Geminal alkene-alkyne cross metathesis using a relay strategy

A relay strategy was employed to achieve an intermolecular ene-yne metathesis between 1,1-disubstituted alkenes and alkynes. The relay serves to activate an unreactive alkene which will not participate in ene-yne metathesis. The new relay cross ene-yne metathesis gives rise to 1,1,3-trisubstituted-1,3-dienes previously inaccessible by direct ene-yne metathesis methods.     

Phase-sensitive multimodal optical parametric amplifier for beam angle amplification

The single-mode phase-sensitive parametric amplifier has been proposed as an approximation to an ideal quantum phase amplifier. We demonstrate numerically that a real, multimode parametric amplifier operated in the spatial domain, and realized by the use of three-wave mixing in nonlinear media, behaves similar to a single-mode quantum phase amplifier, but exhibits smaller phase gain. Constraints for operation in this regime are found to be consistent with small departures of phase from the ideal deamplification condition.     

Cellulose and the twofold screw axis: modeling and experimental arguments

Crystallography indicates that molecules in crystalline cellulose either have twofold screw-axis (2₁) symmetry or closely approximate it, leading to short distances between H4 and H1′ across the glycosidic linkage. Therefore, modeling studies of cellobiose often show elevated energies for 2₁ structures, and experimental observations are often interpreted in terms of intramolecular strain. Also, some computer models of cellulose crystallites have an overall twist as well as twisted individual chains, again violating 2₁ symmetry. To gain insight on the question of inherent strain in 2₁ structures, modeling was employed and crystal structures of small molecules were surveyed. (Residues in a disaccharide cannot be related by 2₁ symmetry because they are not identical but if their linkage geometry would lead to 2₁ symmetry for an infinite cellulose chain, the disaccharide would have 2₁ pseudo symmetry.) Several initial structures in quantum mechanics (QM) studies of cellobiose minimized to structures having 2₁ pseudo symmetry. Similarly, a number of relevant small molecules in experimental crystal structures have pseudo symmetry. While the QM models of cellobiose with 2₁ pseudo symmetry had inter-residue hydrogen bonding, the experimental studies included cellotriose undecaacetate, a molecule that cannot form conventional hydrogen bonds. Limitations in characterizing symmetry based on the linkage torsion angles ϕ and ψ were also explored. It is concluded that 2₁ structures have little intrinsic strain, despite indications from empirical models.     

Three-dimensional molecular mapping in a microfluidic mixing device using fluorescence lifetime imaging

Fluorescence lifetime imaging (FLIM) is used to quantitatively map the concentration of a small molecule in three dimensions in a microfluidic mixing device. The resulting experimental data are compared with computational fluid-dynamics (CFD) simulations. A line-scanning semiconfocal FLIM microscope allows the full mixing profile to be imaged in a single scan with submicrometer resolution over an arbitrary channel length from the point of confluence. Following experimental and CFD optimization, mixing times down to 1.3+/-0.4 ms were achieved with the single-layer microfluidic device.     

On the Normal Structure of NonCommutative Association Schemes of Rank 6

The concept of an association scheme is a far-reaching generalization of the notion of a group. Many group theoretic facts have found a natural generalization in scheme theory. One of these generalizations is the observation that, similar to groups, association schemes of finite order are commutative if they have at most five elements and not necessarily commutative if they have six elements. While there is (up to isomorphism) only one noncommutative group of order 6, there are infinitely many pairwise non-isomorphic noncommutative association schemes of finite order with six elements. (Each finite projective plane provides such a scheme, and non-isomorphic projective planes yield non-isomorphic schemes.) In this note, we investigate noncommutative schemes of finite order with six elements which have a symmetric normal closed subset with three elements. We take advantage of the classification of the finite simple groups.     

Correlation Analysis of the Alternating Step Generator

The alternating step generator is a well-known keystream generator consisting of two stop/go clocked LFSRs, LFSR₁ and LFSR₂, whose clocks are controlled by another LFSR, LFSR₃, which is clocked regularly. A probabilistic analysis of this generator is conducted which shows that the posterior probabilites of individual bits of the first derivatives of the regularly clocked LFSR₁ and LFSR₂ sequences, when conditioned on a given segment of the first derivative of the keystream sequence, can be computed efficiently in a number of probabilistic models of interest. The expected values of these probabilities, for a random keystream sequence, are derived by an approximate theoretical analysis and are also verified by systematic computer experiments. It is pointed out that these posterior probabilities can be enhanced in a resynchronization scenario and thus used for a low-complexity fast correlation attack on the two LFSRs. More generally, it is argued that even without resynchronization these probabilities may be significantly different from one half for fast correlation attacks based on iterative decoding algorithms to be successful, although with incresead complexity. A related method for computing the posterior probabilities of individual bits of the LFSR₃ sequence, when conditioned on both the keystream sequence and the LFSR₁ and LFSR₂ sequences, is also developed. As these posterior probabilities are much more different from one half, they can be used for a low-complexity fast correlation attack on LFSR₃, provided that the initial states of LFSR₁ and LFSR₂ are previously reconstructed.     

Non-critically phase-matched,Ti:Sapphire-pumped picosecond optical parametric oscillator using LiB3O5

We report a new source of high-repetition rate and widely tunable picosecond pulses for the near infrared. A singly resonant, cw, picosecond optical parametric oscillator based on temperature-tuned LiB₃O₅ and synchronously pumped by 1.8 ps pulses from a self-mode-locked Ti:Sapphire laser is demonstrated. The oscillator can provide average output powers of up to 90 mW under non-critical type-I phase matching at a pulse repetition rate of 81 MHz. Without dispersion compensation, transform-limited signal pulses with 720 fs durations have been generated at 1.2 times threshold. With the available mirror set, signal tuning over 1.374–1.530 µm and idler tuning over 1.676–1.828 µm is demonstrated for a range of pump wavelengths and phase-matching temperatures. With additional mirrors, continuous tuning throughout 1–2.7 µm should be readily attainable with a single LiB₃O₅ crystal.