The role of hyperplanes for characterizing suspicious units in DEA

In this paper, the suspicious units including anchor, terminal, and exterior units are investigated as important subsets of vertex units. Based on the concept of separating hyperplanes, an alternative definition of vertex units in data envelopment analysis is presented. Moreover, an advanced mathematical model for obtaining the separating hyperplane that splits up a vertex unit from the other units is proposed. Utilizing the core concept of separating hyperplanes, the special geometry of terminal units enables us to introduce a new definition for terminal units. Thus, some theorems have been proved which provide necessary and sufficient conditions for obtaining terminal units. We made use of the concept of supporting hyperplanes to provide a basic definition for exterior units and present a careful model for discovering exterior units. Also, based on the concept of supporting hyperplanes, different definitions of anchor units have been represented. Finally, the relationship between the sets of exterior, terminal and anchor units have been demonstrated in a theorem.

     

Investigation on Impurity Profiling and Degradation Behavior of WCK 771

Chromatographia - WCK 771 is a novel antibacterial drug recently launched in India for the treatment of acute bacterial skin and skin structure infections (ABSSSI). This report describes...     

The recovery of the acoustic stiffness coefficient

We are concerned with the reconstruction of a non‐differentiable acoustic stiffness reactance coefficient of a one‐dimensional hyperbolic equation using the smallest possible number of boundary readings generated by classical initial conditions. To this end, a complete set of spectral data of a string is extracted from either a single or at most two readings of the trace of the solution on the boundary. The sought coefficient is then uniquely recovered by the Krein inverse spectral theory. Copyright © 2013 John Wiley & Sons, Ltd.     

Synthesis,characterization, and biological investigation of new mixed-ligand complexes

A novel series of mixed-ligand complexes of 5,5′-{(1E,1E′)-1,4-phenelynebis(diazene-2,1-diyl)}bis(quinolin-8-ol) (H₂L₁) as a primary ligand and 4-aminoantipyrine(L₂) as a secondary ligand with Mn(II) ion were prepared using two general formulae: [Mn₂(H₂L₁)₂(L₂)₂X₄].4Cl (X = OH₂( 1 ), ONO₂⁻( 2 ), Cl=nil; OAc( 3 ), Cl = nil) and [Mn₂(H₂L₁)(L₂)₂(O₂SO₂)₂]( 4 ). Free ligands and their complexes were characterized. Electronic absorption spectra of the mixed-ligand complexes indicate a distorted octahedral geometry around the central metal ion, and the anions X⁻ are in the axial positions for all compounds. The ligands behave in a neutral bidentate manner, through nitrogen atoms and oxygen atoms of the carbonyl group (L₂), whereas H₂L₁ coordinated through nitrogen and OH groups as a neutral bidentate ligand. All complexes do not contain coordinated water molecules, but complex ( 1 ) contains four water molecules. The water molecules are removed in a single step. The complexes exhibited magnetic susceptibility corresponding to five unpaired electrons. The antimicrobial activity of the Mn(II) mixed-ligand complexes ( 1–4 ) against two gram-positive bacteria, three local gram-negative bacteria, and three fungi species was tested. Mn(II) mixed-ligand complex ( 2 ) exhibited significant antibacterial activity against Bacillus cereus, Staphylococcus aureus, Escherichia coli, Klebsiella pneumoniae, and Pseudomonas sp. Mixed-ligand complex ( 2 ) exhibited a high potential cytotoxicity against the growth of human lung cancer cells.     

Microwave-Assisted Chemoselective Regeneration of Carbonyl Compounds from Oximes by Silica Chromate/WET SiO2 Under Solvent-Free Conditions

The regeneration of carbonyl compounds from oximes were performed by using silica chromate and wet SiO ₂ (w/w 50%) under microwave irradiation and solvent-free conditions with excellent yields.