The regression model yt = tjt(9u . . . . 0m) + s,; (i"= 1 , . . . , JV, 0 £ (9) is considered, with ;/; nonlinear and continuously twice differentiable and with («j, . . . , ejv) ~ V(0, £ ) , £ k n o w n . The one-dimensional case (i.e. m = 1) is investigated mainly. A nonlinear geometry of the sample space R is proposed and curves parallel to the set {(t/^9),..., tjN(0)); 6 e &} are considered...

We prove results on solvability of nonlinear elliptic partial differential systems of principle type of second order. They are consequences of existence of non-radial solutions for nonlinear partial differential systems of Poisson type. As applications to geometry, we prove the exsitence of local harmonic maps with given tangent plane at a point between any Riemannan manifolds. More generally g...

We report on the observation of second-harmonic conical waves generated in a novel geometry of the transverse excitation of an annular periodically poled nonlinear photonic structure by a fundamental Gaussian beam. We show that the conical beams are formed as a result of the higher-order nonlinear Bragg diffraction involving two parametric processes in which an ordinary fundamental wave is conv...

One has believed that low energy effective theories of the Higgs branch of gauged linear sigma models correspond to supersymmetric nonlinear sigma models, which have been already investigated by many works. In this paper we discuss a explicit derivation of supersymmetric nonlinear sigma models from gauged linear sigma models. In this process we construct Kähler potentials of some two-dimensiona...

In recent years, there has been a large interest in the applications of the Frenet-Serret equations for a space curve in various contexts, and interesting connections between geometry and integrable nonlinear evolution equations have been revealed. The subject of how space curves evolve in time is of great interest and has been investigated by many authors. Hasimoto showed that the evolution of...

We fabricate and characterize waveguides composed of closely spaced and longitudinally oriented silicon ridges etched into silicon-on-insulator wafers. Through both guided mode and bulk measurements, we demonstrate that the patterning of silicon waveguides on such a deeply subwavelength scale is desirable for nonlinear and sensing applications alike. The proposed waveguide geometry simultaneous...

We generalize the nonlinear one-dimensional equation for a fluid layer surface to any geometry and we introduce a new infinite order differential equation for its traveling solitary waves solutions. This equation can be written as a finite-difference expression, with a general solution that is a power series expansion with coefficients satisfying a nonlinear recursion relation. In the limit of ...

We report simultaneous generation of multiple conical second-harmonic waves in a two-dimensional nonlinear photonic structure when illuminated by two overlapping noncollinear fundamental beams. We show that this phenomenon is caused by the nonlinear Čerenkov radiation emitted due to the interaction of photons from each constituent fundamental beam as well as the virtual one propagating along th...

We study the instantaneous nonlinear index change in Al,,,Gac,sAs waveguides below the twophoton absorption edge and find Sphase shifts with 80 pJ, 0.4 ps pulses at wavelengths near 1.6 pm. These large phase shifts are obtained with less than 1 dB of loss from multiphoton absorption. Our results indicate that AlGaAs waveguides, which have a mature fabrication technology, can be used as compact ...

A nonlinear scale-space theory discovered by G. Bluman and S. Kumei is revisited and brought to the attention of computer vision community. Bluman and Kumei found that there exist a unique class of di usivity functions depending only on the local image grey-values that allows the related nonlinear scale-space of an image to be brought in a one-to-one correspondence with a linear scale-space of ...