Revisiting Generalized Nash Games and Variational Inequalities

Generalized Nash games with shared constraints represent an extension of Nash games in which strategy sets are coupled across players through a shared or common constraint. The equilibrium conditions of such a game can be compactly stated as a quasi-variational inequality (QVI), an extension of the variational inequality (VI). In (Eur. J. Oper. Res. 54(1):81–94, 1991), Harker proved that for any QVI, under certain conditions, a solution to an appropriately defined VI solves the QVI. This is a particularly important result, given that VIs are generally far more tractable than QVIs. However Facchinei et al. (Oper. Res. Lett. 35(2):159–164, 2007) suggested that the hypotheses of this result are difficult to satisfy in practice for QVIs arising from generalized Nash games with shared constraints. We investigate the applicability of Harker’s result for these games with the aim of formally establishing its reach. Specifically, we show that if Harker’s result is applied in a natural manner, its hypotheses are impossible to satisfy in most settings, thereby supporting the observations of Facchinei et al. But we also show that an indirect application of the result extends the realm of applicability of Harker’s result to all shared-constraint games. In particular, this avenue allows us to recover as a special case of Harker’s result, a result provided by Facchinei et al. (Oper. Res. Lett. 35(2):159–164, 2007), in which it is shown that a suitably defined VI provides a solution to the QVI of a shared-constraint game.     

Luminescence studies of fresh water diatom frustules

Siliceous frustules were extracted from fresh water diatoms by treating with concentrated HCl. The diatom frustules consist of nano-porous silica structures that exhibit unique optoelectronic and photonic properties. Photoluminescence (PL) properties of diatom frustules at various excitation wavelengths were done. A visible PL band centered at 440 nm was observed when excited at 300 nm, 370 nm and 380 nm wavelengths. The observed PL activity of the diatom frustules has the potential for use in optoelectronic and photonic devices.     

Nature of intramolecular transannular interaction in group 13 atranes: a theoretical study

Ab initio molecular orbital (MO) calculations at the MP2/6-31+G* level coupled with quantum theory of atoms in molecules (QTAIM) analysis were carried out on group 13 atranes (M = B, Al, Ga) with special emphasis on the nature of the transannular M···N interaction present in these molecules. Substituents at the equatorial position were found to influence the extent of transannular interaction. Boratrane molecules were found to have the strongest M···N interaction and consequently have higher stabilization energies. QTAIM analysis revealed the presence of significant covalent character in the transannular M···N bonds which decreases down the group.     

Synthesis of chiral macrocyclic sugar-peptide hybrids by ring closing metathesis approach

Furanoside and peptide appended bis-olefins afforded monomeric 12- to 18-membered cyclic olefins fused to furanoside rings via RCM approach using Grubbs’ Catalyst.     

Photodissociation dynamics of 3-bromo-1,1,1-trifluoro-2-propanol and 2-(bromomethyl) hexafluoro-2-propanol at 234 nm: resonance-enhanced multiphoton ionization detection of Br (2P(j))

The photodissociation dynamics of 3-bromo-1,1,1-trifluoro-2-propanol (BTFP) and 2-(bromomethyl) hexafluoro-2-propanol (BMHFP) have been studied at 234 nm, and the C-Br bond dissociation investigated using resonance-enhanced multiphoton ionization coupled with time-of-flight mass spectrometer (REMPI-TOFMS). Br formation is a primary process and occurs on a repulsive surface involving the C-Br bond of BTFP and BMHFP. Polarization dependent time-of-flight profiles were measured, and the translational energy distributions and recoil anisotropy parameters extracted using forward convolution fits. A strong polarization dependence of time-of-flight profiles suggest anisotropic distributions of the Br((2)P(3/2)) and Br((2)P(1/2)) fragments with anisotropy parameter, β, of respectively 0.5 ± 0.2 and 1.2 ± 0.2 for BTFP, and 0.4 ± 0.1 and 1.0 ± 0.3 for BMHFP. The measured velocity distributions consist of a single velocity component. The average translational energies for the Br((2)P(3/2)) and Br((2)P(1/2)) channels are 9.2 ± 1.0 and 7.4 ± 0.9 kcal/mol for BTFP, and 15.4 ± 1.8 and 15.1 ± 2.0 kcal/mol for BMHFP. The relative quantum yields of Br((2)P(3/2)) and Br((2)P(1/2)), which are 0.70 ± 0.14 and 0.30 ± 0.06 in BTFP and 0.81 ± 0.16 and 0.19 ± 0.04 in BMHFP, indicate that the yield of the former is predominant. The measured anisotropy parameters for the Br((2)P(3/2)) and Br((2)P(1/2)) channels suggest that the former channel has almost equal contributions from both the parallel and the perpendicular transitions, whereas the latter channel has a significant contribution from a parallel transition. Non-adiabatic curve crossing plays an important role in the C-Br bond dissociation of both BTFP and BMHFP. The estimated curve crossing probabilities suggest a greater value in BTFP, which explains a greater observed value of the relative quantum yield of Br((2)P(1/2)) in this case.     

