Elliptic equations with transmission and Wentzell boundary conditions and an application to steady water waves in the presence of wind

In this paper, we present results about the existence and uniqueness of solutions of elliptic equations with transmission and Wentzell boundary conditions. We provide Schauder estimates and existence results in H\"older spaces. As an application, we develop an existence theory for small-amplitude two-dimensional traveling waves in an air-water system with surface tension. The water region is assumed to be irrotational and of finite depth, and we permit a general distribution of vorticity in the atmosphere.Comment: 33 page

Uncountable families of prime z-ideals in C_0(R)

Denote by \continuum=2^{\aleph_0} the cardinal of continuum. We construct an intriguing family (P_\alpha: \alpha\in\continuum) of prime $z$-ideals in \C_0(\reals) with the following properties: If $f\in P_{i_0}$ for some i_0\in\continuum, then $f\in P_i$ for all but finitely many i\in \continuum; \bigcap_{i\neq i_0} P_i \nsubset P_{i_0} for each \i_0\in \continuum. We also construct a well-ordered increasing chain, as well as a well-ordered decreasing chain, of order type $\kappa$ of prime $z$-ideals in \C_0(\reals) for any ordinal $\kappa$ of cardinality \continuum.Comment: 12 page

On neutrino and charged lepton masses and mixings: A view from the electroweak-scale right-handed neutrino model

We present a model of neutrino masses within the framework of the EW-$\nu_R$ model in which the experimentally desired form of the PMNS matrix is obtained by applying an $A_4$ symmetry to the \emph{Higgs singlet sector} responsible for the neutrino Dirac mass matrix. This mechanism naturally avoids potential conflict with the LHC data which severely constrains the Higgs sector, in particular the Higgs doublets. Moreover, by making a simple $ans\ddot{a}tz$ we extract $\mathcal{M}_l {\mathcal{M}_l}^\dagger$ for the charged lepton sector. A similar $ans\ddot{a}tz$ is proposed for the quark sector. The sources of masses for the neutrinos are entirely different from those for the charged leptons and for the quarks and this might explain why $U_{PMNS}$ is {\em very different} from $V_{CKM}$.Comment: 19 pages. Two figure

Dense Piecewise Planar RGB-D SLAM for Indoor Environments

The paper exploits weak Manhattan constraints to parse the structure of indoor environments from RGB-D video sequences in an online setting. We extend the previous approach for single view parsing of indoor scenes to video sequences and formulate the problem of recovering the floor plan of the environment as an optimal labeling problem solved using dynamic programming. The temporal continuity is enforced in a recursive setting, where labeling from previous frames is used as a prior term in the objective function. In addition to recovery of piecewise planar weak Manhattan structure of the extended environment, the orthogonality constraints are also exploited by visual odometry and pose graph optimization. This yields reliable estimates in the presence of large motions and absence of distinctive features to track. We evaluate our method on several challenging indoors sequences demonstrating accurate SLAM and dense mapping of low texture environments. On existing TUM benchmark we achieve competitive results with the alternative approaches which fail in our environments.Comment: International Conference on Intelligent Robots and Systems (IROS) 201

Isometries between quantum convolution algebras

Given locally compact quantum groups \G_1 and \G_2, we show that if the convolution algebras L^1(\G_1) and L^1(\G_2) are isometrically isomorphic as algebras, then \G_1 is isomorphic either to \G_2 or the commutant \G_2'. Furthermore, given an isometric algebra isomorphism \theta:L^1(\G_2) \rightarrow L^1(\G_1), the adjoint is a *-isomorphism between L^\infty(\G_1) and either L^\infty(\G_2) or its commutant, composed with a twist given by a member of the intrinsic group of L^\infty(\G_2). This extends known results for Kac algebras (although our proofs are somewhat different) which in turn generalised classical results of Wendel and Walter. We show that the same result holds for isometric algebra homomorphisms between quantum measure algebras (either reduced or universal). We make some remarks about the intrinsic groups of the enveloping von Neumann algebras of C$^*$-algebraic quantum groups.Comment: 23 pages, typos corrected, references adde