Equations n/a...

Homework Statement Show that for plane waves, the following result holds: \oint \textbf{S}\cdot d \ell = 0. Homework Equations -- The Attempt at a Solution \oint \textbf{S}\cdot d \ell = \frac{1}{\mu_{0}}\oint (\textbf{E} \times \textbf{B})\cdot d \ell Now do I just use...

The question is:Let $\pi=\left \{ x\in\mathbb{R}^n\;|\;x=(x_1,...,x_{n-1}, 0) \right \}$. Prove that if $E\subset\pi$ is a closed Jordan domain, and $f:E\rightarrow\mathbb{R}$ is Riemann integrable, then $\int_{E}f(x)dV=0$.(How to relate the condition it's Riemann integrable to the value is $0$...

Hi all, I've a square force sensitive resistor with a resistance larger than 1MΩ when no pressure is applied. When I apply pressure with my hand, the resistance drops to about 480kΩ I'd like to know if there is a way to make the resistance drop to almost 0Ω when any pressure is applied and...

This is a question about the proper form for thermal noise from a resistor. This is purely academic for me - I always work in the regime where \hbar \omega << k T so the noise spectrum is simply P \approx kT. When this no longer holds, quantum effects matter of course. Then I have seen...

Hello! I have a problem with one proof. The task is: Suppose that X is linear space, x belongs to X and λ is real number. Proof if λx=0 so λ=0 or x=0. And there are conditions. Can use only this properties μ also is real number: I tryed to prove that but completely fails. Let λ=0...

Hi I’m having a problem with a concept, well actually with a force. After watching a program about sending man to the other end of the galaxy in which a huge tube was created in where people lived and gravity was simulated by spinning it and producing Centripetal force. My problem is that I...

I'm trying to understand when a vector field is equal to the curl of a vector potential. Why is it possible that there is always a vector potential with zero divergence? Relevent Equation: B=∇χA I'm trying to understand the proof that the above vector potential A can be one with zero divergence.

Homework Statement Does the sequence \frac{1}{n}+\frac{1}{n}i converge to zero with respect to the metric d(z,w) = |z|+|w|. The Attempt at a Solution So I realize I want √(\frac{1}{n}2+\frac{1}{n}2)=\frac{√2}{n} to be less than ε. So for all n greater than \frac{√2}{ε} the order...

Find [FONT=MathJax_Math]$$x$$ such that trigonometric $$\dfrac{\sin (3x) \cos (60^{\circ}-x)+1}{\sin (60^{\circ}-7x)-\cos (30^{\circ}+x)+m}=0$$ where $$m$$ is a fixed real number. Hi all, I know the expression in the numerator has no real roots by checking it at W|A (plot the graph of...

The problem states: "In what direction is the directional derivative of f(x,y) = \frac{x^2 - y^2}{x^2 + y^2} at (1,1) equal to zero?" I know that ##D_uf = \nabla{f}\cdot{{\bf{u}}}##. I believe the problem simply is asking for me to determine what vector ##{\bf{u}}## will yield zero. Thus...

From the POV of light it shouldn't be moving at all as the closer you get to c the shorter the distance in the axis of direction. As light is at c there is no distance. But then there is no axis of direction either. And light neither moved nor took any "time" to move or not move because time has...

At absolute zero, I understand that atoms have a minimum vibration (the atoms are not completely still). Because of this minimal vibration, He atoms can not freeze at absolute zero. But if enough pressure is applied, the liquid then becomes a solid. Does the pressure eliminate or reduce the...

Hi I know that BCS theory predicts Cooper pairs which move as a Bose condensate in superconductors. But why would scattering lead to a zero resisitance state because surely the Cpairs would provide resistance. I realize that superconductors have zero resistance but just can't really seee why?

