Approximation of low rank solutions for linear quadratic control of partial differential equations

Algebraic Riccati equations (ARE) of large dimension arise when using approximations to design controllers for systems modeled by partial differential equations. We use a modified Newton method to solve the ARE that takes advantage of several special features of these problems. The modified Newton method leads to a right-hand side of rank equal to the number of inputs regardless of the weights. Thus, the resulting Lyapunov equation can be more efficiently solved. The Cholesky-ADI algorithm is used to solve the Lyapunov equation resulting at each step. The algorithm is straightforward to code. Performance is illustrated with a number of standard examples. An example on controlling the deflection of the Euler-Bernoulli beam indicates that for weakly damped problems a low rank solution to the ARE may not exist. Further analysis supports this point.     

Simplifying native chemical ligation with an N-acylsulfonamide linker

We report a simplified procedure for the chemical ligation of peptides by using the sulfamylbutyryl linker as a mildly activating group capable of participating in ligation. When the peptidyl N-methylsulfonamide is directly added with excess thiols to ligation reactions, the speed of reaction is comparable to native chemical ligation.     

Rhodium-catalysed isomerisation/formal 1,3-dipolar cycloaddition cascades to fused-ring heterocycles

Fused ring heterocycles were synthesised via the rhodium catalysed isomerisation/regio and stereoselective 1,3-dipolar cycloaddition cascades in good yields.     

High-performance fiber-laser-based terahertz spectrometer

We have developed a rapid scanning terahertz (THz) spectrometer based on a synchronized two-fiber-laser system. When the system is set to the asynchronous optical sampling mode, THz spectra extending to 3 THz can be acquired within 1 μs at a signal-to-noise ratio of the electric field of better than 20. Signal averaging results in a dynamic range of more than 60 dB, and frequency components of more than 4 THz can be detected. When the lasers are set to the same repetition rate, electronically controlled optical sampling at a rate of 2.5 kHz is demonstrated, making the system versatile for different spectroscopic applications. Finally, we compare the THz emission spectra of a photoconductive switch that is pumped at 780 nm and a nonlinear DAST crystal excited at 1550 nm. We find that the spectral range of the spectrometer is significantly enhanced at higher frequencies, while the dynamic range remains constant.     

A model for an extensional mode resonator used as a frequency-adjustable vibration energy harvester

In an effort to identify techniques for harvesting energy from ambient vibrations, a prototype device that utilizes stretching piezoelectric film to support a proof mass, with an adjustable support that allows the resonant frequency of the device to be easily altered, has been developed. This extensional mode resonator (XMR) device is described by a model developed in this paper that predicts the power that is harvested as a function of the frequency and amplitude of the external vibration, the elastic and piezoelectric materials properties, and the device geometry. The model provides design guidelines for the effects of device geometry and applied tension through an adjustable support that suggest a strong dependence on mechanical damping and a weak dependence on frequency, as opposed to a bending cantilever device. The model predictions are compared to experimental measures from a prototype device for frequencies between 120 and 180 Hz, and at accelerations between 0.1 and 10 m/s². Up to 9 mW is generated from a device with a mass of ∼82 g, and over the range of frequencies tested the power harvested at 4 m/s² is between 3 and 4 mW.     

Selective removal of the 2'- and 3'-O-acyl groups from 2',3',5'-tri-O-acylribonucleoside derivatives with lithium trifluoroethoxide

Selective cleavage of O2' and O3' ester groups from ribonucleoside derivatives has been accomplished with Dowex 1 x 2 (CF3CH2O-) in 2,2,2-trifluoroethanol (TFE) or lithium trifluoroethoxide/TFE. Deacylations with Li+ -OCH2CF3/TFE proceed at ambient temperature (or with mild heating) to give the 5'-O-acyl derivatives in superior yields and higher purity than prior approaches for selective O2' and O3' ester deprotection.     

Direct cyclopropanation of 1-alkynylphosphonates by Cp2ZrCl2/2EtMgBr/2AlCl3 to afford cyclopropylmethylphosphonates

[reaction: see text] The reagent system Cp2ZrCl2/2EtMgBr/2AlCl3 converts 1-alkynylphosphonates into cyclopropylmethylphosphonates 3 in good isolated yields. Ethers, chlorides, and other cyclopropyl groups are compatible with the reaction conditions. Deuterium labeling is consistent with the formation of stable cyclopropylmethylbimetallic phosphonates by ring contraction of the corresponding aluminacyclopentenylphosphonate. Temperature is crucial; apparently, the cyclopropylmethylbimetallic phosphonates are in equilibrium with the aluminacyclopentenylphosphonates. Low temperature favors the former. We surmise that the negative charges of the intermediate are stabilized by the phosphonate group. Thus, diphenylacetylene and 3-hexyne failed to give cyclopropyl products under the same reaction conditions.     

Structure and synthesis of 6-(substituted-imidazol-1-yl)purines: versatile substrates for regiospecific alkylation and glycosylation at N9

X-ray crystal structures of several 6-(azolyl)purine base and nucleoside derivatives show essentially coplanar conformations of the purine and appended 6-(azolyl) rings. However, the planes of the purine and imidazole rings are twisted approximately 57 degrees in a 2-chloro-6-(4,5-diphenylimidazol-1-yl)purine nucleoside, and a twist angle of approximately 61 degrees was measured between the planes of the purine and pyrrole rings in the structure of a 6-(2,5-dimethylpyrrol-1-yl)purine nucleoside derivative. Shielding "above" N7 of the purine ring by a proximal C-H on the 6-azolyl moiety is apparent with the coplanar compounds, but this effect is diminished in those without coplanarity. Syntheses of 6-(azolyl)purines from both base and nucleoside starting materials are described. Treatment of 2,6-dichloropurine with imidazole gave 2-chloro-6-(imidazol-1-yl)purine. Modified Appel reactions at C6 of trityl-protected hypoxanthine and guanine derivatives followed by detritylation gave 6-(imidazol-1-yl)- and 2-amino-6-(imidazol-1-yl)purines. Imidazole was introduced at C6 of 2',3',5'-tri-O-acetylinosine by a modified Appel reaction, and solvolysis of the glycosyl linkage gave 6-(imidazol-1-yl)purine. Guanosine triacetate was transformed into the protected 2,6-dichloropurine nucleoside, which was subjected to S(N)Ar displacement with imidazoles at C6 followed by glycosyl solvolysis to provide 2-chloro-6-(substituted-imidazol-1-yl)purines. Potential applications of these purine derivatives are outlined.     

An autoxidation study of C2 substituted pyrimidine amino reductones

Three pyrimidine derivatives (8a-c), differing from isouramil and divicine at C2, have been synthesized and their autoxidation rates measured spectrophotometrically. The autoxidation rates of all five pyrimidines (8a-c, isouramil and divicine) were correlated with values (rho=−1.28, r²=0.949).