We propose general variational inclusion problems which are slightly different from corresponding problems considered in several recent papers in the literature and show that they are advantageous. Sufficient conditions for the solution existence are established. As applications we derive consequences for several special cases of variational inclusion problems, quasioptimization problems, equilibrium problems and implicit variational inequalities and show that they improve the results of some recent existing papers.

Vietnam’s forestry sector is facing rising demands for wood to support national and rural economies, and rural livelihoods. A feasible option to meet this demand is to improve productivity in the current plantation estates, especially in those owned by thousands of small growers. Growers have invested in short-rotation acacia plantations primarily for the woodchip market, but are being urged through government policies and pressured by certification bodies and some NGOs to shift to longer rotations, preferentially, for growing saw logs. In this context, we examined the productivity of an Acacia auriculiformis plantation in South Vietnam, over four successive rotations, spanning 25 years. We show that it is possible to increase and sustain wood production in the long term, by applying simple but integrated management practices, recognizing that the conservation of site resources is critical for sustainability. Practices which depleted site organic matter and nutrients lead to a hidden, but high, cumulative loss of production. Given the site and soil damaging practices prevalent in the country, it is likely that production foregone in those sites may be equivalent to the yield from one in every four or five rotations harvested. With sound management including the conservation of site resources, planting the best germplasm, appropriate stocking and judicious use of herbicide, total wood production and the proportion of saw logs (50–70% of the commercial wood at about 7 years of age) can be increased substantially. At the same time, these practices also can promote understory development and diversity in the stand. Such holistic benefits are possible without extending the rotation length and/or thinning, which are likely to raise the levels of risks for small growers, who are not covered by any insurance. Investments and support for small growers to enable higher productivity and value per unit area in their holdings, through sustainable management, would offer practical and low-risk options for the benefits of growers, processors and ecosystems.

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Two new phenolic compounds, caesalpiniaphenols G-H (1 and 2), were isolated from Vietnamese Caesalpinia sappan heartwood. The chemical structures were established mainly by extensive spectroscopic studies and chemical evidence. Compounds 1 and 2 showed potent inhibitory activity against HL-60 cancer cell lines with respective IC50 values of 16.7 and 22.5 µg/mL. Treating HL-60 cells with various concentrations of 1 resulted in growth inhibition and the induction of apoptosis.

Quasivariational inclusion problems, Quasiequilibrium problems, Implicit variational inequalities, The solution existence, Fixed points, Nash equilibria, Traffic networks, 49J40, 91B50, 90B20, 90C29,

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