The mass hierarchy with atmospheric neutrinos at INO

We study the neutrino mass hierarchy at the magnetized Iron CALorimeter (ICAL) detector at India-based Neutrino Observatory with atmospheric neutrino events generated by the Monte Carlo event generator Nuance. We judicially choose the observables so that the possible systematic uncertainties can be reduced. The resolution as a function of both energy and zenith angle simultaneously is obtained for neutrinos and anti-neutrinos separately from thousand years un-oscillated atmospheric neutrino events at ICAL to migrate number of events from neutrino energy and zenith angle bins to muon energy and zenith angle bins. The resonance ranges in terms of directly measurable quantities like muon energy and zenith angle are found using this resolution function at different input values of θ₁₃${\theta }_{13}$. Then, the marginalized χ²s${\chi }^2\mathrm{s}$ are studied for different input values of θ₁₃${\theta }_{13}$ with its resonance ranges taking input data in muon energy and zenith angle bins. Finally, we find that the mass hierarchy can be explored up to a lower value of θ₁₃≈5°${\theta }_{13}\approx 5°$ with confidence level >95% in this set up.     

Nano‐Conjugate Fluorescence Probe for the Discrimination of Phosphate and Pyrophosphate

We describe a pyrophosphate (PPi) probe that is based on a fluorescent dicarboxylate‐substituted poly(para‐phenyleneethynylene) (PPE) and 10 nm cobalt–iron spinel nanoparticles (NPs) in aqueous media. The spinel NPs efficiently quench the fluorescence of the PPE at a concentration of 20–30 pmol. Addition of phosphate anions to the PPE–NP construct displaces the quenched PPE to give rise to a fluorescent response; we found that PPi and phosphate (Pi) have significantly different binding affinities for the self‐assembled materials. We can discern >40 nM PPi in the presence of 0.1 mM Pi at pH 7, which suggests that these assemblies may be useful in bio‐analytical applications. This displacement assay was used to effectively determine the ability of pyrophosphatase to hydrolyze PPi to Pi.     

Solvothermal synthesis and properties control of doped ZnO nanoparticles

Indium and gallium doped ZnO nanoparticles have been prepared by a hydrothermal reaction in ethanol and methoxyethanol. A comprehensive study of the preparation process, including a thorough investigation by TG-FTIR and TG-MS of the thermal-purification procedure, is presented. Moreover, the effect of thermal conditions and dopant concentration on the structural and optical properties is discussed on the basis of XRD, TEM and UV-vis-NIR results. Reported data indicated that the use of methoxyethanol as a solvent allows an enhanced control of nanoparticle size and favours dopant incorporation into zinc oxide. Near infrared absorption of these materials can be strongly affected by increasing the doping level and upon treating nanoparticles under reducing atmosphere. Preliminary study indicated that this effect is greatly enhanced for gallium-doped zinc oxide.     

Nevanlinna-Pick Interpolation for {\mathbb{C}} + BH^\infty

We study the Nevanlinna-Pick problem for a class of subalgebras of H ^∞. This class includes algebras of analytic functions on embedded disks, the algebras of finite codimension in H ^∞ and the algebra of bounded analytic functions on a multiply connected domain. Our approach uses a distance formula that generalizes Sarason’s [23] work. We also investigate the difference between scalar-valued and matrix-valued interpolation through the use of C ^*-envelopes. This research was partially supported by the NSF grant DMS 0300128. This research was completed as part of my Ph.D. dissertation at the University of Houston.     

Asymptotic analysis of option pricing in a Markov modulated market

We address asymptotic analysis of option pricing in a regime switching market where the risk free interest rate, growth rate and the volatility of the stocks depend on a finite state Markov chain. We study two variations of the chain namely, when the chain is moving very fast compared to the underlying asset price and when it is moving very slow. Using quadratic hedging and asymptotic expansion, we derive corrections on the locally risk minimizing option price.     

Organocatalytic enantioselective synthesis of alpha-hydroxy phosphonates

Tertiary alpha-hydroxy phosphonates have been synthesized in good yields and high enantiomeric purity (up to 99% ee) through a novel l-proline-catalyzed cross aldol reaction of alpha-keto phosphonates and ketones.     

Synthesis of Some Novel Class of Peptides from α‐Amino Nitrones and Their Potential Biological Activities

α‐amino nitrones are found to have a great significance in the synthesis of peptides. Simple reaction methodology, high yield, and atom efficiency in these reactions have made this protocol highly attractive. The synthetic route may be extended to the synthesis of dipeptides in enantiomerically pure form. Potential biological activity of the newly synthesized peptides is the major application in this new methodology.     

Optimal harvesting of a two species competition model with imprecise biological parameters

In this paper a two competing species harvesting model with imprecise biological parameters has been developed. We have developed a method to handle these imprecise parameters and discuss the dynamical behaviour of the model. We have discussed the existence of various equilibrium points and stability of the system at these equilibrium points. Also the bionomic equilibrium of the harvesting model has been analysed. Next the equilibrium solution of the control problem has been derived, and then dynamical optimization of the harvest policy is carried out taking combined harvesting effort as a dynamic variable by invoking Pontryagin’s Maximum Principle. Our important analytical findings are illustrated through computer simulation using MATLAB followed by discussions and conclusions.