In this paper, our purpose is twofold. Firstly, the tensor andresiduum operations on $L-$nested systems are introduced under thecondition of complete residuated lattice. Then we show that$L-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. Thus the new representation theorem of$L-$subsets on complete re...

Chlorophylls are essential cofactors for photosynthesis, which sustains global food chains and oxygen production. Billions of tons of chlorophylls are synthesized annually, yet full understanding of chlorophyll biosynthesis has been hindered by the lack of characterization of the Mg-protoporphyrin IX monomethyl ester oxidative cyclase step, which confers the distinctive green color of these pig...

To ensure the safe operation of technical processes, the occurrence of a fault has to be reliably detected for a supervisory component to react in time. We investigate the sensitivity of the measured outputs with respect to abrupt or parametric faults for polynomial hybrid systems. For this we define a sensitivity measure based on the reachable sets of the outputs. The approach allows for the c...

We describe a class of affine toric varieties V that are set-theoretically minimally defined by codimV + 1 binomial equations over fields of any characteristic.

Rough sets theory is an effective mathematical tool dealing with vagueness and uncertainty. It has been applied in a variety of fields such as data mining, pattern recognition or process control. It is very important to compute the attribute reduction in real applications of rough set theory. To compute the optimal attribute reduction is NP-hard. Many heuristic attribute reduction algorithms wi...

Edwards curves were the first curves shown to have a complete addition law. However, the completeness of the addition law depends on the curve parameters and even a complete Edwards curve becomes incomplete over a quadratic field extension. This paper covers arbitrary Edwards curves and gives a set of two addition laws that for any pair of input points P1, P2 produce the sum P1 + P2.

Set constraints are inclusion relations between expressions denoting sets of ground terms over a ranked alphabet They are the main ingredient in set based program analysis In this paper we pro vide a Gentzen style axiomatization for sequents where and are nite sets of set constraints based on the axioms of termset al gebra Sequents of the restricted form correspond to positive set constraints a...

We consider the situation where one is given a set S of points in the plane and a collection D of unit disks embedded in the plane. We show that finding a minimum cardinality subset of D such that any path between any two points in S is intersected by at least one disk is NP-complete. This settles an open problem raised in [1]. Using a similar reduction, we show that finding a minimum cardinali...

Large-scale quantum information processors must be able to transport and maintain quantum information and repeatedly perform logical operations. Here, we show a combination of all of the fundamental elements required to perform scalable quantum computing through the use of qubits stored in the internal states of trapped atomic ions. We quantified the repeatability of a multiple-qubit operation ...