Zero Definition and 1000 Threads

Homework Statement A long, thin wire carrying constant current I1 = 2 A into the page is surrounded by a concentric cylindrical hollow wire of inner radius a = 0.12 m, and outer radius b= 0.26 m, carrying total current I2 = 4 A directed out of the page, as shown. Assume the current in the...

Good day, Homework Statement I want to make a measurement on qubit by using formula von Neumann entropy using Mathematica given as below; Homework Equations (ρ)=−Tr(ρlog2ρ) The Attempt at a Solution The ρ={{0.5,0},{0,0.5}}My problem is, when I make the log2{{0.5,0},{0,0.5}} I get the...

Homework Statement Homework Equations Kirchhoff's laws and I = V/R The Attempt at a Solution I asked a question recently about a Kirchhoff's law problem and I received a lot of great help and I feel I better understand it. Or so I thought. This is my attempt at the problem. I don't...

Hello. Here, I'm asking why total orbital quantum number l and total magnetic quantum number m are zero for closed subshell in atom. Let me review the addition of angular momentum first: Each electron has its own orbital quantum number li and magnetic quantum number mi. Then for two electrons...

Homework Statement Find \int_{0}^{\infty} \frac{\cos(\pi x)}{1-4x^2} dx Homework Equations The residue theorem The Attempt at a Solution The residue of this function at $$x=\pm\frac{1}{2}$$ is zero. Therefore shouldn't the integral be zero, if you take a closed path as a hemisphere in the...

if y=1/x² show that y d²y/dx² +(dy/dx)² -10y³=0 i can work out y′=-2x^-3 and y″=6x^-4 but when i sub these in i can't make the whole expression equal zero

Question: The equation kx2+kx+3-k = 0, where k is a constant, has no real roots a) Show that 5k2-12k < 0 b) Find the set of possible values of k Solution attempted: a) For no real roots, b2-4ac < 0 a = k b = k c = 3 - k k2 - 4k(3 - k) < 0 k2 -12k + 4k2 < 0 5k2 - 12k < 0 Hence shown b) 5k2...

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I came up with a doubt regarding isochoric irreversible processes. Is it always true that, for any isochoric process, reversible or not, the work exchanged by the system is zero and the heat exchanged is ##Q=\Delta U##? I'm asking this because, in a exercise on thermodynamics trasformations of...

I googled a bit about this and managed to find this http://arxiv.org/abs/quant-ph/0505056 http://physics.bu.edu/~mohanty/physica-decoherence.pdf Since I can't make much out of them, maybe except this interesting phrase in the first one "First of all it is intriguing that even at absolute zero...

Homework Statement Consider having a battery, its voltage let's say 20 volts. If you connect this battery to a wire. Its resistance is zero. If you precisely measure the voltage at the end of the wire, Would it equal 20 volts or no? Homework Equations dV = I R The Attempt at a Solution Well...

Formula for Electrostatic Potential due to a point charge is V=1/4π∈ Q1 Q2/r This implies that at r=0 value of the potential should be infinity. Is it True. If that is the case then how we say the terminals of a battery having positive and negative charge are having definite value of...

Homework Statement Hi there, I'm happy with the proof that any odd ordered matrix's determinant is equal to zero. However, I am failing to see how it can be done specifically for a 3x3 matrix using only row and column interchanging. Homework Equations I have attached the determinant as an...

Dear all, I'm trying to think about applying the second law of thermodynamics to a system which is not isolated, but has an energy flowing inwards and an equal (!) energy flowing outwards, such that the total energy does not change (total energy flux is zero). Can we still apply the second law...

Does anyone know if there is any internationally agreed method for determining where zero degrees longitude is when mapping other planets etc.?

Is there a notation for the opposite of epsilon (infinitesimal) in the way that infinity is the opposite of zero?

Is this an abuse of Rolle's theorem? Rolle's theorem If a real-valued function f is continuous on a proper closed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists at least one c in the open interval (a, b) such that f'(c) = 0. ##[x_1, x_1]##...

Homework Statement p(x) = x^3 − x^2 + ax + b is a real polynomial with 1 + i as a zero, find a and b and find all of the real zeros of p(x).The Attempt at a Solution [/B] 1-i is also a zero as it is the conjugate of 1+i so (x-(1+i))(x-(1-i))=x^2-2x+2 let X^3-x^2+ax+b=x^2-2x+2(ax+d)...

