Assigning Grammatical Relations with a Back-off Model

This paper presents a corpus-based method to assign grammatical subject/object relations to ambiguous German constructs. It makes use of an unsupervised learning procedure to collect training and test data, and the back-off model to make assignment decisions.Comment: To appear in Proceedings of the Second Conference on Empirical Methods in Natural Language Processing, 7 pages, LaTe

The anisotropic XY-model on the 1d alternating superlattice

The anisotropic XY-model in a transverse field (s=1/2) on the one-dimensional alternating superlattice (closed chain) is considered. The solution of the model is obtained by introducing a generalized Jordan-Wigner transformation which maps the system onto a non-interacting fermion gas. The exact excitation spectrum is determined by reducing the problem to a diagonalization of a block matrix, and it is shown that it is numerically identical to the one obtained by using the approximate transfer matrix method . The induced magnetization and the susceptibility $\chi ^{zz}$ are determined as a function of the transverse field, and it is shown that, at T=0, the susceptibility presents multiple singularities. It is also shown, as expected, that this critical behaviour driven by transverse field belongs to the same universality class of the model on the alternating chain.Comment: 4 pages, 1 figure, presented at ICM200, to be published in the Proceedings (Journal of Magnetism & Magnetic Materials

Dirac Equation with vector and scalar potentials via Supersymmetry in Quantum Mechanics

In this work, a spin $\frac 12$ relativistic particle described by a generalized potential containing both the Coulomb potential and a Lorentz scalar potential in Dirac equation is investigated in terms of the generalized ladder operators from supersymmetry in quantum mechanics. This formalism is applied for the generalized Dirac-Coulomb problem, which is an exactly solvable potential in relativistic quantum mechanics. We obtain the energy eigenvalues and calculate explicitly the energy eigenfunctions for the ground state and the first excited state.Comment: 14 pages, to be submitted to Phys. Lett.

High temperature specific heat and magnetic measurements in Nd0.5Sr0.5MnO3 and R0.5Ca0.5MnO3 (R=Nd, Sm, Dy and Ho) samples

We have made a magnetic characterization of Nd0.5Sr0.5MnO3, Nd0.5Ca0.5MnO3, Sm0.5Ca0.5MnO3, Dy0.5Ca0.5MnO3 and Ho0.5Ca0.5MnO3 polycrystalline samples. Ferromagnetic, antiferromagnetic and charge ordering transitions in our samples agree with previous reports. We also report specific heat measurements with applied magnetic fields between 0 and 9 T and temperatures between 2 and 300 K in all cases. Each curve was successfully fitted at high temperatures by an Einstein model with three optical phonon modes. Close to the charge ordering and ferromagnetic transition temperatures the specific heat curves showed peaks superposed to the characteristic response of the lattice oscillations. The entropy variation corresponding to the charge ordering transition was higher than the one corresponding to the ferromagnetic transition. The external magnetic field seems to have no effect in specific heat of the CO phase transition.Comment: Submitted to Journal of Applied Physic

Complete Vertical Graphs with Constant Mean Curvature in Semi-Riemannian Warped Products

We obtain necessary conditions for the existence of complete vertical graphs of constant mean curvature in the Hyperbolic and Steady State spaces. In the two-dimensional case we prove Bernstein-type results in each of these ambient spaces.Comment: 13 page

