Pujals*, Enrique; Sambarino, Martin
doi: 10.1007/s00574-007-0032-7pmid: N/A
We study the unique integrability of the center unstable subbundle of a codimension one dominated splitting.
doi: 10.1007/s00574-007-0033-6pmid: N/A
Given an arbitrary real quartic polynomial, we find the exact region containing the coefficients of the polynomial such that all roots have absolute values less than 1.
doi: 10.1007/s00574-007-0034-5pmid: N/A
In this paper we propose a technique of approximation for the generalized Riemann-Stieltjes integral and we found an analogue for Newton-Cotes formulas in the case n = 2 and n = 3.
Koruoğlu, Özden; Sahin, Recep; İkikardes, Sebahattin
doi: 10.1007/s00574-007-0035-4pmid: N/A
We consider the extended Hecke groups $$ \ifmmode\expandafter\bar\else\expandafter\=\fi{H}{\left( \lambda \right)} $$ generated by T(z) = −1/z, S(z) = −1/(z + λ) and R(z) = 1/z with λ ≥ 2. In this paper, firstly, we study the fundamental region of the extended Hecke groups $$ \ifmmode\expandafter\bar\else\expandafter\=\fi{H}{\left( \lambda \right)} $$ . Then, we determine the abstract group structure of the commutator subgroups $$ {\ifmmode\expandafter\bar\else\expandafter\=\fi{H}}\ifmmode{'}\else$'$\fi{\left( \lambda \right)} $$ , the even subgroup $$ \ifmmode\expandafter\bar\else\expandafter\=\fi{H}_{e} {\left( \lambda \right)} $$ , and the power subgroups $$ \ifmmode\expandafter\bar\else\expandafter\=\fi{H}^{m} {\left( \lambda \right)} $$ of the extended Hecke groups $$ \ifmmode\expandafter\bar\else\expandafter\=\fi{H}{\left( \lambda \right)} $$ . Also, finally, we give some relations between them.
doi: 10.1007/s00574-007-0036-3pmid: N/A
Sufficient conditions are given to assert that a perturbed mapping has a zero in a Banach manifold modelled over ℝ n . The zero is estimated by means of sequences of Newton's iterations. The proof of the result is constructive and is based upon continuation methods.
doi: 10.1007/s00574-007-0037-2pmid: N/A
In this paper, we prove that $$ S^{{n - 1}} {\left( {{\sqrt {\frac{{n - m}} {n}} }} \right)} \times S^{1} {\left( {{\sqrt {\frac{m} {n}} }} \right)} $$ and round geodesic spheres are the only n-dimensional compact embedded rotation hypersurfaces with H m = 0 (1 ≤ m ≤ n − 1) in a unit sphere S n+1(1). When m = 1, our result reduces to the result of T. Otsuki [O1], [O2], Brito and Leite [BL].
doi: 10.1007/s00574-007-0038-1pmid: N/A
Contrary to the case of interval exchange transformation, we show that generalized affine interval exchange transformation (affine GIET), with or without flips and admitting dense orbits, may not be conjugated to an isometric GIET. This result is proved by constructing explicitly one such affine GIET.
Baak, Choonkil; Moslehian, Mohammad
doi: 10.1007/s00574-007-0039-0pmid: N/A
We introduce the concept of θ-derivations on JB*-triples and prove the Hyers–Ulam-Rassias stability of θ-derivations on JB*-triples. We deal with the Hyers-Ulam-Rassias stability that was first introduced by Th. M. Rassias in the paper “On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300”.
Iglesias, Jorge; Portela, Aldo
doi: 10.1007/s00574-007-0040-7pmid: N/A
In this article the dynamics of generic C r (r ≥ 3) perturbations of complex polynomials are considered. The attention is focused on the determination of the existence of large or invariant components of the complement of the basin of ∞, where the interesting dynamics occur.
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