Denitrification of simulated nitrate-rich wastewater using sulfamic acid and zinc scrap

An enhanced chemical denitrification process was studied as an alternative treatment of nitrate-rich wastewater which cannot be easily treated using conventional biological methods. To accelerate denitrification and to reduce the conversion to ammonia, nitrite reductants were added. In a batch test with the initial nitrate concentration of 500 mg NO ₃ ^? -N per L, sulfamic acid and zinc were found to be the best nitrite and metal reductants, respectively. In a column test with the initial nitrate concentration of 500 mg NO ₃ ^? -N per L, optimum results were experimentally obtained over a zinc scrap column with a 1.0 molar ratio of [NH₂SO₃H]/[NO ₃ ^? -N] and the recirculating flow rate of 6 L min^?1 at pH 2.5. Approximately 98.8 % of nitrate anions were removed, and the observed reaction rate constant (k) was 0.135 min^?1. Zinc consumption was reduced to 46.6 % compared to the procedure without sulfamic acid, and sulfamic acid consumption was reduced to 40 % compared to the results of our previous study. Based on these experimental results, it was concluded that chemical nitrate denitrification using sulfamic acid and zinc scrap is an effective alternative treatment protocol for nitrate-rich wastewater.     

Ordered Mesoporous Silica as Supports in the Heterogeneous Asymmetric Catalysis

Enantioselective synthesis of organic compounds has been studied by homogeneous catalysts for several years. However, these catalysts have yet to make a significant impact on industrial scales for fine chemical synthesis. A primary reason is the designing of a homogeneous asymmetric catalyst, which requires relatively bulky ligands and catalyst recovery and recycling often causes problems. One of the convincing ways to overcome this problem is to immobilise the asymmetric catalyst onto a solid support and the resulting heterogeneous asymmetric catalyst system can, in principle, be readily re-used. A large number of supports such as inorganic oxides including zeolites, alumina, zirconia, silica and organic polymers have been employed as supports in heterogeneous asymmetric catalysis. Therefore, in this review article we have summarized the work done by us in our laboratory on the immobilization of chiral transition metal complexes such as Ru, Ir, Mn and Ti onto ordered mesoporous silica and its asymmetric catalysis. All these immobilized catalysts were well characterized by different physicochemical techniques to confirm the structural retention of the support as well as the active metal complex after immobilization. This report includes our asymmetric catalytic investigations in enantioselective reactions such as hydrogenation of ketones, olefins, oxidation of sulfides and oxidative kinetic resolution of alcohols and sulfoxides through immobilized heterogeneous catalyst systems.     

Dynamics of Cl (2Pj) atom formation in the photodissociation of fumaryl chloride (ClCO - CH = CH - COCl) at 235 nm: a resonance enhanced multiphoton ionization (REMPI) time-of-flight (TOF) study

The photodissociation dynamics of fumaryl chloride (ClCO-CH═CH-COCl) has been studied in a supersonic molecular beam around 235 nm using resonance enhanced multiphoton ionization (REMPI) time-of-flight (TOF) technique by detecting the nascent state of the primary chlorine atom. A single laser has been used for excitation of fumaryl chloride and the REMPI detection of chlorine atoms in their spin-orbit states, Cl ((2)P(3/2)) and Cl* ((2)P(1/2)). We have determined the translational energy distribution, the recoil anisotropy parameter, β, and the spin-orbit branching ratio for chlorine atom elimination channels. To obtain these, measured polarization-dependent and state-specific TOF profiles are converted into kinetic energy distributions, using a least-squares fitting method, taking into account the fragment recoil anisotropies, β(i). The TOF profiles for both Cl and Cl* are found to be independent of laser polarization; i.e., β is well characterized by a value of 0.0, within the experimental uncertainties. Two components, namely, the fast and the slow, are observed in the translational energy distribution, P(E(T)), of Cl and Cl* atoms, and assigned to be formed from different potential energy surfaces. The average translational energies for the fast components of the Cl and Cl* channels are 14.9 ± 1.6 and 16.8 ± 1.6 kcal/mol, respectively. Similarly, for the slow components, the average translational energies of the Cl and Cl* channels are 3.4 ± 0.8 and 3.1 ± 0.8 kcal/mol, respectively. The energy partitioning into the translational modes is interpreted with the help of various models, such as impulsive and statistical models. Apart from the chlorine atom elimination channel, molecular hydrogen chloride (HCl) elimination is also observed in the photodissociation process. The HCl product has been detected, using a REMPI scheme in the region of 236-237 nm. The observation of the molecular HCl in the dissociation process highlights the importance of the relaxation process, in which the initially excited parent molecule relaxes to the ground state from where the molecular (HCl) elimination takes place.     

Synthesis of 1,2,4-oxadiazole derivatives: anticancer and 3D QSAR studies

Monatshefte für Chemie - Chemical Monthly - A 3D QSAR study was performed on 1,2,4-oxadiazole derivatives using the [(SW) kNN MFA], CoMFA, and CoMSIA techniques. On the basis of 3D QSAR...     

Development of TUSCAT: A software for light scattering studies on spherical, spheroidal and cylindrical particles

An integrated software package TUSCAT (Tezpur University SCATtering Software) incorporated with a graphical user interface (GUI) was developed for modeling electromagnetic scattering from small particles and also to yield characteristic properties of the scattering particles from experimental data. Its interactive features enable the user to observe the changes in output scattering properties in real time. In addition to its ease of use, it has high computational accuracy, efficiency, reliability and adaptability.