A general transformation for theta series associated with the quadratic form $$x^2+ky^2$$

Using elementary techniques, we prove a general transformation for theta series associated with the quadratic form \(x^2+ky^2.\) The transformation is then applied to establish several infinite families of identities involving theta series whose Fourier coefficients are interlinked.     

QSDPNAL: a two-phase augmented Lagrangian method for convex quadratic semidefinite programming

In this paper, we present a two-phase augmented Lagrangian method, called QSDPNAL, for solving convex quadratic semidefinite programming (QSDP) problems with constraints consisting of a large number of linear equality and inequality constraints, a simple convex polyhedral set constraint, and a positive semidefinite cone constraint. A first order algorithm which relies on the inexact Schur complement based decomposition technique is developed in QSDPNAL-Phase I with the aim of solving a QSDP problem to moderate accuracy or using it to generate a reasonably good initial point for the second phase. In QSDPNAL-Phase II, we design an augmented Lagrangian method (ALM) wherein the inner subproblem in each iteration is solved via inexact semismooth Newton based algorithms. Simple and implementable stopping criteria are designed for the ALM. Moreover, under mild conditions, we are able to establish the rate of convergence of the proposed algorithm and prove the R-(super)linear convergence of the KKT residual. In the implementation of QSDPNAL, we also develop efficient techniques for solving large scale linear systems of equations under certain subspace constraints. More specifically, simpler and yet better conditioned linear systems are carefully designed to replace the original linear systems and novel shadow sequences are constructed to alleviate the numerical difficulties brought about by the crucial subspace constraints. Extensive numerical results for various large scale QSDPs show that our two-phase algorithm is highly efficient and robust in obtaining accurate solutions. The software reviewed as part of this submission was given the DOI (Digital Object Identifier)  https://doi.org/10.5281/zenodo.1206980.     

Using one EWMA chart to jointly monitor the process mean and variance

Two control charts are usually used to monitor the process mean and variance separately. The mean is monitored using the [`(X)]{\bar{{X}}} chart while the variance using either the standard deviation, S chart, or the range, R chart. Recently, numerous single variable charts are proposed to jointly monitor the mean and variance. Most approaches transform the sample mean and sample variance into two statistics, each having a standard scale, and either plotting them on the same chart or combining them into a single statistic to be plotted on a chart. The R chart is more widely used than the S chart but no attempt is made to combine the [`(X)]{\bar{{X}}} and R charts in the construction of a single variable chart and to study its properties and performance. In this paper, we transform the [`(X)]{\bar{{X}}} and R statistics into two standard normal random variables, used in the computation of two corresponding exponentially weighted moving average (EWMA) statistics, which are then merged into a single plotting statistic for the proposed chart, called the EWMA [`(X)]-R{\bar{{X}}-R} chart.     

Analysis of a bi-piezoelectric ceramic layer with an interfacial crack subjected to anti-plane shear and in-plane electric loading

The behaviour of a bi-piezoelectric ceramic layer with a centre interfacial crack subjected to anti-plane shear and in-plane electric loading has been studied. The dislocation density functions and the Fourier integral transform method have been employed to eliminate the problem of singular integral equations. The normalized energy release rate, stress and electrical displacement intensity factors, G/G₀,K_III/K_III0 and K_D/K_D0, respectively, were determined for different geometric and property parameters by use of two different crack surface electric boundary conditions, i.e. impermeable and permeable. It has been shown that the effects of the thickness and material constants of the piezoelectric layer on all the three parameters, i.e. G/G₀,K_III/K_III0 and K_D/K_D0 were significant.     

Observation of a new DsJ meson in B+-->D0D0K+ decays

We report the observation of a new DsJ meson produced in B+-->D0DsJ-->D0D0K+. This state has a mass of M=2708+/-9(-10)(+11) MeV/c2, a width Gamma=108+/-23(-31)(+36) MeV/c2 and a 1- spin-parity. The statistical significance of this observation is 8.4 sigma. The results are based on an analysis of 449 x 10(6) BB events collected at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider.     

