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Jul
29
comment Shortest Path Length as mathematical function/expression
the only thing i can think about is $X^n_{ij}$ is the number of $i \to j$ paths of length exactly $n$
Jul
29
comment Finding the horizontal and vertical tangents of a parametric equation.
@Alex updated solution with another approach for you
Jul
29
comment Finding the horizontal and vertical tangents of a parametric equation.
@Alex horizontal tangents have $y'=0$ so you end up with $x=0$ or $x^2+y^2=1$
Jul
29
comment Express as a single logarithm
Welcome to the site. People here don't like to do your homework for you. Please take some hints in the answer below, attempt the problem and put an update into the question or alert the answerer by a comment...
Jul
29
comment Implicit finite differences: Sufficient conditions for non-negativity
it seems $a_n, b_n, c_n \ge 0$ should do it, but it's too restrictive for you.
Jul
29
comment Implicit finite differences: Sufficient conditions for non-negativity
@uranix he is going back in time
Jul
28
comment Differentiability of multi-variable functions
@user160492 not exactly. Note that $f(0,y)=0$ but $f(x,0) \neq 0$. Can you compute $\frac{df(x,0)}{dx}$?
Jul
28
comment Mathematics of Magic Squares
Welcome to Math.SE! Hope you stay and contribute to the site :)
Jul
28
comment Sign of eigenvalues of $A$ by $\det(A-\lambda I)=\lambda \det(B+D-\lambda I).$
You likely mean $D$ not $C$ in the first sentence
Jul
28
comment Partial differential equation
you could find it numerically, do you need an analytic solution?
Jul
28
comment Partial differential equation
i edited to the best of my ability to understand, please check this is what you intended to ask
Jul
28
comment defining a sequence of numbers L n≥1, and prove something about it
@Zero you can, but I don't see how this will help
Jul
28
comment defining a sequence of numbers L n≥1, and prove something about it
@Zero note that $\phi$ and $\Phi$ both satisfy $x^2 = x+1$. Can you use this fact to complete the proof?
Jul
28
comment defining a sequence of numbers L n≥1, and prove something about it
@Zero the hint starts off by assuming that $L_n = \phi^n + \Phi^n$ and $L_{n-1} = \phi^{n-1} + \Phi^{n-1}$. This is the Inductive Assumption, and we should prove the statement for $L_{n+1}$...
Jul
28
comment defining a sequence of numbers L n≥1, and prove something about it
@Rohan you the fact that both $\phi$ and $\Phi$ are solutions of $x^2=x+1$
Jul
28
comment defining a sequence of numbers L n≥1, and prove something about it
@Zero to assume that $L_n$ and $L_{n-1}$ have the desired form, you need strong induction
Jul
23
comment Dividing the square
In what sense are you dividing into 4 equal parts - by area, or by perimeter? What does removing one edge of the square change?
Jul
23
comment How do I solve a under-determined quadratic multi-variate system?
How many data points do you have available? I also don't understand how knowing the distributions of the $X_i$ will help for anything...
Jul
23
comment How do I solve a under-determined quadratic multi-variate system?
I don't understand the question. Do you have the data points $(y,x_1,x_2,x_3)$ and are asking which $\beta_{\cdot}$ were used to make them work?
Jul
21
comment How to solve $z^3 + \overline z = 0$
@robjohn indeed, but not much harder and i wanted the OP to do at least something by himself