The "Integral of Zero Problem" I know that this seems like such a trivial problem, but take a look at this: \frac{df}{dx} = 0, f(x) = \int{0}dx, f(x) = 0\int{}dx, f(x) = 0(x + C), f(x) = 0x + 0C, f(x) = 0, where any general constant multiplied by zero simplifies...

Homework Statement The problem asks us to find deceleration from 60km/h to 0km/h in 1,2 seconds.Homework Equations The speed formulasThe Attempt at a Solution I know how to apply the formula. However, in the problem, it is written 0km/h. How many significant digits is that? How many significant...

I have the equations to determine the rise time, peak time, percent overshoot, and settling time for a generic second-order system with no zeros in the system. Given a unit step input for the open-loop transfer function G(s)=(s+1)/(s2+2s+1) how do I analytically determine the performance...

I have the equations to determine the rise time, peak time, percent overshoot, and settling time for a generic second-order system with no zeros in the system. Given a unit step input for the open-loop transfer function G(s)=(s+1)/(s2+2s+1) how do I analytically determine the performance...

Homework Statement We have the Einstein tensor G_{αβ} = R_{αβ} - \frac{1}{2}g_{αβ}R where R_{\alpha \beta}, R are the Ricci tensor and scalar. Homework Equations We want the metric to be small perturbation of the flat space, so g_{\alpha \beta} = \eta_{\alpha \beta} + h_{\alpha...

Homework Statement if this statement is true: \int_0^\infty f(x) dx= 0 then is this true? f(x) = 0 in domain x\in [0,\infty) Homework Equations -NA- The Attempt at a Solution Hmm.. I can't come out with a formula that refute that. I would think of an odd function that changes...

Homework Statement If the only eigenvalue is zero, can you ever get a set of n linearly independent vectors? Homework Equations The Attempt at a Solution

http://en.wikipedia.org/wiki/Zero-energy_universe The idea relies on negative gravitational energy, but isn't gravitational energy simply negative from convention? http://en.wikipedia.org/wiki/Potential_energy#Why_choose_a_convention_where_gravitational_energy_is_negative.3F

I'm trying to build a simple circuit to detect when a lamp (tail light) is burned out, and light an LED in the dash. I think I can use a couple op amps but not sure how. My plan was to connect non-inv input to the (-) lead of the lamp socket and the other input to chassis ground. But I...

Sometimes we set potential to equal zero at infinity, other times at the origin. What's the general rule of thumb here-how do I know which to choose when doing a problem?

Homework Statement I am looking for the base, collector, and emitter voltages in the following circuit: Homework Equations KCL KVL offset voltage = VB - VE saturation voltage = VC - VE The Attempt at a Solution First I made a matrix without assuming any values for offset or...

Homework Statement For all non zero natural numbers n prove that: 1- 24\mid n(n+1)(n+2)(n+3)(n+4) and that : 2- 120\mid n(n+1)(n+2)(n+3)(n+4)(n+5) The Attempt at a Solution 1- For n=1 we get that 24 divides 120 so we assume that 24 divides n(n+1)(n+2)(n+3)(n+4) and we...

[b]1. Let a != 0 and b be elements of the integers mod n. If the equation ax=b has no solution in Zn then a is a zero divisor in Zn The Attempt at a Solution Not sure where to start on this proof, I keep trying to find something using the properties of modular arithmetic but am coming up empty

Homework Statement Consider the ring Z/mZ, show that S = {[0], [a], [2a], · · · , [m − a]} forms a (possibly nonunitary) subring of Z/mZ when a divides m. (i.e. show that (S,+, ·) is closed the usual addition and multiplication. (We are not require to find a multiplicative identity)...

What is the empiric reason behind the assumption that there is lowest thermodynamic temperature (absolute zero)? And that all other temperatures of bodies in thermodynamic equilibrium are always higher ? I am looking for a reason not using the entropy concept, as the entropy was derived...

