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A former participant of math olypmiads. I started to think about mathematics lately.

Most recent interests:

  • Gauge integrals: did you know that there exists an integral, whose definition is a generalization of Riemann's definition, yet its strength exceeds that of Lebesgue integral? Instead of limiting your partitions by a positive constant $\delta$: $t_{k+1}-t_k <\delta$, you allow restrictions by a positive function (the "guage") $\delta$: $t_{k+1} - t_{k} < \delta(c_k)$, where $c_k \in [t_k,t_{k+1}]$.
  • Primitive parts of sequences: Take a integer linear recurrence sequence $a_n$ arising from a monic quadratic equation in $\mathbb{Z}[x]$: $x^2 + ax +b = 0$. Examples: Fibonacci, Lucas, $\frac{a^n-b^n}{a-b}$ (where either both $a,b$ are integers, or are conjugate algebraic integers). Then: 1) Under some conditions, $a_n$ has a primitive divisor - a prime divisiors not dividing the previous elements (a statement which translates into statement about order of elements) - that's Zsigmondy's Theorem. 2) $\prod_{d|n} a_d^{\mu(\frac{n}{d})}$ is an integer sequence! For $\frac{a^n-b^n}{a-b}$ it yields the Cyclotomic homogeneous polynomials, and for Fibonacci it yields a sequence called its primitive part.

9h
awarded  Popular Question
Sep
7
comment Problem with orientation in Stokes' Theorem
@lmsteffan I point my right hand's thumb in the direction of the normal (at a point near the curve). My other four fingers naturally curl in some direction which dictates the orientation of the curve.
Sep
7
asked Problem with orientation in Stokes' Theorem
Sep
2
comment Stokes' Theorem - Stuck with a non-elementary integral
No mistake - this clever parameterization works (leads to $-8$). Thank you.
Sep
2
accepted Stokes' Theorem - Stuck with a non-elementary integral
Sep
2
comment Stokes' Theorem - Stuck with a non-elementary integral
@Semiclassical - Thanks, that's a useful and clever remark. We can replace $\vec{F}$ with $(4z,0,x)$ and use the parametrization suggested by Jyrki - $(x,y,z)=(\sin(2\theta), 2\sin^2\theta, 2\sin \theta), \theta \in [0,\pi]$.
Sep
2
asked Stokes' Theorem - Stuck with a non-elementary integral
Jul
2
awarded  Curious
Jul
2
awarded  Inquisitive
May
1
awarded  Yearling
Feb
22
awarded  Necromancer
Feb
21
revised Restricted Matrix Elimination - Possible?
added 77 characters in body
Feb
16
accepted Restricted Matrix Elimination - Possible?
Feb
16
revised Restricted Matrix Elimination - Possible?
added 63 characters in body
Feb
16
answered Restricted Matrix Elimination - Possible?
Feb
16
revised Restricted Matrix Elimination - Possible?
added 36 characters in body
Feb
16
revised Restricted Matrix Elimination - Possible?
added 44 characters in body
Feb
15
accepted Is there a continuous injective map from $\mathbb{R}$ that has compact image?
Feb
15
revised Is there a continuous injective map from $\mathbb{R}$ that has compact image?
edited title
Feb
15
asked Is there a continuous injective map from $\mathbb{R}$ that has compact image?