On Tests of Symmetry Against One-Sided Alternatives

To test that an experimental treatment is better than an existing one (or control), one can equivalently consider the difference in their response and test if the distribution of the difference is symmetric (about zero) versus it exhibits positive bias (skewness to the right). In this paper, we test the symmetry (about zero) of a discrete distribution against two particular classes of one sided alternatives. We obtain the maximum likelihood estimators under each alternative. The asymptotic null distributions of the likelihood ratio statistics are shown to have chi-bar square type distributions. A power study is performed to compare these one-sided alternatives with other one-sided tests. The theory developed is illustrated by an example.     

Set Differential Equations and Flow Invariance

The study of Set Differential Equations is initiated in the metric space of nonempty, compact, convex subsets of , endowed with the Hausdorff metric. The existence of a generalized solution for the associated initial value problems is proved when the function involved does not satisfy any continuity assumptions. Utilizing the ideas of nonsmooth analysis, a proximal aiming condition is employed to investigate the weak and strong invariance for these solutions.     

On the neutral stability of mixed strategies in asymmetric contests

Although a mixed strategy can never be evolutionary stable in a truly asymmetric contest, examples show that mixed strategies can satisfy the weaker criterion of neutral stability. This paper shows that such examples are rare, and, generically, a mixed strategy is unstable. We apply our result to the battle of the sexes between males and females over the raising of offspring.     

Glaser oxidative coupling in ionic liquids: an improved synthesis of conjugated 1,3-diynes

Terminal alkynes undergo oxidative-coupling smoothly in the presence of the CuCl-TMEDA catalytic system in hydrophobic [bmim]PF₆ ionic liquid under aerobic conditions to produce 1,3-diynes in excellent yields under mild conditions. The substrates, alkynes, show enhanced reactivity and selectivity in ionic liquids (ILs). The recovery of the catalyst is facilitated by the hydrophobic nature of the [bmim]PF₆ ionic liquid.     

TMSI mediated Prins-type cyclization of ketones with homoallylic and homopropargylic alcohol: synthesis of 2,2-disubstituted-, spirocyclic-4-iodo-tetrahydropyrans and 5,6-dihydro-2H-pyrans

The Prins-type cyclization of ketones with homoallylic and homopropargylic alcohols in the presence of TMSI generated in situ from TMSCl and NaI produced 2,2-disubstituted- or spirocyclic-4-iodo-tetrahydropyrans and spirocyclic-4-iodo-5,6-dihydro-2H-pyrans in good yields. These iodopyrans are reported for the first time.     

A new coumestan from Tephrosia calophylla

A new coumestan, tephcalostan (1) has been isolated from the whole plant of Tephrosia calophylla BEDD. together with two known flavonoids, 7-O-methylglabranin (2) and kaempferol 3-O-beta-D-glucopyranoside (3). The structure of tephcalostan was elucidated as 5'-(R)-8, 9-methylenedioxy-5'-isopropenyl-4', 5'-dihydrofurano[2', 3':2, 3]coumestan by extensive one-and two-dimensional (1D- and 2D-)-NMR techniques including (1)H-(1)H correlation spectroscopy (COSY), heteronuclear single quantum coherence (HSQC), heteronuclear multiple bond connectivity (HMBC) and nuclear Overhauser enhancement spectroscopy (NOESY) experiments.     

Comparison of thermal degradation products from real municipal waste plastic and model mixed plastics

The thermal degradation of real municipal waste plastic (MWP) obtained from Sapporo, Japan and model mixed plastics was carried out at 430 °C in atmospheric pressure by batch operation. The chlorinated hydrocarbons found in PE/PP/PS/PVC [poly(ethylene)/poly(propylene)/poly(styrene)/poly(vinyl chloride)] degradation liquid products were also observed in PE/PP/PS/PVC/PET (poly(ethylene terephalate)) and MWP degradation liquid products. The presence of PET in MWP produced the additional chlorinated hydrocarbons, which are similar to the chlorinated hydrocarbons observed during the PE/PP/PS/PVC/PET degradation liquid products. In addition, the presence of PET facilitated the formation of more organic chlorine content in liquid products and drastic decrease in the formation of inorganic chlorine content.     

Electrospray ionization studies of transition-metal complexes of 2-acetylbenzimidazolethiosemicarbazone using collision-induced dissociation and ion-molecule reactions

The complexes of transition-metal ions (M2+, where M = Fe, Co, Ni, Cu, Zn, Cd, and Hg) with 2-acetylbenzimidazolethiosemicarbazone (L) are studied under electrospray ionization (ESI) conditions. The ESI mass spectra of Fe and Co complexes showed the complex ions corresponding to [M+2L-2H]+, and those of Ni and Zn complexes showed [M+2L-H]+ ions, wherein the metal/ligand ratio is 1:2 and the oxidation state of the central metal ion is +3 in the case of Fe and Co and +2 in the case of Ni and Zn. The Cd and Cu complexes showed preferentially 1:1 complex ions, i.e., [M+L-H]+ or [M+L+Cl]+, whereas Hg formed both 1:1 and 1:2 complex ions. During formation of the above complex ions one or two ligands are deprotonated after keto-enol tautomerism, depending on the nature and oxidation state of central metal ion. The structures and coordination numbers of the metal ions in the complex ions were studied by their collision-induced dissociation spectra and ion-molecule reactions with acetonitrile or propylamine in the collision cell. Based on these results it is concluded that Fe, Co, Ni and Zn form stable octahedral complexes, whereas tetrahedral or square planar complexes are formed preferentially for other metals. In addition, the Cu complex showed a [2L+2Cu-3H]+ ion with a Cu-Cu bond.     

Absorption and emission of light in red emissive carbon nanodots

The structure–function relationship, especially the origin of absorption and emission of light in carbon nanodots (CNDs), has baffled scientists. The multilevel complexity arises due to the large number of by-products synthesized during the bottom-up approach. By performing systematic purification and characterization, we reveal the presence of a molecular fluorophore, quinoxalino[2,3-b]phenazine-2,3-diamine (QXPDA), in a large amount (∼80% of the total mass) in red emissive CNDs synthesized from o-phenylenediamine (OPDA), which is one of the well-known precursor molecules used for CND synthesis. The recorded NMR and mass spectra tentatively confirm the structure of QXPDA. The close resemblance of the experimental vibronic progression and the mirror symmetry of the absorption and emission spectra with the theoretically simulated spectra confirm an extended conjugated structure of QXPDA. Interestingly, QXPDA dictates the complete emission characteristics of the CNDs; in particular, it showed a striking similarity of its excitation independent emission spectra with that of the original synthesized red emissive CND solution. On the other hand, the CND like structure with a typical size of ∼4 nm was observed under a transmission electron microscope for a blue emissive species, which showed both excitation dependent and independent emission spectra. Interestingly, Raman spectroscopic data showed the similarity between QXPDA and the dot structure thus suggesting the formation of the QXPDA aggregated core structure in CNDs. We further demonstrated the parallelism in trends of absorption and emission of light from a few other red emissive CNDs, which were synthesized using different experimental conditions.

Herein we unveil the presence of a molecular fluorophore quinoxalino[2,3-b]phenazine-2,3-diamine (QXPDA) in a colossal amount in red emissive CNDs synthesized from o-phenylenediamine, a well-known precursor molecule used for CND synthesis.