Extensions of holomorphic motions

We prove that a normalized holomorphic motion of a closed set E is induced by a holomorphic map into the Teichmüller space of E, denoted by T(E), if and only if it can be extended to a normalized continuous motion of the Riemann sphere. We also prove that the extension can be chosen to have additional properties. This research was partially supported by a PSC-CUNY grant.     

Quasi-elastic neutron scattering study of dynamics in condensed matter

Quasi-elastic neutron scattering (QENS) technique, known to study stochastic motions has been successfully used to elucidate the molecular motions and physical properties related to them, in a variety of systems. QENS is a unique technique that provides information on the time-scale of the motion as well as the geometry of the motions. In this paper, results of some of the systems studied using the facility available at Dhruva, Trombay and other mega-facilities are discussed. Emphasis is given on the results obtained from three different systems studied using QENS, namely, (1) alkyl chain motions in monolayer protected metal clusters, (2) molecular motions of propane in Na-Y zeolitic systems and (3) the study of reorientational motions of liquid crystal innO.m series in different mesophases.     

Two New Octahedral Cd(II) Complexes [Cd(L)2] and {[Cd(LH)2(SCN)2]H2O} [L = C6H5C(OH)NN = C(CH3)C5H4N]: Synthesis and Structural Studies

Two new octahedral Cd(II) complexes [Cd(L)₂] (1) and {[Cd(LH)₂(SCN)₂]H₂O} (2) [where LH = C₁₄H₁₃N₃O] are synthesized using a tridentate hydrazone ligand (LH) and they are characterized by elemental analysis, IR spectra, NMR spectra, thermal studies and finally the structures have been determined by single crystal X-ray diffraction. Complex 1 crystallizes in monoclinic system, space group C2/c with a = 22.565(6) ?, b = 10.252(3) ?, c = 12.187(4) ?, β = 118.851(2)^∘, and Z = 4. Complex 2 also crystallizes in the monoclinic system, space group P2₁/c with a = 9.257(9)?, b = 17.809(2)?, c = 9.548(9)?, β = 107.439(4)^∘, and Z = 2. In 1 the ligand binds the Cd(II) ion in tridentate fashion, whereas in 2 it acts as a bidentate ligand.     

Geometry on the quantum Heisenberg manifold

A class of C∗-algebras called quantum Heisenberg manifolds were introduced by Rieffel in (Comm. Math. Phys. 122 (1989) 531) as strict deformation quantization of Heisenberg manifolds. Using the ergodic action of Heisenberg group we construct a family of spectral triples. It is shown that associated Kasparov modules are homotopic. We also show that they induce cohomologous elements in entire cyclic cohomology. The space of Connes-deRham forms have been explicitly calculated. Then we characterize torsionless/unitary connections and show that there does not exist a connection that is simultaneously torsionless and unitary. Explicit examples of connections are produced with negative scalar curvature. This part illustrates computations involving some of the concepts introduced in Frohlich et al. (Comm. Math. Phys. 203 (1999) 119), for which to the best of our knowledge no infinite-dimensional example is known other that the noncommutative torus.     

Discovery of a Cryptic Intermediate in Late Steps of Mithramycin Biosynthesis

MtmOIV and MtmW catalyze the final two reactions in the mithramycin (MTM) biosynthetic pathway, the Baeyer–Villiger opening of the fourth ring of premithramycin B (PMB), creating the C3 pentyl side chain, strictly followed by reduction of the distal keto group on the new side chain. Unexpectedly this results in a C2 stereoisomer of mithramycin, iso‐mithramycin (iso‐MTM). Iso‐MTM undergoes a non‐enzymatic isomerization to MTM catalyzed by Mg²⁺ ions. Crystal structures of MtmW and its complexes with co‐substrate NADPH and PEG, suggest a catalytic mechanism of MtmW. The structures also show that a tetrameric assembly of this enzyme strikingly resembles the ring‐shaped β subunit of a vertebrate ion channel. We show that MtmW and MtmOIV form a complex in the presence of PMB and NADPH, presumably to hand over the unstable MtmOIV product to MtmW, yielding iso‐MTM, as a potential self‐resistance mechanism against MTM toxicity.     

Angular momentum dependence of the giant dipole resonance width in excited nuclei of mass

Gamma ray spectra in the energy range of 4–25 MeV were measured in the reaction ²⁸Si + ¹²⁴Sn at E(²⁸Si) 150 MeV in coincidence with low energy γ-multiplicities. The spectra were analysed using a simulated Monte Carlo CASCADE code. The centroid energy and width of the giant dipole resonance were extracted for various multiplicity windows. The average angular momentum and temperature of the final states populated after the giant dipole photon emission range from 25 and 1.5 MeV to 56 and 1.3 MeV, respectively. The extracted widths are almost constant for the lower multiplicity windows and show an increase of 1.4 MeV at the highest window. The nuclei are expected to be near the liquid drop regime and the experimental results are not inconsistent with the liquid drop behaviour.     

Kinetics and mechanism of oxidation of glycine by iron(iii)-1,10-phenanthroline complex in perchloric acid medium

Kinetics and mechanism of oxidation of glycine by iron (III)-1,10-phenanthroline complex has been studied in perchloric acid medium. The reaction is first order with respect to iron(III) and glycine. An increase in (phenanthroline) increases the rate, while increase in [H⁺] decreases the rate. Hence it can be inferred that the reactive species of the substrate is the zwitterionic form and that of the oxidant is [Fe(phen)₂(H₂O)₂]³⁺. The proposed mechanism leads to the rate law as elucidated.     

Dynamics of different molecules adsorbed in porous media

We present in this paper a comparative study on the dynamics of benzene, cyclohexane, and methanol molecules, confined in the pores of MCM-41 molecular sieve and HZSM-5 zeolite. The quasi-elastic neutron scattering (QENS) measurements revealed that the physical state of these adsorbed molecules depended not only on the structural characteristics of the host matrix but also on the chemical properties, such as dipole moment, of the guest molecules. Thus, while no motion was observed in the time-scale of 10⁻¹⁰−10⁻¹² s in the case of methanol, the larger size benzene and cyclohexane molecules are found to perform six-fold and three-fold jump rotation, respectively, when adsorbed inside the cages of HZSM-5 at room temperature. At the same time, all the three molecules are found to undergo a translational motion inside the pores of MCM-41 molecular sieves, the value of diffusion constant being the lowest in case of methanol because of its higher polarity. Translationl motion of the guest molecules inside the pores of MCM-41 can be satisfactorily described by Chudley-Eliott fixed jump length diffusion and accordingly the residence time, jump length and diffusion constant are estimated.     

Triangular range counting query in 2D and its application in finding k nearest neighbors of a line segment

We present an efficient algorithm for finding k nearest neighbors of a query line segment among a set of points distributed arbitrarily on a two dimensional plane. Along the way to finding this algorithm, we have obtained an improved triangular range searching technique in 2D. Given a set of n points, we preprocess them to create a data structure using O(n²) time and space, such that given a triangular query region Δ, the number of points inside Δ can be reported in O(logn) time. Finally, this triangular range counting technique is used for finding k nearest neighbors of a query straight line segment in O(log²n+k) time.