PROBABILISTIC AND AVERAGE LINEAR WIDTHS OF SOBOLEV SPACE WITH GAUSSIAN MEASURE IN SPACE S_Q(T)(1≤Q≤∞)

Probabilistic linear （N, δ）-widths and p-average linear N-widths of Sobolev space W2^r（T）, equipped with a Gaussian probability measure #, are studied in the metric of Sq （T） （1 ≤ Q ≤∞）, and determined the asymptotic equalities：λN,δ（W2^r（T）,μ,Sq（T））={（N^-1）^r＋p/2-1/q√1＋1/N·ln1/δ, 1≤q≤2, （N^-1）^r＋p/2-1/q（1＋N^-1/q√ln1/δ）,2〈q〈∞, （N^-1）^r＋p/2√lnN/δ, q=∞,and λN^（a）（W2^r（T）,μ,Sq（T））p={（N^-1）^r＋p/2-1/q, 1≤q〈∞, （N^-1）^r＋p/2-1/q√lnN, q=∞,where 0 〈 p 〈 ∞, δ∈ （0, 1/2], ρ 〉 1, and Sq（T） is a subspace of L1（T）, in which the Fourier series is absolutely convergent in lq sense.

Spherical Linear Diophantine Fuzzy Sets with Modeling Uncertainties in MCDM

The existing concepts of picture fuzzy sets(PFS),spherical fuzzy sets(SFSs),T-spherical fuzzy sets(T-SFSs)and neutrosophic sets(NSs)have numerous applications in decision-making problems,but they have various strict limitations for their satisfaction,dissatisfaction,abstain or refusal grades.To relax these strict constraints,we introduce the concept of spherical linearDiophantine fuzzy sets(SLDFSs)with the inclusion of reference or control parameters.A SLDFSwith parameterizations process is very helpful formodeling uncertainties in themulti-criteria decisionmaking(MCDM)process.SLDFSs can classify a physical systemwith the help of reference parameters.We discuss various real-life applications of SLDFSs towards digital image processing,network systems,vote casting,electrical engineering,medication,and selection of optimal choice.We show some drawbacks of operations of picture fuzzy sets and their corresponding aggregation operators.Some new operations on picture fuzzy sets are also introduced.Some fundamental operations on SLDFSs and different types of score functions of spherical linear Diophantine fuzzy numbers(SLDFNs)are proposed.New aggregation operators named spherical linear Diophantine fuzzy weighted geometric aggregation(SLDFWGA)and spherical linear Diophantine fuzzy weighted average aggregation(SLDFWAA)operators are developed for a robust MCDM approach.An application of the proposed methodology with SLDF information is illustrated.The comparison analysis of the final ranking is also given to demonstrate the validity,feasibility,and efficiency of the proposed MCDM approach.

OPTIMAL ALGORITHMS FOR DIAGONAL OPERATORS ON N-WIDTHS IN DIFFERENT COMPUTATIONAL SETTING——In Memory of Professor Sun Yongsheng

In this paper, we give some optimal algorithms for diagonal operator T from space lp（1≤p≤2） to l2 on n-widths in different computational setting.

A real-time data smoothness method based on xPC-Target

A method of real-time data smoothness which is applied in a hardware-in-the-loop （HIL） simulation platform for a plug-in hybrid electric vehicle synthetical power device is described. The input signal of the platform comes from a AC/DC switch power with output containing noises. A linear slide average arithmetic is applied to smooth the noises. To average a certain number input sample signals, this method can decrease the noises voltage level, which meet the requirement of the simulation platform. The efficiency and signal delay time are presented to describe the result of this method, and a statistical index is used to judge the arithmetic＇ s efficiency. The tests results show that the arithmetic fit the requirement of the HIL simulation platform.

THE CALCULATION OF THE PROFILE-LINEAR AVERAGE VELOCITY IN THE TRANSITION REGION FOR ULTRASONIC HEAT METER BASED ON THE METHOD OF LES

The measurement accuracy of an ultrasonic heat meter depends on the relationship of the profile-linear average velocity.There are various methods for the calculation of the laminar and turbulence flow regions,but few methods for the transition region.At present,the traditional method to deal with the transition region is to adopt the relationship for the turbulent flow region.In this article,a simplified model of the pipe is used to study the characteristics of the transition flow with specific Reynolds number.The k-εmodel and the Large Eddy Simulation（LES）model are,respectively,used to calculate the flow field of the transition region,and a comparison with the experiment results shows that the LES model is more effective than the k-εmodel,it is also shown that there will be a large error if the relationship based on the turbulence flow is used to calculate the profile-linear average velocity relationship of the transition flow.The profile-linear average velocity for the Reynolds number ranging from 5 300 to 10 000 are calculated,and the relationship curve is obtained.The results of this article can be used to improve the measurement accuracy of ultrasonic heat meter and provide a theoretical basis for the research of the whole transition flow.