Atomic Ring Invariant and Modified CANON Extended Connectivity Algorithm for Symmetry Perception in Molecular Graphs and Rigorous Canonicalization of SMILES

We propose new invariant (the product of the corresponding primes for the ring size of each bond of an atom) as a simple unambiguous ring invariant of an atom that allows distinguishing symmetry classes in the highly symmetrical molecular graphs using traditional local and distance atom invariants. Also, we propose modifications of Weininger’s CANON algorithm to avoid its ambiguities (swapping and leveling ranks, incorrect determination of symmetry classes in non-aromatic annulenes, arbitrary selection of atom for breaking ties). The atomic ring invariant and the Modified CANON algorithm allow us to create a rigorous procedure for the generation of canonical SMILES which can be used for accurate and fast structural searching in large chemical databases.

Atomic Ring Invariant and Modified CANON Extended Connectivity Algorithm for Symmetry Perception in Molecular Graphs and Rigorous Canonicalization of SMILES

We propose new invariant (the product of the corresponding primes for the ring size of each bond of an atom) as a simple unambiguous ring invariant of an atom that allows distinguishing symmetry classes in the highly symmetrical molecular graphs using traditional local and distance atom invariants. Also, we propose modifications of Weininger’s CANON algorithm to avoid its ambiguities (swapping and leveling ranks, incorrect determination of symmetry classes in non-aromatic annulenes, arbitrary selection of atom for breaking ties). The atomic ring invariant and the Modified CANON algorithm allow us to create a rigorous procedure for the generation of canonical SMILES which can be used for accurate and fast structural searching in large chemical databases.

Atomic Ring Invariant and Modified CANON Extended Connectivity Algorithm for Symmetry Perception in Molecular Graphs and Rigorous Canonicalization of SMILES

We propose new invariant (product of corresponding primes for ring size of each bond of an atom) as a simple unambiguous ring invariant of the atom which allows to distinguish symmetry classes in highly symmetrical molecular graphs (with using of traditional local atom invariants). Also, we propose modifications of Weininger’s CANON algorithm which let to avoid its ambiguities (swapping and leveling of ranks, incorrect determination of symmetry classes in non-aromatic annulenes, arbitrary selection of atom for breaking ties). The atomic ring invariant and the Modified CANON algorithm allow us to create a rigorous procedure for the generation of canonical SMILES which can be used for accurate and fast structural search in large chemical databases.

Effects of Gamma Radiation on the Elastic Properties of Thulium Doped Zinc Borotellurite Glass

Effects of gamma radiation on the elastic properties of {[(TeO2)0.7(B2O3)0.3]0.7[ZnO]0.3}0.99{Tm2O3}0.01 (thulium doped zinc borotellurite glass) were investigated. Glass samples were prepared using the melt-quenching technique. Density and ultrasonic velocity of glasses before and after irradiation process were measured using Electronic Densimeter MD-300S and Ritec Ram-5000 Snap System, respectively. Next, elastic moduli and Poisson’s ratio of the glasses were calculated. Atomic ring size of the glass network was also calculated to support the attained results. Results show that density varied after radiation and maximised at 20 kGy. This is attributed to the breaking and rearrangement of chemical bonding in the glass network due to radiation. Furthermore, all elastic parameters exhibited an increasing trend that indicated the strengthening of the glass samples as well as increment of its rigidity. Besides that, atomic ring size was found to decrease as radiation dose increased. This indicate that compaction of glass network took place as the samples were exposed to gamma rays which in turn contributed to the elevation of elastic moduli of the prepared glass.

ATOMISTIC VIEWS OF DYNAMICAL FRACTURE INSTABILITIES IN SILICON: MOLECULAR DYNAMICS STUDIES

This study investigates the crystallographic orientations most widely known to exhibit fractures in silicon, such as those on the (111) plane cracks travelling along the [Formula: see text] direction ([Formula: see text] cracks). The (111) crack plane is believed to be the most stable fracture plane. However, fracture instabilities caused by brittle crack jumps remain on (111) the crack plane in a discontinuous manner. In this study, molecular dynamics simulations were performed to investigate the atomistic-level studies of fracture properties under a uniaxial tensile load (mode I load) in the (111) [Formula: see text] Si system. Our simulation results suggest that the formation of untypical-membered Si atomic rings in the vicinity of the crack tip, which can be induced by atomic stress near the crack tip, has an important role in the behavior of crack propagation instabilities. The presence of untypical-membered Si atomic rings acts as a self-protecting mechanism that contribute in maintaining the crack on the (111) fracture plane. Notably, our simulations also presented that the situation when a seven- Si atomic ring moves away from the crack tip associated with a sudden jump of crack speed can be regarded as the origin of the peculiar speed advancement behavior of the [Formula: see text] systems. Moreover, several of our simulation results are in agreement with related experimental measurements.

SOME REMARKS ON PRINCIPAL PRIME IDEALS

In this paper we investigate principal prime ideals in commutative rings. Among other things we characterize the principal prime ideals that are both minimal and maximal and characterize the maximal ideals of a polynomial ring that are principal. Our main result is that if (p) is a principal prime ideal of an atomic ring R, then ht(p)≤1.