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Dirac-harmonic maps with the trivial index

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Science China mathematics 2024年

作者： Jürgen Jost Linlin Sun Jingyong Zhu max planck institute for mathematics in the sciences School of mathematics and Statistics Guangxi Normal University School of mathematics Sichuan University

For a homotopy class [u] of maps between a closed Riemannian manifold M and a general manifold N, we want to find a Dirac-harmonic map with the map component in the given homotopy class. Most known results require the index to be nontrivial. When the index is trivial, the few known results are all constructive and produce uncoupled solutions. In this paper, we define a new quantity. As a byproduct of proving the homotopy invariance of this new quantity, we find a new simple proof for the fact that all the Dirac-harmonic spheres in surfaces are uncoupled. More importantly, by using the homotopy invariance of this new quantity,we prove the existence of Dirac-harmonic maps from manifolds in the trivial index case. In particular, when the domain is a closed Riemann surface, we prove the short-time existence of the α-Dirac-harmonic map flow in the trivial index case. Together with the density of the minimal kernel, we get an existence result for Dirac-harmonic maps from closed Riemann surfaces to K¨ahler manifolds, which extends the previous result of the first and third authors. This establishes a general existence theory for Dirac-harmonic maps in the context of the trivial index.

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From the unknown to spotlight:newly identified hormone adjusts hepatic cholesterol synthesis to dietary uptake

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Signal Transduction and Targeted Therapy 2024年第7期9卷 2845-2847页

作者： Yakum Bertrand Nkeh Resul Gökberk Elgin Gesine Saher Project Group Biology of Lipids Department of NeurogeneticsMax Planck Institute for Multidisciplinary SciencesGöttingenGermany

In a study published in Cell,Hu and colleagues discovered that the signaling activity of the intestinal hormone Cholesin leads to the attenuation of hepatic cholesterol synthesis in response to intestinal absorption thereby maintaining homeostatic levels of circulating cholesterol.1 These findings have major translational implications as they provide a potential new target for the management of hypercholesterolemia and associated disorders.

关键词： cholesterol hepatic synthesis

Steroidal scaffold decorations in Solanum alkaloid biosynthesis

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Molecular Plant 2024年第8期17卷 1236-1254页

作者： Rosalind Lucier Mohamed O.Kamileen Yoko Nakamura Sofiia Serediuk Ranjit Barbole Jens Wurlitzer Maritta Kunert Sarah Heinicke Sarah E.O'Connor Prashant D.Sonawane Department of Natural Product Biosynthesis Max Planck Institute for Chemical Ecology07745 JenaGermany Research Group Biosynthesis and NMR Max Planck Institute for Chemical Ecology07745 JenaGermany Biochemical sciences Division CSIR-National Chemical LaboratoryPune 411008MaharashtraIndia

Steroidal glycoalkaloids(SGAs)are specialized metabolites produced by hundreds of Solanum species,including important vegetable crops such as tomato,potato,and *** it has been known that SGAs play important roles in defense in plants and“anti-nutritional"effects(e.g.,toxicity and bitterness)to humans,many of these molecules have documented anti-cancer,anti-microbial,antiinflammatory,anti-viral,and anti-pyretic *** these,α-solasonine andα-solamargine isolated from black nightshade(Solanum nigrum)are reported to have potent anti-tumor,anti-proliferative,and anti-inflammatory ***,α-solasonine andα-solamargine,along with the core steroidal aglycone solasodine,are the most widespread SGAs produced among the Solanum ***,it is still unknown how plants synthesize these bioactive steroidal *** comparative metabolomictranscriptome-guided approach,biosynthetic logic,combinatorial expression in Nicotiana benthamiana,and functional recombinant enzyme assays,here we report the discovery of 12 enzymes from *** that converts the starting cholesterol precursorto solasodine aglycone,and the downstreamα-solasonine,α-solamargine,and malonyl-solamargine SGA *** further identified six enzymes from cultivated eggplant that catalyze the production ofα-solasonine,α-solamargine,and malonyl-solamargine SGAs from solasodine aglycone via glycosylation and atypical malonylation *** work provides the gene tool box and platform for engineering the production of high-value,steroidal bioactive molecules inheterologoushosts usingsyntheticbiology.

关键词： steroidal glycoalkaloids Solanum biosynthetic pathway α-solamargine malonyl-solamargine specialized metabolites

Pseudoeffective thresholds and cohomology of twisted symmetric tensor fields on irreducible Hermitian symmetric spaces

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Science China mathematics 2024年第11期67卷 2433-2452页

作者： Feng Shao institute of mathematics Academy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical sciences University of Chinese Academy of Sciences

Let X be an irreducible Hermitian symmetric space of compact type(IHSS for short).In this paper,we give the irreducible decomposition of *** a by-product,we give a cohomological characterization of the rank of ***,we introduce pseudoeffective thresholds to measure the bigness of tangent bundles of smooth complex projective varieties precisely and calculate them for irreducible Hermitian symmetric spaces of compact type.

