Authors:M. Dajczer; J. H. de Lira Pages: 187 - 198 Abstract: Abstract In this paper, we provided conditions for an entire constant mean curvature Killing graph lying inside a possible unbounded region to be necessarily a slice. PubDate: 2017-06-01 DOI: 10.1007/s00574-016-0019-3 Issue No:Vol. 48, No. 2 (2017)

Authors:Wolfgang Ebeling; Sabir M. Gusein-Zade Pages: 199 - 208 Abstract: Abstract For a complex analytic variety with an action of a finite group and for an invariant 1-form on it, we give an equivariant version (with values in the Burnside ring of the group) of the local Euler obstruction of the 1-form and describe its relation with the equivariant radial index defined earlier. This leads to equivariant versions of the local Euler obstruction of a complex analytic space and of the global Euler obstruction. PubDate: 2017-06-01 DOI: 10.1007/s00574-016-0022-8 Issue No:Vol. 48, No. 2 (2017)

Authors:Jiryo Komeda; Akira Ohbuch Pages: 209 - 218 Abstract: Abstract Let (C, P) be a pointed non-singular curve of genus g such that the Weierstrass semigroup H(P) of P is \(\gamma \) -hyperelliptic. We prove that there exists a double covering \(\pi :C\longrightarrow C'\) such that P is its ramification point if \(g=6\gamma +1\) , \(6\gamma \) and \(H(P)\not \ni 4\) . Torres showed that the above statement holds if \(g\ge 6\gamma +4\) . Kato and the authors also obtained the same result even in the cases \(g=6\gamma +3\) and \(6\gamma +2\) . PubDate: 2017-06-01 DOI: 10.1007/s00574-016-0002-z Issue No:Vol. 48, No. 2 (2017)

Authors:F. E. Brochero Martínez; M. Corrêa; A. M. Rodríguez Pages: 219 - 235 Abstract: Abstract We give an upper bound of the degree of quasi-smooth hypersurfaces which are invariant by a one dimensional holomorphic foliation on a weighted projective space. This bound depends only on the degree of the foliation and the weights of the space. PubDate: 2017-06-01 DOI: 10.1007/s00574-016-0003-y Issue No:Vol. 48, No. 2 (2017)

Authors:Edileno de Almeida Santos Pages: 237 - 251 Abstract: Abstract We consider singular holomorphic foliations on compact complex surfaces with invariant rational nodal curve of positive self-intersection. Then, under some assumptions, we list all possible foliations. PubDate: 2017-06-01 DOI: 10.1007/s00574-016-0011-y Issue No:Vol. 48, No. 2 (2017)

Authors:Ricardo Abreu-Blaya; Lianet De la Cruz-Toranzo; Tania R. Gómez-Santiesteban; Yulieth Ramírez-Leyva; Juan Bory-Reyes Pages: 253 - 260 Abstract: Abstract In this note, we consider poly-analytic Cauchy integral operators introduced in a rather natural way on the higher order Lipschitz classes. We prove some boundary properties of the function represented by such an integral operator in the general context of rectifiable Jordan curves. PubDate: 2017-06-01 DOI: 10.1007/s00574-016-0013-9 Issue No:Vol. 48, No. 2 (2017)

Authors:Aziz El Kacimi Alaoui Pages: 261 - 282 Abstract: Abstract Let \(\mathcal{F}\) be a complex foliation by Riemann surfaces defined by a trivial (in the differentiable sense) fibration \(\pi :M\longrightarrow B\) but for which the complex structure on each fibre \(\pi ^{-1}(t)\) may depend on t. Let \(\sigma :B\longrightarrow M\) be a section of \(\pi \) contained in a \(\mathcal{F}\) -relatively compact subset of M. We prove: for any \(\mathcal{F}\) -relatively compact open set U containing \(\Sigma =\sigma (B)\) and any integer \(s\ge 0\) , there exists a function \(U\longrightarrow {\mathbb {C}}\) of class \(C^s\) nonconstant on any leaf of \((U,\mathcal{F})\) , meromorphic along the leaves and whose set of poles is exactly \(\Sigma \) . PubDate: 2017-06-01 DOI: 10.1007/s00574-016-0020-x Issue No:Vol. 48, No. 2 (2017)

Authors:Cícero Carvalho; Victor G. L. Neumann; Hiram H. López Pages: 283 - 302 Abstract: Abstract In this paper we introduce a new family of codes, called projective nested cartesian codes. They are obtained by the evaluation of homogeneous polynomials of a fixed degree on a certain subset of \(\mathbb {P}^n(\mathbb {F}_q)\) , and they may be seen as a generalization of the so-called projective Reed–Muller codes. We calculate the length and the dimension of such codes, an upper bound for the minimum distance and the exact minimum distance in a special case (which includes the projective Reed–Muller codes). At the end we show some relations between the parameters of these codes and those of the affine cartesian codes. PubDate: 2017-06-01 DOI: 10.1007/s00574-016-0010-z Issue No:Vol. 48, No. 2 (2017)

