Étale covers of affine spaces in positive characteristicRevêtements étales des espaces affines en caractéristique positive

We prove that every projective, geometrically reduced scheme of dimension n over an infinite field k of positive characteristic admits a finite morphism over some finite radicial extension k′ of k to projective n-space, étale away from the hyperplane H at infinity, which maps a chosen Weil divisor into H and a chosen smooth geometric point of X not on the divisor to some point not in H. To cite this article: K.S. Kedlaya, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 921–926.     

Third-order nonlinear optical studies of newly synthesized polyoxadiazoles containing 3,4-dialkoxythiophenes

The third-order nonlinear optical properties of newly synthesized soluble polyoxadiazoles containing 3,4-dialkoxythiophenes were investigated by using Z-scan and degenerate four-wave mixing (DFWM) techniques. The measurements were performed at 532 nm with 7 ns pulses from a Nd:YAG laser. We found a good agreement between the values of χ⁽³⁾ determined from both the experiments. Z-scan results indicate a negative nonlinear refractive index, n₂, whose magnitude is of the order of 10⁻¹⁰ esu for all the copolymers. The variation of nonlinear response among the copolymers clearly indicates the dependence of χ⁽³⁾ on donor and acceptor type of units present in these copolymers. The copolymers exhibit strong reverse saturable absorption and good optical limiting properties at 532 nm.     

Effective atomic number studies in clay minerals for total photon interaction in the energy region 10 keV–10 MeV

Effective atomic numbers (Z_eff) of different clay minerals are calculated for total photon interaction in the energy region 10 keV–10 MeV. The variation of Z_eff with energy is discussed by comparing with the similar studies made for alloys and compounds from our laboratory.     

Modeling and simulation of WDM optical networks under traffic control protocols

A proper node architecture design capable to support different network protocol enhances the data transport capability of a wavelength division multiplexed system. In the present paper a simple node architecture model has been developed to simulate the node throughput based on media access control protocols for bursty data traffic of variable time slot duration and data rate. An appropriate mathematical model has been derived to evaluate different types of traffic reservation protocols used in WDM networks. It has been observed that the network performance is well controlled through implemented protocols and network design parameters.     

TDDFT Investigation of the Electronic Structures and Photophysical Properties of Fluorescent Extended Styryl Push-Pull Chromophores Containing Carbazole Unit

Push-pull chromophores attached to carbazole based π-conjugating spacers bearing N-alkylamino donors, cyanovinyl and carbethoxy acceptors have been studied by the means of UV-Visible measurements. The intramolecular charge transfer (ICT) of these π-conjugated systems has also been tested by investigating the ability of the solute molecules to undergo shifts in their fluorescence emission maxima with increasing solvent polarity. Density Functional Theory [B3LYP/6-31G(d)] and Time Dependent Density Functional Theory [TD-B3LYP/6-31G(d)] computations have been used to have more understanding of the structural, molecular, electronic and photophysical parameters of push-pull dyes. The largest wavelength difference between the experimental and computed electronic absorption maxima was 45 nm. For emission, a largest difference of 61 nm was observed. The ground state and excited state dipole moments in different solvents were determined using experimental solvatochromic data and computed Onsager radii. The dipole moments of the molecules in the excited state were observed to be higher than in the ground state.     

Coherent States and Modified de Broglie-Bohm Complex Quantum Trajectories

This paper examines the nature of classical correspondence in the case of coherent states at the level of quantum trajectories. We first show that for a harmonic oscillator, the coherent state complex quantum trajectories and the complex classical trajectories are identical to each other. This congruence in the complex plane, not restricted to high quantum numbers alone, illustrates that the harmonic oscillator in a coherent state executes classical motion. The quantum trajectories we consider are those conceived in a modified de Broglie-Bohm scheme. Though quantum trajectory representations are widely discussed in recent years, identical classical and quantum trajectories for coherent states are obtained only in the present approach. We may note that this result for standard harmonic oscillator coherent states is not totally unexpected because of their holomorphic nature. The study is extended to coherent states of a particle in an infinite potential well and that in a symmetric Poschl-Teller potential by solving for the trajectories numerically. For the Gazeau-Klauder coherent state of the infinite potential well, almost identical classical and quantum trajectories are obtained whereas for the Poschl-Teller potential, though classical trajectories are not regained, a periodic motion results as t→∞. Similar features were found for the SUSY quantum mechanics-based coherent states of the Poschl-Teller potential too, but this time the pattern of complex trajectories is quite different from that of the previous case. Thus we find that the method is a potential tool in analyzing the properties of generalized coherent states.     

