Trace lead measurement and on-line removal of matrix interference in seawater by isotope dilution coupled with flow injection and ICP-MS

Isotope dilution analysis method coupled with flow injection and inductively coupled plasma mass spectrometry (ID-FI-ICP-MS), enabled trace lead concentration in seawater to be determined and the high salt concentration in the matrix, such as Na⁺, Ca²⁺ and Mg²⁺, to be removed on-line. The operational parameters of the FI system including pH for the chelating reaction, concentration of 8-hydroxyquinoline-5-sulfonic acid (8-HQS), sample loading time and injection speed, washing time and speed, eluting acid concentration and eluting speed, and instrumental parameters for ICP-MS were optimized and selected. Accurate results could be achieved because the isotope ratios required can be precisely measured in the range of the eluting peak by means of ID-FI-ICP-MS. The 3σ detection limit was 0.204 ng ml⁻¹. The trace lead concentration of seawater in south Xiamen, China was 0.988 ± 0.039 ng ml⁻¹. The recoveries of spiked Pb standard in seawater and standard reference water (GBW 08607) were 97.9 and 101.0%, respectively, with a relative standard deviation of 0.98%. This method can be used to determine trace lead concentration in high salt matrix samples, and is especially useful when the eluting peaks do not have a Gaussian-distribution.     

Study of a Monod–Haldene type food chain chemostat with pulsed substrate

In this paper, we introduce and study a model of a Monod–Haldene type food chain chemostat with pulsed substrate. We investigate the subsystem with substrate and prey and study the stability of the periodic solutions, which are the boundary periodic solutions of the system. The stability analysis of the boundary periodic solution yields an invasion threshold. By use of standard techniques of bifurcation theory, we prove that above this threshold there are periodic oscillations in substrate, prey, and predator. Simple cycles may give way to chaos in a cascade of period-doubling bifurcations. Furthermore, by comparing bifurcation diagrams with different bifurcation parameters, we can see that the impulsive system shows two kinds of bifurcations, whose are period-doubling and period-halfing.     

Diffusion-induced Spatio-temporal Oscillations in an Epidemic Model with Two Delays

We investigate a diffusive, stage-structured epidemic model with the maturation delay and freelymoving delay. Choosing delays and diffusive rates as bifurcation parameters, the only possible way to destabilize the endemic equilibrium is through Hopf bifurcation. The normal forms of Hopf bifurcations on the center manifold are calculated, and explicit formulae determining the criticality of bifurcations are derived. There are two different kinds of stable oscillations near the first bifurcation: ...     

Tris(hydroxymethyl)phosphine,P(CH2OH)3 – A convenient and effective new reagent for the fixation of protein samples for SEM imaging

Tris(hydroxymethyl)phosphine [P(CH₂OH)₃, THP] is demonstrated to be an alternative fixative to glutaraldehyde for preparation of proteinaceous specimens for SEM analysis. THP is easily prepared from commercially-available [P(CH₂OH)₄]Cl, and unlike many other alkylphosphines, is reasonably air-stable [>7 days at pH 7–8]. Experiments carried out with chicken breast muscle, cross-sectioned perpendicular to the muscle fibres and imaged using SEM, indicate that THP effectively fixes the muscle structure with minimal discolouration of the sample.     

Determination of arsenic species in Solanum Lyratum Thunb using capillary electrophoresis with inductively coupled plasma mass spectrometry

A simple and highly efficient interface to couple capillary electrophoresis with inductively coupled plasma mass spectrometry by a microflow polyfluoroalkoxy nebulizer and a quadruple ion deflector was developed in this study. By using this interface, six arsenic species, including arsenite, arsenate, monomethylarsonic acid, dimethylarsinic acid, arsenobetaine, and arsenocholine, were baseline‐separated and determined in a single run within 11 min under the optimized separation conditions. The instrumental detection limit was in the range of 0.02–0.06 ng/mL for the six arsenic compounds. Repeatability expressed as the relative standard deviation (n = 5) of both migration time and peak area were better than 2.5 and 4.3% for six arsenic compounds. The proposed method, combined with a closed‐vessel microwave‐assisted extraction procedure, was successfully applied for the determination of arsenic species in the Solanum Lyratum Thunb samples from Anhui province in China with the relative standard deviations (n = 5) ≤4%, method detection limits of 0.2–0.6 ng As/g and a recovery of 98–104%. The experimental results showed that arsenobetaine was the main speciation of arsenic in the Solanum Lyratum Thunb samples from different provinces in China, with a concentration of 0.42–1.30 μg/g.     