Authors:Enrique Fernández-Cara; Ivaldo Tributino de Sousa Pages: 303 - 315 Abstract: Abstract This paper deals with the local null control of a free-boundary problem for the 1D semilinear heat equation with distributed controls (locally supported in space) or boundary controls (acting at \(x=0\) ). In the main result we prove that, if the final time T is fixed and the initial state is sufficiently small, there exists controls that drive the state exactly to rest at time \(t=T\) . PubDate: 2017-06-01 DOI: 10.1007/s00574-016-0001-0 Issue No:Vol. 48, No. 2 (2017)

Authors:Henrique Vitório Pages: 317 - 333 Abstract: Abstract We propose a unified approach to the theory of connections in the geometry of sprays and Finsler metrics which, in particular, gives a simple explanation of the well-known fact that all the classical Finslerian connections provide exactly the same formulas appearing in the calculus of variations. PubDate: 2017-06-01 DOI: 10.1007/s00574-016-0014-8 Issue No:Vol. 48, No. 2 (2017)

Authors:Yin Chen Abstract: Abstract We study modular invariants of finite affine linear groups over a finite field \(\mathbb {F}_{q}\) under affine actions and linear actions. We generalize a result of Chuai (J Algebra 318:710–722, 2007, Theorem 4.2) to any m-folds affine actions. Suppose \(G\leqslant \mathrm{GL}(n,\mathbb {F}_{q})\) is a subgroup and W denotes the canonical module of \(\mathrm{GL}(n,\mathbb {F}_{q})\) . We denote by \(\mathbb {F}_{q}[W]^{G}\) the invariant ring of G acting linearly on W and denote by \(\mathbb {F}_{q}[W_{n+1}]^{AG(W^{*})}\) the invariant ring of the affine group \(AG(W^{*})\) of G acting canonically on \(W_{n+1}:=W\oplus \mathbb {F}_{q}\) . We show that if \(\mathbb {F}_{q}[W]^{G}=\mathbb {F}_{q}[f_{1},f_{2},\ldots ,f_{s}]\) , then \(\mathbb {F}_{q}[W_{n+1}]^{AG(W^{*})}=\mathbb {F}_{q}[f_{1},f_{2},\ldots ,f_{s},h_{n+1}]\) , where \(h_{n+1}\) denotes the \((n+1)\) -th Mui’s invariant of degree \(q^{n}\) . Let \(\mathrm{AGL}_{1}(\mathbb {F}_{p})\) be the 1-dimensional affine general linear groups over the prime field \(\mathbb {F}_{p}\) . We find a generating set for the ring of vector invariants \(\mathbb {F}_{p}[mW_{2}]^{\mathrm{AGL}_{1}(\mathbb {F}_{p})}\) and determine the Noether’s number \(\upbeta _{mW_{2}}(\mathrm{AGL}_{1}(\mathbb {F}_{p}))\) for any \(m\in \mathbb {N}^{+}\) . PubDate: 2017-07-24 DOI: 10.1007/s00574-017-0050-z

Authors:Talat Körpinar; Rıdvan Cem Demirkol Abstract: Abstract In this work, we firstly describe conditions for being elastica for a moving particle corresponding to different type of space curves in Minkowski space \(\mathsf{E}_2^4\) . Then, we investigate the energy on the elastic curves corresponding to a particular particle in the space and we also exploit its relationship with energy on the same particle in the Frenet vector fields. Finally, we characterize non-elastic curves in \(\mathsf{E}_2^4\) and we compute their energy to see the distinction between energies for the curves of elastic and non-elastic case in Minkowski space \(\mathsf{E}_2^4\) . PubDate: 2017-07-10 DOI: 10.1007/s00574-017-0047-7

Authors:Jeovanny de Jesus Muentes Acevedo Abstract: Abstract Let M be a compact Riemannian manifold. The set \(\text {F}^{r}(M)\) consisting of sequences \((f_{i})_{i\in {\mathbb {Z}}}\) of \(C^{r}\) -diffeomorphisms on M can be endowed with the compact topology or with the strong topology. A notion of topological entropy is given for these sequences. I will prove this entropy is discontinuous at each sequence if we consider the compact topology on \(\text {F}^{r}(M)\) . On the other hand, if \( r\ge 1\) and we consider the strong topology on \(\text {F}^{r}(M)\) , this entropy is a continuous map. PubDate: 2017-07-07 DOI: 10.1007/s00574-017-0049-5

Authors:Mário Bessa; Jairo Bochi; Michel Cambrainha; Carlos Matheus; Paulo Varandas; Disheng Xu Abstract: Abstract A theorem of Viana says that almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents. In this note we extend this result to cocycles on any noncompact classical semisimple Lie group. PubDate: 2017-07-04 DOI: 10.1007/s00574-017-0048-6