Hi! When dealing with a pn homojunction, it is easy to see the features it has at equilibrium, and also the features it has with forward/reverse bias. Plots show the constant Fermi level at equilibrium and the different Fermi levels for a forward bias; moreover, examples show how much the bands...

For example if we could bring a radioactive atom to absolute zero, would it still be subject to the random radioactive decay? Or would absolute zero inhibit the normal half-life decay of the element? Perhaps in other words, would absolute zero inhibit the elapsing of time?

Homework Statement \frac{d\vec{Y}}{dt} = \begin{bmatrix} 2 & 4 \\ 3 & 6 \end{bmatrix} \vec{Y} Find the eigenvalues and eigenvectors Homework EquationsThe Attempt at a Solution I found the eigenvectors to be \vec{v_1} = \begin{bmatrix} 2 \\ 1 \end{bmatrix} , \vec{v_2} = \begin{bmatrix} 2...

I used a function called ind2patch to make a big 3D block which contains a number of smaller blocks in 3 dimensions. Each small block has a value which the magnitude is represented by a color.One example is shown below: However, most of the boxes have very low or zero value and I don't need to...

Homework Statement .[/B] I am attempting to determine the group refractive index of a laser cavity at it's resonance frequency. Homework Equations .[/B] \begin{align*} \frac{2\omega n L}{c} &= 2m\pi \end{align*} \begin{align*} n_g &= n + \omega \frac{dn}{d\omega} \end{align*} 3. The attempt...

Homework Statement "design a band pass circuit having a midband gain of 20 dB with -3 dB frequencies at 20 Hz and 20 KHz the amplifier should not produce any phase shift." does midband gain strictly apply to voltage gain (because that's how i look at it)? I was going to use a common collector...

If I were to move a positive charge from infinity to a location between two positive charges where the net electric field is zero, the electric field would do zero work because there is no potential difference right? I am confused about why this is though. As you move the charge from infinity...

This is probably a very trivial question, but my brain isn't "playing ball" today so I'm hoping someone can help me with this. Suppose I have a system of ##N## mutually interacting particles, then the force on the ##i##-th particle due to the other ##N-1## particles is given by...

Homework Statement A person of weight w is in an upward-moving elevator when the cable suddenly breaks. What is the person's apparent weight immediately after the elevator starts to fall?

Homework Statement A billiard ball moving at 2 m/s collides (0 degrees) with another of the same weight and at rest, in a perfectly elastic collision. Demonstrate with equations why the balls trade velocities. Homework EquationsThe Attempt at a Solution In the provided explanation, I can...

Homework Statement [/B] Finding equation allowing to calculate time of zero-g (weightlessness) in a parabolic flight using non-powered glider (no thrust). Homework Equations [/B] I have found a few ways to calculate the time (here is one example which is basing on aircraft's velocity only -...

Good morning, How do we prove that the number zero is a negative or positive number?

Why absolute zero of temperature doesn't depend upon properties of substance?

I've searched around and all I can find are people quoting the equations. I see it in the math, but it seems contradictory. Here is my line of thought: 1. A source maintains a voltage difference across its terminals. 2. The difference in voltage causes charge to flow from higher to lower...

What if you were in a spaceship in outer space and had a sphere filled with water and some fish in it and then carefully removed the shell, leaving behind only a bubble of water. Would the water hold together and could the fish would swim outside the bubble and suffocate?

Homework Statement Using the Generating function for Legendre polynomials, show that: ##P_n(0)=\begin{cases}0 & n \ is \ odd\\\frac{(-1)^n (2n)!}{2^{2n} (n!)^2} & n \ is \ even\end{cases}## Homework Equations Generating function: ##(1-2xt+t^2)^{-1/2}=\displaystyle\sum\limits_{n=0}^\infty...

Came across this problem while reading and I can't understand what it wants. I've tried solving for units to get zero divisors but that doesn't work. It's not the end of the world if I can't figure it out, it's just bothering me because I'm confused. Here's the problem: Let $R$ and $S$ be...

