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In this paper, we consider a class of functionals subject to a duality restriction. The functional is of the form J(Ω,Ω*)=∫Ωf+∫Ω*g $\mathcal{J}\left({\Omega},{{\Omega}}^{{\ast}}\right)={\int }_{{\Omega}}f+{\int }_{{{\Omega}}^{{\ast}}}g$ , where f, g are given nonnegative functions in a manifold. The duality is a relation α(x, y) ≤ 0 ∀ x ∈ Ω, y ∈ Ω*, for a suitable function α. This model covers several geometric and physical applications. In this paper we review two topological methods introduced in the study of the functional, and discuss possible extensions of the methods to related problems.

Yungui Plateau is rich in fungal diversity. Hyphomycetes, growing on submerged wood, can promote the degradation of organisms and the reuse of rotten wood energy. During an investigation of hyphomycetes in this region, 19 species of dematiaceous hyphomycetes were collected in Yungui Plateau.Both morphological identification and multi-gene phylogenetic analyses of ITS, tef1 and LSU sequences supported Coryneum sevenseptatis as a new species. Phaeoisaria guizhouensis and Pleurothecium yunanensis were introduced, based on morphology. Morphological descriptions and illustrations of the new species were detailed. Known species are listed with notes.

In this article, we study the Musielak-Orlicz-Gauss image problem based on the Gauss curvature flow in Li et al. We deal with some cases in which there is no uniform estimate for the Gauss curvature flow. By the use of the topological method in Guang et al., a special initial condition is chosen such that the Gauss curvature flow converges to a solution of the Musielak-Orlicz-Gauss image problem.

The genus Xylaria comprises a diverse group of fungi with a global distribution and significant ecological importance, known for being a source of bioactive secondary metabolites with antibacterial, antioxidative, anticarcinogenic, and additional properties. In this study, we present a comprehensive taxonomic revision of the species of Xylaria found in some parts of southern China, characterized by an extensive multilocus phylogeny analysis based on internal transcribed spacer (ITS), TUB2 (β‐tubulin), and DNA‐directed RNA polymerase II subunit 2 (rpb2) gene regions. Morphological examination and detailed comparative analyses of the collected specimens were conducted to determine the distinctiveness of each species. The multilocus phylogeny approach allowed us to infer evolutionary relationships and assess species boundaries accurately, leading to the identification of 40 novel Xylaria species hitherto unknown to science. The newly described species are: X. baoshanensis, X. bawanglingensis, X. botryoidalis, X. dadugangensis, X. doupengshanensis, X. fanglanii, X. glaucae, X. guizhouensis, X. japonica, X. jinghongensis, X. jinshanensis, X. kuankuoshuiensis, X. liboensis, X. negundinis, X. orbiculati, X. ovata, X. pseudoanisopleura, X. pseudocubensis, X. pseudobambusicola, X. pseudoglobosa, X. pseudohemisphaerica, X. pseudohypoxylon, X. puerensis, X. qianensis, X. qiongzhouensis, X. rhombostroma, X. serratifoliae, X. shishangensis, X. shuqunii, X. shuangjiangensis, X. sinensis, X. tongrenensis, X. umbellata, X. xishuiensis, X. yaorenshanensis, X. yinggelingensis, X. yumingii, X. yunnanensis, X. zangmui, and X. zonghuangii. The study's findings shed light on the distinctiveness of the newly described species, supported by both morphological distinctions and phylogenetic relationships with their close relatives. This taxonomic revision significantly contributes to our understanding the diversity of Xylaria in China and enriches the knowledge of fungal biodiversity worldwide. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of solutions to the centroaffine Minkowski problem, namely the existence of closed convex hypersurfaces in the Euclidean space \mathbb {R}^{n+1} with prescribed centroaffine curvature. This problem can be described as a variational problem with a functional resembling Kantorovich's dual functional in optimal transportation. By using the Gauss curvature flow, we obtain new conditions for the existence of solutions to the problem. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of functionals subject to a duality restriction. The functional is of the form J (Ω , Ω * ) = ∫ Ω f + ∫ Ω * g , where f, g are given nonnegative functions in a manifold. The duality is a relation α(x, y) ≤ 0 ∀ x ∈ Ω, y ∈ Ω*, for a suitable function α. This model covers several geometric and physical applications. In this paper we review two topological methods introduced in the study of the functional, and discuss possible extensions of the methods to related problems. [ABSTRACT FROM AUTHOR]

Sophora flavescens is a widely used traditional Chinese herbal medicine. In this work, a new pterocarpan glycoside, kurarinol C (1) together with six known compounds, sophoracarpan A (2), trifohrhizin-6'-monoacetate (3), trifohrhizin (4), maackiain (5), (6S,6aS,11aR）-6α-methoxy-pterocarpin (6), L-maackiain (7) were isolated from the roots of S. flavescens. Among them, compounds 2 and 6 were discovered from S. flavescens for the first time. Their chemical structures were elucidated on the basis of extensive NMR and MS analyses. Furthermore, the antioxidant activities of these compounds were evaluated by the ABTS and DPPH free radical scavenging assay. Three compounds (5, 6, 7) exhibited stronger antioxidant capacity against the ABTS enzyme at 20 µg/mL (scavenging rates > 55%). [ABSTRACT FROM AUTHOR]