Authors:Tiago Macedo; Thiago Castilho de Mello Abstract: Abstract Let R be a commutative integral domain with unit, f be a nonconstant monic polynomial in R[t], and \(I_f \subset R[t]\) be the ideal generated by f. In this paper we study the group of R-algebra automorphisms of the R-algebra without unit \(I_f\) . We show that, if f has only one root (possibly with multiplicity), then \({{\mathrm{Aut}}}(I_f) \cong R^\times \) . We also show that, under certain mild hypothesis, if f has at least two different roots in the algebraic closure of the quotient field of R, then \({{\mathrm{Aut}}}(I_f)\) is a cyclic group and its order can be completely determined by analyzing the roots of f. PubDate: 2017-07-04 DOI: 10.1007/s00574-017-0046-8

Authors:Thaís Maria Dalbelo; Marcelo Messias; Alisson C. Reinol Abstract: Abstract In this paper we give the normal form of all polynomial differential systems in \(\mathbb {R}^3\) having a weighted homogeneous surface \(f=0\) as an invariant algebraic surface and characterize among these systems those having a Darboux invariant constructed uniquely using this invariant surface. Using the obtained results we give some examples of stratified vector fields, when \(f=0\) is a singular surface. We also apply the obtained results to study the Vallis system, which is related to the so-called El Niño atmospheric phenomenon, when it has a cone as an invariant algebraic surface, performing a dynamical analysis of the flow of this system restricted to the invariant cone and providing a stratification for this singular surface. PubDate: 2017-06-27 DOI: 10.1007/s00574-017-0045-9

Authors:Jairo K. Mengue Abstract: Abstract Given a Lipschitz function \(f:\{1,\ldots ,d\}^\mathbb {N} \rightarrow \mathbb {R}\) , for each \(\beta >0\) we denote by \(\mu _\beta \) the equilibrium measure of \(\beta f\) and by \(h_\beta \) the main eigenfunction of the Ruelle Operator \(L_{\beta f}\) . Assuming that \(\{\mu _{\beta }\}_{\beta >0}\) satisfy a large deviation principle, we prove the existence of the uniform limit \(V= \lim _{\beta \rightarrow +\infty }\frac{1}{\beta }\log (h_{\beta })\) . Furthermore, the expression of the deviation function is determined by its values at the points of the union of the supports of maximizing measures. We study a class of potentials having two ergodic maximizing measures and prove that a L.D.P. is satisfied. The deviation function is explicitly exhibited and does not coincide with the one that appears in the paper by Baraviera-Lopes-Thieullen which considers the case of potentials having a unique maximizing measure. PubDate: 2017-06-23 DOI: 10.1007/s00574-017-0044-x

Authors:Henrique F. de Lima; Eraldo Lima; Adriano Medeiros; Márcio S. Santos Abstract: Abstract We establish Liouville type results concerning two-sided hypersurfaces immersed in a weighted Killing warped product, under suitable constraints either on the Bakry-Émery-Ricci tensor of the base of the ambient space or on the height function of the hypersurface. PubDate: 2017-06-20 DOI: 10.1007/s00574-017-0043-y

Authors:Somorjit Konthoujam Singh; Hemant Kumar Singh; Tej Bahadur Singh Abstract: Abstract Let \(G=\mathbb {Z}_p,\) \(p>2\) a prime, act freely on a finitistic space X with mod p cohomology ring isomorphic to that of \(\mathbb {F}P^m\times \mathbb {S}^3\) , where \(m+1\not \equiv 0\) mod p and \(\mathbb {F}=\mathbb {C}\) or \(\mathbb {H}\) . We wish to discuss the nonexistence of G-equivariant maps \(\mathbb {S}^{2q-1}\rightarrow X\) and \( X\rightarrow \mathbb {S}^{2q-1}\) , where \(\mathbb {S}^{2q-1}\) is equipped with a free G-action. These results are analogues of the celebrated Borsuk-Ulam theorem. To establish these results first we find the cohomology algebra of orbit spaces of free G-actions on X. For a continuous map \(f\!:\! X\rightarrow \mathbb {R}^n\) , a lower bound of the cohomological dimension of the partial coincidence set of f is determined. Furthermore, we approximate the size of the zero set of a fibre preserving G-equivariant map between a fibre bundle with fibre X and a vector bundle. An estimate of the size of the G-coincidence set of a fibre preserving map is also obtained. These results are parametrized versions of the Borsuk-Ulam theorem. PubDate: 2017-06-03 DOI: 10.1007/s00574-017-0040-1

Authors:Cícero Aquino; Halyson Baltazar Abstract: Abstract The purpose of this article is to study the uniqueness of complete hypersurfaces satisfying some pinching curvature condition. Here, we use the generalized maximum principle of Omori–Yau to obtain uniqueness results for complete spacelike hypersurfaces immersed in a Lorentzian product space. In addition, we obtain the analogue results for complete hypersurfaces immersed in a Riemannian product space. PubDate: 2017-06-02 DOI: 10.1007/s00574-017-0041-0