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Intersect a quartic to extract its roots

100%

Kulkarni R. G.

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

2017

tom 16

In this note we present a new method for determining the roots of a quartic polynomial, wherein the curve of the given quartic polynomial is intersected by the curve of a quadratic polynomial (which has two unknown coefficients) at its root point; so the root satisfies both the quartic and the quadratic equations. Elimination of the root term from the two equations leads to an expression in the two unknowns of quadratic polynomial. In addition, we introduce another expression in one unknown, which leads to determination of the two unknowns and subsequently the roots of quartic polynomial.

On the computation of the Nielsen numbers and the converse of the Lefschetz coincidence theorem

100%

Wong P.

Fundamenta Mathematicae

1991-1992

tom 140

nr 2

191-196

Let $f,g:M_1 → M_2$ be maps where $M_1$ and $M_2$ are connected triangulable oriented n-manifolds so that the set of coincidences $C_{f,g}= {x ∈ M_1 | f(x)=g(x)}$ is compact in $M_1$. We define a Nielsen equivalence relation on $C_{f,g}$ and assign the coincidence index to each Nielsen coincidence class. In this note, we show that, for n ≥ 3, if $M_2= \widetilde M_2/K$ where $\widetilde M_2$ is a connected simply connected topological group and K is a discrete subgroup then all the Nielsen coincidence classes of f and g have the same coincidence index. In particular, when $M_1$ and $M_2$ are compact, f and g are deformable to be coincidence free if the Lefschetz coincidence number L(f,g) vanishes.

Corrections to "On the computation of the Nielsen numbers and the converse of the Lefschetz coincidence theorem" (Fund. Math. 140 (1992), 191–196)

100%

Wong P.

Fundamenta Mathematicae

1992

tom 141

nr 1

97-99

Ograniczanie wyników

2 Fundamenta Mathematicae

1 Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

2 Wong P.

1 Kulkarni R. G.

1 2017

2 1992

Wyniki wyszukiwania

Intersect a quartic to extract its roots

On the computation of the Nielsen numbers and the converse of the Lefschetz coincidence theorem

Corrections to "On the computation of the Nielsen numbers and the converse of the Lefschetz coincidence theorem" (Fund. Math. 140 (1992), 191–196)