Higher-order cone-pseudoconvex, quasiconvex and other related functions in vector optimization

Recently Bhatia (Optim. Lett. doi:10.1007/s11590-010-0248-0, 2010) introduced higher-order cone-convex functions and used them to obtain higher-order sufficient optimality conditions and duality results for a vector optimization problem over cones. The concepts of higher-order (strongly) cone-pseudoconvex and cone-quasiconvex functions were also defined by Bhatia (Optim. Lett. doi:10.1007/s11590-010-0248-0, 2010). In this paper we introduce the notions of higher-order naturally cone-pseudoconvex, strictly cone-pseudoconvex and weakly cone-quasiconvex functions and study various interrelations between the above mentioned functions. Higher-order sufficient optimality conditions have been established by using these functions. Generalized Mond–Weir type higher-order dual is formulated and various duality results have been established under the conditions of higher-order strongly cone-pseudoconvexity and higher-order cone quasiconvexity.     

Molecular dynamics simulations of biotin carboxylase

Biotin carboxylase catalyzes the ATP-dependent carboxylation of biotin and is one component of the multienzyme complex acetyl-CoA carboxylase that catalyzes the first committed step in fatty acid synthesis in all organisms. Biotin carboxylase from Escherichia coli, whose crystal structures with and without ATP bound have been determined, has served as a model system for this component of the acetyl-CoA carboxylase complex. The two crystal structures revealed a large conformational change of one domain relative to the other domains when ATP is bound. Unfortunately, the crystal structure with ATP bound was obtained with an inactive site-directed mutant of the enzyme. As a consequence the structure with ATP bound lacked key structural information such as for the Mg2+ ions and contained altered conformations of key active-site residues. Therefore, nanosecond molecular dynamics studies of the wild-type biotin carboxylase were undertaken to supplant and amend the results of the crystal structures. Specifically, the protein-metal interactions of the two catalytically critical Mg2+ ions bound in the active site are presented along with a reevaluation of the conformations of active-site residues bound to ATP. In addition, the regions of the polypeptide chain that serve as hinges for the large conformational change were identified. The results of the hinge analysis complemented a covariance analysis that identified the individual structural elements of biotin carboxylase that change their conformation in response to ATP binding.     

Large deflection angle fan-out element based on dislocated grating array

We study the possibility of designing and fabricating a fan-out element based on a computer-generated hologram (CGH) which is capable of providing a large deflection angle without using excessively small CGH cells. The recent development of CGHs using dislocated grating arrays was employed to design the fan-out element. Experimental results show that a deflection angle of 41° was achieved using a CGH cell size of 10 μm×10 μm and an operating optical wavelength of 0.98 μm. Further experimental results and theoretical analysis are also presented in order to investigate the characteristics of this type of fan-out element.     

Numerical simulation of low loss silicon photonic wire waveguide with multiple cladding layers

A different silicon photonic wire waveguide is proposed, which uses multiple thin cladding layers in order to reduce the index contrast between core and cladding interface. The reduced index contrast in the proposed waveguide has led to reduction in the scattering losses by 37% as compared to silicon wire waveguide for 400 nm × 220 nm waveguide dimension. The proposed waveguide has shown significant reduction in bending losses. It offers the bending loss of 0.0118 dB at the radius of 1 μm and 0.0063 dB for a radius of 2 μm at 1.55 μm wavelength as compared to 0.086 and 0.013 dB at the radius of 1 and 2 μm, respectively, offered by silicon photonic wire waveguide at 1.5 μm wavelength. The use of polymer material as top cladding layer resulted in decreasing the sensitivity of effective index against temperature for the designed waveguide by a factor of 2 as compared to silicon wire waveguide.     

The Curtius rearrangement of some organic azides: A DFT mechanistic study

The reaction mechanism for the thermal Curtius reaction of formyl azide has been investigated using B3LYP/6‐311+G(d,p). It is found that, while the synisomer undergoes nitrogen elimination via a concerted mechanism, yielding isocyanic acid directly, the anti‐isomer cannot undergo reaction via the concerted mechanism and first eliminates nitrogen, yielding oxazirene, via a transition state which is higher in energy than that for the concerted mechanism. Singlet formyl nitrene does not exist as an independent moiety. Rather, the strong N? O interaction yields the cyclic isomer oxazirene. The isomerization of oxazirene to isocyanic acid goes through a transition state which is even higher in energy than that for nitrogen elimination. It is hence proposed that this reaction should take place via the concerted mechanism only, the anti‐isomer undergoing isomerization first to the syn isomer since the activation barrier for this step is very small. The same mechanism is found to prevail for acetyl and benzoyl azide. These findings are in accord with all experimental data. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

A comparison of three analytical techniques for the measurement of steroidal estrogens in environmental water samples

Research into the analysis and monitoring of steroidal estrogens has grown significantly over the last decade, resulting in the emergence of a range of applicable techniques. In this study, three popular techniques, gas chromatography-mass spectrometry (GC-MS), gas chromatography-tandem mass spectrometry (GC-MS-MS) and liquid chromatography-tandem mass spectrometry (LC-MS-MS) for the analysis of three highly potent steroidal estrogens in the aquatic environment have been compared. It has been observed that overall, the three techniques appear comparable in generating similar estrogen concentrations for river and effluent samples. Of the three techniques, the GC-MS technique is the simplest to operate, but fails to detect the estrogens at the lower-end of environmentally relevant concentrations. The tandem MS techniques are more selective than MS, and therefore able to detect lower concentration levels of the three steroidal estrogens of interest. However, the LC-MS-MS technique is more susceptible to matrix interferences for the analysis of samples, resulting in a reduction of the signal-to-noise ratio and a subsequent reduction in reliability and stability compared to GC-MS-MS. With the GC-MS-MS technique offering increased selectivity, the lowest limits of detection, and no false positive identification, it is recommended to be the preferred analytical technique for routine analysis of estrogens in environmental water samples.     

Steric interference modification of the hammerhead ribozyme

Although the structure of the hammerhead ribozyme is well characterized, many questions remain about its catalytic mechanism. Extensive evidence suggests the necessity of a conformational change en route to the transition state. We report a steric interference modification approach for investigating this change. By placing large 2' modifications at residues insensitive to structurally conservative 2'-deoxy modifications, we hoped to discover structural effects distal to the site of modification. Of twenty residues tested, six were identified where the addition of 2' bulk inhibits cleavage, even though these bulky modifications could be accommodated in the crystal structure without steric clash. It is proposed that these 2'-modifications inhibit cleavage by preventing formation of the alternate, active conformation. Since these 2' effects are present in both domain I and domain II of the hammerhead, the entire catalytic core must undergo conformational changes during catalysis.     

Reversal of Klein reflection by magnetic barriers in bilayer graphene

Massless Dirac fermions in monolayer graphene exhibit total transmission when normally incident on a scalar potential barrier, a consequence of the Klein paradox originally predicted by O Klein for relativistic electrons obeying the 3 + 1 dimensional Dirac equation. For bilayer graphene, charge carriers are massive Dirac fermions and, due to different chiralities, electron and hole states are not coupled to each other. Therefore, the wavefunction of an incident particle decays inside a barrier as for the non-relativistic Schr?dinger equation. This leads to exponentially small transmission upon normal incidence. We show that, in the presence of magnetic barriers, such massive Dirac fermions can have transmission even at normal incidence. The general consequences of this behavior for multilayer graphene consisting of massless and massive modes are mentioned. We also briefly discuss the effect of a bias voltage on such magnetotransport.