Condition Definition and 587 Threads

Homework Statement 8.02 × 10−1 moles of nitrogen gas ( γ= 1.40) is contained in a volume of 2.00 × 10−2 m3 at a pressure of 1.00 × 105 Pa and temperature of 300 K. The sample is adiabatically compressed to half its original volume. IT behaves as an ideal gas. (i) What is the change in...

In solving the Navier Stokes equation, the typical boundary condition imposed on the tangential velocity at a solid surface is that of no-slip. However, it is known that for gaseous flow there always exists a non-zero velocity near the wall, especially at relatively big Knudsen number. Is there...

Hi, I'm looking at the Jacobian condition which is ## J= a \frac{dy_{0}}{ds}-b\frac{dx_0}{ds}## where the pde takes the form ##c= a\frac{\partial u}{\partial x} + b \frac{\partial u}{\partial y} ##, where ##a=\frac{\partial x}{\partial \tau } ##, ##b=\frac{\partial y}{\partial \tau }##...

I'm reading "The variational principles of mechanics", written by C. Lanczos and he said that, if one have the condition dq_3 = B_1 dq_1 + B_2 dq_2 and one want to know if there is a finite relation between the q_i, on account the given condition, one must have the condition \frac{\partial...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am trying to understand Chapter 4, Section 4.2 on Noetherian and Artinian modules and need help with the definition of a noetherian module - in particular I need help with the nature of an ascending chain of submodule ...

Dear All, Please help me clear some doubts about Theorem 3.3.1 in the 1st attachment. The condition ## |a| = |b| ## has only 8 cases right? ## { x+iy. x - iy, -x + iy, -x - iy, y + ix, y - ix, -y + ix, -y - ix } ## so for the condition ## |a| = |b| ## and ## b \bar c = \bar a c...

Homework Statement A hot solid sphere of initial radius ##a## with a uniform initial temperature ##T_{0}## is allowed to cool under stagnant air at ambient temperature, ##T_{\infty}## . Assume the temperature within the sphere is uniform throughout the cooling process. Show that under...

Hello, I have two different discrepancies to this system: a) How and when is possible to have more solution of differential eq. or their system for same initial problem? For example this is happening in following system. It is written about this system: "Different value of constant \dot{M}=4\pi...

How did they derive equation (6)? I don't like how they say -Φm instead of Φm, but that aside, I get that both rays 1A and 2A' travel the same distance, but AC incurs a phase change due to total internal reflection (-Φm) and it travels AC from there. Meanwhile, A'C is the distance the other...

Hello, I have an extreme question :) Let's assume that here are Primordial Black Holes (PBH) in range 10^15 - 10^24 g for example. What would happen if some of them get into the some other object(Sun, Planet or compact object) and settle in the center (ideal case). I have computed radius of...

Hello, I would like to examine or learn something about accretion to Primordial Black Hole (PBH) captured by some compact object (sitting in the center). How is this happening? What is happening to material, "blob", which is falling to PBH? How much is squeezed? Can you somebody let me know...

Homework Statement [/B] One mole of 2-D ideal gas is confined in an isotropic cone potential: U = \lambda |r| where \lambda is a positive parameter and r is the displacement vector (2-dimensional) from the origin. The...

Hello I'm getting confused when I want to use magnetic boundary equation could you tell me how we define the unit vector(an) in this equation? for example you assume that we have two different region (A in red and B in yellow) which vector (1,2,3,4) is right for equation and which is right...

So say I have Pr(Z|X&Y) I'm guessing that it follows the standard Pr(A|B)=[Pr(B|A)Pr(A)]/Pr(B) So Pr(Z|X&Y)=[Pr(X&Y|Z)Pr(Z)]/Pr(X&Y)?Also, if X&Y are independent, then would I get Pr(X&Y|Z)=Pr(X|Z)Pr(Y|Z)?

Hey! :o I need some help at the following exercise: Show that the polynomial $f(x)=x^n+1 \in \mathbb{Q}[x]$ is irreducible if and only if $n=2^k$ for some integer $k \geq 0$. Could you give me some hints what I could do?? (Wondering)

I'm arguing with a friend regarding the condition for a table to flip over assuming that the right contact point of its right leg with the ground (denoted hereafter by O) is held fixed i.e. the table cannot slip. The upper horizontal plate is a sort of a rod with mass m and both legs are...

