Search

The forward-backward operator splitting algorithm is one of the most important methods for solving the optimization problem of the sum of two convex functions, where one is differentiable with a Lipschitz continuous gradient and the other is possibly nonsmooth but proximable. It is convenient to solve some optimization problems in the form of dual or primal-dual problems. Both methods are mature in theory. In this paper, we construct several efficient first-order splitting algorithms for solving a multi-block composite convex optimization problem. The objective function includes a smooth function with a Lipschitz continuous gradient, a proximable convex function that may be nonsmooth, and a finite sum of a composition of a proximable function and a bounded linear operator. To solve such an optimization problem, we transform it into the sum of three convex functions by defining an appropriate inner product space. On the basis of the dual forward-backward splitting algorithm and the primal-dual forward-backward splitting algorithm, we develop several iterative algorithms that involve only computing the gradient of the differentiable function and proximity operators of related convex functions. These iterative algorithms are matrix-inversion-free and completely splitting algorithms. Finally, we employ the proposed iterative algorithms to solve a regularized general prior image constrained compressed sensing (PICCS) model that is derived from computed tomography (CT) image reconstruction under sparse sampling of projection measurements. Numerical results show that the proposed iterative algorithms outperform other algorithms., 27 pages, 4 figures, J. Comp. Math. 2018

A migratory fluoro-alkenylation of unactivated alkyl bromides is reported; the reaction is enabled by fluorine effects and involves an alkyl nickel chain-walking mechanism., We describe a nickel-catalyzed highly regio- and stereoselective migratory fluoro-alkenylation of unactivated alkyl bromides. A unique catalytic cycle merging alkyl nickel chain-walking and defluorinative coupling enables the introduction of a broad array of fluoroalkenyl moieties into carbon chains. Control experiments with other halogenated alkenes demonstrated the essential role of fluorine atoms in this reaction. Notably, the reaction proceeds under mild conditions and allows for the synthesis of a variety of valuable monofluoroalkenes.

Background Douyu Village, inhabited by the Lhoba people, is situated within the Eastern Himalayas, in southeastern Tibet, China. The village is located among high mountains and valleys, which feature complex terrain with cold and dry climates and distinctive vegetation types and species. The Lhoba people in this village are isolated from other groups in China. The Lhoba people have lived in this village since the 15th century and mainly depended on gathering, hunting, and swidden agriculture before the 1960s. Because they have a long history and live under extreme climatic, geographical, and ecological conditions, the Lhoba people in Douyu Village may have unique traditional knowledge about wild plants. Thus, this research aims to record the traditional botanical knowledge of the Lhoba people in Douyu. Methods An ethnobotanical study was conducted on the Lhoba people in Douyu Village in Longzi County, Tibet, China. Semi-structured interviews and group discussions with informed consent were used in the study. We interviewed 41 informants (14 key informants) between 18 and 75 years of age. All information was collected, organized, and compiled into “use reports” for quantitative analysis. The informant consensus factor (ICF) was used to determine the homogeneity of the informants’ knowledge of medicinal plants, while the cultural importance index (CI) was used to estimate the cultural importance of shared species. Results A total of 91 wild species (90 vascular plants and 1 fungus) belonging to 71 genera and 39 families utilized by the Lhoba people in Douyu were documented. Of these species, Pimpinella xizangense and Wikstroemia lungtzeensis are endemic to Longzi County, while Sinopodophyllum hexandrum and Paeonia ludlowii are endangered species in China. All habitats, from the field vegetation at the valley bottoms to the alpine shrubland and meadows, were used for plant collection, and the numbers of species of plants collected from the various vegetation types (except for fields) decreased with increasing altitude. Our study found that 55 species are edible plants and fungi, 29 species are medicinal plants, and 38 species are used for other purposes. Medicinal plants are used for 11 categories of diseases, among which diseases of blood-forming organs (ICF = 0.96) and gastrointestinal diseases (ICF = 0.95) exhibited the highest ICF values. Based on the CI values, the most important plants in this study area are Berberis xanthophloea, B. kongboensis, Sinopodophyllum hexandrum, Vicatia thibetica, and Hippophae rhamnoides subsp. gyantsensis. Moreover, a comparison of the wild plants used by Lhoba ethnic groups in three counties in China showed significant differences among these regions. Conclusions Our study demonstrates that the wild plants utilized by the Lhoba people in Douyu Village are highly diverse, at 90 plant and one fungal species, which reflects not only the number of species but also their diversified functions. The extreme climatic, geographical, and ecological conditions of Douyu within the high mountains and valleys of the Eastern Himalayas potentially affect the Lhoba people’s culture, including plant utilization practices, and contribute to the rich diversity of the wild plants used by the local people.