Viidennen asteen yhtälön ratkaisukaavan olemassaolon mahdottomuus Galois'n teorian pohjalta
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Polynomial and horizontally polynomial functions on Lie groups
Antonelli, Gioacchino; Le Donne, Enrico (Springer, 2022)We generalize both the notion of polynomial functions on Lie groups and the notion of horizontally affine maps on Carnot groups. We fix a subset S of the algebra g of left-invariant vector fields on a Lie group G and we ... -
Matriisin Hessenbergin muoto
Holopainen, Niko (2013) -
On a Continuous Sárközy-Type Problem
Kuca, Borys; Orponen, Tuomas; Sahlsten, Tuomas (Oxford University Press (OUP), 2023)We prove that there exists a constant ϵ>0ϵ>0 with the following property: if K⊂R2K⊂R2 is a compact set that contains no pair of the form {x,x+(z,z2)}{x,x+(z,z2)} for z≠0z≠0, then dimHK≤2−ϵdimHK≤2−ϵ. -
Computational Experiments with the Roots of Fibonacci-like Polynomials as a Window to Mathematics Research
Abramovich, Sergei; Kuznetsov, Nikolay V.; Leonov, Gennady A. (MDPI AG, 2022)Fibonacci-like polynomials, the roots of which are responsible for a cyclic behavior of orbits of a second-order two-parametric difference equation, are considered. Using Maple and Wolfram Alpha, the location of the largest ... -
On several notions of complexity of polynomial progressions
Kuca, Borys (Cambridge University Press, 2023)For a polynomial progression (x, x + P1(y), . . . , x + Pt(y)), we define four notions of complexity: Host Kra complexity, Weyl complexity, true complexity and algebraic complexity. The first two describe the smallest ...