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Jan
29
answered Is the following fractional function convex?
Jan
29
answered Polynomial with bounded coefficients and real root
Jan
28
comment relation between equallity of hermitian parts and numerical range
The numerical range is the set of $x^\star M x$ for all $x$ with $x^\star x = 1$. $x^\star A_H x$ is the real part of $x^\star A x$. So what depends only on the Hermitian part is the projection of the numerical range on the real axis.
Jan
28
answered Are the solutions to $1+1/2^s+1/3^s=0$ known?
Jan
28
revised relation between equallity of hermitian parts and numerical range
added 107 characters in body
Jan
28
answered relation between equallity of hermitian parts and numerical range
Jan
28
comment Type of polynomial where leading coefficient is to the power of $6$
Sextic is the name in common use. I don't think I've ever seen "hexic" used for a polynomial.
Jan
27
answered why does the equation $(-x^2 + 2x)/(5x - 4) = 6$ have 2 solutions?
Jan
27
comment Numerical integration of a system of stiff ODEs starting at a singular point
And you still won't tell us the actual corrected equations. There's nothing more I can say about it.
Jan
27
comment Product of two sums, one finite and one infinite
For the finite sum, use the binomial theorem. For the infinite sum, the variant form of the binomial series.
Jan
27
answered Calculating determinant of 100x100 matrix
Jan
27
comment Numerical integration of a system of stiff ODEs starting at a singular point
If you've made changes, you haven't let us in on the changes. As far as I can see, $\dot{x}_1$ is still singular on $x_1 = x_2$, the initial point $(1,1,1)$ is on that singular plane, and you haven't told us what the final point is supposed to be.
Jan
27
comment An intuitive explanation for the negatives of divergent summations?
Of course I wasn't evaluating the same summation. I'm simply saying that "it comes out negative" is not any kind of general rule. You have so far given two examples where a summability method gives a negative result. It's like looking at Condaleeza Rice and Hilary Clinton and asking "why is every Secretary of State female?"
Jan
27
answered An intuitive explanation for the negatives of divergent summations?
Jan
27
comment integrals with no analytic answer - intuition and proof
Certainly not that. Constant functions are elementary, so every real number is a value of an elementary function at a rational $x$.
Jan
27
comment integrals with no analytic answer - intuition and proof
Of course there are various methods that sometimes produce such a closed form. When none of the known methods apply, and numerical evaluation produces a number that isn't easily recognizable, we might strongly suspect that there is no closed form, but to prove such a statement (for any reasonable definition of "closed form") is essentially hopeless.
Jan
27
comment integrals with no analytic answer - intuition and proof
AFAIK very little is known in general about closed forms for definite integrals of elementary functions.
Jan
26
comment Numerical integration of a system of stiff ODEs starting at a singular point
If your trajectory is going to be in the singular plane, you can treat that as a constraint: substitute $x_1 = x_2$ and have two nonsingular differential equations in the two unknowns $x_2, x_3$.
Jan
26
answered Eccentricity of a general ellipse
Jan
26
comment Proof for the length of plane curves
@Jasser That's just the convergence of Riemann sums to the integral. Note that $\sqrt{f'(t)^2 + g'(t)^2}$ is continuous since $f'$ and $g'$ are continuous.