Constraint-induced restriction and extension operators with applications

The Stokes operator is a differential-integral operator induced by the Stokes equations. In this paper, we analyze the Stokes operator from the point of view of the Helmholtz minimum dissipation principle. We show that, through the Hodge orthogonal decomposition, a pair of bounded linear operators, a restriction operator and an extension operator, are induced from the divergence-free constraint. As a consequence, we use it to calculate the eigenvalues of the Stokes operator.

Aggregation Operators for Decision Making Based on q-Rung Orthopair Fuzzy Hypersoft Sets:An Application in Real Estate Project

In this paper,a decision-making problem with a q-rung orthopair fuzzy hypersoft environment is developed,and two operators of ordered weighted average and induced ordered weighted average are developed.Several fundamental features are also derived.The induced ordered weighted average operator is essential in a q-ROFH environment as the induced ordered aggregation operators are special cases of the existing aggregation operators that already exist in q-ROFH environments.The main function of these operators is to help decision-makers gain a complete understanding of uncertain facts.The proposed aggregation operator is applied to a decision-making problem,with the aim of selecting the most promising real estate project for investment.

A CLASS OF REACTION-DIFFUSION EQUATIONS WITH HYSTERESIS DIFFERENTIAL OPERATOR

In this paper, the classical and weak derivatives with respect to spatial variable of a class of hysteresis functional are discussed. Some conclusions about solutions of a class of reaction-diffusion equations with hysteresis differential operator are given.

An anomaly detection method for spacecraft solar arrays based on the ILS-SVM model

Solar arrays are important and indispensable parts of spacecraft and provide energy support for spacecraft to operate in orbit and complete on-orbit missions.When a spacecraft is in orbit,because the solar array is exposed to the harsh space environment,with increasing working time,the performance of its internal electronic components gradually degrade until abnormal damage occurs.This damage makes solar array power generation unable to fully meet the energy demand of a spacecraft.Therefore,timely and accurate detection of solar array anomalies is of great significance for the on-orbit operation and maintenance management of spacecraft.In this paper,we propose an anomaly detection method for spacecraft solar arrays based on the integrated least squares support vector machine(ILS-SVM)model:it selects correlated telemetry data from spacecraft solar arrays to form a training set and extracts n groups of training subsets from this set,then gets n corresponding least squares support vector machine(LS-SVM)submodels by training on these training subsets,respectively;after that,the ILS-SVM model is obtained by integrating these submodels through a weighting operation to increase the prediction accuracy and so on;finally,based on the obtained ILS-SVM model,a parameterfree and unsupervised anomaly determination method is proposed to detect the health status of solar arrays.We use the telemetry data set from a satellite in orbit to carry out experimental verification and find that the proposed method can diagnose solar array anomalies in time and can capture the signs before a solar array anomaly occurs,which reflects the applicability of the method.

Uncertainty and Reduction in Intuitionistic Fuzzy Covering Based Rough Sets

This paper proposes a novel pair of induced IF covering approximation operators in an IF covering approximation space,and discusses some basic properties about definable IFSs.A measure is defined to describe the uncertainty of IFSs in IF covering approximation spaces.Finally,we study the properties of reductions of an IF covering respectively based on induced IF covering approximation operators and IF covering approximation operators.