概率度量空间中φ-压缩映象的不动点定理

摘要本文给出概率度量空间中Ф—压缩映象的一个新的不动点定理,它改进和推广了文献[1—5]中的某些主要结果。     

Biomimetic nanochannels for the discrimination of sialylated glycans via a tug-of-war between glycan binding and polymer shrinkage

Sialylated glycans that are attached to cell surface mediate diverse cellular processes such as immune responses, pathogen binding, and cancer progression. Precise determination of sialylated glycans, particularly their linkage isomers that can trigger distinct biological events and are indicative of different cancer types, remains a challenge, due to their complicated composition and limited structural differences. Here, we present a biomimetic nanochannels system integrated with the responsive polymer polyethyleneimine-g-glucopyranoside (Glc-PEI) to solve this problem. By using a dramatic “OFF–ON” change in ion flux, the nanochannels system achieves specific recognition for N-acetylneuraminic acid (Neu5Ac, the predominant form of sialic acid) from various monosaccharides and sialic acid species. Importantly, different “OFF–ON” ratios of the conical nanochannels system allows the precise and sensitive discrimination of sialylated glycan linkage isomers, α2–3 and α2–6 linkage (the corresponding ion conductance increase ratios are 96.2% and 264%, respectively). Analyses revealed an unusual tug-of-war mechanism between polymer-glycan binding and polymer shrinkage. The low binding affinity of Glc-PEI for the α2–6-linked glycan caused considerable shrinkage of Glc-PEI layer, but the high affinity for the α2–3-linked glycan resulted in only a slight shrinkage. This competition mechanism provides a simple and versatile materials design principle for recognition or sensing systems that involve negatively charged target biomolecules. Furthermore, this work broadens the application of nanochannel systems in bioanalysis and biosensing, and opens a new route to glycan analysis that could help to uncover the mysterious and wonderful glycoworld.

A glycan-responsive polymer-modified nanochannels system enables the precise discrimination of sialylated glycan linkage isomers via the different “OFF–ON” changes resulting from a “tug-of-war” between polymer-glycan binding and polymer shrinkage.     

Color-kinematics duality for Sudakov form factor in non-supersymmetric pure Yang–Mills theory

We study the duality between color and kinematics for the Sudakov form factors of $\mathrm{tr}({F}^{2})$ in non-supersymmetric pure Yang-Mills theory. We construct the integrands that manifest the color-kinematics duality up to two loops. The resulting numerators are given in terms of Lorentz products of momenta and polarization vectors, which have the same powers of loop momenta as that from the Feynman rules. The integrands are checked by d-dimensional unitarity cuts and are valid in any dimension. We find that massless-bubble and tadpole topologies are needed at two loops to realize the color-kinematics duality. Interestingly, the two-loop solution contains a large number of free parameters suggesting the duality may hold at higher loop orders.     

On probabilistic norm of a linear operators and space of operators

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ［１］,ＸｉａｏｉｎｔｒｏｄｕｃｅｄｔｈｅｎｏｔｉｏｎｏｆｐｒｏｂａｂｉｌｉｓｔｉｃｎｏｒｍｏｆａｌｉｎｅａｒｏｐｅｒａｔｏｒｏｎＭｅｎｇｅｒｐｒｏｂａｂｉｌｉｓｔｉｃｎｏｒｍｅｄｓｐａｃｅ（ｂｒｉｅｆｙ,ＭｅｎｇｅｒＰＮ＿ｓｐａｃｅ）．Ａｎｄｂｙｕｓｉｎｇｔｈｅｎｏｔｉｏｎ,ｕｎｄｅｒｔｈｅｃｏｎｄｉｔｉｏｎｏｆｔ＿ｎｏｒｍΔｓａｔｉｓｆｙｉｎｇΔ（ｔ,ｔ）≥ｔ（ｔ∈（０,１］）,ｈｅｇａｖｅａｄｅｓｃｒｉｐｔｉｏｎｏｆｂｏｕｎｄｅｄｎｅｓｓｏｆｌｉｎｅａｒｏｐｅ…     

Oriented Circular Dichroism Analysis of Chiral Surface‐Anchored Metal–Organic Frameworks Grown by Liquid‐Phase Epitaxy and upon Loading with Chiral Guest Compounds

Oriented circular dichroism (OCD) is explored and successfully applied to investigate chiral surface‐anchored metal–organic frameworks (SURMOFs) based on camphoric acid (D‐ and Lcam) with the composition [Cu₂(Dcam)_2x(Lcam)_2?2x(dabco)]_n (dabco=1,4‐diazabicyclo‐[2.2.2]‐octane). The three‐dimensional chiral SURMOFs with high‐quality orientation were grown on quartz glass plates by using a layer‐by‐layer liquid‐phase epitaxy method. The growth orientation, as determined by X‐ray diffraction (XRD), could be switched between the [001] and [110] direction by using either OH‐ or COOH‐terminated substrates. These SURMOFs were characterized by using OCD, which confirmed the ratio as well as the orientation of the enantiomeric linker molecules. Theoretical computations demonstrate that the OCD band intensities of the enantiopure [Cu₂(Dcam)₂(dabco)]_n grown in different orientations are a direct result of the anisotropic nature of the chiral SURMOFs. Finally, the enantiopure [Cu₂(Dcam)₂(dabco)]_n and [Cu₂(Lcam)₂(dabco)]_n SURMOFs were loaded with the two chiral forms of ethyl lactate [(+)‐ethyl‐D ‐lactate and (?)‐ethyl‐L ‐lactate)]. An enantioselective enrichment of >60 % was observed by OCD when the chiral host scaffold was loaded from the racemic mixture.     

Photoinduced Charge‐Carrier Generation in Epitaxial MOF Thin Films: High Efficiency as a Result of an Indirect Electronic Band Gap?

For inorganic semiconductors crystalline order leads to a band structure which gives rise to drastic differences to the disordered material. An example is the presence of an indirect band gap. For organic semiconductors such effects are typically not considered, since the bands are normally flat, and the band‐gap therefore is direct. Herein we show results from electronic structure calculations demonstrating that ordered arrays of porphyrins reveal a small dispersion of occupied and unoccupied bands leading to the formation of a small indirect band gap. We demonstrate herein that such ordered structures can be fabricated by liquid‐phase epitaxy and that the corresponding crystalline organic semiconductors exhibit superior photophysical properties, including large charge‐carrier mobility and an unusually large charge‐carrier generation efficiency. We have fabricated a prototype organic photovoltaic device based on this novel material exhibiting a remarkable efficiency.