An inverse spectral problem

In this article an infinite periodic Jacobi matrix is under consideration. It is shown that the spectrum of the matrix consists of a single finite interval if and only if the period of the matrix is equal to unity.     

Far-infrared laser magnetic resonance spectrum of34S16O in X3Σ− state

The far-infrared laser magnetic resonance spectrum of³⁴S¹⁶O in the ground X³Σ^? state has been observed using five optically pumped laser lines as sources. The isotopic sulfur monoxide radical was produced by the reaction of oxygen gas with sulfur vaporized from an oven. The construction and design of such an oven have been discussed. A merged least squares fit of the earlier EPR and microwave results, and the present data yield better-determined molecular constants.     

Simulations on the thermal decomposition of a poly(dimethylsiloxane) polymer using the ReaxFF reactive force field

To investigate the failure of the poly(dimethylsiloxane) polymer (PDMS) at high temperatures and pressures and in the presence of various additives, we have expanded the ReaxFF reactive force field to describe carbon-silicon systems. From molecular dynamics (MD) simulations using ReaxFF we find initial thermal decomposition products of PDMS to be CH(3) radical and the associated polymer radical, indicating that decomposition and subsequent cross-linking of the polymer is initiated by Si-C bond cleavage, in agreement with experimental observations. Secondary reactions involving these CH(3) radicals lead primarily to formation of methane. We studied temperature and pressure dependence of PDMS decomposition by following the rate of production of methane in the ReaxFF MD simulations. We tracked the temperature dependency of the methane production to extract Arrhenius parameters for the failure modes of PDMS. Furthermore, we found that at increased pressures the rate of PDMS decomposition drops considerably, leading to the formation of fewer CH(3) radicals and methane molecules. Finally, we studied the influence of various additives on PDMS stability. We found that the addition of water or a SiO(2) slab has no direct effect on the short-term stability of PDMS, but addition of reactive species such as ozone leads to significantly lower PDMS decomposition temperature. The addition of nitrogen monoxide does not significantly alter the degradation temperature but does retard the initial production of methane and C(2) hydrocarbons until the nitrogen monoxide is depleted. These results, and their good agreement with available experimental data, demonstrate that ReaxFF provides a useful computational tool for studying the chemical stability of polymers.     

Minimal triangulation of a graph and optimal pivoting order in a sparse matrix

This paper considers the problem of finding a minimal triangulation of an undirected graph G = (V, E), where a triangulation is a set T such that every cycle in G = (V, E ∪ T) has a chord. A triangulation T is minimal (minimum) if no triangulation F exists such that F is a proper subset of $\text{T (¦F¦ < ¦T¦)}$, and an ordering α is optimal (optimum) if a minimal (minimum) triangulation is generated by α. A minimum triangulation (optimum ordering) is necessarily minimal (optimal), but the converse is not necessarily true. A necessary and sufficient condition for a triangulation to be minimal is presented. This leads to an algorithm for finding an optimal ordering α which produces a minimal set of “fill-in” when the process is viewed as triangular factorization of a sparse matrix.     

Design and fabrication of automated sedimentation-based separation and siphon-based extraction for detection of allergic reaction on a centrifugal microfluidic disc

We report the design and fabrication of a novel and fully integrated polymer-based centrifugal microfluidic disc for rapid automatic allergens detection. All essential steps for a single test including flow valving, sequencing, mixing, separation, extraction, and sedimentation for final detection are automatically conducted within 30 min on a centrifugal microfluidic disc. Our design features a siphon-based valving and analyte extraction structure where the released analyte is separated and subsequently extracted by a siphon valve into the detection chamber. Incorporating the siphon valve and a series of capillary valves, we realize automated detection of allergic reaction on a centrifugal microfluidic disc.     

Understanding the structural properties of a dendrimeric material directly from powder X-ray diffraction data

Complete structure determination of an early-generation dendrimeric material has been carried out directly from powder X-ray diffraction data, using the direct-space genetic algorithm technique for structure solution followed by Rietveld refinement. This work represents the first application of modern direct-space techniques for structure determination from powder X-ray diffraction data in the case of a dendrimeric material and paves the way for the future application of this approach to enable complete structure determination of other dendrimeric materials that cannot be prepared as single crystal samples suitable for single crystal X-ray diffraction studies.