Prolate and Oblate Shape Coexistence in 188Pt

A standard in-beam γ-spectroscopy experiment for ¹⁸⁸Pt is performed via the¹⁷⁶Yb(¹⁸O, 6n) reaction at beam energies of 88 and 95MeV, and the level scheme for ¹⁸⁸Pt is established. Prolate and oblate shape coexistence has been demonstrated to occur in ¹⁸⁸Pt by applying the projected shell model. The rotation alignment of i_13/2 neutrons drives the yrast sequence changingsuddenly from prolate to oblate shape at angular momentum 10h, indicating likely a new type of shape phase transition along the yrast line in ¹⁸⁸Pt.     

Lower limit of determination values for trace elements in iron certified reference materials by neutron activation analysis with multiple gamma-ray detection

Recycling steel products demands a new technique for determining tramp elements in steel. Tramp elements, As and Sb, in some iron certified reference materials were determined by neutron activation analysis with multiple gamma-ray detection method and reported in MTAA11. In MTAA12, the authors reported the lower limit of determination values (LDL) and the dispersion of this method. The values of the LDLs for As and Sb in high purity iron were 0.002 and 0.0009 μg·g⁻¹. The dispersion is small enough to satisfy the demand from materials science.     

Kinetic analysis of superoxide anion radical-scavenging and hydroxyl radical-scavenging activities of platinum nanoparticles

There are few reports on the physiological effects of metal nanoparticles (nps), especially with respect to their functions as scavengers for superoxide anion radical (O2(.-)) and hydroxyl radical (.OH). We tried to detect the scavenging activity of Pt nps using a hypoxanthine-xanthine oxidase system for O2(.-) and using a Fenton and a UV/H2O2 system for .OH. Electron spin resonance analysis revealed that 2 nm particle size Pt nps have the ability to scavenge O2(.-) and .OH. The calculated rate constant for the O2(.-)-scavenging reaction was 5.03 +/- 0.03 x 10(7) M (-1) s (-1). However, the analysis of the Fenton and UV/H 2O 2 system in the presence of Pt nps suggested that the .OH-scavenging reaction cannot be determined in both systems. Among particle sizes tested from 1 to 5 nm, 1 nm Pt nps showed the highest O2(.-)-scavenging ability. Almost no cytotoxicity was observed even after adherent cells (TIG-1, HeLa, HepG2, WI-38, and MRC-5) were exposed to Pt nps at concentrations as high as 50 mg/L. Pt nps scavenged intrinsically generated reactive oxygen species (ROS) in HeLa cells. Additionally, Pt nps significantly reduced the levels of intracellular O2(.-) generated by UVA irradiation and subsequently protected HeLa cells from ROS damage-induced cell death. These findings suggest that Pt nps may be a new type of antioxidant capable of circumventing the paradoxical effects of conventional antioxidants.     

Integrating sensitive quantification of hepatic metabolic functions by capillary electrophoresis with laser-induced fluorescence detection

We report the establishment of capillary electrophoresis with laser-induced fluorescence (CE-LIF) detection as a common analytical platform for sensitive quantification of both phase I and II metabolism in various hepatic in vitro models.     

A novel 3D mammalian cell perfusion-culture system in microfluidic channels

Mammalian cells cultured on 2D surfaces in microfluidic channels are increasingly used in drug development and biological research applications. These systems would have more biological or clinical relevance if the cells exhibit 3D phenotypes similar to the cells in vivo. We have developed a microfluidic channel based system that allows cells to be perfusion-cultured in 3D by supporting them with adequate 3D cell-cell and cell-matrix interactions. The maximal cell-cell interaction was achieved by perfusion-seeding cells through an array of micropillars; and 3D cell-matrix interactions were achieved by a polyelectrolyte complex coacervation process to form a thin layer of matrix conforming to the 3D cell shapes. Carcinoma cell lines (HepG2, MCF7), primary differentiated (hepatocytes) and primary progenitor cells (bone marrow mesenchymal stem cells) were perfusion-cultured for 72 hours to 1 week in the microfluidic channel, which preserved their 3D cyto-architecture and cell-specific functions or differentiation competence. This transparent 3D microfluidic channel-based cell culture system also allows direct optical monitoring of cellular events for a wide range of applications.