Imaginary-time path-integral (PI) molecular simulations can be used to calculate exact quantum statistical mechanical properties for complex systems containing many interacting atoms and molecules. The limiting computational factor in a PI simulation is typically the evaluation of the potential energy surface (PES) and forces at each ring-polymer "bead"; for an n-bead ring-polymer, a PI simulat...

let $r$ be a ring and $m$ a right $r$-module with $s=end_r(m)$. a module $m$ is called semi-projective if for any epimorphism $f:mrightarrow n$, where $n$ is a submodule of $m$, and for any homomorphism $g: mrightarrow n$, there exists $h:mrightarrow m$ such that $fh=g$. in this paper, we study sgq-projective and$pi$-semi-projective modules as two generalizations of semi-projective modules. a m...

let $r$ be an associative ring with identity. an element $x in r$ is called $mathbb{z}g$-regular (resp. strongly $mathbb{z}g$-regular) if there exist $g in g$, $n in mathbb{z}$ and $r in r$ such that $x^{ng}=x^{ng}rx^{ng}$ (resp. $x^{ng}=x^{(n+1)g}$). a ring $r$ is called $mathbb{z}g$-regular (resp. strongly $mathbb{z}g$-regular) if every element of $r$ is $mathbb{z}g$-regular (resp. strongly $...

Alonso P. Moreno, Viviana M. Berthoud, Gregorio Pérez-Palacios, and E. Martha Pérez-Armendariz Krannert Institute of Cardiology, Indiana School of Medicine, Indianapolis, Indiana; Section of Hematology/Oncology, Department of Pediatrics, University of Chicago, Chicago, Illinois; and Facultad de Medicina, Departmento de Medicina Experimental, Unidad de Investigación, Enseñanza y Comunicación Ens...

An instance I of Ring Grooming consists of m sets A1, A2, . . . , Am from the universe {0, 1, . . . , n − 1} and an integer g ≥ 2. The unrestricted variant of Ring Grooming, referred to as Unrestricted Ring Grooming, seeks a partition {P1, P2, . . . , Pk} of {1, 2, . . . , m} such that |Pi | ≤ g for each 1 ≤ i ≤ k and ∑k i=1 | ⋃ r∈Pi Ar | is minimized. The restricted variant of Ring Grooming, r...

Necessary and sufficient conditions for an Ore extension S = R[x;σ, δ] to be a PI ring are given in the case σ is an injective endomorphism of a semiprime ring R satisfying the ACC on annihilators. Also, for an arbitrary endomorphism τ of R, a characterization of Ore extensions R[x; τ ] which are PI rings is given, provided the coefficient ring R is noetherian.

Density functional theory (UB3LYP/6-31G(d,p)) was used to determine substituent effects on the singlet-triplet-state energy gap for 21 meta-substituted phenylnitrenium ions. It was found that strongly electron-donating substituents stabilize the triplet state relative to the singlet state. With sufficiently strong meta electron donors (e.g., m,m'-diaminophenylnitrenium ion) the triplet is predi...