Revealing the order of a vortex through its intensity record

We show that the intensity distribution of an optical vortex contains information of its order. Specifically, the number of dark rings in the Fourier transform of the intensity is found to be equal to the order of the vortex. Based on this property and the orthogonality of Laguerre polynomials, we demonstrate the feasibility of an experimental technique for determining the order of optical vortices. It shows the beauty of going to complementary spaces, which has been employed earlier also to find the information not available in other domains.     

Ortho-branched ladder-type oligophenylenes with two-dimensionally π-conjugated electronic properties

The synthesis, photochemical and electrochemical properties, and electronic structures of a series of star-shaped ladder-type oligophenylenes Sn (n = 7, 10, 13, 16, 19, and 22), including one multibranched case S19mb, are reported and compared with the linear para-phenylene ladders Rn (n = 2-5 and 8) and the stepladder analogues SFn (n = 10, 16, and 22). The n value refers to the number of π-conjugated phenylene rings. Functionalized isotruxenes are the key synthetic building blocks, and S22 is the largest monodispersed ladder-type oligophenylene known to date. The Sn systems possess the structural rigidity of Rn and the ortho-para phenylene connectivity of SFn. Consequently, Sn represents the first class of branched chromophores with fully two-dimensional conjugation in both ground- and excited-state configurations. Evidences include the excellent linear correlations for the optical 0-0 energies or the first oxidation potentials of Sn and Rn against the reciprocal of their n values, delocalized HOMO and LUMO based on density functional theory calculations, and molecule-like fluorescence anisotropy. The resulting model of effective conjugation plane (ECP) for the two-dimensional π-conjugated systems compliments the concept of effective conjugation length (ECL) for one-dimensional oligomeric systems. Other implications of the observed structure-property relationships are also included.     

Role of bond strength on the lattice thermal expansion and oxide ion conductivity in quaternary pyrochlore solid solutions

Quaternary pyrochlore-type solid solutions, CaGdZrNb(1-x)Ta(x)O(7) (x = 0, 0.2, 0.4, 0.6, 0.8, 1), were prepared by a high-temperature ceramic route. The pyrochlore phases of the compounds were confirmed by powder X-ray diffraction (XRD), Raman spectroscopy, and transmission electron microscopy. The crystallographic parameters of the pyrochlore compounds were accurately determined by Rietveld analysis of the powder XRD data. The isovalent substitution of Ta in place of Nb at the B site can reveal the effect of chemical bonding on lattice thermal expansion and oxide ion conductivity because both Nb and Ta have the same ionic radius (0.64 ?). Lattice thermal expansion coefficients of the samples were calculated from high-temperature XRD measurements, and it was found that the thermal expansion coefficient decreases with substitution of Ta. Oxide ion conductivity measured by a two-probe method also shows the same trend with substitution of Ta, and this can be attributed to the high bond strength of the Ta-O bond compared to that of the Nb-O bond. Microstructural characterization using scanning electron microscopy proves that the size of the grains has a small effect on the oxide ion conductivity. Our studies established the role of chemical bonding in deciding the conductivity of pyrochlore oxides and confirmed that the 48f-48f mechanism of oxide ion conduction is dominant in pyrochlore oxides.     

Gas sensing properties of single crystalline ZnO nanowires grown by thermal evaporation technique

The ZnO NWs were applied as effective material for the fabrication of ethanol (C₂H₅OH) and carbon monoxide (CO) gas sensor. The ZnO NWs were grown by thermal evaporation techniques on non-catalytic Si (100) substrates. The average width and length of ZnO NWs was 60 nm and 20 μm, respectively and they were single crystalline in nature. The maximum response was 51.64 at 300 °C for 1000 ppm of CO gas, while 104.23 at 400 °C for 250 ppm of ethanol gas. The response of ZnO NWs was very high for ethanol compared to the CO, whereas the recovery time for ethanol was very poor compare to CO gas. The response of ZnO NWs was about 25 times higher for ethanol compare to CO, at 400 °C for 100 ppm of each gas. The high response for ethanol is related to electron donating effect of ethanol (10e^?) which was higher than the CO gas (2e^?). The high response of ZnO NWs was attributed to large contacting surface area for electrons, oxygen, target gas molecule, and abundant channels for gas diffusion.     

Stereoselective total synthesis of simplactone A

The efficient and simple stereoselective approach toward the total synthesis of simplactone A is described. The key features of this synthetic strategy include stereoselective C-ethylation, selective triol protection, and Wittig olefination for the formation of the six-membered ring.     

Monads on projective spaces

Let be a vector bundle on P ⁿ . There is a strong relationship between and its intermediate cohomology modules. In the case where has low rank, we exploit this relationship to provide various splitting criteria for . In particular, we give a splitting criterion for in terms of the vanishing of certain intermediate cohomology modules. We also show that the Horrocks-Mumford bundle is the only non-split rank two bundle on P ⁴ with a Buchsbaum second cohomology module.Partially supported by NSF Grants.     

Randomized rounding: A technique for provably good algorithms and algorithmic proofs

We study the relation between a class of 0–1 integer linear programs and their rational relaxations. We give a randomized algorithm for transforming an optimal solution of a relaxed problem into a provably good solution for the 0–1 problem. Our technique can be a of extended to provide bounds on the disparity between the rational and 0–1 optima for a given problem instance. This work was supported by Semiconductor Research Corporation grant SRC 82-11-008 and an IBM Doctoral Fellowship.