Recent content by ihggin

Hi, so I am trying to build a cell counting apparatus using light scattering. The setup is a (green) laser shining through a clear bottle full of (Dicty) cells suspended in a stirred solution. The idea is to put a photodetector at some angle by the bottle; a greater cell density should result in...

Hi, I was wondering if it is possible to adapt the conjugate gradient method (or if there's a variation of the method) for nonsymmetrical boundary value problems. For example, I want to solve something like a 2D square grid, where f(x)=0 for all x on the boundary of the square...

Okay, thanks again for the help! (I used Ohm's law and it worked out fine enough.)

Thanks for the help. I haven't studies load lines before, but I just read the wiki, and it mostly makes sense now. Just a clarifying question though: in the Fig. 5 plot, the slope that gives resistance shouldn't be of the line on the log-log graph, right? (I'm pretty sure this is the case...

What is 2*(2^n) equal to? [Hint: not 2^(2n)]

Homework Statement Use the following phototransistor (http://www.vishay.com/docs/81532/bpw96.pdf) to design a circuit that gives an output voltage of 8 V when irradiance is 0.05 mW/cm^2 and 1 V when irradiance is 1 mW/cm^2 (both at wavelength 950 nm). Homework Equations The...

Try using 'Exp[-x]' for the exponential rather than 'e^(-x)'.

Suppose f_1 is a linear map between vector spaces V_1 and U_1, and f_2 is a linear map between vector spaces V_2 and U_2 (all vector spaces over F). Then f_1 \otimes f_2 is a linear transformation from V_1 \otimes_F V_2 to U_1 \otimes_F U_2. Is there any "nice" way that we can write the kernel...

Okay, thanks for the tips. Either way, I get \dim_R C\otimes_RC = 4.

Let U and V be vector spaces over the complex numbers C. Then the tensor product over C, U\otimes_CV is also a complex vector space. Note that U, V, and U\otimes_CV can be regarded as vector spaces over the real numbers R as well. Also note that we can form U\otimes_RV. Question: are U\otimes_CV...

Let R be a Principal Ideal Domain. Let a,b \in R, at least one of which is non-zero. Determine precisely all solutions (s,t), where s,t \in R, of the equation sa+tb= \gcd (a,b). My attempt: since \gcd (a,b) divides both a and b, we can divide both sides by \gcd (a,b) to get the equation s...

Here is a potentially neat problem. Let x(t),y(t) (for all t\in \mathbb{R}) be polynomials in t. Prove that for any x(t),y(t) there exists a non-zero polynomial f(x,y) in 2 variables such that f(x(t),y(t))=0 for all t. The strategy is to show that for n sufficiently large, the polynomials...

Thank you! So basically (T-cI)\alpha=0 so the dimension of the kernel is greater than zero, which means the dimension of the image is less than that of V. We can then take a vector x that is not in the image and generate a basis from it. We then define f so that it's zero on all the basis...

Let V be a finite-dimensional vector space over the field F and let T be a linear operator on V. Let c be a scalar and suppose there is a non-zero vector \alpha in V such that t \alpha = c \alpha. Prove that there is a non-zero linear functional f on V such that T^{t}f=cf, where T^{t}f=f\circ T...