Oscillatory integral operators with homogeneous polynomial phases in several variables

We obtain L² decay estimates in λ for oscillatory integral operators Tλ whose phase functions are homogeneous polynomials of degree m and satisfy various genericity assumptions. The decay rates obtained are optimal in the case of (2+2)-dimensions for any m, while in higher dimensions the result is sharp for m sufficiently large. The proof for large m follows from essentially algebraic considerations. For cubics in (2+2)-dimensions, the proof involves decomposing the operator near the conic zero variety of the determinant of the Hessian of the phase function, using an elaboration of the general approach of Phong and Stein [D.H. Phong, E.M. Stein, Models of degenerate Fourier integral operators and Radon transforms, Ann. of Math. (2) 140 (1994) 703-722].     

Mercury assisted fluorescent supramolecular assembly of hexaphenylbenzene derivative for femtogram detection of picric acid

Aggregates of hexaphenylbenzene derivatives 3, having pyrene groups form network of fluorescent nanofibres in presence of mercury ions. Further, fluorescent nanofibres of 3-Hg²⁺ supramolecular ensemble exhibit sensitive and pronounced response towards the picric acid. In addition, the solution coated paper strips of 3-Hg²⁺ supramolecular ensemble can detect picric acid in the range of 2.29 fg/cm², thus, providing a simple, portable and low cost method for detection of picric acid in solution and in contact mode.     

A Toggle Nanoswitch Alternately Controlling Two Catalytic Reactions

Reversible switching between two states of the triangular nanoswitch [Cu( 1 )]⁺ was accomplished by alternate addition of 2‐ferrocenyl‐1,10‐phenanthroline ( 2 ) and copper(I) ions. The two switching states regulate the binding and release of two distinct catalysts, piperidine and [Cu( 2 )]⁺, in a fully interference‐free manner and allow alternating on/off switching of two orthogonal catalytic processes. In switching state I, piperidine is released from the nanoswitch and catalyzes a Knoevenagel addition between 4‐nitrobenzaldehyde and diethyl malonate (ON‐1 and OFF‐2), while in state II the released [Cu( 2 )]⁺ catalyzes a click reaction between 4‐nitrophenylacetylene and benzylazide (OFF‐1 and ON‐2). Upon addition of one equivalent of 2 to the (OFF‐1 and ON‐2)‐state, both catalytically active processes are shut down (OFF‐1 and OFF‐2).     

Arjunolic acid: A promising new building block for nanochemistry

Arjunolic acid, the major extractable constituent of the heavy wood ofTerminalia Arjuna, has the potential to be used as a rigid and functional molecular framework for the construction of nanosized supramolecular architectures and nanomaterials. The nanosized triterpenoid, arjunolic acid, showed efficient gelation of various organic solvents at low concentrations. The low molecular mass gelator molecules self-assembled in the solvents to form fibers of nanometer diameters. The movement of the solvent molecules was hindered inside the fibrous network leading to the formation of a gel     

Band structure in104Ag

The level structure of¹⁰⁴Ag has been studied through the¹⁰³Rh (α, 3nγ) reaction at E_α=40 and 45 MeV. The principal features of the proposed level scheme are in agreement with those obtained earlier through heavy ion reaction. Two quasiparttcle-plus-rotor model calculation has been performed, and the results are compared with experimental data.     

Electro-optical properties of a new series of fluorinated antiferroelectric orthoconic liquid crystalline esters

The electro-optical properties of orthoconic antiferroelectric liquid crystals of some analogues of (S)?MHPOBC ((S)?4?(1?methylheptyloxy)carbonylphenyl 4'-octyloxy-4-biphenylcarboxylate) have been investigated and discussed in terms of the structure property correlations of liquid crystalline molecules. Polarisation field reversal technique has been used for their characterisation. In this study the occurrence of such a high value of spontaneous polarisation (P_s) for the investigated compound is especially noteworthy as they comprise a bulky chiral unit, zigzag ester linkage and polar fluorinated terminal. Lengthening of oligomethylene spacer in the terminal chain and placement of fluorine atom in the molecular core structure leads to reduction in the value of P_s. The P_s data suggest that the nature of the chiral smectic C (SmC*) to smectic A (SmA) phase transition is of second order and the critical exponent β is in the range 0.19–0.34. The ‘V-shaped’ mode or thresholdless switching in such high-polarisation ferroelectric liquid crystals has also been discussed.     

Impedance spectroscopy study of the nanocrystalline ferroelectric (PbMg)(ZrTi)O3 system

Nanosized ceramic powder having a general formula Pb_1-xMg_xZr_0.05Ti_0.95O₃ (PMZT) with x=0, 0.03, 0.06 and 0.09 has been synthesized by a metal ion complex precursor solution method. Preliminary structural analysis of PMZT compounds using the X-ray diffraction technique suggests that they exhibit a single phase with tetragonal crystal structure. Complex impedance spectroscopy analysis has been carried out to investigate the electrical properties. The physical structure of the samples has been visualized most prominently near 400 °C from the Nyquist plot as consisting of grains separated by grain boundaries. The presence of a single arc in the complex modulus spectrum at different temperatures confirms the single-phase character of the PMZT compounds. PACS 77.22.Ch; 77.22.Ej; 77.22.Gm; 77.80.Bh     

Synthesis of 3-carbonyl pyrazole-5-phosphonates via 1,3-dipolar cycloaddition of Bestmann–Ohira reagent with ynones

The present work explores the hitherto unexplored reactivity of ynones as dipolarophiles with Bestmann–Ohira reagent. The reaction offers a convenient route for the synthesis of regioisomerically pure 3,5-disubstituted or 3,4,5-trisubstituted pyrazoles in excellent yields. However, di-ynones and molecules possessing both ynone and enone functionalities provide only monocycloaddition products, whereas another multiple bond undergoes Michael addition with the methoxide anion.     

Wet-chemical synthesis of crystalline BaTiO3 from stable chelated titanium complex: formation mechanism and dispersibility in organic solvents

Crystalline barium titanate nanoparticles were synthesized in solution at low temperature (70 degrees C) from acetylacetone chelated titanium complex and barium hydroxide. Very fine crystalline solids were characterized to cubic phase of BaTiO(3) by X-ray diffraction studies of the air-dried samples. It was observed that the crystalline barium titanate was formed in solution at Ba/Ti molar ratio > or =2.5. The dependence of the reaction temperature and the Ba(OH)(2) concentration (in terms of Ba/Ti molar ratio) on formation of crystalline BaTiO(3) in solution-phase was studied, and a plausible mechanism toward the formation of crystalline BaTiO(3) was also proposed. Crystallite sizes of the BaTiO(3) were found to be in the range 33-50 nm, while the average particle sizes, measured by dynamic light scattering method were in the range 70-100 nm. The crystalline BaTiO(3) prepared from acetylacetone chelated titanium complex was highly dispersible in organic medium such as N-methyl-2-pyrillidone (NMP) and N,N-dimethyl formamide (DMF).