Coefficient rings of numerical semigroup algebras

Numerical semigroup rings are investigated from the relative viewpoint. It is known that algebraic properties such as singularities of a numerical semigroup ring are properties of a flat numerical semigroup algebra. In this paper, we show that arithmetic and set-theoretic properties of a numerical semigroup ring are properties of an equi-gcd numerical semigroup algebra.

     

Diindeno-Fused Dibenzo[a,h]anthracene and Dibenzo[c,l]chrysene: Syntheses,Structural Analyses,and Properties

Diindeno-fused dibenzo[a,h]anthracene 6 and diindeno-fused dibenzo[c,l]chrysene 9 contain the key moieties 1,4-quinodipropene (1,4-QDP) and 2,6-naphthoquinodipropene (2,6-NQDP), respectively, and they both have an open-shell singlet ground state. The latter compound exhibits a strong biradical character and interesting properties, including a low ΔE_T−S (2.44 kcal mol⁻¹), a small HOMO–LUMO gap (1.06 eV), a wide photoabsorption range (250–1172 nm), and a large two-photon absorption cross-section (σ=1342±56 GM). This work verifies that 6 has a slightly larger HOMO–LUMO gap and ΔE_T−S than its helical isomer diindeno[2,1-f:1′,2′-j]picene (DIP), but is a much stronger two-photon absorber, verifying the important effect of geometry on the photophysical properties.     

Redox Communication within Multinuclear Iron–Sulfur Complexes Related to Electronic Interplay in the Active Site of [FeFe]Hydrogenase

The one‐electron oxidations of a Fe₂ complex lead to the formation of a persistent metal‐stabilized thiyl radical Fe₂ species, mixed‐valent Fe₄, and Fe₈ complexes. The unpaired spin in the Fe₂ radical species delocalizes over the Fe₂ and the aromatic dithiolate, mostly on the terminal sulfur. The subsequent dimerization of the singly oxidized Fe₂ to the Fe₄ retains the partial thiyl radical character. For an analogue with less steric hindrance, the π–π stacking interaction between the dithiolato aromatic rings induces generation of the Fe₈, in which process electronic structures of the species are modulated through reducing the thiyl radical to the thiolate. Electronic reorganization repeats when the Fe₈ is converted to Fe₄. Electronic interplay in the complexes decreases the energy gap of frontier MOs and buffers electronic impacts upon redox events. Easier accessible redox potentials and increased stability of the species are facilitated. The results demonstrate that electronic versatility of the benzenedithiolate exerts pronounced influences on electronic and coordination structure of the metal complexes.     

Modified Lagrangian vortex method with improved boundary conditions for water waves past a thin bottom‐standing barrier

Herein, the modified Lagrangian vortex method (LVM), a hybrid analytical‐numerical algorithm per se, is devised to simulate the process of vortex formation and shedding from the sharp edge of a zero‐thickness vertical plate under linear water‐wave attack. Application of the Helmholtz decomposition facilitates a convenient switch between the inviscid‐ and viscous‐flow models, thereby enabling easy incorporation of vorticity effects into the potential‐flow calculations for the viscous‐dominated region. In evaluating the potential‐flow component, making good use of the quickly convergent technique with singular basis functions, correctly capturing the singular behavior in velocity fields near the tip of the plate, leads to a considerable reduction of computational burdens and to 12‐decimal‐place accuracy. The viscous correction is carried out via the meshless LVM with improved boundary conditions. Comparisons with previously published results show good agreement. Simulations of vortex generation and evolution illuminate the ability of the present method, and provide a supplement to pertinent experimental works. The hybrid scheme proposed herein allows flexibility for the former LVM and convenience in the code development. Such a compromise fits particularly well for the high‐resolution modeling of sharp‐edged vortex shedding without heavy numerical developments. Copyright © 2014 John Wiley & Sons, Ltd.     

Functional Groups Assisted Tunable Dielectric Permittivity of Guest-Free Zn-Based Coordination Polymers for Gate Dielectrics

The dielectric properties of coordination polymers has been a topic of recent interest, but the role of different functional groups on the dielectric properties of these polymers has not yet been fully addressed. Herein, the effects of electron-donating (R=NH₂) and electron-withdrawing (R=NO₂) groups on the dielectric behavior of such materials were investigated for two thermally stable and guest-free Zn-based coordination polymers, [Zn(L₁)(L₂)]_n ( 1 ) and [Zn(L₁)(L₃)]_n ( 2 ) [L₁=2-(2-pyridyl) benzimidazole (Pbim), L₂=5-aminoisophthalate (Aip), and L₃=5-nitroisophthalate (Nip)]. The results of dielectric studies of 1 revealed that it possesses a high dielectric constant (κ=65.5 at 1 kHz), while compound 2 displayed an even higher dielectric constant (κ=110.3 at 1 kHz). The electron donating and withdrawing effects of the NH₂ and NO₂ substituents induce changes in the polarity of the polymers, which is due to the inductive effect from the aryl ring for both NO₂ and NH₂. Theoretical results from density functional theory (DFT) calculations, which also support the experimental findings, show that both compounds have a distinct electronic behavior with diverse wide bandgaps. The significance of the current work is to provide information about the structure-dielectric property relationships. So, this study promises to pave the way for further research on the effects of different functional groups on coordination polymers on their dielectric properties.     

Cyclic orbifolds of lattice vertex operator algebras having group-like fusions

Letters in Mathematical Physics - Let L be an even (positive definite) lattice and $$g\in O(L)$$. In this article, we prove that the orbifold vertex operator algebra $$V_{L}^{{\hat{g}}}$$ has...     

DNA dynamics and organization in sub-micron scale: Bacterial chromosomes and plasmids in vivo and in vitro

Decades of research have witnessed that the mechanical properties of DNA and the associated protein interactions are crucial to the structural organizations and dynamic behaviors of bacterial DNA molecules. Packaged in a restricted cellular space and respective compositions, the entropic force due to confinement is a major factor driving the basal structural formation of the bacterial chromosome and the distribution of plasmids. The dynamic responses of the DNA-protein interactions also modulate the DNA organization when the cellular functions proceed. In this review, we survey the in-vivo and in-vitro evidence and the current understandings of the cellular phenomena of DNA molecules in the sub-micron scale of the bacterial cellular environment. The physical nature and constraints of DNA in cells and the related biological factors, especially the effects induced by gene expressions, are also discussed. We anticipate that by the methodological advances in vivo and in vitro as well as their combinations, the fundamental insights of the coupling from the physical environment and DNA-protein interactions on bacterial DNA dynamics and organization may be revealed.