A Criterion for Projective Modules

In case G is a finite group, there is a well-known criterion for projective modules: A ? G-module M is projective if and only if it is ? -free and has finite projective dimension. We first investigate whether only finite groups satisfy the above criterion. In the class of groups L H 𝔉, we conclude that this is true. Secondly, we consider the problem when a stably flat Γ-module is projective, where Γ is an arbitrary group. We show that if Γ is an L H 𝔉-group, then every stably flat cofibrant ? Γ-module is projective.     

Generalized MacWilliams identities and their applications to perfect binary codes

We present generalized MacWilliams identities for binary codes. These identities naturally lead to the concepts of the local weight distribution of a binary code with respect to a word u and its MacWilliams u-transform. In the case that u is the all-one word, these ones correspond to the weight distribution of a binary code and its MacWilliams transform, respectively. We identify a word v with its support, and consider v as a subset of {1, 2,..., n}. For two words u,w of length n such that their intersection is the empty set, define the u-face centered at w to be the set . A connection between our MacWilliams u-transform and the weight distribution of a binary code in the u-face centered at the zero word is presented. As their applications, we also investigate the properties of a perfect binary code. For a perfect binary code C, the main results are as follows: first, it is proved that our local weight distribution of C is uniquely determined by the number of codewords of C in the orthogonal u-face centered at the zero word. Next, we give a direct proof for the known result, concerning the weight distribution of a coset of C in the u-face centered at the zero word, by A. Y. Vasil’eva without using induction. Finally, it is proved that the weight distribution of C in the orthogonal u-face centered at w is uniquely determined by the codewords of C in the u-face centered at the zero word.      

MAO‐free and extremely active catalytic system for ethylene tetramerization

The original Sasol catalytic system for ethylene tetramerization is composed of a Cr source, a PNP ligand, and MAO (methylaluminoxane). The use of expensive MAO in excess has been a critical concern in commercial operation. Many efforts have been made to replace MAO with non‐coordinating anions (e.g., [B(C₆F₅)₄]^?); however, most of such attempts were unsuccessful. Herein, an extremely active catalytic system that avoids the use of MAO is presented. The successive addition of two equivalent [H(OEt₂)₂]⁺[B(C₆F₅)₄]^? and one equivalent CrCl₃(THF)₃ to (acac)AlEt₂ and subsequent treatment with a PNP ligand [CH₃(CH₂)₁₆]₂C(H)N(PPh₂)₂ ( 1 ) yielded a complex presumably formulated as [ 1 ‐CrAl (acac)Cl₃(THF)]²⁺[B(C₆F₅)₄]^?₂, which exhibited high activity when combined with iBu₃Al (1120 kg/g‐Cr/h; ~4 times that of the original Sasol system composed of Cr (acac)₃, iPrN(PPh₂)₂, and MAO). Via the introduction of bulky trialkylsilyl substituents such as –SiMe₃, –Si(nBu)₃, or –SiMe₂(CH₂)₇CH₃ at the para‐position of phenyl groups in 1 (i.e., by using [CH₃(CH₂)₁₆]₂C(H)N[P(C₆H₄‐p‐SiR₃)₂]₂ instead of 1 ), the activities were dramatically improved, i.e., tripled (2960–3340 kg/g‐Cr/h; more than 10 times that of the original Sasol system). The generation of significantly less PE (<0.2 wt%) even at a high temperature is another advantage achieved by the introduction of bulky trialkylsilyl substituents. NMR studies and DFT calculations suggest that increase of the steric bulkiness on the alkyl‐N and P‐aryl moieties restrict the free rotation around (alkyl)N–P (aryl) bonds, which may cause the generation of more robust active species in higher proportion, leading to extremely high activity along with the generation of a smaller amount of PE.     

Prediction of African Swine Fever Virus Inhibitors by Molecular Docking-Driven Machine Learning Models

African swine fever virus (ASFV) causes a highly contagious and severe hemorrhagic viral disease with high mortality in domestic pigs of all ages. Although the virus is harmless to humans, the ongoing ASFV epidemic could have severe economic consequences for global food security. Recent studies have found a few antiviral agents that can inhibit ASFV infections. However, currently, there are no vaccines or antiviral drugs. Hence, there is an urgent need to identify new drugs to treat ASFV. Based on the structural information data on the targets of ASFV, we used molecular docking and machine learning models to identify novel antiviral agents. We confirmed that compounds with high affinity present in the region of interest belonged to subsets in the chemical space using principal component analysis and k-means clustering in molecular docking studies of FDA-approved drugs. These methods predicted pentagastrin as a potential antiviral drug against ASFVs. Finally, it was also observed that the compound had an inhibitory effect on AsfvPolX activity. Results from the present study suggest that molecular docking and machine learning models can play an important role in identifying potential antiviral drugs against ASFVs.     