关键词： tangent bundle pseudoeffective threshold irreducible Hermitian symmetric space of compact type (IHSS) multiplicity free action

Chemically robust superhydrophobic surfaces with a self‐replenishing nanoscale liquid coating

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Droplet 2024年第1期3卷 136-148页

作者： Xiaoteng Zhou Pranav Sudersan Diego Diaz Benjamin Leibauer Chirag Hinduja Fahimeh Darvish Pravash Bista Lukas Hauer Manfred Wagner Werner Steffen Jie Liu Michael Kappl Hans‐Jürgen Butt max planck institute for Polymer Research MainzGermany Key Laboratory of Green Printing Institute of ChemistryChinese Academy of SciencesBeijingChina School of Chemical sciences University of Chinese Academy of SciencesBeijingChina

Due to poor chemical robustness,superhydrophobic surfaces become susceptible to failure,especially in a highly oxidative *** ensure the longterm efficacy of these surfaces,a more stable and environmentally friendly coating is required to replace the conventional salinization ***,soottemplated surfaces with re‐entrant nanostructures are precoated with polydimethylsiloxane(PDMS)*** additional nanometer‐thick lubricant layer of PDMS was then applied to increase chemical *** surface is superhydrophobic with a nanoscale liquid *** the lubricant layer is thin,ridge formation is suppressed,which leads to low drop sliding friction and fast drop *** introducing a bottom“reservoir”of a free lubricant as an oil source for self‐replenishing to the upper layer,the superhydrophobic surface becomes more stable and heals spontaneously in response to alkali erosion and O2 plasma *** design also leads to a higher icing delay time and faster removal of impacting cooled water drops than for uncoated surfaces,preventing icing at low temperatures.

关键词： coating friction liquid

2-local unstable homotopy groups of indecomposable A3～2-complexes

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Science China mathematics 2024年第3期67卷 607-626页

作者： Zhongjian Zhu Jianzhong Pan College of mathematics and Physics Wenzhou University Hua Loo-Keng Key Laboratory of mathematics Institute of MathematicsAcademy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical sciences University of Chinese Academy of Sciences

In this paper,we calculate the 2-local unstable homotopy groups of indecomposable A3～*** main technique used is analysing the homotopy property of J（A,X）,defined by Gray（1973） for a CW-pair（X,A）,which is homoto... 详细信息

关键词： homotopy groups A 2 n -complexes fibration sequence relative James construction 55P15

Density peak clustering using tensor network

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Science China(Information sciences) 2024年第3期67卷 321-322页

作者： Xiao SHI Yun SHANG institute of mathematics Academy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical sciences University of Chinese Academy of Sciences National Center for mathematics and Interdisciplinary sciences Key Laboratory of ManagementDecision and Information SystemsAcademy of Mathematics and Systems ScienceChinese Academy of Sciences

Tensor networks have been a powerful tool in simulating many-body physics and have recently gained recognition in the machine learning community due to their remarkable representation capabilities. However, using tens... 详细信息

关键词： Tensors

Differential roles of C-3 and C-6 phosphate monoesters in affecting potato starch properties

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Grain & Oil Science and Technology 2024年第2期7卷 79-86页

作者： Li Ding Andreas Blennow Yuyue Zhong Department of Plant and Environmental sciences Faculty of ScienceUniversity of CopenhagenDenmark Department of Sustainable and Bio-inspired Materials Max-Planck Institute of Colloids and InterfacesPotsdamGermany

The effects of starch phosphate monoester content(SPC),namely C-3(C3P)and C-6 phosphate monoesters(C6P),on the starch properties were investigated using four potato starches with varied SPC/C3P/C6P and two nonphosphorylated maize starches with a similar range of amylose content(AC)as *** starch property results showed that a higher SPC is associated with lower turbidity,storage and loss modulus after storage,and water solubility,but higher swelling power(SP)and pasting *** findings suggested that SPC inhibited molecular rearrangement during storage and starch leaching during heating,and enhanced swelling and viscosities due to increased hydration and water uptake caused by the repulsion effect of phosphate groups and a less ordered crystalline *** SPC also resulted in lower resistant starch(RS)content in a native granular state but higher RS after *** correlations further indicated that SPC/C3P/C6P were positively correlated with peak(r^(2)=0.925,0.873 and 0.930,respectively),trough(r^(2)=0.994,0.968 and 0.988,respectively),and final viscosities(r^(2)=0.981,0.968 and 0.971,respectively).Notably,SPC,mainly C3P,exhibited a significantly positive correlation with SP(r^(2)=0.859)and setback viscosity(r^(2)=0.867),whereas SPC,mainly C6P,showed a weak positive correlation with RS after retrogradation(r^(2)=0.746).However,SPC had no significant correlations with water solubility,turbidity and rheology properties,which were more correlated with *** findings are helpful for the food industry to select potato starches with desired properties based on their contents of SPC,C3P,or C6P.

关键词： Starch phosphate monoesters C-3 phosphate monoesters C-6 phosphate monoesters Physicochemical properties In vitro digestibility

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A Deep Learning Method for Computing Eigenvalues of the Fractional Schrödinger Operator

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Journal of Systems Science & Complexity 2024年第2期37卷 391-412页

作者： GUO Yixiao MING Pingbing LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

The authors present a novel deep learning method for computing eigenvalues of the fractional Schrödinger *** proposed approach combines a newly developed loss function with an innovative neural network architecture that incorporates prior knowledge of the *** improvements enable the proposed method to handle both high-dimensional problems and problems posed on irregular bounded *** authors successfully compute up to the first 30 eigenvalues for various fractional Schrödinger *** an application,the authors share a conjecture to the fractional order isospectral problem that has not yet been studied.

关键词： Eigenvalue problem deep learning fractional Schrödinger operator isospectral problem

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