Recent content by Gh. Soleimani

Thank you so much for your answer. Finally, I need to obtain local minimum, local maximum and saddle points. As you know, we have to use Hessian matrix which will be made by second derivative. In fact, to examine eigenvalues of H - matrix in critical point says to us where is local minimum and...

Sorry. I think that I took a mistake to introduce the function. First of all, let me write true function as follows: ƒ(x, y, z) = x +yz - xy ∇ƒ = (1-y) i +(z-x) j + y k where: ∂ƒ/∂x = 1 - y =0 ∂ƒ/∂y = z - x =0 ∂ƒ/∂z = y =0 As you can see, there are not any answer for critical point...

Hi everybody If we have not any answers for critical points after first partial derivatives equal to zero, how can we continue to find local MAX, local MIN and Saddle point?. For example: Suppose we have below equations for first partial derivatives: ∂ƒ/∂x = y + 5 , ∂ƒ/∂y = 2z , ∂ƒ/∂z = y As...

Thanks. I found my answer on below link: https://ocw.mit.edu/courses/mathematics/18-03sc-differential-equations-fall-2011/unit-ii-second-order-constant-coefficient-linear-equations/damped-harmonic-oscillators/MIT18_03SCF11_s13_2text.pdf

If you consider b^2/m > 4*k, you can get the solution by using classic method (b = damping constant, m = mass and k = spring constant) otherwise you have to use complex numbers. How have the references books proved the solution for this differential equation?

Natural frequency is the frequency at which a system tends to oscillate in the absence of any driving or damping force. Free vibrations of an elastic body are called natural vibrations and occur at a frequency called the natural frequency. Now, assume we want to calculate the natural frequency...

Can we find the natural frequency of water's molecules by using of Newton's law of cooling and resonance phenomena?

Therefore, you believe that we should not apply MB for velocities close (but less than it) to the speed of light. But indeed, what is upper limit of velocity in which MB gives us a good approximation to calculate number of molecules? Because the companies still use MB to design Turbo Molecular...

Yes, previous experiments showed that Newtonian mechanics is contrary to modern experimental results and is clearly a limited theory in which velocity of the particles in the Universe always remains less than the speed of light. But, here there is a strange case and the interesting point...

Let me tell you another example about velocity of Gases. According to below links, Physicists at CERN generated ions with temperatures of more than 1.6 trillion degrees Celsius. At the Brookhaven National Laboratory in Upton, have set a new record for the highest temperature ever measured: 4...

oh. sorry. I mixed everything. thanks

Regarding to mo (equal to mass of one molecule), could you please tell me how you calculate the mass of 0.5 mole hydrogen? Is below calculation true? 0.5 u = (1.6766E-24)/2 g = 8.383E-28 kg

Thanks. I understood my mistake.

Do you mean that mo = M?

Let me tell you above mentioned in another view. According to all references books, we have: Vrms = (3kBT/mo)^0.5 = (3RT/ M)^0.5 There is a discrepancy between (3kBT/mo)^0.5 and (3RT/ M)^0.5. In the case of kB, we have two variables of "T" and "mo" but the case of "R" tells us that there is...