We describe some general geometric properties of the fiber product preserving bundle functors. Special attention is paid to the vertical Weil bundles. We discuss namely the flow natural maps and the functorial prolongation of connections. The main purpose of the present paper is to describe some geometric properties of the category FMm of fibered manifolds with m-dimensional bases and local fib...

In this paper, we propose an efficient framework for edge-preserving stereo matching. Local methods for stereo matching are more suitable than global methods for real-time applications. Moreover, we can obtain accurate depth maps by using edge-preserving filter for the cost aggregation process in local stereo matching. The computational cost is high, since we must perform the filter for every n...

Let $mathcal {A} $ and $mathcal {B} $ be C$^*$-algebras. Assume that $mathcal {A}$ is of real rank zero and unital with unit $I$ and $k>0$ is a real number. It is shown that if $Phi:mathcal{A} tomathcal{B}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $Phi(|A|^k)=|Phi(A)|^k $ for all normal elements $Ainmathcal A$, $Phi(I)$ is a projection, and there exists a posit...

A large class of neural network models have their units organized in a lattice with fixed topology or generate their topology during the learning process (usually unsupervised). These network models can be used as neighborhood preserving map and some of them generate a perfect topology preserving map of the input manifold using competitive Hebbian rule. But such a structure is difficult to mana...

In the paper, we investigate the duality of categories of complete lattices and maps preserving suprema or infima according to [15, p. 179–183; 1.1–1.12]. The duality is based on the concept of the Galois connection. Let S, T be complete lattices. Note that there exists a connection between S and T which is Galois. One can prove the following proposition (1) Let S, T , S , T be non empty relati...