New locally conservative finite element methods on a rectangular mesh

A new family of locally conservative, finite element methods for a rectangular mesh is introduced to solve second-order elliptic equations. Our approach is composed of generating PDE-adapted local basis and solving a global matrix system arising from a flux continuity equation. Quadratic and cubic elements are analyzed and optimal order error estimates measured in the energy norm are provided for elliptic equations. Next, this approach is exploited to approximate Stokes equations. Numerical results are presented for various examples including the lid driven-cavity problem.     

The McCoy Condition on Noncommutative Rings

We introduce the multiplication algebra of a Bernstein algebra, establish its Peirce decomposition relative to an idempotent of A and state some basic properties of this algebra of endomorphtsms     

Enantiomerically pure synthesis of beta-substituted gamma-butyrolactones: a key intermediate to concise synthesis of pregabalin

Chiral beta-substituted gamma-butyrolactones are known to be important intermediates for many biologically active compounds such as gamma-aminobutyric acid (GABA) derivatives and lignans. We have developed a general, convenient, and scalable synthetic method for enantiomerically pure beta-substituted gamma-butyrolactones, with either configuration, via nucleophilic cyclopropane ring opening of (1S,5R)- or (1R,5S)-bicyclic lactone followed by decarbethoxylation. The utility of our method was demonstrated by streamlined synthesis of pregabalin ((S)-3-isobutyl-gamma-aminobutyric acid), an anticonvulsant drug for the treatment of peripheral neuropathic pain.     

Synthesis of tri-, hexa-, and nonasaccharide subunits of the atypical O-antigen polysaccharide of the lipopolysaccharide from Danish Helicobacter pylori strains

Synthesis of trisaccharide repeating unit, -->3)-alpha-D-Rhap-(1-->2)-alpha-D-Manp3CMe-(1-->3)-alpha-L-Rha p-(1-->, and its dimeric hexa- and trimeric nonasaccharide subunits of the atypical O-antigen polysaccharide of the lipopolysaccharide from Danish H. pylori strains D1, D3, and D6 has been accomplished. Successful synthesis of the hexasaccharide and the nonasaccharide was possible by dimerization and trimerization of the suitably protected trisaccharide repeating unit, in which three monosaccharide moieties were arranged in a proper order by placing the sterically demanding 3-C-methyl-D-mannose moiety in between D- and L-rhamnoses. Key steps include the coupling of three monosaccharide moieties and dimerization and trimerization of the trisaccharide unit by glycosylations employing the 2'-carboxybenzyl glycoside method. Also presented is a method for the synthesis of the novel branched sugar, 3-C-methyl-D-mannose moiety by elaboration of its equatorial hydroxyl and axial methyl groups at C-3' in the disaccharide stage.     

Vascular mimetics based on microfluidics for imaging the leukocyte--endothelial inflammatory response

We describe the development, validation, and application of a novel PDMS-based microfluidic device for imaging leukocyte interaction with a biological substrate at defined shear force employing a parallel plate geometry that optimizes experimental throughput while decreasing reagent consumption. The device is vacuum bonded above a standard 6-well tissue culture plate that accommodates a monolayer of endothelial cells, thereby providing a channel to directly observe the kinetics of leukocyte adhesion under defined shear flow. Computational fluid dynamics (CFD) was applied to model the shear stress and the trajectory of leukocytes within the flow channels at a micron length scale. In order to test this model, neutrophil capture, rolling, and deceleration to arrest as a function of time and position was imaged in the transparent channels. Neutrophil recruitment to the substrate proved to be highly sensitive to disturbances in flow streamlines, which enhanced the rate of neutrophil-surface collisions at the entrance to the channels. Downstream from these disturbances, the relationship between receptor mediated deceleration of rolling neutrophils and dose response of stimulation by the chemokine IL-8 was found to provide a functional readout of integrin activation. This microfluidic technique allows detailed kinetic studies of cell adhesion and reveals neutrophil activation within seconds to chemotactic molecules at concentrations in the picoMolar range.     

Self-assembled peptide architecture with a tooth shape: folding into shape

Molecular self-assembly is the spontaneous association of molecules into structured aggregates by which nature builds complex functional systems. While numerous examples have focused on 2D self-assembly to understand the underlying mechanism and mimic this process to create artificial nano- and microstructures, limited progress has been made toward 3D self-assembly on the molecular level. Here we show that a helical β-peptide foldamer, an artificial protein fragment, with well-defined secondary structure self-assembles to form an unprecedented 3D molecular architecture with a molar tooth shape in a controlled manner in aqueous solution. Powder X-ray diffraction analysis, combined with global optimization and Rietveld refinement, allowed us to propose its molecular arrangement. We found that four individual left-handed helical monomers constitute a right-handed superhelix in a unit cell of the assembly, similar to that found in the supercoiled structure of collagen.     