I understand(or assume understand) that geodesic deviation describes how much parallel geodesics diverge/converge on manifolds while moving along these geodesic. But is not it a definition for intrinsic curvature? If it is same as Riemann curvature tensor in terms of describing curvature, why...

Not sure if the correct term is indefinite or undefined... I mean something like an infinite series that does not sum to a particular value, like this: X = 1 - 1 + 1 - 1 + 1 - 1 + 1... where pending the placement of parentheses one can infer multiple answers for X So, is it proper to say X...

Suppose ##T## is an operator in a finite dimensional complex vector space and it has a zero eigenvalue. If ##v## is the corresponding eigenvector, then $$ Tv=0v=0 $$ Does it mean then that ##\textrm{null }T## consists of all eigenvectors with the zero eigenvalue? What if ##T## does not have zero...

hi there, Why does we need to have a signal which always has the average amplitude of zero. i read some where that it would be inefficient for over transmission medium to carry a signal which have amplitude great than zero. Why?

Homework Statement Let F(ℝ) = {ƒ:ℝ->ℝ} define (f+g)(x) = f(x)+g(x) (f*g)(x) = f(x)*g(x) F(ℝ) is a commutative ring. ƒ_0(x) = 0 and ƒ_1(x) = 1 a) Describe all units and zero divisors b) Find a function f such that ƒ≠ƒ_0, ƒ≠ƒ_1, and ƒ^2 = ƒ Homework Equations A unit is an element r ∈ R, which...

Prove $$\frac{ab}{a+b+ab}+\frac{bc}{b+c+bc}+\frac{ca}{c+a+ca}\le \frac{a^2+b^2+c^2+6}{9}$$ for all positive real $a,\,b$ and $c$ and $a,\,b,\,c\ne 0$.

Homework Statement Lecturer says that: Generalized Coordinate: θ = q1 Generalized Force: Q1 = 0 I don't understand why Q1 equals to zero. Homework Equations Q_i = \sum_j \underline F_j \frac{\delta \underline r_j}{\delta q_i} The Attempt at a Solution First i need to find partial...

To show that the Lagrangian ##L## is invariant under a rotation of ##\theta##, it is common practice to show that it is invariant under a rotation of ##\delta\theta##, an infinitesimal angle, and then use the fact that a rotation of ##\theta## is a composite of many rotations of...

If I am sitting, not moving, my velocity can be zero along with my acceleration but in truth the Earth is moving along with the solar system and so on but i want to know theoretically if a massless object in space can have zero velocity and zero acceleration, in essence what i am askimg is can...

Homework Statement A well insulated container consists of two equal volumes separated by a partition - one half an ideal gas while the other is a vacuum. The partition is removed, and the gas expands. What is the entropy change per mole? Homework Equations dS = dQrev/T S/R = Cp/R dT/T -...

Hello Forum, It is said that astronauts on the International Space Station (ISS) experience microgravity and not complete zero gravity. The acceleration of gravity at the ISS altitude is still pretty significant (~8.7 m/s^2), far from zero. However the free fall motion of the ISS and its...

I'm confused about how this related to the roots of an equation. Here's the definition: We say that ##f## has a zero of order ##m## at ##z_0## if ##f^{(k)}(z_0)=0## for ##k=0,\dots , m-1##, but ##f^{(m)}(z_0)\ne 0## or equivalently that ##f(z) = \sum_{k=m}^\infty a_k(z-z_0)^k##, ##a_m \ne 0##...

when i have lim x->0 (x-sinx)/(sinx)^3 why can't I replace it with 1/(sinx)^2-1/(sinx)^2? thanks

$$\lim_{{x}\to{0}}\frac{\cos\left({3x}\right)-1}{{x}^{2}}$$ $$\frac{f'}{g'} =-\frac{3\sin\left({3x}\right)}{2x} =-\frac{9}{2}\cdot\frac{\sin\left({3x}\right)}{3x}$$ $x\to 0$ is $-\frac{9}{2}$ Just seeing if this is correct or better way to do it

Consider a common circuit with some resistors in series. The nodes should have approximately the same potential. I know that truthfully the wire just has small resistance compared to resistors. However, even though the gradient of potential is approximately zero in a node, the same current flows...