T he symmetry of a ring system is crucial for classical and quantum effects. Mathematically speaking a ring is a nonsingly connected geometry. In quantum mechanics the ring symmetry of the benzene molecule gives rise to its delocalized electronic states [1]. In ring geometries strongly connected to external leads the electron wave packets can take two different paths around the ring which gives...

circularly-polarized antenna is built based on new siw(substrate integrated waveguide)structure which contains cavity-backed resonator and a conventional polarized ring with twosquare slits in inner and outer ring that differ 90° at position and is proposed for right-handedcircular polarization (rhcp) and fabricated in two separate layers. a broadband impedancebandwidth of 13.9% and a rhcp axia...

circularly-polarized antenna is built based on a new siw (substrate integrated waveguide)structure which contains cavity-backed resonator and a conventional polarized ring with twosquare slits in inner and outer ring that differ 90° at position and is proposed for right-handedcircular polarization (rhcp) and fabricated in two separate layers. a broadband impedancebandwidth of 13.9% and a rhcp a...

Quantum computing has shown great potential in various quantum chemical applications such as drug discovery, material design, and catalyst optimization. Although significant progress been made simulation of simple molecules, ab initio solid-state materials on computers is still its early stage, mostly owing to the fact that system size quickly becomes prohibitively large when approaching thermo...

circularly-polarized antenna is built based on new SIW(substrate integrated waveguide)structure which contains cavity-backed resonator and a conventional polarized ring with twosquare slits in inner and outer ring that differ 90° at position and is proposed for right-handedcircular polarization (RHCP) and fabricated in two separate layers. A broadband impedancebandwidth of 13.9% and a RHCP axia...

There is a local ring E of order 4, without identity for the multiplication, defined by generators and relations as $$E=\langle a,b \mid 2a=2b=0,\, a^2=a,\, b^2=b,\,ab=a,\, ba=b\rangle .$$ We study special construction self-orthogonal codes over E, based on combinatorial matrices related to two-class association schemes, Strongly Regular Graphs (SRG), Doubly Tournaments (DRT). construct quasi s...

Tetracyclines and tetracycline analogues are prepared by a convergent, single-step Michael-Claisen condensation of AB precursor 1 or 2 with D-ring precursors of wide structural variability, followed by removal of protective groups (typically in two steps). A number of procedural variants of the key C-ring-forming reaction are illustrated in multiple examples. These include stepwise deprotonatio...

Inspired by a recent work of Buchweitz and Flenner, we show that, for a semidualizing bimodule $C$, $C$--perfect complexes have the ability to detect when a ring is strongly regular.It is shown that there exists a class of modules which admit minimal resolutions of $C$--projective modules.

Let $R$ be a commutative ring and let $I$ be an ideal of $R$. In this paper, we will introduce the notions of 2-absorbing $I$-prime and 2-absorbing $I$-second submodules of an $R$-module $M$ as a generalization of 2-absorbing and strongly 2-absorbing second submodules of $M$ and explore some basic properties of these classes of modules.