Homework Statement Let f_k\rightarrow f in L^2(\Omega) where |\Omega| is finite. If \int_{\Omega}{f_k(x)}dx=0 for all k=1,2,3,\ldots, then \int_{\Omega}{f(x)}dx=0. Homework Equations The Attempt at a Solution I started by playing around with Holder's inequality and constructing...

Homework Statement Find positions on the x-axis for the charges Q1 = -1 C and Q2 = +3 C so that the electric field is zero at x = 0. Homework Equations F=Eq where E=kq/r^2 The Attempt at a Solution I put q1 and q2 1 meter apart and then found where a third charge would go so the...

Hi, is there a median number between zero and one? There are countless numbers between zero and one - an infinite set. If we pick any number at random (say 0.2) then could we always say it is the median as there is an infinite set of numbers on either side? What if I pick another...

For a certain problem I have non-zero electrical field E, non-zero electric flux density D, and non-zero volumic charge density ρV. When I integrate pV dV over the given region, I get 0. How is this possible?

I'm looking for the deeper meaning behind this law/theorem/statement (I don't know what it is, please correct me). My textbook just told us a matrix is not invertible if the determinant is zero.

What would happen to things on Earth if transported to the moon? For instance, say that a house, with furniture and fixtures in place, were dropped gently onto the moon's surface? How about food - meat, vegetables, fruit? Would things crack? Or would they survive the experience so that if...

I have a larger problem involving divergences and curls, but the correct answer requires ∇°B (divergence of B) = 0. I understand the proof of this in Griffiths, but the definition of divergence in cylindrical coordinates is: After using the product rule to split the first term, we get the...

An infinitely long "mass-spring transmission line", consisting of masses (m) connected by springs (spring constant s) obeys the following dispersion relation: ω = \sqrt{4s/m} sin(kd/2). The group velocity is dω/dk = d/2 \sqrt{4s/m} cos(kd/2). What does zero group velocity "mean" for...

New to cosmology and somewhat confused. I get all the ideas indvidually, that inflation is the exponential growth in the beginning of the universe, than that gravity and matter cancel each other out to make the zero energy universe, and that a flat universe is the only one that is zero energy...

hi guys, is it possible for electron to have zero K.E in a confined region in space? My guessed is, due to the wave nature of electron, if electron were to possesses zero KE, its wavelength will have to approach infinity since p = h / wavelength. therefore its not possible for electron to have...

Hi, I am designing a device which has cameras need to see through a sheet of glass at angle very low, near zero. And at that angle most of light is reflected so it is very hard to see. - The surface of the transparent material must be flat and smooth - The camera must see outside object...

I am trying to prove if f and g are Riemann integrable, then fg is also Riemann integrable using Lebesgue's integrability criterion. I already proved that a Riemann integrable function is bounded. Not much harder to show fg is too bounded. How do I show that [a,b] is of measure zero? I can't...

https://www.khanacademy.org/science/physics/work-and-energy/work-and-energy-tutorial/v/work-and-energy--part-2 I was watching a video at Khan Academy on Work & Energy (link above). At 2:50, he describes a situation with an elevator doing work against gravity. My question is pretty simple: If...

Suppose F(x,y,z) = 0 grad (F) = 0 ? e.g. F = x + y + z grad (F) = <1,1,1> =/= <0,0,0> ?? I don't know why I get an opposite result

Ok, so I know that the laws of physics say reaching absolute zero temperature is impossible, but suppose we took a box that was perfectly insulated in completely empy space, and I took all the particles out of it to create a vacuum. Now, since there are no particles in the box, then wouldn't...

Homework Statement The diagram shows two charges, +4 μC and –16 μC, 120 mm apart. What is the distance from the +4 μC charge to the point between the two charges where the resultant electric potential is zero? A 24mm B 40mm C 80mm D 96mm Homework Equations potential equation...

Homework Statement Which one of the following statements about electric field strength and electric potential is incorrect? A Electric potential is a scalar quantity. B Electric field strength is a vector quantity. C Electric potential is zero whenever the electric field strength is zero. D...