Helicoids and Catenoids in M×RM\times\mathbb{R}

Given an arbitrary $C^\infty$ Riemannian manifold $M^n$, we consider the problem of introducing and constructing minimal hypersurfaces in $M\times\mathbb{R}$ which have the same fundamental properties of the standard helicoids and catenoids of Euclidean space $\mathbb{R}^3=\mathbb{R}^2\times\mathbb{R}$. Such hypersurfaces are defined by imposing conditions on their height functions and horizontal sections, and then called $vertical\, helicoids$ and $vertical \, catenoids$. We establish that vertical helicoids in $M\times\mathbb{R}$ have the same fundamental uniqueness properties of the helicoids in $\mathbb{R}^3.$ We provide several examples of vertical helicoids in the case where $M$ is one of the simply connected space forms. Vertical helicoids which are entire graphs of functions on ${\rm Nil}_3$ and ${\rm Sol}_3$ are also presented. We give a local characterization of hypersurfaces of $M\times\mathbb{R}$ which have the gradient of their height functions as a principal direction. As a consequence, we prove that vertical catenoids exist in $M\times\mathbb{R}$ if and only if $M$ admits families of isoparametric hypersurfaces. If so, they can be constructed through the solutions of a certain first order linear differential equation. Finally, we give a complete classification of the hypersurfaces of $M\times\mathbb{R}$ whose angle function is constant

Convexity, Rigidity, and Reduction of Codimension of Isometric Immersions into Space Forms

We consider isometric immersions of complete connected Riemannian manifolds into space forms of nonzero constant curvature. We prove that if such an immersion is compact and has semi-definite second fundamental form, then it is an embedding with codimension one, its image bounds a convex set, and it is rigid. This result generalizes previous ones by M. do Carmo and E. Lima, as well as by M. do Carmo and F. Warner. It also settles affirmatively a conjecture by do Carmo and Warner. We establish a similar result for complete isometric immersions satisfying a stronger condition on the second fundamental form. We extend to the context of isometric immersions in space forms a classical theorem for Euclidean hypersurfaces due to Hadamard. In this same context, we prove an existence theorem of hypersurfaces with prescribed boundary and vanishing Gauss-Kronecker curvature. Finally, we show that isometric immersions into space forms which are regular outside the set of totally geodesic points admit a reduction of codimension to one

Metallic nanolines ruled by grain boundaries in graphene: an ab initio study

We have performed an ab initio investigation of the energetic stability, and the electronic properties of transition metals (TMs = Mn, Fe, Co, and Ru) adsorbed on graphene upon the presence of grain boundaries (GBs). Our results reveal an energetic preference for the TMs lying along the GB sites (TM/GB). Such an energetic preference has been strengthened by increasing the concentration of the TM adatoms; giving rise to TM nanolines on graphene ruled by GBs. Further diffusion barrier calculations for Fe adatoms support the formation of those TM nanolines. We find that the energy barriers parallel to the GBs are sligthly lower in comparision with those obtained for the defect free graphene; whereas, perpendicularly to the GBs the Fe adatoms face higher energy barriers. Fe and Co (Mn) nanolines are ferromagnetic (ferrimagnetic), in contrast the magnetic state of Ru nanolines is sensitive to the Ru/GB adsorption geometry. The electronic properties of those TM nanolines were characterized through extensive electronic band structure calculations. The formation of metallic nanolines is mediated by a strong hybridization between the TM and the graphene ($\pi$) orbitals along the GB sites. Due to the net magnetization of the TM nanolines, our band structure results indicate an anisotropic (spin-polarized) electronic current for some TM/GB systems

CαC^{\alpha}-regularity of Laplace equation with singular data on boundary

In this paper we are interested in regularity $C^{\alpha}$ and existence of solutions for Laplace equation on the upper half-space with nonlinear boundary condition with singular data in Morrey-type spaces. To overcome lack of real interpolation property and trace theorems, we introduce a new functional space in order to show existence and regularity. To this end, we prove sharp estimates for Riesz potential $I_{\delta}$. As a byproduct, in particular, we get $C^{1-n/\mu}(\overline{\mathbb{R}^n_+})$-regularity of solutions with singular data, covering known results in $L^p$ and Morrey space $\mathcal{M}_p^\nu$.Comment: We have changed the title of the article and update introduction and sections, inspired by anonymous referee comment

q-Deformed Kink Solutions

The q-deformed kink of the $\lambda\phi^4-$model is obtained via the normalisable ground state eigenfunction of a fluctuation operator associated with the q-deformed hyberbolic functions. The kink mass, the bosonic zero-mode and the q-deformed potential in 1+1 dimensions are found