The map x y p x y x of the plane is area preserving and has the remarkable property that in numerical studies it shows exact integrability The plane is a union of smooth disjoint invariant curves of the map However the integral has not explicitly been known In the current paper we will show that the map does not have an algebraic integral i e there is no non constant function F x y such that F ...

In this article, we study local holomorphic conformal embeddings from B into B1 × · · · ×BNm with respect to the normalized Bergman metrics. Assume that each conformal factor is smooth Nash algebraic. Then each component of the map is a multi-valued holomorphic map between complex Euclidean spaces by the algebraic extension theorem derived along the lines of Mok and Mok-Ng. Applying holomorphic...

In this paper we discuss the packing properties of invariant disks defined by periodic behavior of a model for a bandpass Σ–∆ modulator. The periodically coded regions form a packing of the forward invariant phase space by invariant disks. For this one-parameter family of PWIs, by introducing codings underlying the map operations we give explicit expressions for the centers of the disks by anal...

This paper is a continuation of [4, 9, 13]. To classify algebraic varieties is one of the goals in algebraic geometry. One way to study a given variety is to understand the behavior of its pluricanonical maps. The objects concerned here are complex projective 3-folds of general type over C. Let X be such an object and denote by φm the m-th pluricanonical map of X , which is the rational map ass...

In this article we introduce the notion of Split Variational Autoencoder (SVAE), whose output $\hat{x}$ is obtained as a weighted sum $\sigma \odot \hat{x_1} + (1-\sigma) \hat{x_2}$ two generated images $\hat{x_1},\hat{x_2}$, and $\sigma$ {\em learned} compositional map. The composing well $\sigma$-map are automatically synthesized by model. network trained usual with negative loglikelihood los...

In this article, we study local holomorphic isometric embeddings from Bn into BN1 × · · · × BNm with respect to the normalized Bergman metrics up to conformal factors. Assume that each conformal factor is smooth Nash algebraic. Then each component of the map is a multi-valued holomorphic map between complex Euclidean spaces by the algebraic extension theorem derived along the lines of Mok and M...