Homework Statement Take the action S = \int d^4x \frac{1}{2} \left( \partial_{\mu}\phi(x)\partial^{\mu}\phi(x) - m^2\phi^2(x) - g\phi(x)^p \right) , and consider the following transformations: x^{\mu} \rightarrow x^{'\mu} = \lambda x^{\mu} \phi(x) \rightarrow \phi^{'}(x) =...

Hello, Let's suppose we are given a function f:\mathbb{R}\rightarrow \mathbb{R}, and we assume its Fourier transform F=\mathcal{F}(f) exists and has compact support. What sufficient condition could we impose on f, in order to be sure that F is also bounded?

i only can integrate a k-form in a n-dimensional manifold, if k=n right?

P -> Q P Q P->Q T T T T F F F T T F F T I understand the condition "P is sufficient for Q". But I'm not getting the meaning of why "Q is necessary for P". What does this signifies, Please explain ..

Hello All, I'm currently testing a product for environmental test but i don't know what test do i conduct for this one. I would like to ask your help if which is more severe environment. 1. Damp Heat Test (85°C / 85% R.H) 2. Damp Heat Test (85°C / 95% R.H) 3. Water Immersion Test...

What is the full load condition of a transformer. Then in reference to the equation: Vp = aVs + Req*Ip + jXeq*Ip (the very common complex equation of a simple equivalent circuit ) Should I use Vs= 230 V or Vp = 2300 V in full load load condition or will the magnitude of the primary voltage be...

how can i find the sets from following situation. i have three numbers,{1 2 3} which will always be in this order {123}, i want to find out number of cases can be made. but 2 can come at frist position that is before 1 or at second position or at third position that is after 3. and all are...

The same thing as title.

Hello! (Wave) I am looking at the following exercise: Suppose that we have an algorithm,which cost is $f(n) \ \mu sec (10^{-6} sec)$. If $f(n)=n \log{n}$,to what should $n$ be equal,so that the cost is $10^6 \ \mu sec$? So,it must be: $$n \log{n}=10^6 \Rightarrow n^n=10^{10^6}$$ But how...

Hi, I am a research student in Theoretical Dark Matter Cosmology. I am currently working on the evolution of dark matter WIMP in the early universe. I am trying to understand how to derive the famous condition for dark matter decoupling,T = m/26. How do you get this condition from the...

Hello, i had studied the problem in 1D, but i thinking the problem in 2d, an i have the following question: in a potential -V between (-a,a) an 0 otherwise. One dimensional case: One of the boundary condition are : ##\phi_I \in (-a,a)##, and ##\phi_{II} \in (a,\infty)## ##...

Hi, all. I'll be brief. Can Airy functions [those who solve the differential equation y''-xy=0] be considered orthogonal over some interval? If so, what is their orthogonality condition? Given that the Airy functions have a representation in terms of Bessel functions, I would be inclined to...

Hey there, I have modeled a propagating wave in a 1D dispersive media, in which square and cubic nonlinear terms are present. u′′=au3+bu2+cu the propagating pulse starts to steepen with time which is the effect of nonlinearity, but there is an effect which I can't understand. so...

Homework Statement I was told that for an object to execute SHM, the x (distance displaced from the spring) can't be greater than e . Why is this so? i can't understand. can someone explain please? Homework Equations The Attempt at a Solution

I have a PDE of the following form: f_t(t,x,y) = k f + g(x,y) f_x(t,x,y) + h(x,y) f_y(t,x,y) + c f_{yy}(t,x,y) \\ \lim_{t\to s^+} f(t,x,y) = \delta (x-y) Here k and c are real numbers and g, h are (infinitely) smooth real-valued functions. I have been trying to learn how to do this...

Hi all, I found the following statement on a magazine page and cannot understand it. It is possibly very distant from the little maths I know, but made me very curious. It is therein said that if a number $$n$$ is a Fibonacci number, then one of the conditions $$ 5n^2 + 4$$ or $$5n^2-4$$ is...

I have two question one of them I have solved but a bit differently and the second is something I need more help with. First question I have solved previously but bit different and I am not too sure how it should be solved in part b given above. Here is my similar solution Can you comment...

For two positive real numbers $x$ and $y$ that satisfy the condition $x^3=x+1$ and $y^6=3x+y$, show that $x>y$.

Homework Statement IF A is nxn matrix, and k(A)=||A||||A^-1|| then a large k(A) means the solution has more significant digits than is k(A) were small true or false? Homework Equations The Attempt at a Solution Well k(A) is defined as 10^(k) right so the larger the condition...

