Global Solution and Blow-up for a Class of p-Laplacian Evolution Equations with Logarithmic Nonlinearity

The main goal of this work is to study an initial boundary value problem for a quasilinear parabolic equation with logarithmic source term. By using the potential well method and a logarithmic Sobolev inequality, we obtain results of existence or nonexistence of global weak solutions. In addition, we also provided sufficient conditions for the large time decay of global weak solutions and for the finite time blow-up of weak solutions.     

一般状态空间马氏链随机泛函的指数矩

本文研究了一般状态空间马氏链随机泛函的指数矩.利用最小非负解理论,得到了随机泛函的指数矩是相应方程的最小非负解,推广了可数状态空间马氏链的结果,作为应用,证明了随机泛函的指数矩与漂移条件等价.     

Muckenhoupt–Wheeden conjectures for sparse operators

We provide an explicit example of a pair of weights and a dyadic sparse operator for which the Hardy–Littlewood maximal function is bounded from \(L^p(v)\) to \(L^p(u)\) and from \(L^{p'}(u^{1-p'})\) to \(L^{p'}(v^{1-p'})\) while the sparse operator is not bounded on the same spaces. Our construction also provides an example of a single weight for which the weak-type endpoint does not hold for sparse operators.     

Can Tetrylone Act in a Similar Fashion to Tetrylene in Ni(CO)2 Complexes? A Theoretical Study based on a Comparison using DFT Calculations

A comparison was made to investigate the structures and bonding of nickel complex that carry tetrylone and tetrylene ligands [(CO)₂Ni‐{E(PH₃)₂}] ( Ni1E ) and [(CO)₂Ni‐{NHE_Me}] ( Ni2E ) (E = C to Pb) using quantum chemical calculations at the BP86 level with various basis sets (SVP, TZVPP, TZ2P+). The nature of the Ni–E bonds was analyzed with charge‐ and energy decomposition methods. The structures of tetrylone complexes Ni1E exhibit an interesting trend with the ligands E(PH₃)₂ are bonded in a tilted orientation relative to the fragment Ni(CO)₂. In contrast, the calculated equilibrium structures of complexes Ni2E exhibit the NHE_Me ligands (E = C to Sn) bonded in a head‐on way to the Ni(CO)₂ fragment, while the bending angle gives the strongest side‐on bonded ligand NHPb_Me when E = Pb. The interesting trend of the bond dissociation energy (BDE) is observed for the tetrylone, which has the same trend BDEs compared with tetrylene complexes. The EDA‐NOCV results indicate that the tetrylone ligands {E(PH₃)₂} in complexes are similar to the tetrylene ligands NHE_Me as strong σ‐donors and weak π‐acceptors. The BDEs calculated for the Ni–E bonds in Ni1E and Ni2E show that the effect of bulky ligands may obscure the intrinsic Ni–E bond strength. The bonding analysis shows that the tetrylone ligands in Ni1E may act in a similar fashion to the tetrylene ligands in Ni2E . All complexes Ni1E and Ni2E are suitable targets for synthesis.     

Weakly automorphism invariant modules and essential tightness

While a module is pseudo-injective if and only if it is automorphism-invariant, it was not known whether automorphism-invariant modules are tight. It is shown that weakly automorphism-invariant modules are precisely essentially tight. We give various examples of weakly automorphism-invariant and essentially tight modules and study their properties. Some particular results: (1) R is a semiprime right and left Goldie ring if and only if every right (left) ideal is weakly injective if and only if every right (left) ideal is weakly automorphism invariant; (2) R is a CEP-ring if and only if R is right artinian and every indecomposable projective right R-module is uniform and essentially R-tight.     

Platinum-catalyzed hydrofunctionalization of unactivated alkenes with carbon, nitrogen and oxygen nucleophiles

The transition metal-catalyzed addition of the X-H bond of a carbon, nitrogen or oxygen nucleophile across the C[double bond]C bond of an unactivated alkene (hydrofunctionalization) represents an attractive, atom-economical approach to the synthesis of carbocyclic and heterocyclic molecules and for the elaboration of ethylene and 1-alkenes. We have developed a family of Pt(II)-catalyzed protocols for the inter- and intramolecular hydrofunctionalization of unactivated alkenes with a range of H-X nucleophiles including beta-diketones, indoles, amines, carboxamides and alcohols. These transformations display good functional group compatibility, low moisture sensitivity, and often good generality.     

Rationally designing molecularly imprinted polymer towards predetermined high selectivity by using metal as assembled pivot

This article presents an original work aiming at rationally designing a molecularly imprinted polymer (MIP) towards high selective recognition. Assembled with (S)-naproxen as a template and 4-vinylpyridine as a functional monomer, a certain amount of cobalt, as pivot, is added for the preparation of MIP. The result indicates that the use of pivot plays obviously a positive role in increasing the specificity of MIP, so as to adsorb more for the template and less for its enantiomer. Related information indicates that this, in logic, can be a result of increasing match between binding sites and the templates, which makes the polymer capable of selectively recognizing the imprint species.     

Evaluation of the protective capabilities of nucleosome STRs obtained by large‐scale sequencing

Partial DNA profiles are often obtained from degraded forensic samples and are hard to analyze and interpret. With in‐depth studies on degraded DNA, an increasing number of forensic scientists have focused on the intrinsic structural properties of DNA. In theory, nucleosomes offer protection to the bound DNA by limiting access to enzymes. In our study, we performed large‐scale DNA sequencing on nucleosome core DNA of human leucocytes. Five nucleosome short tandem repeats (STRs) were selected (including three forensic common STRs (i.e. TPOX, TH01, and D10S1248) and two unpublished STRs (i.e. AC012568.7 and AC007160.3)). We performed a population genetic investigation and forensic genetic statistical analysis of these two unpublished loci on 108 healthy unrelated individuals of the HeBei Han population in China. We estimated the protective capabilities of five selected nucleosome loci and MiniFiler? loci with artificial degraded DNA and case samples. We also analyzed differences between sequencing results and software predicted results. Our findings showed that nucleosome STRs were more likely to be detected than MiniFiler? loci. They were well protected from degradation by nucleosomes and could be candidates for further nucleosome multiplex construction, which would increase the chances of obtaining a better balanced profile with fewer allelic drop‐outs.