Effective Isometric Embeddings for Certain Hermitian Holomorphic Line Bundles

We consider bihomogeneous polynomials on complex Euclidean spacesthat are positive outside the origin and obtain effective estimateson certain modifications needed to turn them into squares ofnorms of vector-valued polynomials on complex Euclidean space.The corresponding results for hypersurfaces in complex Euclideanspaces are also proved. The results can be considered as Hermitiananalogues of Hilbert's seventeenth problem on representing apositive definite quadratic form on Rⁿ as a sum of squares ofrational functions. They can also be regarded as effective estimateson the power of a Hermitian line bundle required for isometricprojective embedding. Further applications are discussed.     

Trace of heat kernel,spectral zeta function and isospectral problem for sub-laplacians

In this article, we first study the trace for the heat kernel for the sub-Laplacian operator on the unit sphere in ℂ ⁿ⁺¹. Then we survey some results on the spectral zeta function which is induced by the trace of the heat kernel. In the second part of the paper, we discuss an isospectral problem in the CR setting.     

Recommender systems

The ongoing rapid expansion of the Internet greatly increases the necessity of effective recommender systems for filtering the abundant information. Extensive research for recommender systems is conducted by a broad range of communities including social and computer scientists, physicists, and interdisciplinary researchers. Despite substantial theoretical and practical achievements, unification and comparison of different approaches are lacking, which impedes further advances. In this article, we review recent developments in recommender systems and discuss the major challenges. We compare and evaluate available algorithms and examine their roles in the future developments. In addition to algorithms, physical aspects are described to illustrate macroscopic behavior of recommender systems. Potential impacts and future directions are discussed. We emphasize that recommendation has great scientific depth and combines diverse research fields which makes it interesting for physicists as well as interdisciplinary researchers.     

Nickel-Catalyzed Chemoselective Arylation of Amino Alcohols

A systematic evaluation of competitive bisphosphine/Ni-catalyzed C−N versus C−O cross-couplings involving model compounds enabled development of hitherto unknown chemoselective O- and N-arylation of amino alcohols with (hetero)aryl chloride electrophiles, without recourse to protection group chemistry. Use of the CyPAd-DalPhos pre-catalyst C2 enabled particularly challenging O-arylation chemoselectivity in amino alcohols featuring branched primary and secondary alkylamine groups, while selective N-arylation was observed in substrates featuring less-hindered linear alkylamine and aniline reacting groups. Useful reaction scope in the (hetero)aryl chloride was achieved throughout, and the ability to conduct such transformations using benchtop handling of materials is demonstrated.     

Anisotropic fluctuations in ordered copolymer phases

The random phase approximation is reformulated to investigate the anisotropic fluctuations about an ordered polymer phase. This very general method is applied to the lamellar phase of block copolymers. The calculated anisotropic scattering intensity captures the main features observed experimentally including the secondary peaks due to fluctuations with hexagonal symmetry. We also determined the limits of metastability of the lamellar phase as well as the bending and elastic moduli of the lamellae.     

Practical and General Alcohol Deoxygenation Protocol

Herein, we describe a practical protocol for the removal of alcohol functional groups through reductive cleavage of their benzoate ester analogs. This transformation requires a strong single electron transfer (SET) reductant and a means to accelerate slow fragmentation following substrate reduction. To accomplish this, we developed a photocatalytic system that generates a potent reductant from formate salts alongside Brønsted or Lewis acids that promote fragmentation of the reduced intermediate. This deoxygenation procedure is effective across structurally and electronically diverse alcohols and enables a variety of difficult net transformations. This protocol requires no precautions to exclude air or moisture and remains efficient on multigram scale. Finally, the system can be adapted to a one-pot benzoylation-deoxygenation sequence to enable direct alcohol deletion. Mechanistic studies validate that the role of acidic additives is to promote the key C(sp³)−O bond fragmentation step.     

Synthesis,Redox and Optical Properties of Low‐Bandgap Platinum(II) Polyynes with 9‐Dicyanomethylene‐Substituted Fluorene Acceptors

In view of the strong electron‐withdrawing nature of the cyano substituent, a blue donor/acceptor‐type organometallic polymer (trans‐[—Pt(PBu₃)₂—C≡C—R—C≡C—]_n (R = 9‐dicyanomethylenefluorene‐2,7‐diyl)) was prepared in good yield by CuI‐catalyzed polymerization involving the dehydrohalogenating coupling of trans‐[Pt(PBu₃)₂Cl₂] and H—C≡C—R—C≡C—H. The thermal, redox and photoconducting properties of the polymer are reported. Electronic absorption studies indicate that it has a bandgap of 1.58 eV which is the lowest among any of the metal polyyne polymers reported in the literature. The derivatization of the polymer backbone with electron deficient dicyano‐substituted electron acceptor in the side chain is found to be effective to tune the bandgap of this class of materials while maintaining their solubility and processability.     

Peptide Amphiphile Mediated Co-assembly for Nanoplasmonic Sensing

Aromatic interactions are commonly involved in the assembly of naturally occurring building blocks, and these interactions can be replicated in an artificial setting to produce functional materials. Here we describe a colorimetric biosensor using co-assembly experiments with plasmonic gold and surfactant-like peptides (SLPs) spanning a wide range of aromatic residues, polar stretches, and interfacial affinities. The SLPs programmed in DDD−(ZZ)_x−FFPC self-assemble into higher-order structures in response to a protease and subsequently modulate the colloidal dispersity of gold leading to a colorimetric readout. Results show the strong aggregation propensity of the FFPC tail without polar DDD head. The SLPs were specific to the target protease, i.e., M^pro, a biomarker for SARS-CoV-2. This system is a simple and visual tool that senses M^pro in phosphate buffer, exhaled breath condensate, and saliva with detection limits of 15.7, 20.8, and 26.1 nM, respectively. These results may have value in designing other protease testing methods.