Singularly Perturbed Markov Chains with Two Small Parameters: A Matched Asymptotic Expansion

AbstractThis work is concerned with asymptotic properties of solutions to forward equations for singularly perturbed Markov chains with two small parameters. It is motivated by the model of a cost-minimizing firm involving production planning and capacity expansion and a two-level hierarchical decomposition. Our effort focuses on obtaining asymptotic expansions of the solutions to the forward equation. Different from previous work on singularly perturbed Markov chains, the inner expansion terms are constructed by solving certain partial differential equations. The methods of undetermined coefficients are used. The error bound is obtained

Simultaneous Determination of Palladium and Platinum by On-line Enrichment and HPLC with 4-(2-Hydroxynaphthalene- 1-ylmethylene)-thiazolidine-2,5-Dithione as Pre-column Derivatization Reagent

In this paper, a new reagent, 4-(2-hydroxy-naphthalene-1-ylmethylene)-thiazolidine-2,5-dithione (HNMTD) was synthesized. A new method for the simultaneous determination of palladium and platinum ions as metal-HNMTD chelates was developed using high performance liquid chromatography equipped with an on-line enrichment technique. Prior to chromatography the palladium and platinum ions were derivatized with HNMTD to coloured chelate complexes. The Pd-HNMTD and Pt-HNMTD complexes were then enriched on an enrichment column(ZORBAXReversed Phase StableBoundC18, 4.6×10mm,1.8 μm) using a buffer solution of 0.05 mol L–1 sodium acetate-acetic acid buffer (pH 3.8) as mobile phase.After the enrichment was completed, the retained chelates were back-flushed to the analytical column. The separation of chelates on the analytical column (ZORBAX Reversed Phase Stable Bound C18, 4.6 × 50 mm, 1.8 μm) was satisfactory when 72% methanol (containing 0.05 mol L–1 of pH 3.8 sodium acetate-acetic acid buffer salt and 0.1% of TritonX-100) was used as mobile phase. The Pt-HNMTD and Pd-HNMTD chelates were separated completely within 2 min. The detection limits (S/N = 3) for palladium and platinum were 1.2 ng L–1 and 1.4 ng L–1, respectively. The method was applied with good results to the determination of palladium and platinum in water and urine samples.Keywords: Palladium, platinum, 4-(2-hydroxy-naphthalene-1-ylmethylene)-thiazolidine-2,5-dithione, high performance liquid chromatography, on-line enrichment

Wilson ratio of Fermi gases in one dimension

We calculate the Wilson ratio of the one-dimensional Fermi gas with spin imbalance. The Wilson ratio of attractively interacting fermions is solely determined by the density stiffness and sound velocity of pairs and of excess fermions for the two-component Tomonaga-Luttinger liquid (TLL) phase. The ratio exhibits anomalous enhancement at the two critical points due to the sudden change in the density of states. Despite a breakdown of the quasiparticle description in one dimension, two important features of the Fermi liquid are retained, namely the specific heat is linearly proportional to temperature whereas the susceptibility is independent of temperature. In contrast to the phenomenological TLL parameter, the Wilson ratio provides a powerful parameter for testing universal quantum liquids of interacting fermions in one, two and three dimensions.Comment: 5+2 pages, 4+1 figures, Eq. (4) is proved, figures were refine

Multi-View Label Prediction for Unsupervised Learning Person Re-Identification

Person re-identification (ReID) aims to match pedestrian images across disjoint cameras. Existing supervised ReID methods utilize deep networks and train them with identity-labeled images, which suffer from limited annotations. Recently, clustering-based unsupervised ReID attracts more and more attention. It first clusters unlabeled images and assigns cluster index to the pseudo-identity-labels, then trains a ReID model with the pseudo-identity-labels. However, considering the slight inter-class variations and significant intra-class variations, pseudo-identity-labels learned from clustering algorithms are usually noisy and coarse. To alleviate the problems above, besides clustering pseudo-identity-labels, we propose to learn pseudo-patch-labels, which brings two advantages: (1) Patch naturally alleviates the effect of backgrounds, occlusions, and carryings since they usually occupy small parts in images, thus overcome noisy labels. (2) It is plausible that patches from different pedestrians belong to the same pseudo-identity-label. For example, pedestrians have a high probability of wearing either the same shoes or pants but a low possibility of wearing both. The experiments demonstrate our proposed method achieves the best performance by a large margin on both image- and video-based datasets

