Ideal-Symmetric and Semiprime Rings

Lambek extended the usual commutative ideal theory to ideals in noncommutative rings, calling an ideal A of a ring R symmetric if rst ∈ A implies rts ∈ A for r, s, t ∈ R. R is usually called symmetric if 0 is a symmetric ideal. This naturally gives rise to extending the study of symmetric ring property to the lattice of ideals. In the process, we introduce the concept of an ideal-symmetric ring. We first characterize the class of ideal-symmetric rings and show that this ideal-symmetric property is Morita invariant. We provide a method of constructing an ideal-symmetric ring (but not semiprime) from any given semiprime ring, noting that semiprime rings are ideal-symmetric. We investigate the structure of minimal ideal-symmetric rings completely, finding two kinds of basic forms of finite ideal-symmetric rings. It is also shown that the ideal-symmetric property can go up to right quotient rings in relation with regular elements. The polynomial ring R[x] over an ideal-symmetric ring R need not be ideal-symmetric, but it is shown that the factor ring R[x]/xⁿR[x] is ideal-symmetric over a semiprime ring R.     

High-field NMR using resistive and hybrid magnets

Resistive and resistive-superconducting hybrid magnets can generate dc magnetic fields much higher than conventional superconducting NMR magnets but the field spatial homogeneity and temporal stability are usually not sufficient for high-resolution NMR experiments. Hardware and technique development addressing these issues are presented for high-resolution NMR at magnetic fields up to 40T. Passive ferromagnetic shimming and magic-angle spinning are used effectively to reduce the broadening from inhomogeneous magnetic field. A phase correction technique based on simultaneous heteronuclear detection is developed to compensate magnetic field fluctuations to achieve high spectral resolution.     

Oxygen Vacancy Diffusion and Condensation in Lithium‐Ion Battery Cathode Materials

Oxygen vacancies (OV) are native defects in transition metal (TM) oxides and their presence has a critical effect on the physicochemical properties of the oxide. Metal oxides are commonly used in lithium‐ion battery (LIB) cathodes and there is still a lack of understanding of the role of OVs in LIB research field. Here, we report on the behavior of OVs in a single‐crystal LIB cathode during the non‐equilibrium states of charge and discharge. We found that microcrack evolution in a single crystal occurs due to OV condensation in specific crystallographic orientations generated by the continuous migration of OVs and TM ions. Moreover, understanding the effects of the presence and diffusion of OVs in metal oxides enables the elucidation of most of the conventional mechanisms of capacity fading in LIBs and provides new insights for new electrochemical applications.     

Key Role of a-Top CO on Terrace Sites of Metallic Pd Clusters for CO Oxidation

Pd-based catalysts are the most widely used for CO oxidation because of their outstanding catalytic activity and thermal stability. However, fundamental understanding of the detailed catalytic processes occurring on Pd-based catalysts under realistic conditions is still lacking. In this study, we investigated CO oxidation on metallic Pd clusters supported on Al₂O₃ and SiO₂. High-angle annular dark-field scanning transmission electron microscopy revealed the formation of similar-sized Pd clusters on Al₂O₃ and SiO₂. In contrast, CO chemisorption analysis indicated a gradual change in the dispersion of Pd (from 0.79 to 0.2) on Pd/Al₂O₃ and a marginal change in the dispersion (from 0.4 to 0.24) on Pd/SiO₂ as the Pd loading increased from 0.27 to 5.5 wt %; these changes were attributed to differences in the metal-support interactions. Diffuse reflectance infrared Fourier-transform spectroscopy revealed that fewer a-top CO species were present in Pd supported on Al₂O₃ than those in Pd supported on SiO₂, which is related to the morphological differences in the metallic Pd clusters on these two supports. Despite the different dispersion profiles and surface characteristics of Pd, O₂ titration demonstrated that linearly bound CO (with an infrared signal at 2090 cm⁻¹) reacted first with oxygen in the case of CO-saturated Pd on Al₂O₃ and SiO₂, which suggests that a-top CO on the terrace site plays an important role in CO oxidation. The experimental observations were corroborated by periodic density functional calculations, which confirmed that CO oxidation on the (111) terrace sites is most plausible, both kinetically and thermodynamically, compared to that on the edge or corner sites. This study will deepen the fundamental understanding of the effect of Pd clusters on CO oxidation under reaction conditions.     

