A note on an SOR-like method for augmented systems

Golub et al. (2001, BIT, 41, 71–85) gave a generalizedsuccessive over-relaxation method for the augmented systems.In this paper, the connection between the SOR-like method andthe preconditioned conjugate gradient (PCG) method for the augmentedsystems is investigated. It is shown that the PCG method isat least as accurate (fast) as the SOR-like method. Numericalexamples demonstrate that the PCG method is much faster thanthe SOR-like method.     

Structure and magnetostriction of RFex (1.6 ? x ? 2.0) and R(Fe1−yTiy)1.8 (y ? 0.2) alloys (RDy0.65Tb0.25Pr0.1)

Structure, Curie temperature and magnetostriction of RFe_x (1.6 ? x ? 2.0) and R(Fe_1−yTi_y)_1.8 (y ? 0.2) alloys (RDy_0.65Tb_0.25Pr_0.1) have been investigated using optical microscopy, X-ray diffraction, AC initial susceptibility and standard strain gauge techniques. The homogenized RFe_x alloys are found to be essentially single phase in the range of 1.8 ? x ? 1.85. The second phase is a rare-earth-rich phase when x ? 1.8, and (Dy, Tb, Pr)Fe₃ phase when x ? 1.85. X-ray diffraction indicates that the R(Fe_1−yTi_y)_1.8 alloys contain a small amount of Fe₂Ti phase when y ? 0.05, which increases with the increment of Ti content. The Curie temperature of R(Fe₁−_yTi_y)_1.8 alloys slightly enhances with increasing Ti concentration when y ? 0.05, then remains almost unchanged in the range of 0.05 ? y ? 0.20. The magnetostriction of RFe_x alloys is improved when x ? 1.80 and reduced by increasing Fe content when x ? 1.85. The magnetostriction of R(Fe_1−yTi_y)_1.8 alloys is lowered by increasing Ti content.     

Phase diagram and tricritical behavior of an metamagnet in uniform and random fields

A two-sublattice Ising metamagnet in both uniform and random fields is studied within the mean-field approach based on Bogoliubov’s inequality for the Gibbs free energy. We show that the qualitative features of the phase diagrams are dependent on the parameters of the model and the uniform field values. The tricritical point and reentrant phenomenon can be observed on the phase diagram. The reentrance is due to the competition between uniform and random interactions.     

Solubility of Mannitol in Aqueous Sodium Chloride by the Isopiestic Method

Using a method for determination of solubilities of nonelectrolytes in electrolyte solutions based on isopiestic equilibration and precise chemical analyses, we have measured and report the solubilities of mannitol in sodium chloride solutions. Our results are, in general, in good agreement with the data of Kelly et al. The method is described and its advantages discussed.     

Enzymatic Determination of Glucose by Optical-Fiber Sensor Sequential Injection Renewable Surface Spectrophotometry

Introduction Determinationofglucoseisrequiredinmedicine industry,foodindustry,clinicaldiagnosisaswellas variousresearchfields.Therefore,intensiveefforts havebeendirectedtothedevelopmentofanalytical methodsfordeterminationofglucose,suchasthose basedonbiose…     

On-line sample-pre-treatment schemes for trace-level determinations of metals by coupling flow injection or sequential injection with ICP-MS

Within the last decade, the first generation of flow injection (FI) has been supplemented by sequential injection (SI), also termed the second generation, and, recently, by the third generation, i.e., SI-Lab-on-Valve (SI-LOV). As apparent from the literature, FI and/or SI have become dominant as substitutes for labor-intensive, manual, sample-pre-treatment and/or solution-handling procedures prior to analyte detection by inductively coupled plasma mass spectrometry (ICP-MS). The present review presents and discusses the progress of the state of the art in implementing miniaturized FI/SI systems for on-line matrix separation and pre-concentration of trace levels of metals with detection by ICP-MS. It highlights some of the frequently applied on-line, sample-pre-treatment schemes, including solid phase extraction (SPE), on-wall molecular sorption and precipitate/(co)-precipitate retention using a polytetrafluoroethylene (PTFE) knotted reactor (KR), solvent extraction-back extraction and hydride/vapor generation. It also addresses a novel, robust approach, whereby the protocol of SI-LOV-bead injection (BI) on-line separation and pre-concentration of ultra-trace levels of metals by a renewable microcolumn is interfaced to ICP-MS, as conducted in the present authors' group. It discusses the future outlook in this field.     

Exact results of a dimerized S=1 Ising chain with single-ion anisotropy

The dimerized spin-1 Ising chain with both longitude and transverse single-ion anisotropies D_z and D_x is solved exactly by means of a mapping to the spin- Ising chain with the alternating transverse fields and the Jordan-Wigner transformation. The analytical expressions of the quasi-particles’ spectra Λ_k, the minimal energy gap Δ₀ for exciting a fermion quasi-particle, the minimal energy gap Δ_h for exciting a hole, and the ground-state energy E_g are obtained. The phase diagram of the ground state is also given. The results show that the system exhibits a series of quantum phase transitions depending on the dimerization strength of the crystal fields, while the quantum critical points are determined exactly.