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The variations of the concentration and characteristics of particulate matter (PM) are influenced by several factors, such as emission sources and meteorological conditions. In this study, fine particles (PM2.5) and ultrafine particles (PM0.1) were simultaneously collected during summer and winter in Hanoi, Vietnam, to clarify the behavior of PM0.1 (which is rarely observed in this region) by characterizing the chemical components of each particle size in order to clarify particle formation and growth in two seasons with different humidity. The results showed that organic carbon (OC) and elemental carbon (EC) were the major compounds in both size ranges of PM, accounting for up to 56% and 80% of the analyzed components in PM2.5 and PM0.1, respectively. Secondary organic carbon (SOC) accounted for 36–41% and 37–47% of the total OC in PM2.5 and PM0.1, respectively, indicating an important contribution of secondary sources to OC. The strong correlations between water-soluble organic carbon (WSOC) and both sulfate (SO42−) and nitrate (NO3−) showed that photochemical reactions contributed considerably to WSOC formation. Furthermore, the correlations between absolute humidity and other chemical components suggest that the PM2.5 collected in Hanoi was formed by secondary processes in the aqueous phase on the aerosol surface. In contrast, no correlation was found between the relative humidity and other chemical components. These observations indicate that particle growth is dependent on the number of water molecules above a certain level under drizzle-like weather conditions particular to the study region, whereas occasional heavy rain during the sampling period might have hindered those processes.

In this paper, in order to solve a variational inequality problem over the fixed point set of a nonexpansive mapping on uniformly smooth or reflexive and strictly convex Banach spaces with a uniformly Gâteaux differentiable norm, we investigate an explicit iteration method, based on the steepest-descent and Krasnosel’skii–Mann algorithms. We also show that some modifications of the last and Halpern-type algorithms are special cases of our result.

The purpose of this paper is to present a regularization method for finding a common fixed point of a nonexpansive semigroup in a real Hilbert space. A combination of the considered regularization scheme with the proximal point algorithm and another one of the regularization method with an iterative scheme is studied in this research. We also discuss an application of the proposed methods for an initial value problem in Hilbert spaces.

In this paper, we propose a new simple explicit iterative algorithm to find a solution for variational inequalities over the set of common fixed points of an infinite family of nonexpansive mappings on real reflexive and strictly convex Banach spaces with a uniformly Gâteaux differentiable norm. Two numerical examples also are given for illustration.

Polychlorinated benzenes (PCBzs) including penta- and hexachlorobenzene can be unintentionally formed from thermal processes in different industrial activities, and very little information is available on the contamination and emission characteristics of these new persistent organic pollutants from industries in Vietnam. In this study, contamination of PCBzs (including penta- and hexachlorobenzene, named PeCBz and HCB, respectively) and PCBs (including CB-28, 52, 101, 153, 138, 180) in fly ash, bottom ash and soil from combustion processes of waste incineration, metallurgy (steel making and zinc production) and cement production from several provinces in the Northern Vietnam, including Hai Duong, Hanoi, Bac Ninh, Hai Phong and Thai Nguyen, was preliminary investigated. The PCBzs concentrations in fly ash, bottom ash and soil ranged from 2.7 to 100 ng g(-1), from 2.7 to 159 ng g(-1) and from 0.28 to 33.9 ng g(-1), respectively. Relatively high residues of PeCBz in fly ash and bottom ash from municipal waste incinerators in some provinces from the Northern Vietnam were encountered. Total PCBs concentrations ranged from 18.0 to 8260 ng g(-1), from 1.0 to 10600 ng g(-1) and from 14.5 to 130 ng g(-1) for the fly ash, bottom ash and soil, respectively. Daily intakes of PeCBz, HCB and PCBs through soil ingestion and dermal exposure estimated for children ranged 0.33-9.93 (mean 3.14), 0.39-21.1 (mean 4.9) and 6.09-1530 ng/kg bw/day (mean 346), respectively; and these intakes were about 4.7-5.4 times higher than those estimated for adult. The intakes of PeCBz and HCB were relatively low, while those for PCBs exceeded WHO TDI for some samples.

We consider a regularization method based on the Browder–Tikhonov and iterative regularization method that can be used to find a solution of a class of accretive variational inequalities in a q-uniformly smooth Banach space, and the solutions are sought in the set of common fixed points of a countable family of nonexpansive mappings. We also introduce an iteration method, which is implicit and converges strongly, based on the steepest descent method with a strongly accretive and strictly pseudocontractive mapping. Our results generalize and extend some well-known regularization methods in the literature.

The purpose of this paper is to present a new iteration method based on the hybrid method in mathematical programming, extragradient method, and Mann’s method for finding a common element of the solution set of equilibrium problems, the solution set of variational inequality problems for a monotone, Lipschitz continuous mapping and the set of fixed points for a nonexpansive semigroup in Hilbert spaces. We obtain a strong convergence theorem for the sequences generated by this process. The results in this paper generalize and extend some well-known strong convergence theorems in the literature.

In this paper, we introduce a new iteration method based on the hybrid method in mathematical programming, the descent-like method and the Halpern’s iteration method for finding a common element of the solution set for a variational inequality and the set of common fixed points of a countably infinite family of nonexpansive mappings in Hilbert spaces. The result in this paper modifies and improves some well-known results in the literature for a more general problem.

In this paper, we introduce some new iteration methods combining the hybrid method in mathematical programming with Mann’s iterative method and the Halpern method for finding a fixed point of an asymptotically nonexpansive mapping and a common fixed point of an asymptotically nonexpansive semigroup in a Hilbert space. The main results in this paper modify and improve some well-known results in the literature.

The aim of this paper is to develop a class of constant step size parallel-iterated pseudo two-step Runge–Kutta methods (PIPTRK methods) for nonstiff first-order ODE problems into variable step size methods. Embedded formulas are provided for giving a cheap error estimate used in the step size control. Methods with variable parameters approach were applied for overcoming the difficulty in using two-step methods with variable step size. By applications to a few widely used test problems, we compare the efficiency of the resulting PIPTRK methods with step size control (PIPTRKSC methods) with the codes PIRK, DOPRI5, DOP853 and ODEX. This numerical comparison shows that these new PIPTRKSC methods are by far superior to the PIRK, DOPRI5, DOP853 and ODEX codes.