Pl Help:Finding velocity using pythagorasTheorem and other velocities. \left[Homework Statement Three particles start moving simultaneously from a point on a horizontal smooth plane. First particle moves with speed ##v_1## towards east, second particle moves towards north with speed ##v_2##...

For an imperfect conductor, when there is current, an electric field is set up inside the wire along the direction of the current flow, and is parallel to the wire. If this is true, then what I don't understand is boundary condition tells me the tangential E-field is always continuous, if...

Homework Statement Find all the holomorphic functions ##f: \mathbb C \to \mathbb C## such that ##f'(0)=1## and for all ##x,y \in \mathbb R##, ##f(x+iy)=e^xf(iy)## I am completely stuck with this exercise, for the second condition, I know that...

Homework Statement Show that the stability condition for a circular orbit of radius a, i.e. f(a) + \frac{a}{3} (\frac{df}{dr})_{r=a} < 0 is equivalent to the condition \frac{d^2V(r)}{dr^2} > 0 for r=a where V(r) is the effective potential given by V(r) = U(r) +...

Homework Statement How to derive equation (22) on page 31 of Kittel's Intro to Solid State Physics 8th edition. The equation is: 2\vec{k}\cdot\vec{G}+G^2=0 Homework Equations The diffraction condition is given by \Delta\vec{k}=\vec{G} which from what I can surmise is the starting...

Homework Statement a small object is mounted to the perimeter of a hoop of radius r. The mass of the object and the hoop is the same. The hoop is placed into a fixed semi-cylinder shaped rough trough of radius R, such that the small mass is at the top. Find the least R/r ratio such that the...

Hi all, Generally boundary condition (Dirichlet and Neumann) are applied on the Load Vector, in FEM formulation. The equation i solved, is Generalized eigenvalue equation for Scalar Helmholtz equation in homogeneous wave guide with perfectly conducting wall ( Kψ =λMψ ), and found, doesn't...

Hello guys, suppose we have an eigenvalue problem \left\{ \begin{array}{ll} u'' + λu = 0, \quad x \in (0,\pi) \\ u(0)=0 \quad \\ \left( \int_0^\pi \! {(u^+)}^2 \, \mathrm{d}x \right)^{\frac{1}{2}} = \left( \int_0^\pi \! {(u^-)}^4 \, \mathrm{d}x \right)^\frac...

Homework Statement U= { (x1, x2, x3, x4) | x1 x3 ≥ -5 } The Attempt at a Solution Let x = (1,2,3,4) and y = (1,2,3,4) x+ y = (2,4,6,8) x1x3 = 2x6 = 12 12 >-5 so closure by addition is fulfilled. I've been hearing contradicting information-some state that any 1 test of...

If a vector field ##\vec{v}## is non-divergent, so the identity is satisfied: ##\vec{\nabla}\cdot\vec{v}=0##; if is non-rotational: ##\vec{\nabla}\times\vec{v}=\vec{0}##; but if is "non-linear" Which differential equation the vector ##\vec{v}## satisfies? EDIT: this isn't an arbritrary...

If a holomorphic function is a function that \frac{\partial f}{\partial \bar{z}} =0 Thus, an antiholomorphic function is a function that \frac{\partial f}{\partial z} =0 ?

Homework Statement Stuck on two similar problems: "State the normal stress boundary condition at an interface x_3-h(x_1,x_2,t)=0between an invisicid incompressible fluid and a vacuum. You may assume that the interface has a constant tension." The second question in the same but the fluid is...

Homework Statement Consider a ##j=1, SU(2)## representation (or fundamental ##S0(3)## representation). Suppose that ##a_i, b_i## and ##c_i## (i=1,2,3) are vectors transforming under this representation i.e ##a_i' = [\rho_1 (x)]_{ij} a_j = \rho_{ij} a_j## and similarly for b and c. Consider...

I see on StackOverflow people doing stuff like [FONT="Courier New"] for (int k = 0; k < something.length(); k++) where the body of the for loop never has any chance of modify something's length. I thought that was considered bad coding practice. The implementation of something's class might...

Hello guys, I'm trying rather hard to find a real square matrix that will satisfy this ##AA^T=-I##. The first thing that comes to my mind is of course orthogonal matrix. But clearly it isn't. In fact, ##A^T=-A^{-1}## in order for it to work. The condition is pretty strict if you also consider...