Fourier transform versus Hilbert transform

Certain relations between the Fourier transform of a function and the Hilbert transform of its derivative are revealed. They concern the integrability/non-integrability of both transforms. Certain applications are discussed.     

A multiplier method with automatic limitation of penalty growth

This paper presents a multiplier method for solving optimization problems with equality and inequality constraints. The method realizes all the good features that were foreseen by R. Fletcher for this type of algorithm in the past, but which suffers from none of the drawbacks of the earlier attempts.Research sponsored by the National Science Foundation (RANN) Grant ENV76-04264 the National Science Foundation Grant ENG73-08214-A01 and the Sweden-American Foundation.     

Multiplexed inkjet functionalization of silicon photonic biosensors

The transformative potential of silicon photonics for chip-scale biosensing is limited primarily by the inability to selectively functionalize and exploit the extraordinary density of integrated optical devices on this platform. Silicon biosensors, such as the microring resonator, can be routinely fabricated to occupy a footprint of less than 50 × 50 μm; however, chemically addressing individual devices has proven to be a significant challenge due to their small size and alignment requirements. Herein, we describe a non-contact piezoelectric (inkjet) method for the rapid and efficient printing of bioactive proteins, glycoproteins and neoglycoconjugates onto a high-density silicon microring resonator biosensor array. This approach demonstrates the scalable fabrication of multiplexed silicon photonic biosensors for lab-on-a-chip applications, and is further applicable to the functionalization of any semiconductor-based biosensor chip.     

Impacts of professional development focused on teaching engineering applications of mathematics and science

With the recent national emphasis on preparing children for future careers in science, technology, engineering, and mathematics, K-12 teachers are being called upon to include engineering in their instruction. This study explores the impacts of a summer professional development (PD) program focused on the engineering applications of mathematics and science on in-service K-12 teachers' (a) personal engineering efficacy, (b) engineering teaching efficacy, and (c) perceived barriers to teaching engineering. This quantitative study revealed that a single engineering-focused PD could increase teachers' personal engineering efficacy and engineering teaching efficacy and reduce particular perceived barriers to teaching engineering. No differences existed in pre- to post workshop assessment scores based on grade level taught, gender, or years of teaching experiences. However, pre- to post workshop assessment differences existed between participants depending on the discipline they taught and wether or not they had previously used engineering activities in their classrooms. These findings suggest that a single engineering PD can have significant impacts on in-service teachers' personal engineering efficacy, engineering teaching efficacy, and perceived barriers to teaching engineering, but a one-size-fits-all approach to such PD is not equally effective for all participants.     

Molecular cloning and biochemical characterization of a family-9 endoglucanase with an unusual structure from the gliding bacteria <Emphasis Type="Italic">Cytophaga hut chinsonii</Emphasis>

Cytophaga hutchinsonii was originally isolated from sugarcane piles. This microorganism therefore probably produces an array of enzymes allowing it to digest cellulosic substrates. C. hutchinsonii thus represents a rich source of potentially effective cellulase enzymes that can be harnessed for conversion of biomass to simple sugars. These sugars can then be used as feedstock for ethanol production or other chemical syntheses. In this study, we report the PCR cloning of an endoglucanase gene (Cel9A) from C. hutchinsonii using degenerated primers directed at the catalytic domain. Alignment of the amino acids sequence revealed that Cel9A has a gene structure totally different from the other known cellulose degraders. The most striking feature of this cloned protein is the absence of a cellulose-binding domain (CBD), which to date was believed to be imperative in cellulose hydrolysis. Consequently, the Cel9A gene, encoding β-1,4 endoglucanase from C. hutchinsonii was over-expressed in Escherichia coli with a His-Tag based expression vector. The resulting polypeptide, with a molecular mass of 105 KDa, was purified from cell extracts by affinity chromatography on cellulose. Mature Cel9A was optimally active at pH 5.0 and 45°C. The enzyme efficiently hydrolyzes carboxymethyl-cellulose (CMC). Analysis of CMC and filter paper hydrolysis suggests that Cel9A is a nonprocessive enzyme with endo-cellulase activities.     

Selective bromination of perylene diimides under mild conditions

A novel method for the bromination of perylene diimides, PDI (1), under mild conditions is reported. Variation of the reaction conditions allows mono- and dibromination of PDIs to afford 2 and 3 (these can be separated through standard procedures) or exclusive dibromination to afford 3. Pure 1,7 regioisomers are obtained through repetitive crystallization. The structure of 1,7-3b was elucidated by a single-crystal X-ray analysis. The facility of the bromination reaction, which decreases in the order 1a > 1b > 1c, depends on PDI aggregation propensities. Monobrominated PDIs were utilized for the syntheses of novel unsymmetrical piperidinyl (4a and 4b) and trimethylsilylethynyl derivatives (5a and 5b). Computational studies (DFT) on imide substituent rotation in PDIs reveal that in the case of bulky groups there is a restricted rotation leading to isomers, in agreement with our experimental results. An aromatic core twist in PDIs bearing one and two bromine substituents was also investigated by DFT.     

Influence of the colloidal environment on the magnetic behavior of cobalt nanoparticles

The magnetic properties of 10 nm diameter surfactant-coated cobalt (Co) nanoparticles in 1,2-dichlorobenzene (DCB) are investigated by a series of sequential magnetic moment (m) vs temperature (T) measurements. A rapid rise in magnetic moment around 250 K during warming and an abrupt drop at 234 K during cooling are observed when a nonsaturating external magnetic field is applied. Differential scanning calorimetry (DSC) measurements demonstrate that the rapid rise and abrupt drop in magnetization are associated with the melting and freezing of the solvent. Magnetic measurements of these Co nanoparticles in DCB are also used to probe their aging over a period of 70 days. The saturation magnetic moment of Co nanoparticles in DCB stored in air at room temperature decreases by nearly 40% over 70 days. Transmission electron microscopy (TEM) characterizations are reported to show the time evolution in the size, shape, and crystalline structures of DCB-immersed nanoparticles.