Goal programming approaches for data envelopment analysis cross efficiency evaluation

Cross efficiency evaluation has long been proposed as an alternative method for ranking the decision making units (DMUs) in data envelopment analysis (DEA). This study proposes goal programming models that could be used in the second stage of the cross evaluation. Proposed goal programming models have different efficiency concepts as classical DEA, minmax and minsum efficiency criteria. Numerical examples are provided to illustrate the applications of the proposed goal programming cross efficiency models.     

Mixed modulus of smoothness with Muckenhoupt weights and approximation by angle

Mixed modulus of smoothness in weighted Lebesgue spaces with Muckenhoupt weights are investigated. Using mixed modulus of smoothness we obtain Potapov type direct and inverse estimates of angular trigonometric approximation of functions in these spaces. Also we obtain equivalences between mixed modulus of smoothness and K-functional and realization functional. Fractional order modulus of smoothness is considered as well.     

Synthesis,Structural, and Physicochemical Study of First- and Second-Generation Melamine-Based Dendrimers

Abstract

First-tier (G₁) 2,4,6-tridiethymalonate-triazine (2,4,6-TDEMTA) and second-tier (G₂) 2,4,6-hexadiethylmalonate-triazine (2,4,6-HDEMTA) dendrimers were prepared with melamine (1,3,5-triazine) as core (G₀) and sodium malonate ester for bifurcation of chains. The trichlorotriazine (TCT) and sodium diethyl malonate (SDEM) aqueous solutions were mixed, and a creamy white precipitate of G₁ was obtained. The G₁ was hydrolyzed in alkaline medium to prepare 2,4,6-tridisodiummalonate-triazine (2,4,6-TDSMTA) by replacing ?C₂H₅ groups of COOC₂H₅ by Na, which was further neutralized by dilute HCl to obtain 2,4,6-trimalonicacid-triazine (2,4,6-TMATA). The TMATA was treated with PCl₅(s) to form –COCl, which was treated with SDEM to form the G₂.     

Rubio de Francía's weighted extrapolation in mixed-norm spaces and applications

Weighted extrapolation for pairs of functions in mixed-norm Banach function spaces defined on the product of quasi-metric measure spaces $(X,d,\mu )$ and $(Y,\rho ,\nu )$ are derived. As special cases, we have appropriate results for mixed-norm Lebesgue, Lorentz, and Orlicz spaces. Some of the derived results are applied to get weighted extrapolation in mixed-norm grand Lebesgue spaces.     

Poincaré's inequality and Sobolev spaces with monomial weights

In this paper, we use a weighted version of Poincaré's inequality to study density and extension properties of weighted Sobolev spaces over some open set $\mathrm{\Omega }\subseteq {\mathbb{R}}^N$. Additionally, we study the specific case of monomial weights $w(x_1,\text{…},x_N)={\prod }_{i=1}^N{\left|x_i\right|}^{a_i},a_i\ge 0$, showing the validity of a weighted Poincaré inequality together with some embedding properties of the associated weighed Sobolev spaces.     

Impact of Correlated Activity and STDP on Network Structure

Synaptic strengths between neurons are plastic and modified by spontaneous activity and information from the outside. There is increasing interest in the impact of correlated neuron activity and learning rules on global network structure. Here the networks of exponential integrate-and-fire neurons with spike timing-dependent plasticity (STDP) learning rules are considered, by providing the theoretical approximation of spiking cross-covariance between connected neurons and the theory for the evolution of synaptic weights. Background input mean and variance highly affect the spiking covariance, even for the fixed baseline firing rate and connection. Through analyzing the effects of covariance and STDP on vector fields for pairwise correlated neurons under fixed baseline firing rate, we show that the connections from a neuron with lower input mean to that with higher one will strengthen for balanced Hebbian STDP. However, this situation is reversed for Anti-Hebbian cases. Moreover, for potentiation dominated STDP, the synaptic weights for the networks of neurons with lower input mean are more likely to be enhanced. In addition, these properties found from coupled neurons also hold for large recurrent networks in both theories and simulations. This study provides a self-consistent theoretical method for understanding how correlated spiking activity and STDP shape the network structure and an approach for predicting structures of large networks through the analysis of simple neural circuits.     

Prediction of Sol Fraction and Average Molecular Weights after Gelation for Non‐Linear Free Radical Polymerizations Using a Kinetic Approach

Mass balance equations in terms of the moment generating function of the distribution of mole concentrations of polymer species for free radical copolymerizations of mono/divinyl monomers could be numerically solved after gel point using open source code ACDC, needed for extremely stiff two‐point boundary value problems. For the first time, it became possible to compare the error of earlier well‐known approximated estimation methods for the weight fraction of sol and average molecular weights to this accurate mathematical solution. It turns out that predictions by the pseudo‐kinetic method are reasonable only when equal reactivity of double bonds prevails, causing early gelation in the batch reactor. Otherwise the discrepancies between the exact and approximate solutions are quite important.

Comparison between predicted number‐average and weight‐average degrees of polymerization of sol in batch non‐linear free radical polymerizations of model system III.