Significance of plaque morphology in modifying flow characteristics in a diseased coronary artery: Numerical simulation using plaque measurements from intravascular ultrasound imaging

The paper deals with numerical investigation of the effect of plaque morphology on the flow characteristics in a diseased coronary artery using realistic plaque morphology. The morphological information of the lumen and the plaque is obtained from intravascular ultrasound imaging measurements of 42 patients performed at Cleveland Clinic Foundation, Ohio. For this data, study of Bhaganagar et al. (2010) [1] has revealed the stenosis for 42 patients can be categorized into four types – type I (peak-valley), type II (ascending), type III (descending), and type IV (diffuse). The aim of the present study is to isolate the effect of shape of the stenosis on the flow characteristics for a given degree of the stenosis. In this study, we conduct fluid dynamic simulations for the four stenosis types (type I–IV) and analyze the differences in the flow characteristics between these types. Finely refined tetrahedral mesh for the 3-D solid model of the artery with plaques has been generated. The 3-D steady flow simulations were performed using the turbulence (k–ε) model in a finite volume based computational fluid dynamics solver. The axial velocity, the radial velocity, turbulence kinetic energy and wall shear stress profiles of the plaque have been analyzed. From the axial and radial velocity profiles results the differences in the velocity patterns are significantly visible at proximal as well as distal to the throat, region of maximum stenosis. Turbulent kinetic energy and wall shear stress profiles have revealed significant differences in the vicinity of the plaque. Additional unsteady flow simulations have been performed to validate the hypothesis of the significance of plaque morphology in flow alterations in diseased coronary artery. The results revealed the importance of accounting for plaque morphology in addition to plaque height to accurately characterize the turbulent flow in a diseased coronary artery.     

High-field NMR using resistive and hybrid magnets

Resistive and resistive-superconducting hybrid magnets can generate dc magnetic fields much higher than conventional superconducting NMR magnets but the field spatial homogeneity and temporal stability are usually not sufficient for high-resolution NMR experiments. Hardware and technique development addressing these issues are presented for high-resolution NMR at magnetic fields up to 40T. Passive ferromagnetic shimming and magic-angle spinning are used effectively to reduce the broadening from inhomogeneous magnetic field. A phase correction technique based on simultaneous heteronuclear detection is developed to compensate magnetic field fluctuations to achieve high spectral resolution.     

Synthesis and Characterization of Novel 1‐Methyl‐3‐(4‐phenyl‐4H‐1,2,4‐triazol‐3‐yl)‐1H‐indazole Derivatives

A series of novel 1‐methyl‐3‐(4‐phenyl‐4H‐1,2,4‐triazol‐3‐yl)‐1H‐indazoles was synthesized in three steps from 5‐(1‐methyl‐1H‐indazol‐3‐yl)‐4‐phenyl‐2H‐1,2,4‐triazole‐3(4H)‐thiones. 5‐(1‐Methyl‐1H‐indazol‐3‐yl)‐4‐phenyl‐2H‐1,2,4‐triazole‐3(4H)‐thiones were converted into 1‐methyl‐3‐(5‐(methylsulfonyl)‐4‐phenyl‐4H‐1,2,4‐triazol‐3‐yl)‐1H‐indazoles upon methylation followed by treatment with aq. KMnO₄. The reaction of 1‐methyl‐3‐(5‐(methylsulfonyl)‐4‐phenyl‐4H‐1,2,4‐triazol‐3‐yl)‐1H‐indazoles with Raney nickel resulted in desulphonylation to afford corresponding 1‐methyl‐3‐(4‐phenyl‐4H‐1,2,4‐triazol‐3‐yl)‐1H‐indazoles. All the new synthesized compounds were characterized by spectral techniques.