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.

     

Cubane,Bicyclo[1.1.1]pentane and Bicyclo[2.2.2]octane: Impact and Thermal Sensitiveness of Carboxyl-, Hydroxymethyl- and Iodo-substituents

With the burgeoning interest in cage motifs for bioactive molecule discovery, and the recent disclosure of 1,4-cubane-dicarboxylic acid impact sensitivity, more research into the safety profiles of cage scaffolds is required. Therefore, the impact sensitivity and thermal decomposition behavior of judiciously selected starting materials and synthetic intermediates of cubane, bicyclo[1.1.1]pentane (BCP), and bicyclo[2.2.2]octane (BCO) were evaluated via hammer test and sealed cell differential scanning calorimetry, respectively. Iodo-substituted systems were found to be more impact sensitive, whereas hydroxymethyl substitution led to more rapid thermodecomposition. Cubane was more likely to be impact sensitive with these substituents, followed by BCP, whereas all BCOs were unresponsive. The majority of derivatives were placed substantially above Yoshida thresholds—a computational indicator of sensitivity.     

PhI(OTf)2 Does Not Exist (Yet)**

PhI(OTf)₂ has been used for the past 30 years as a strong I(III) oxidant for organic and inorganic transformations. It has been reported to be generated in situ from the reactions of either PhI(OAc)₂ or PhI=O with two equivalents of trimethylsilyl trifluoromethanesulfonate (TMS-OTf). In this report it is shown that neither of these reactions generate a solution with spectroscopic data consistent with PhI(OTf)₂, with supporting theoretical calculations, and thus this compound should not be invoked as the species acting as the oxidant for transformations that have been associated with its use.     

Cyclooctatetraenes through Valence Isomerization of Cubanes: Scope and Limitations

The scope and limitations of Eaton's rhodium(I)-catalyzed valence isomerization of cubane to cyclooctatetraene (COT) were investigated in the context of functional group tolerability, multiple substitution modes and the ability of cubane-alcohols to undergo one-pot tandem Ley–Griffith Wittig reactions in the absence of a transition metal catalyst.     

Quantum rings as a perfect spin-splitter and spin-filter by using the Rashba effect

Spin related conductance and polarization via an open ballistic quantum nanoringconnected to one input lead and two output ones are studied by considering the Rashbaeffect based on the transfer matrix method. Our probes show that controlling on Rashbastrength leads to 100 percent spin polarization while we have high efficiency for thesystem. In addition, it is possible to design the position of input and output leads insuch a way as to optimize the system to work as a spin filtering or spin switching nanodevice. Also, this apparatus can work as a Stern-Gerlach tool which can be used in someimportant practical nano-industrial applications. By controlling on Rashba strength in aspecial design of two output lead positions, it is possible to divide the input chargecurrent into any output ones while the partial output charge current has substantial valuein one of two output leads and it is reduced in the other one simultaneously. Bycontrolling on Rashba strength in a special design of output lead positions, the spinconductance can attain a considerable value in one output lead despite an insignificantvalue in the other one simultaneously.     

Stachyonic Acid: A Dengue Virus Inhibitor from Basilicum polystachyon

Stachyonic acid A, arising from the first in-depth phytochemical investigation of the herb Basilicum polystachyon, was found to display potent inhibitory activity against dengue virus, with limited cytotoxicity. Andrographolide, a known dengue virus inhibitor and closely related labdane-type diterpene, is structurally more complex but displayed poor antiviral activity in the PRNT assay, and increased cytotoxicity in comparison. Furthermore, a Diels–Alder reaction with PTAD identified the active pharmacophore of stachyonic acid to be the conjugated diene.     

Investigating the Role of Vacancies on the Thermoelectric Properties of EuCuSb-Eu2ZnSb2 Alloys

AMX compounds with the ZrBeSi structure tolerate a vacancy concentration of up to 50 % on the M-site in the planar MX-layers. Here, we investigate the impact of vacancies on the thermal and electronic properties across the full EuCu_1−xZn_0.5xSb solid solution. The transition from a fully-occupied honeycomb layer (EuCuSb) to one with a quarter of the atoms missing (EuZn_0.5Sb) leads to non-linear bond expansion in the honeycomb layer, increasing atomic displacement parameters on the M and Sb-sites, and significant lattice softening. This, combined with a rapid increase in point defect scattering, causes the lattice thermal conductivity to decrease from 3 to 0.5 W mK⁻¹ at 300 K. The effect of vacancies on the electronic properties is more nuanced; we see a small increase in effective mass, large increase in band gap, and decrease in carrier concentration. Ultimately, the maximum zT increases from 0.09 to 0.7 as we go from EuCuSb to EuZn_0.5Sb.