Phosphonated Near‐Infrared Fluorophores for Biomedical Imaging of Bone

The conventional method for creating targeted contrast agents is to conjugate separate targeting and fluorophore domains. A new strategy is based on the incorporation of targeting moieties into the non‐delocalized structure of pentamethine and heptamethine indocyanines. Using the known affinity of phosphonates for bone minerals in a model system, two families of bifunctional molecules that target bone without requiring a traditional bisphosphonate are synthesized. With peak fluorescence emissions at approximately 700 or 800 nm, these molecules can be used for fluorescence‐assisted resection and exploration (FLARE) dual‐channel imaging. Longitudinal FLARE studies in mice demonstrate that phosphonated near‐infrared fluorophores remain stable in bone for over five weeks, and histological analysis confirms their incorporation into the bone matrix. Taken together, a new strategy for creating ultra‐compact, targeted near‐infrared fluorophores for various bioimaging applications is described.     

Anti‐Inflammatory Activity of a Novel Acetylene Isolated from the Roots of Angelica tenuissima Nakai

Three polyacetylenes, one novel and two known, were isolated from the root of Angelica tenuissima. Using ¹H‐ and ¹³C‐NMR, COSY, HMBC, and HMQC, their structures were found to be (3R,8S)‐heptadeca‐1‐en‐4,6‐diyne‐3,8‐diol ( 1 ), falcarindiol ( 2 ), and oplopandiol ( 3 ). Absolute configurations of compound 1 were established using Mosher's esterification. In addition, the polyacetylenes ( 1 – 3 ) were evaluated for their anti‐inflammatory activity. Compounds 1 and 3 showed potent inhibitory activity against lipopolysaccharide‐induced nitric oxide (NO) production in RAW267.7 macrophage cells with IC₅₀ values of 4.31 and 5.06 μm, respectively. Compound 1 strongly inhibited inducible nitric oxide synthase (iNOS) and cyclooxygenase (COX)‐2 in a concentration‐dependent manner.     

Cost‐Effective,High‐Performance Porous‐Organic‐Polymer Conductors Functionalized with Sulfonic Acid Groups by Direct Postsynthetic Substitution

We demonstrate the facile microwave‐assisted synthesis of a porous organic framework 1 and the sulfonated solid ( 1S ) through postsubstitution. Remarkably, the conductivity of 1S showed an approximately 300‐fold enhancement at 30 °C as compared to that of 1 , and reached 7.72×10^?2 S cm^?1 at 80 °C and 90 % relative humidity. The superprotonic conductivity exceeds that observed for any conductive porous organic polymer reported to date. This material, which is cost‐effective and scalable for mass production, also revealed long‐term performance over more than 3 months without conductivity decay.     

Theoretical investigation of the structures and spectroscopic properties of (H2O4)n (n = 1–4) clusters

Density functional theory and ab initio calculations were performed to elucidate the hydrogen interactions in (H₂O₄)_n (n = 1–4) clusters. The optimized geometries, binding energies, and harmonic vibrational frequencies were predicted at various levels of theory. The trans conformer of the H₂O₄ monomer was predicted to be the most stable structure at the CCSD(T)/aug‐cc‐pVTZ level of theory. The binding energies per H₂O₄ monomer increased in absolute value by 9.0, 10.1, and 11.8 kcal/mol from n = 2 to n = 4 at the MP2/cc‐pVTZ level of theory (after the zero‐point vibrational energy and basis set superposition error corrections). This result implies that the intermolecular hydrogen bonds were stronger in the long‐chain clusters, that is, the formation of the longer chain in the (H₂O₄)_n clusters was more energetically favorable.     

The basis set superposition error in multilevel methods: a test on the H2O and HF dimer

The basis set superposition error (BSSE) is often very important in the accurate calculation of dimerization energies. Accurate prediction of thermochemical properties requires appropriate consideration of the basis set incompleteness error. Multilevel methods introduce adjustable parameters to reproduce experimental data, that is, the higher level correction (HLC) in G3 and adjustable coefficients in the MCCM. However, the HLC term is cancelled out and the adjustable coefficients in the MCCM do not remove the BSSE completely. We have calculated the BSSE involved in the multilevel methods. The H₂O and HF dimer systems were used as a test case. This study shows that empirical coefficients do reduce the BSSE in some cases and an MCCM with good parameters can be used to reproduce dimerization energies within chemical accuracy without the BSSE correction.