An experimental and numerical study of fracture coalescence in pre-cracked specimens under uniaxial compression

This study presents crack initiation, propagation and coalescence at or near pre-existing open cracks or flaws in a specimen under uniaxial compression. The flaw geometry in the specimen was a combination of a horizontal flaw and an inclined flaw underneath. This flaw geometry is different from those reported in the previous studies, where a pair of parallel flaws was used. Three materials were used, PMMA (Poly Methyl MethAcrylate), Diastone (types of molded gypsum), and Hwangdeung granite. Crack initiation and propagation showed similar and different patterns depending on the material. In PMMA, tensile cracks initiated at the flaw tips and propagated to the tip of the other flaw in the bridge area. The cracks then coalesced at a point of the inclined flaw, which is affected by the flaw inclination angle. For Diastone and Hwangdeung granite, tensile cracks were observed followed by the initiation of shear cracks. Coalescence occurred mainly through the tensile cracks or tensile and shear cracks. Crack coalescence was classified according to the crack coalescence types of parallel flaws for overlapping flaw geometry in the past works. In addition, crack initiation and coalescence stresses in the double-flawed specimens were analyzed and compared with those in the single-flawed specimen. Numerical simulations using PFC^2D (Particle Flow Code in two dimensions) based on the DEM (Discrete Element Method) were carried out and showed a good agreement with the experimental results in the coalescence characteristics in Hwangdeung granite. These experimental and numerical results are expected to improve the understanding of the characteristics of cracking and crack coalescence and can be used to analyze the stability of rock and rock structures, such as the excavated underground openings or slopes, tunneling construction, where pre-existing cracks or fractures play a crucial role in the overall integrity of such structures.     

Cobalt-phosphate complexes catalyze the photoelectrochemical water oxidation of BiVO4 electrodes

BiVO(4) semiconductor electrodes were coupled with cobalt-phosphate complexes (CoPi) to enhance the photoelectrochemical (PEC) performance for water oxidation reaction. CoPi was deposited on a 550 nm-thick BiVO(4) film via electrodeposition (ED) and photodeposition (PD) methods for comparison of their effects. The CoPi on BiVO(4) exhibited Co?:?P atomic ratios of approximately 1?:?7 for the electrodeposited sample and approximately 1?:?18 for the photodeposited sample, and Co(2+) and Co(3+) co-existed in both samples. Optimized CoPi ED resulted in a CoPi overlayer of approximately 850 nm thick, which showed an electrochromic-like behavior that was likely due to limited access of phosphate into BiVO(4) across the CoPi layer. Optimized CoPi PD, however, had very thin and rather uniform CoPi dispersion and did not show electrochromic-like behavior. Despite the lesser amount of CoPi, the PEC performance of BiVO(4)/CoPi (PD) was comparable to that of BiVO(4)/CoPi (ED). Real-time measurements of the headspace molecular oxygen that evolved from water oxidation indicated that CoPi enhances O(2) production and photocurrent generation at BiVO(4) by a factor of around 15 and a maximum of 20, respectively, at 0.576 V(SCE) (equivalent to 1.23 V(RHE)) under air mass 1.5 irradiation (400 mW cm(-2)). Prolonged irradiation of BiVO(4)/CoPi (ED) resulted in a reduced Co?:?P ratio to 1?:?1.77 without changing the mixed valency of Co(II/III). This finding indicates that incorporation of phosphate into the CoPi was kinetically slower than water oxidation. The primary role of CoPi has been suggested as a hole-conducting electrocatalyst making the photogenerated electrons more mobile and, consequently, increasing conductivity and boosting the PEC water oxidation performance of BiVO(4).     

A simple and smart telemedicine device for developing regions: a pocket-sized colorimetric reader

We have proposed a novel mobile healthcare platform, combining a pocket-sized colorimetric reader (13.5 × 6.5 × 2.5 cm(3)) and commercially available 10-parameter urinalysis paper strips (glucose, protein, glucose, bilirubin, urobilinogen, ketones, nitrite, pH, specific gravity, erythrocytes, and leukocytes), capable of sending data with a smart phone. The reader includes a novel colorimetric multi-detection module, which consists of three-chromatic light-emitting diodes, silicon photodiodes and a novel poly(methylmethacrylate) (PMMA) optical splitter. We employed data reading methods using conversions of the signal data (red, blue, and green) to the hue (H) color map or the Y model data, and used a curve-fitting method for the quantification. The reader is battery-powered, inexpensive, light-weight, and very speedy in analysis. And, it was applied to detection of a thousand of human urine samples and demonstrated reliable quantification of urinary glucose and protein. The features can be used by unskilled people on-site to transfer the analyzed data to experts off-site.