Coherent control of resonance-mediated reactions: F+HD

Cross sections resulting from scattering that proceeds via an intermediate resonance are shown to be exceptionally controllable using a coherent superposition of only two initial states. Full quantum computations on F+HD(v=0;j=0,1)-->H+DF, D+HF, which exhibits a resonance in one of the reactive channels, support the formal arguments, showing that control is indeed vast. In this case the ratio of reactive integral cross sections can be altered by a factor of 62 (compared to a noncoherent factor of only 3.3), while the ratio of reactive differential cross sections can be altered by a factor of over 6000 (compared to a noncoherent factor of less than 7). These results constitute the first prediction of extensive quantum control in a collisional process.     

Approaches for introducing high molecular diversity in scaffolds: Fast parallel synthesis of highly substituted 1H-quinolin-4-one libraries

We have developed a two steps strategy for the parallel synthesis of highly diversified quinolin-ones. In the first step we have combined and improved different synthetic methods for generating quinolin-4-ones bearing four different substitutions at specific positions using round bottomed flasks. The synthesis was assessed for a large number of substituted quinolin-4-ones. In the second step, the improved method was adapted to a parallel array synthesis using a 12 positions carrousel as demonstrated for the synthesis of 42-variable quinolin-4-ones. The first combinatorial library set 14(a-x) was obtained with a chemical purity of more than 95% without purification, the second library set 15(a-r), which included two synthetic steps, needed combinatorial purification using an innovative parallel purifier. The proposed approach contributes to a more extensive diversification of molecular scaffolds in general and provides access to highly substituted quinolinones in particular.     

Catalytic beacons for the detection of DNA and telomerase activity

DNA and telomerase activity are detected by a DNAzyme generated upon hybridization and opening of a functional catalytic beacon.     

Susceptibility-matched envelope for the correction of EPI artifacts

Fast gradient echo sequences, such as echo planer imaging (EPI) and spiral imaging, are vulnerable to artifacts resulting from B(0) inhomogeneities. A major contribution to these artifacts is the susceptibility variation across the head, which is most severe in regions adjacent to air-tissue interfaces, such as the mouth, nasal sinuses, ears and the cortex. Susceptibility artifacts can cause geometrical distortions in the image as well as loss of signal due to T(2)* dephasing. The extent of these artifacts increases with the main field, thus compromising the signal-to-noise ratio (SNR) benefit gained in higher fields. In the current work, inhomogeneity caused by susceptibility variations at the external boundary of the human body has been corrected by surrounding the organs with a liquid without hydrogen atoms and whose susceptibility is similar to that of the imaged organ. EPI experiments were conducted on head-sized phantom, human brain, hand and legs. This method causes minimal patient inconvenience and no interference with any function of the scanner, thus yielding a simple and efficient solution for the correction of B(0) variation.     

Experimental reconstruction of a long-period grating from its core-to-core transmission spectrum

We demonstrate, for the first time to our knowledge, reconstruction of the structure of a long-period grating from its measured core-to-core transmission spectrum intensity. The reconstruction is obtained by writing an auxiliary grating in cascade to the interrogated grating. Our reconstruction technique is based on using the Hilbert transform and a phase-retrieval algorithm. Using our method, we have reconstructed the structure of a uniform long-period grating with a 47% coupling efficiency.     

Production of radially or azimuthally polarized beams in solid-state lasers and the elimination of thermally induced birefringence effects

Production and amplification of radially and azimuthally (tangentially) polarized laser beams are demonstrated. Based on the different focusing between radially and tangentially polarized light in thermally stressed isotropic laser rods, Nd:YAG laser oscillators were developed to produce low-loss stable oscillation in a single polarization. Pure radially polarized light at 70 W with M2 = 2 and on-axis impure radially polarized light at 150 W with M2 = 2.5 were achieved. The radially polarized beams were then amplified while good beam quality and polarization purity were retained. Complete elimination of thermal-birefringence-induced aberrations was demonstrated. This should allow much better beam quality from rod-based high-power lasers.     

Existence and uniqueness results for large solutions of general nonlinear elliptic equations

We study under what condition there exists a solution of -u+f(u)=0 in a domain which blows-up on the boundary, independently of the regularity of the boundary, and we provide criteria for uniqueness. We apply our results to the case f(u)= e^au.     

The density of 0's in recurrence double sequences

Let be a double sequence over a finite field satisfying a linear recurrence with constant coefficients, with at most finitely many nonzero elements on each row. Given a nonzero element g of , we show how to obtain an explicit formula for the number of g's in the first qⁿ rows of A. We also characterize the cases when the density of 0's is 1.