We investigate inverse limits with set-valued bonding functions. We generalize theorems of W. T. Ingram and William S. Mahavier, and of Van Nall, on the connectedness of the inverse limit space. We establish a fixed point theorem and show that under certain conditions, inverse limits with set-valued bonding functions can be realized as ordinary inverse limits. We also obtain some results that a...

Semi-supervised learning methods using Generative Adversarial Networks (GANs) have shown promising empirical success recently. Most of these methods use a shared discriminator/classifier which discriminates real examples from fake while also predicting the class label. Motivated by the ability of the GANs generator to capture the data manifold well, we propose to estimate the tangent space to t...

A subset A of a space X is called regular open if A = IntA, and regular closed if X\A is regular open, or equivalently, if A= IntA. A is called semiopen [16] (resp., preopen [17], semi-preopen [3], b-open [4]) ifA⊂ IntA (resp.,A⊂ IntA,A⊂ IntA ,A⊂ IntA∪ IntA). The concept of a preopen set was introduced in [6] where the term locally dense was used and the concept of a semi-preopen set was introd...

We continue the study, begun in [11], of inverse Chevalley formulas for equivariant K-group semi-infinite flag manifolds. Using language alcove paths, we reformulate and extend our combinatorial formula to arbitrary weights all simply-laced types (conjecturally also type E8).

Abstract Seven-degree-of-freedom redundant manipulators with link offset have many advantages, including obvious geometric significance and suitability for configuration control. Their is similar to that of the experimental module manipulator (EMM) in Chinese Space Station Remote Manipulator System. However, finding analytical solution an EMM on basis arm angle parameterization difficult. This ...

Analytical techniques are used to solve a class of inverse radiative-transfer problems relevant to 1nite and semi-in1nite plane-parallel media. While the assumption of isotropic scattering is made, di*use re+ection is allowed at the surface, for the semi-in1nite case, and at both surfaces for the case of a 1nite layer. For the general case based on a semi-in1nite medium, a cubic algebraic equat...