A formal construction of a divergence-free basis in the nonconforming virtual element method for the Stokes problem

Numerical Algorithms - We develop a formal construction of a pointwise divergence-free basis in the nonconforming virtual element method of arbitrary order for the Stokes problem introduced in Zhao...     

Classification of reflexible regular embeddings and self-Petrie dual regular embeddings of complete bipartite graphs

In this paper, we classify the reflexible regular orientable embeddings and the self-Petrie dual regular orientable embeddings of complete bipartite graphs. The classification shows that for any natural number n, say (p₁,p₂,…,p_k are distinct odd primes and a_i>0 for each i?1), there are t distinct reflexible regular embeddings of the complete bipartite graph K_n,n up to isomorphism, where t=1 if a=0, t=2^k if a=1, t=2^k+1 if a=2, and t=3·2^k+1 if a?3. And, there are s distinct self-Petrie dual regular embeddings of K_n,n up to isomorphism, where s=1 if a=0, s=2^k if a=1, s=2^k+1 if a=2, and s=2^k+2 if a?3.     

Label-free aptasensor for platelet-derived growth factor (PDGF) protein

A label-free aptasensor for platelet-derived growth factor (PDGF) protein is reported. The aptasensor uses mixed self-assembled monolayers (SAMs) composed of a thiol-modified PDGF binding aptamer and 6-mercaptohexanol (MCH) on a gold electrode. The SAMs were characterized by cyclic voltammetry (CV), electrochemical impedance spectroscopy (EIS), and differential pulse voltammetry (DPV) before and after binding of the protein using [Fe(CN)₆]^3−/4−, a redox marker ion as an indicator for the formation of a protein-aptamer complex. The CVs at the PDGF modified electrode showed significant differences, such as changes in the peak currents and peak-to-peak separation, before and after binding of the target protein. The EIS spectra, in the form of Nyquist plots, were analyzed with a Randles circuit while the electron transfer resistance R_ct was used to monitor the binding of the target protein. The results showed that, without any modification to the aptamer, the target protein can be recognized effectively at the PDGF binding aptamer SAMs at the electrode surface. Control experiments using non-binding oligonucleotides assembled at the electrode surfaces also confirmed the results and showed that there was no formation of an aptamer-protein complex. The DPV signal at the aptamer functionalized electrode showed a linearly decreased marker ion peak current in a protein concentrations range of 1-40 nM. Thus, label-free detection of PDGF protein at an aptamer modified electrode has been demonstrated.     

Thin-thick surface phase coexistence and boundary tension of the square-well fluid on a weak attractive surface

Prewetting transition is studied for the square-well fluid of attractive-well diameter lambda(ff)sigma(ff)=1.5 in the presence of a homogeneous surface modeled by the square-well potential of attractive well from 0.8sigma(ff) to 1.8sigma(ff). We investigate surface phase coexistence of thin-thick film transition using grand-canonical transition matrix Monte Carlo (GC-TMMC) and histogram reweighting techniques. Molecular dynamics (MD) and GC-TMMC are utilized to predict the properties of the fluid for various surface fluid affinities. Occurrences of prewetting transition with the variation of surface affinity are observed for a domain of reduced temperature from T(*)=0.62 to 0.75. We have used MD and GC-TMMC+finite size scaling (FSS) simulations to calculate the boundary tension as a function of temperature as well as surface affinity. Boundary tensions via MD and GC-TMMC+FSS methods are in good agreement. The boundary tension increases with the decrease of wall-fluid affinity. Prewetting critical properties are calculated using rectilinear diameter approach and scaling analysis. We found that critical temperature and density increase with the decrease of wall-fluid affinity.     

A Unique Tryptophan C‐Prenyltransferase from the Kawaguchipeptin Biosynthetic Pathway

Cyanobactins are a rapidly growing family of linear and cyclic peptides produced by cyanobacteria. Kawaguchipeptins A and B, two macrocyclic undecapeptides reported earlier from Microcystis aeruginosa NIES‐88, are shown to be products of the cyanobactin biosynthetic pathway. The 9 kb kawaguchipeptin (kgp) gene cluster was identified in a 5.26 Mb draft genome of Microcystis aeruginosa NIES‐88. We verified that this gene cluster is responsible for the production of the kawaguchipeptins through heterologous expression of the kgp gene cluster in Escherichia coli. The KgpF prenyltransferase was overexpressed and was shown to prenylate C‐3 of Trp residues in both linear and cyclic peptides in vitro. Our findings serve to further enhance the structural diversity of cyanobactins to include tryptophan‐prenylated cyclic peptides.