THE FUNDAMENTAL GROUP OF THE SPACE OF MAPS FROM A SURFACE INTO THE PROJECTIVE PLANE

In this work we compute the fundamental group of each connected component of the function space of maps from it closed surface into the projective space

Rigidity theorems for complete spacelike hypersurfaces with constant scalar curvature in De Sitter space

In this paper we give a partially affirmative answer to the following question posed by Haizhong Li: is a complete spacelike hypersurface in De Sitter space S(1)(n+1)(c), n >= 3, with constant normalized scalar curvature R satisfying n-2/nc <= R <= c totally umbilical? (C) 2008 Elsevier B.V. All rights reserved.

A Boolean algebra and a Banach space obtained by push-out iteration

Under the assumption that c is a regular cardinal, we prove the existence and uniqueness of a Boolean algebra B of size c defined by sharing the main structural properties that P(omega)/fin has under CH and in the N(2)-Cohen model. We prove a similar result in the category of Banach spaces. (C) 2011 Elsevier B.V. All rights reserved.

The Borsuk-Ulam theorem for homotopy spherical space forms

In this work, we show for which odd-dimensional homotopy spherical space forms the Borsuk-Ulam theorem holds. These spaces are the quotient of a homotopy odd-dimensional sphere by a free action of a finite group. Also, the types of these spaces which admit a free involution are characterized. The case of even-dimensional homotopy spherical space forms is basically known.

Bjorling problem for timelike surfaces in the Lorentz-Minkowski space

We solve the Bjorling problem for timelike surfaces in the Lorentz-Minkowski space through a split-complex representation formula obtained for this kind of surface. Our approach uses the split-complex numbers and natural split-holomorphic extensions. As applications, we show that the minimal timelike surfaces of revolution as well as minimal ruled timelike surfaces can be characterized as solutions of certain adequate Bjorling problems in the Lorentz-Minkowski space. (C) 2010 Elsevier Inc. All rights reserved.

The Gauss-Kronecker curvature of minimal hypersurfaces in four-dimensional space forms

LetQ(4)( c) be a four-dimensional space form of constant curvature c. In this paper we show that the infimum of the absolute value of the Gauss-Kronecker curvature of a complete minimal hypersurface in Q(4)(c), c <= 0, whose Ricci curvature is bounded from below, is equal to zero. Further, we study the connected minimal hypersurfaces M(3) of a space form Q(4)( c) with constant Gauss-Kronecker curvature K. For the case c <= 0, we prove, by a local argument, that if K is constant, then K must be equal to zero. We also present a classification of complete minimal hypersurfaces of Q(4)( c) with K constant.

Construction of Hamiltonian-Minimal Lagrangian submanifolds in Complex Euclidean Space

We describe several families of Lagrangian submanifolds in complex Euclidean space which are H-minimal, i.e. critical points of the volume functional restricted to Hamiltonian variations. We make use of various constructions involving planar, spherical and hyperbolic curves, as well as Legendrian submanifolds of the odd-dimensional unit sphere.

The Wijsman hyperspace of a metric hereditarily Baire space is Baire

In this paper, we show that the Wijsman hyperspace of a metric hereditarily Baire space is Baire. This solves a recent question posed by Zsilinszky. (C) 2009 Elsevier B.V. All rights reserved.

A FREE BOUNDARY ISOPERIMETRIC PROBLEM IN HYPERBOLIC 3-SPACE BETWEEN PARALLEL HOROSPHERES

We investigate the isoperimetric problem of finding the regions of prescribed volume with minimal boundary area between two parallel horospheres in hyperbolic 3-space (the part of the boundary contained in the horospheres is not included). We reduce the problem to the study of rotationally invariant regions and obtain the possible isoperimetric solutions by studying the behavior of the profile curves of the rotational surfaces with constant mean curvature in hyperbolic 3-space. We also classify all the connected compact rotational surfaces M of constant mean curvature that are contained in the region between two horospheres, have boundary partial derivative M either empty or lying on the horospheres, and meet the horospheres perpendicularly along their boundary.

Spherical space forms - Homotopy self-equivalences and homotopy types, the case of the groups Z/a x (Z/b x TL(2)(F(p)))

Let G = Z/a x(mu) (Z/b x TL(2)(F(p))) and X(n) be an n-dimensional CW-complex with the homotopy type of the n-sphere. We determine the automorphism group Aut(G) and then compute the number of distinct homotopy types of spherical space forms with respect to free and cellular G-actions on all CW-complexes X(2dn - 1), where 2d is a period of G. Next, the group E(X(2dn - 1)/alpha) of homotopy self-equivalences of spherical space forms X(2dn - 1)/alpha, associated with such G-actions alpha on X(2dn - 1) are studied. Similar results for the rest of finite periodic groups have been obtained recently and they are described in the introduction. (C) 2009 Elsevier B.V. All rights reserved.

DNA strand breaks and base modifications induced by cholesterol hydroperoxides

Cholesterol (Ch) can be oxidized by reactive oxygen species, forming oxidized products such as Ch hydroperoxides (ChOOH). These hydroperoxides can disseminate the peroxidative stress to other cell compartments. In this work, the ability of ChOOH to induce strand breaks and/or base modifications in a plasmid DNA model was evaluated. In addition, HPLC/MS/MS analyses were performed to investigate the formation of 8-oxo-7,8-dihydro-2`-deoxyguanosine (8-oxodGuo) after the incubation of 2`-deoxyguanosine (dGuo) with ChOOH and Cu(2+). In the presence of copper ions, ChOOH induced DNA strand breaks in time and concentration-dependent manners. Purine and pyrimidine base modifications were also observed, as assessed respectively by the treatment with Fpg and Endo III repair enzymes. The detection of 8-oxodGuo by HPLC/MS/MS is in agreement with the dGuo oxidation in plasmid DNA. ChOOH-derived DNA damage adds further support to the role of lipid peroxidation in inducing DNA modifications and mutation.

Double-strand DNA cleavage induced by oxindole-Schiff base copper(II) complexes with potential antitumor activity

Some oxindole-Schiff base copper(II) complexes have already shown potential antitumor activity towards different cells, inducing apoptosis in a process modulated by the ligand, and having nuclei and mitochondria as main targets. Here, three novel copper(II) complexes with analogous ligands were isolated and characterized by spectroscopic techniques, having their reactivity compared to the so far most active complex in this class. Cytotoxicity experiments carried out toward human neuroblastoma SH-SY5Y cells confirmed its proapoptosis property. DNA cleavage studies were then performed in the presence of these complexes, in order to verify the influence of ligand structural features in its nuclease activity. All of them were able to cause double-strand DNA scissions, giving rise to nicked circular Form II and linear Form III species, in the presence of hydrogen peroxide. Additionally, DNA Form II was also detected in the absence of peroxide when the most active complex, [Cu(isaepy)(2)](2+) 1, was used. In an effort to better elucidate their interactions with DNA, solutions of the different complexes titrated with DNA had their absorption spectra monitored. An absorbance hyperchromism observed at 260 nm pointed to the intercalation of these complexes into the DNA structure. Further, investigations of 2-deoxy-D-ribose (DR) oxidation catalyzed by each of those complexes, using 2-thiobarbituric acid reactive species (TBARS) method, and detection of reactive oxygen species (ROS) formation by spin-trapping EPR, suggested that their mechanism of action in performing efficiently DNA cleavage occurs preferentially, but not only by oxidative pathways. (C) 2007 Elsevier Inc. All rights reserved.