Determination of Heavy Metal Ions in Tobacco and Tobacco Additives

This paper describes a new method for the simultaneous determination of heavy metal ions in tobacco and tobacco additives by microcolumn high-performance liquid chromatography. The samples were digested by microwave digestion. The lead, cadmium, mercury, nickel, cobalt and tin ions in the digested samples were pre-column derivatized with tetra-(o-aminophenyl)- porphyrin (To-APP) to form coloured chelates. The Hg-To-APP, Cd-To-APP, Pb-To-APP, Ni-To-APP, Co-To-APP and Sn-To-APP chelates were enriched by solid phase extraction with a C18 cartridge resulting in an enrichment factor of 50. The chelates were separated on aWaters Xterra™ RP18 microcolumn (50mm×1.0 mm, 2.5 μm) with a mixture of methanol-tetrahydrofuran (95:5, v/v, containing 0.05 mol L–1 pyrrolidine-acetic acid buffer salt, pH=10.0) as mobile phase at a flow rate of 0.2 mL min–1 and identified with a photodiode array detector at 350–600 nm. The metal chelates were fully separated in 2.0 min. The detection limits for lead, cadmium, mercury, nickel, cobalt and tin in the original digested samples were 4 ng L–1, 3 ngL–1, 6 ngL–1, 5 ngL–1, 5 ngL–1 and 4 ng L–1, respectively. The relative standard deviation for five replicate samples was 2.65~3.24%. The standard recoveries were 95.6~108%. The method was applied with good results to the determination of lead, cadmium, mercury, nickel, cobalt and tin in tobacco and tobacco additives.KEYWORDS: Microcolumn high-performance liquid chromatography, tetra-(o-aminophenyl)-porphyrin, heavy metal ions

Renewed Search for Evidence of 26Al as the Heat Source for Igneous Differentiation in Achondrites.

第2回極域科学シンポジウム/第34回南極隕石シンポジウム 11月18日（金） 国立国語研究所 2階講

Study on the Solid Phase Extraction and Spectrophotometric Determination of Mercury in Water and Biological Samples with 5-(p-Aminobenzylidene)-thiorhodanine

This paper presents the synthesis and application of  5-(p-aminobenzylidene)-thiorhodanine (ABTR) as a new chromogenic reagent for the determination of mercury. Based on the rapid reaction of mercury(II) with ABTR and the solid phase extraction of the coloured chelate with a C18 disk, a highly sensitive, selective and rapid method for the determination of mercury has been developed. In the presence of pH 3.5 sodium acetate-acetic acid buffer solution and emulsifier-OP medium, ABTR reacted with mercury(II) to form a red chelate in a molar ratio 1:2 (mercury to ABTR). This chelate was enriched by solid phase extraction with a C18 disk and eluted from the disk with dimethyl formamide (DMF). An enrichment factor of 50 was achieved. The molar absorptivity of the chelate in DMF was found to be 1.21 × 105 L mol–1 cm–1 at 555 nm. Beer’s law was obeyed in the range of 0.01~ 3 μgmL–10/. The relative standard deviation for eleven replicates with a concentration of 0.01 μgmL–1 was 1.98%. This method was applied with good results to the determination of mercury in water and biological samples.Keywords: Mercury, solid phase extraction, spectrophotometry,  5-(p-aminobenzylidene)-thiorhodanine