Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 7

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

Two remarks on non-zero constant Jacobian polynomial maps of ℂ²

100%
Chau N.
Annales Polonici Mathematici
|
2003
|
tom 82
|
nr 1
39-44
EN
We present some estimates on the geometry of the exceptional value sets of non-zero constant Jacobian polynomial maps of ℂ² and their components.
2
Content available remote

Note on the Jacobian condition and the non-proper value set

100%
Chau N.
Annales Polonici Mathematici
|
2004
|
tom 84
|
nr 3
203-210
EN
We show that the non-proper value set of a polynomial map (P,Q): ℂ² → ℂ² satisfying the Jacobian condition detD(P,Q) ≡ const ≠ 0, if non-empty, must be a plane curve with one point at infinity.
3
Content available remote

Non-zero constant Jacobian polynomial maps of $ℂ²$

100%
Chau N.
Annales Polonici Mathematici
|
1999
|
tom 71
|
nr 3
287-310
EN
We study the behavior at infinity of non-zero constant Jacobian polynomial maps f = (P,Q) in ℂ² by analyzing the influence of the Jacobian condition on the structure of Newton-Puiseux expansions of branches at infinity of level sets of the components. One of the results obtained states that the Jacobian conjecture in ℂ² is true if the Jacobian condition ensures that the restriction of Q to the curve P = 0 has only one pole.
4
Content available remote

A note on the plane Jacobian conjecture

100%
Chau N.
Annales Polonici Mathematici
|
2012
|
tom 105
|
nr 1
13-19
EN
It is shown that every polynomial function P:ℂ² → ℂ with irreducible fibres of the same genus must be a coordinate. Consequently, there do not exist counterexamples F = (P,Q) to the Jacobian conjecture such that all fibres of P are irreducible curves with the same genus.
5
Content available remote

Plane Jacobian conjecture for simple polynomials

100%
Chau N.
Annales Polonici Mathematici
|
2008
|
tom 93
|
nr 3
247-251
EN
A non-zero constant Jacobian polynomial map F=(P,Q):ℂ² → ℂ² has a polynomial inverse if the component P is a simple polynomial, i.e. its regular extension to a morphism p:X → ℙ¹ in a compactification X of ℂ² has the following property: the restriction of p to each irreducible component C of the compactification divisor D = X-ℂ² is of degree 0 or 1.
6
Content available remote

Integer points on a curve and the plane Jacobian problem

100%
Chau N.
Annales Polonici Mathematici
|
2006
|
tom 88
|
nr 1
53-58
EN
A polynomial map F = (P,Q) ∈ ℤ[x,y]² with Jacobian $JF:= P_xQ_y - P_yQ_x ≡ 1$ has a polynomial inverse with integer coefficients if the complex plane curve P = 0 has infinitely many integer points.
7
Content available remote

On nonsingular polynomial maps of ℝ²

64%
Chau N., Gutierrez C.
Annales Polonici Mathematici
|
2006
|
tom 88
|
nr 3
193-204
EN
We consider nonsingular polynomial maps F = (P,Q): ℝ² → ℝ² under the following regularity condition at infinity $(J_∞)$: There does not exist a sequence ${(p_k,q_k)} ⊂ ℂ²$ of complex singular points of F such that the imaginary parts $(ℑ(p_k),ℑ(q_k))$ tend to (0,0), the real parts $(ℜ(p_k),ℜ(q_k))$ tend to ∞ and $F(ℜ(p_k),ℜ(q_k))) → a ∈ ℝ²$. It is shown that F is a global diffeomorphism of ℝ² if it satisfies Condition $(J_∞)$ and if, in addition, the restriction of F to every real level set $P^{-1}(c)$ is proper for values of |c| large enough.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.