A Special Algorithm for an Additive Model in Data Envelopment Analysis

A special algorithm is presented for the additive model in data envelopment analysis (DEA). The special algorithm first classifies a data set into several subsets. Then the subset is solved by a different algorithmic framework. In simulation studies, the algorithm outperformed available DEA codes. The proposed algorithm can efficiently deal with a large data set.     

An improved entry to a key intermediate for thienamycin synthesis from methyl (R)-3-hydroxybutanoate via direct epimerization at C-3 on 2-azetidinone rings

An improved entry to a key thienamycin intermediate is described which relies upon the direct epimerization at C-3 of the 3-(1-hydroxyethyl)-2-azetidinone derivatives readily obtained from methyl ($\text{R}$)-3-hydroxybutanoate.     

Pd(II)-catalyzed condensation reaction of ketoximes and dichloromethane using potassium superoxide

Methylene dioximes are formed from ketoximes and CH₂Cl₂ using either KO₂ with a catalytic amount of Pd(II) complex $\text{3}$ or K₂CO₃ with 18-crown-6 catalyst. The reactivity of ketoximes towards CH₂Cl₂ is reversed between these two methods.     

Contribution of interstitial diffusion in drug absorption from perfused rabbit muscle: effect of hyaluronidase on absorption.

[3H]Water and [14C]inulin were injected into perfused rabbit muscle with or without hyaluronidase (300 units/ml) and their absorption into venous effluent from muscle was determined. Hyaluronidase accelerated the absorption of both compounds but the enhancement of [14C]inulin was much larger than that for [3H]water. The pharmacokinetic analysis of venous appearance curves based on a physiological diffusion model elucidated that interstitial diffusion of [14C]inulin was remarkably increased by hyaluronidase treatment, suggesting the existence of steric hindrance for it by the polysaccharide network under normal conditions. Enhancement of [3H]water diffusion was also detected although enhancement ratio was about one-half of that of [14C]inulin. Mean time necessary for each process was calculated using the statistical moment concepts. The results suggested predominant contribution of the interstitial diffusion process and secondary and little contribution of local perfusion flow and permeation process across the capillary wall, respectively, in total absorption of [14C]inulin. Effect of hyaluronidase on transcapillary movement of [14C]inulin was studied using an in vitro diffusion experiment with cultured endothelial cell monolayer and no enhancing effect was shown on [14C]inulin transport across the cell monolayer. The contribution of the local perfusion flow, on the other hand, was shown to be almost equivalent to that of the diffusion process in the total absorption of [3H]water.     

SYNTHESES AND CHARACTERIZATION OF A NEW TYPE OF LIQUID CRYSTALLINE POLYESTERS

A new type of liquid crystalline polyesters with resorcin as one part of the mesogenic unitconnected together by polymethylene, or phenylene group, and lateral groups consisting of arigid azobenzene as another part of the mesogenic unit were synthesized by interfacialpolymerization of diacyl chlorides in 1, 2-dichloroethane and 2, 4-dihydroxy-4'-nitroazobenzen inaqueous alkaline solution. The polyester structures were confirmed by proton NMR and IRspectra. Their phase transition behavior and texture were studied by polarizing microscopy andDSC.     

Differential symmetry breaking operators: II. Rankin–Cohen operators for symmetric pairs

Rankin–Cohen brackets are symmetry breaking operators for the tensor product of two holomorphic discrete series representations of \(SL(2,\mathbb {R})\). We address a general problem to find explicit formulæ  for such intertwining operators in the setting of multiplicity-free branching laws for reductive symmetric pairs. For this purpose, we use a new method (F-method) developed in Kobayashi and Pevzner (Sel. Math. New Ser., (2015). doi: 10.1007/s00029-15-0207-9) and based on the algebraic Fourier transform for generalized Verma modules.The method characterizes symmetry breaking operators by means of certain systems of partial differential equations of second order. We discover explicit formulæ  of new differential symmetry breaking operators for all the six different complex geometries arising from semisimple symmetric pairs of split rank one and reveal an intrinsic reason why the coefficients of orthogonal polynomials appear in these operators (Rankin–Cohen type) in the three geometries and why normal derivatives are symmetry breaking operators in the other three cases. Further, we analyze a new phenomenon that the multiplicities in the branching laws of Verma modules may jump up at singular parameters.