Enhanced Russell measure in fuzzy DEA

The radial measures of classical DEA models (CCR, BCC) are incomplete, they are only separate measures of input and output efficiency and their efficiency index omit the non-zero input and output slacks. Enhanced Russell graph measure (ERM) eliminates these deficiencies. All of the existing fuzzy DEA models are extension of CCR or BCC model, efficiencies of DMUs, ultimately, are solution of CCR or BCC model. Based on ERM model, a fuzzy DEA model is proposed to deal with the efficiency evaluation problem with the given fuzzy input and output data, by using a ranking method based on the comparison of α-cuts. The proposed framework is illustrated through an application to performance assessment of flexible manufacturing system and comparative results are presented. The efficiency measure of the proposed approach is relatively more reasonable than those of fuzzy DEA models based on CCR or BCC model and represents some real-life processes more appropriately.non-radial measures; fuzzy DEA; data envelopment analysis; FMS; flexible manufacturing system; FMS performance; enhanced Russell measure; Russell graph; performance evaluation.

A class of singular n-dimensional impulsive Neumann systems

Abstract This paper investigates the existence of infinitely many positive solutions for the second-order n-dimensional impulsive singular Neumann system −x″(t)+Mx(t)=λg(t)f(t,x(t)),t∈J,t≠tk,−Δx′|t=tk=μIk(tk,x(tk)),k=1,2,…,m,x′(0)=x′(1)=0. $$\begin{aligned}& -\mathbf{x}^{\prime\prime}(t)+ M\mathbf{x}(t)=\lambda {\mathbf{g}}(t)\mathbf{f} \bigl(t,\mathbf{x}(t) \bigr),\quad t\in J, t\neq t_{k}, \\& -\Delta {\mathbf{x}}^{\prime}|_{t=t_{k}}=\mu {\mathbf{I}}_{k} \bigl(t_{k},\mathbf{x}(t_{k}) \bigr),\quad k=1,2,\ldots ,m, \\& \mathbf{x}^{\prime}(0)=\mathbf{x}^{\prime}(1)=0. \end{aligned}$$ The vector-valued function x is defined by x=[x1,x2,…,xn]⊤,g(t)=diag[g1(t),…,gi(t),…,gn(t)], $$\begin{aligned}& \mathbf{x}=[x_{1},x_{2},\dots ,x_{n}]^{\top }, \qquad \mathbf{g}(t)=\operatorname{diag} \bigl[g_{1}(t), \ldots ,g_{i}(t), \ldots , g_{n}(t) \bigr], \end{aligned}$$ where gi∈Lp[0,1] $g_{i}\in L^{p}[0,1]$ for some p≥1 $p\geq 1$, i=1,2,…,n $i=1,2,\ldots , n$, and it has infinitely many singularities in [0,12) $[0,\frac{1}{2})$. Our methods employ the fixed point index theory and the inequality technique

Symmetric positive solutions for fourth-order n-dimensional m-Laplace systems

Abstract This paper investigates the existence, multiplicity, and nonexistence of symmetric positive solutions for the fourth-order n-dimensional m-Laplace system {ϕm(x″(t)))″=Ψ(t)f(t,x(t)),0<t<1,x(0)=x(1)=∫01g(s)x(s)ds,ϕm(x″(0))=ϕm(x″(1))=∫01h(s)ϕm(x″(s))ds. $$\left \{ \textstyle\begin{array}{l} \phi_{m}(\mathbf{x}{''}(t))){''}=\Psi(t)\mathbf{f}(t,\mathbf{x}(t)), \quad 0< t< 1,\\ \mathbf{x}(0)=\mathbf{x}(1)=\int_{0}^{1}\mathbf{g}(s)\mathbf{x}(s)\, ds,\\ \phi_{m}(\mathbf{x}{''}(0))=\phi_{m}(\mathbf{x}{''}(1))=\int _{0}^{1}\mathbf{h}(s)\phi_{m}(\mathbf{x}{''}(s))\,ds. \end{array}\displaystyle \right .$$ The vector-valued function x is defined by x=[x1,x2,…,xn]⊤ $\mathbf {x}=[x_{1},x_{2},\dots,x_{n}]^{\top}$, Ψ(t)=diag[ψ1(t),…,ψi(t),…,ψn(t)] $\Psi(t)=\operatorname{diag}[\psi_{1}(t), \ldots, \psi _{i}(t), \ldots, \psi_{n}(t)]$, where ψi∈Lp[0,1] $\psi_{i}\in L^{p}[0,1]$ for some p≥1 $p\geq1$. Our methods employ the fixed point theorem in a cone and the inequality technique. Finally, an example illustrates our main results

Necessary and Sufficient Conditions for the Existence of Positive Solution for Singular Boundary Value Problems on Time Scales

By constructing available upper and lower solutions and combining the Schauder&#39;s fixed point theorem with maximum principle, this paper establishes sufficient and necessary conditions to guarantee the existence of Cld[0,1]&#x1D54B; as well as Cld&#x0394;[0,1]&#x1D54B; positive solutions for a class of singular boundary value problems on time scales. The results significantly extend and improve many known results for both the continuous case and more general time scales. We illustrate our results by one example

Detection system for coal mine electrical inspection instrument with digital display based on machine visio

In view of problems of low measurement efficiency, high labour intensity and being influenced by subjective factors in manually calibrating coal mine electrical inspection instrument with digital display, an automatic inspection system for coal mine electrical inspection instrument with digital display was designed based on machine vision. The system controls power on of the instrument and a video to get booting process, and uses high lights statistics mode to identify key display frame of the electrical inspection instrument, uses template matching to complete automatic identification of the display image, and uses digit recognition with threading method to detect the measurement accuracy automaticly. Validity of the designed system is verified with experiment results from industrial prototype system

Synthesis and Biological Activity of Novel 1-(Substituted Phenoxyacetoxy) Alkyl Phosphonates and Phosphinates

To investigate the influence of nitro group on the biological activity of phenoxyacetoxy phosphonates and phosphinates, a series of novel 1-(substituted phenoxyacetoxy) alkyl phosphonates and phosphinates were synthesized and screened for herbicidal activity and plant growth regulatory activity. Compounds 5a, 5b and 5j exhibited notable bioactivity. Results indicated that nitro groups had a great influence on the biological activity, and the improvement of biological activity required a reasonable combination of a nitro group and other substituents