Floating point round-off causes erroneous and inconsistent decisions in geometric modelling algorithms. These errors lead to the generation of topologically invalid boundary models for CSG objects and significantly reduce the reliability of CAD applications. Previously known methods that guarantee topological consistency by relying on arbitrary precision rational arithmetic or on symbol-manipul...

The origin of this paper is in a question that was asked of the author by Michael Wellman, a computer scientist who works in artificial intelligence at Wright Patterson Air Force Base in Dayton, Ohio. He wanted to know if, starting with R and its usual topology and product partial order, he could linearly reorder every finite subset and still obtain a continuous function from R into R that was ...

generally ordering policies are done by two methods, including fix order quantity (foq) and fix order period (fop). these methods are static and either the quantity of ordering or the procedure of ordering is fixing in throughout time horizon. in real environments, demand is varying in any period and may be considered as uncertainty. when demand is variable in any period, the traditional and st...

in this work, we introduce notion of connectedness on fuzzy soft topological spaces and present fundamentals properties. we also investigate effect to fuzzy soft connectedness. moreover, c_i-connectedness which plays an important role in fuzzy topological space extend to fuzzy soft topological spaces.

Problem 540 of J. D. Lawson and M. Mislove in Open Problems in Topology asks whether the process of taking duals terminate after finitely many steps with topologies that are duals of each other. The problem for T1 spaces was already solved by G. E. Strecker in 1966. For certain topologies on hyperspaces (which are not necessarily T1), the main question was in the positive answered by Bruce S. B...

Abstract Topological defects in liquid crystals (LCs) dominate molecular alignment/motion many cases. Here, the neural network (NN) function has been introduced to predict LC orientation condition (orientation angle and order parameter) at local positions around topological from phase/polarization microscopic color images. The NN was trained advance by using information of an a planar alignment...

In this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. It gives some criterions to study locally convex topological spaces in a discrete approach.

in this paper, a mathematical method is proposed to formulate a generalized ordering problem. this model is formed as a linear optimization model in which some variables are binary. the constraints of the problem have been analyzed with the emphasis on the assessment of their importance in the formulation. on the one hand, these constraints enforce conditions on an arbitrary subgraph and then g...

In this paper, we study the separtion axioms $T_0,T_1,T_2$ and $T_{5/2}$ on topological and semitopological residuated lattices and we show that they are equivalent on topological residuated lattices. Then we prove that for every infinite cardinal number $alpha$, there exists at least one nontrivial Hausdorff topological residuated lattice of cardinality $alpha$. In the follows, we obtain some ...