Existence of solutions on weak vector equilibrium problems

Weak vector equilibrium problems with bi-variable mappings from product space of two bounded complete locally convex Hausdorff topological vector spaces to another topological vector space are studied. The existence theorems of solutions are proved by the FKKM fixed point theorem. Viscosity principle of vector equilibrium problems is dealt with. The relations between solutions of the vector equilibrium problem and those of its perturbation problem are presented.     

Enumeration of perfect matchings of a type of Cartesian products of graphs

Let G be a graph and let Pm(G) denote the number of perfect matchings of G.We denote the path with m vertices by P_m and the Cartesian product of graphs G and H by G×H. In this paper, as the continuance of our paper [W. Yan, F. Zhang, Enumeration of perfect matchings of graphs with reflective symmetry by Pfaffians, Adv. Appl. Math. 32 (2004) 175-188], we enumerate perfect matchings in a type of Cartesian products of graphs by the Pfaffian method, which was discovered by Kasteleyn. Here are some of our results:1. Let T be a tree and let C_n denote the cycle with n vertices. Then Pm(C₄×T)=∏(2+α²), where the product ranges over all eigenvalues α of T. Moreover, we prove that Pm(C₄×T) is always a square or double a square.2. Let T be a tree. Then Pm(P₄×T)=∏(1+3α²+α⁴), where the product ranges over all non-negative eigenvalues α of T.3. Let T be a tree with a perfect matching. Then Pm(P₃×T)=∏(2+α²), where the product ranges over all positive eigenvalues α of T. Moreover, we prove that Pm(C₄×T)=[Pm(P₃×T)]².     

The Exact Hausdorff Measure Function of the Level Sets of Multi-parameter Symmetric Stable Process

In this paper, we investigate the Hausdorff measure for level sets of N-parameter Rd-valued stable processes, and develop a means of seeking the exact Hausdorff measure function for level sets of N-parameter Rd-valued stable processes. We show that the exact Hausdorff measure function of level sets of N-parameter Rd-valued symmetric stable processes of index α is Ф（r） = r^N-d/α （log log l/r）d/α when Nα 〉 d. In addition, we obtain a sharp lower bound for the Hausdorff measure of level sets of general （N, d, α） strictly stable processes.     

Removable edges in a 5-connected graph and a construction method of 5-connected graphs

An edge e of a k-connected graph G is said to be a removable edge if G?e is still k-connected. A k-connected graph G is said to be a quasi (k+1)-connected if G has no nontrivial k-separator. The existence of removable edges of 3-connected and 4-connected graphs and some properties of quasi k-connected graphs have been investigated [D.A. Holton, B. Jackson, A. Saito, N.C. Wormale, Removable edges in 3-connected graphs, J. Graph Theory 14(4) (1990) 465-473; H. Jiang, J. Su, Minimum degree of minimally quasi (k+1)-connected graphs, J. Math. Study 35 (2002) 187-193; T. Politof, A. Satyanarayana, Minors of quasi 4-connected graphs, Discrete Math. 126 (1994) 245-256; T. Politof, A. Satyanarayana, The structure of quasi 4-connected graphs, Discrete Math. 161 (1996) 217-228; J. Su, The number of removable edges in 3-connected graphs, J. Combin. Theory Ser. B 75(1) (1999) 74-87; J. Yin, Removable edges and constructions of 4-connected graphs, J. Systems Sci. Math. Sci. 19(4) (1999) 434-438]. In this paper, we first investigate the relation between quasi connectivity and removable edges. Based on the relation, the existence of removable edges in k-connected graphs (k?5) is investigated. It is proved that a 5-connected graph has no removable edge if and only if it is isomorphic to K₆. For a k-connected graph G such that end vertices of any edge of G have at most k-3 common adjacent vertices, it is also proved that G has a removable edge. Consequently, a recursive construction method of 5-connected graphs is established, that is, any 5-connected graph can be obtained from K₆ by a number of θ⁺-operations. We conjecture that, if k is even, a k-connected graph G without removable edge is isomorphic to either K_k+1 or the graph H_k/2+1 obtained from K_k+2 by removing k/2+1 disjoint edges, and, if k is odd, G is isomorphic to K_k+1.     

A generalization of Browder’s fixed point theorem with applications

In this paper, the concept of c$c$-compact mapping is introduced. A generalization of Browder’s fixed point theorem and some equivalence forms are given. As applications, the existence of solutions for some variational inequalities and monotone operator equations is discussed.