Determination of Bone Trabeculae Modulus—An Ultrasonic Scanning and MicroCT (μCT) Imaging Combination Approach

To date, there is no method to measure non-destructively the modulus of trabeculae within cancellous bone, whilst retaining its structural integrity. In this study ultrasonic scanning, coupled with microCT imaging, is employed to determine trabeculae modulus along the three major anatomical axes non-destructively. The proposed method allows cancellous bone specimens to remain intact, for possible use in subsequent studies. Volume rendering of the microCT images allows three-dimensional visualization of cancellous bone specimens to be tested. This facilitates trabeculae selection and accurate measurement of distance traveled by the ultrasonic wave, thus yielding a good degree of confidence in the acoustic velocity measured. For all the three principal anatomical directions, the measured acoustic speeds ranged from 2,115 to 3,077 m/s, giving an average of 2,505 m/s. Average wave velocities in the superior–inferior, medial–lateral and anterior–posterior anatomical directions were found to be 2,295, 2,469 and 2,754 m/s, respectively; the differences corresponding to the three directions do not appear to be significant. Subsequently, the modulus was then determined using elastic wave propagation theory.     

A ligand-free copper(I) oxide catalyzed strategy for the N-arylation of azoles in water

A simple and practical protocol has been developed for the cross-coupling of azoles and aryl iodides under ligand-free copper(I) oxide catalyzed conditions in water. The protocol uses tetrabutylammonium bromide (TBAB) as the phase-transfer catalyst, and water as the solvent, and shows good tolerance towards various functional groups.     

Biomimetic anchors for antifouling and antibacterial polymer brushes on stainless steel

Barnacle cement (BC) was beneficially applied on stainless steel (SS) to serve as the initiator anchor for surface-initiated polymerization. The amine and hydroxyl moieties of barnacle cement reacted with 2-bromoisobutyryl bromide to provide the alkyl halide initiator for the surface-initiated atom transfer radical polymerization (ATRP) of 2-hydroxyethyl methacrylate (HEMA). The hydroxyl groups of HEMA polymer (PHEMA) were then converted to carboxyl groups for coupling of chitosan (CS) to impart the SS surface with both antifouling and antibacterial properties. The surface-functionalized SS reduced bovine serum albumin adsorption, bacterial adhesion, and exhibited antibacterial efficacy against Escherichia coli (E. coli). The effectiveness of barnacle cement as an initiator anchor was compared to that of dopamine, a marine mussel inspired biomimetic anchor previously used in surface-initiated polymerization. The results indicate that the barnacle cement is a stable and effective anchor for functional surface coatings and polymer brushes.     

Determination of metabolites in Uncaria sinensis by HPLC and GC-MS after green solvent microwave-assisted extraction

Uncaria sinensis (Oliv.) Havil (Rubiaceae) has been used as an important Traditional Chinese Medicine (TCM) herb for the treatment of fevers and various nervous disorders. The major bioactive secondary metabolites from different classes of chemical compounds, i.e. organic acid, flavonoid and alkaloid, present in this TCM herb, namely catechin, caffeic acid, epicatechin and rhynchophylline, were extracted by microwave-assisted extraction (MAE) method with ultra-pure water as the extraction solvent. The optimal extraction conditions for this green solvent MAE method were found to be 100 °C for 20 min. The recoveries of the compounds were found to be comparable to that of heating under reflux using ultra-pure water for 60 min. The method precision (RSD, n = 6) was found to vary from 0.19% to 5.60% for the proposed method on different days for the secondary metabolites. Simultaneously, the key primary metabolites such as sucrose and phenylalanine for the biosynthesis of bioactive secondary metabolites were successfully characterized by GC-MS. Furthermore, an approach using the combination of primary and secondary metabolite profiling based on their chemical fingerprints with Principal Component Analysis (PCA) was successfully developed to evaluate the quality of U. sinensis obtained from different sources. This approach was shown to be feasible in discriminating U. sinensis from different origins and thus a potential application for the quality control of other medicinal herbs.     

Determination of melamine in milk powder using gas chromatography-high-resolution isotope dilution mass spectrometry

A GC-high-resolution isotope dilution MS (IDMS) method for the quantification of melamine in milk powder is described. The developed technique is compared to the LC-IDMS/MS technique, typically used for the determination of melamine in various matrices. The accuracy of the GC-high-resolution IDMS method was demonstrated when a small degree of equivalence was obtained in a regional comparative study involving the determination of melamine in milk powder.     

Robust suboptimal control of nonlinear systems

In this paper, we consider a nonlinear dynamic system with uncertain parameters. Our goal is to choose a control function for this system that balances two competing objectives: (i) the system should operate efficiently; and (ii) the system’s performance should be robust with respect to changes in the uncertain parameters. With this in mind, we introduce an optimal control problem with a cost function penalizing both the system cost (a function of the final state reached by the system) and the system sensitivity (the derivative of the system cost with respect to the uncertain parameters). We then show that the system sensitivity can be computed by solving an auxiliary initial value problem. This result allows one to convert the optimal control problem into a standard Mayer problem, which can be solved directly using conventional techniques. We illustrate this approach by solving two example problems using the software MISER3.     

Hölder continuity and upper estimates of solutions to vector quasiequilibrium problems

In this paper, we establish the Hölder continuity of solution mappings to parametric vector quasiequilibrium problems in metric spaces under the case that solution mappings are set-valued. Our main assumptions are weaker than those in the literature, and the results extend and improve the recent ones. Furthermore, as an application of Hölder continuity, we derive upper bounds for the distance between an approximate solution and a solution set of a vector quasiequilibrium problem with fixed parameters.     

Spherical Photon Orbits Around a Kerr Black Hole

Two circular photon orbits are known to exist in the equatorial plane of the Kerr black hole. In this paper, we investigate so-called spherical photon orbits—orbits with constant coordinate radii that are not confined to the equatorial plane. A one-parameter class of solutions is found, which includes the circular orbits as special cases. The properties of these spherical orbits are then analyzed, with the aim of classifying them by qualitative differences in their behavior. Finally, representative orbits from each class are plotted out, including a zero-angular momentum photon orbit and one with non-fixed azimuthal direction.