Let B be the unit ball in the complex space C. Write Rat(B,B) for the space of proper rational holomorphic maps from B into B and Poly(B,B ) for the set of proper polynomial holomorphic maps from B into B . We say that F and G ∈ Rat(B,B) are equivalent if there are automorphisms σ ∈ Aut(B) and τ ∈ Aut(B ) such that F = τ ◦G◦σ. Proper rational holomorphic maps from B into B with N ≤ 2n− 2 are eq...

Recall that a continuous function $fcolon Xto Y$ between Tychonoff spaces is proper if and only if the Stone extension $f^{beta}colon beta Xtobeta Y$ takes remainder to remainder, in the sense that $f^{beta}[beta X-X]subseteq beta Y-Y$. We introduce the notion of ``taking remainder to remainder" to frames, and, using it, we define a frame homomorphism $hcolon Lto M$ to be $beta$-proper, $lambd...

CID map (similar results obtained for CIR and inclination maps) obtainable in as little as one minute following CA injection, compared to (b) T2w and (c) SSFP imaging that visualize a more homogeneous lesion. (d) Delayed enhancement imaging acquired many minutes post-contrast injection demonstrate similar lesion core and border regions after subtraction with pre-contrast data. a b c d VISUALIZA...

Production and prediction of land-use/land cover changes (LULCC) map are among the significant issues regarding input of many environmental and hydrological models. Among various introduced methods, similarity-weighted instance-based machine learning algorithm (SimWeight) and Markov-chain with lower complexity and proper performnce are frequently used. The main aim of this study is utilizing Si...

In this paper, numerical investigation of upward two phase flow of air-water has been studied. Different conditions of flow regimes including annular, wispy annular, slug, churn and bubbly are simulated based on Hewitt and Roberts map, and a good agreement between the experimental data of the map and the numerical simulation has been observed. Accordingly, a proper CFD model in CFD software of ...

We prove that the Reeb space of a proper definable map in an arbitrary o-minimal expansion of the reals is realizable as a proper definable quotient. We also show that the Betti numbers of the Reeb space of a map f can be arbitrarily large compared to those of X, unlike in the special case of Reeb graphs of manifolds. Nevertheless, in the special case when f : X → Y is a semi-algebraic map and ...