Let A be a commutative ring, B a commutative A-algebra and M a complex of B-modules. We begin by constructing the square SqB/A M , which is also a complex of B-modules. The squaring operation is a quadratic functor, and its construction requires differential graded (DG) algebras. If there exists an isomorphism ρ : M ≃ −→ SqB/A M then the pair (M,ρ) is called a rigid complex over B relative to A...

keyword: α-actinin rod domain, α-spectrin, Steered Molecular Dynamics. Abstract: α−actinin, an actin binding protein, plays a key role in cell migration, cross-links actin filaments in the Z-disk, and is a major component of contractile muscle apparatus. The flexibility of the molecule is critical to its function. The flexibility of various regions of the molecule, including the linker connecti...

Nomenclature A k , a k Fourier series coefficients, d mean difference between theoretical and experimental stress values, i square root of –1, m mapping function shape descriptor, r, θ polar coordinates in the mapping plane, s standard deviation in the difference between stress values, t distance from the crack tip, x, y Cartesian coordinates in the physical plane, z complex coordinate in the p...

Let A be a commutative ring, B a commutative A-algebra and M a complex of B-modules. We begin by constructing the square SqB/A M , which is also a complex of B-modules. The squaring operation is a quadratic functor, and its construction requires differential graded (DG) algebras. If there exists an isomorphism ρ : M ≃ −→ SqB/A M then the pair (M,ρ) is called a rigid complex over B relative to A...

The title compound, C(15)H(22)O(4), consists of two trans-fused six-membered rings and a trans-fused five-membered γ-lactone. The ep-oxy and hydroxyl groups are α-oriented. The cyclo-hexane rings adopt half-chair and chair conformations and the lactone ring is in an envelope conformation. The mol-ecular structure is stabilized by one O-H⋯O and three C-H⋯O intra-molecular hydrogen bonds.

A comprehensive survey of pathways leading to the generation of α-trifluoromethyl monocyclic piperidinic derivatives is provided (65 references). These compounds have been synthesized either from 6-membered rings e.g., pipecolic acid or lactam derivatives by introduction a trifluoromethyl group, from pyridine or pyridinone derivatives by reduction, and from 5-membered rings e.g., prolinol deriv...

let $r$ be an associative ring with identity and $z^*(r)$ be its set of non-zero zero divisors.  the zero-divisor graph of $r$, denoted by $gamma(r)$, is the graph whose vertices are the non-zero  zero-divisors of  $r$, and two distinct vertices $r$ and $s$ are adjacent if and only if $rs=0$ or $sr=0$.  in this paper, we bring some results about undirected zero-divisor graph of a monoid ring ov...

OBJECTIVE Considering the importance of annular dynamics in the valvular and ventricular function, we sought to evaluate the effects of treated pericardial annuloplasty rings on mitral annular dynamics and left-ventricular (LV) function after mitral valve repair. The results were compared with the mitral annular dynamics and LV function in patients with rigid and flexible rings and also in thos...

The introduction of multiple carbon rings is one of the common ways for graphene modification. Starting from warped C80H30 nanographene, which consists of a number of six- and seven-membered carbon rings (C6 and C7) centering at a five-membered carbon ring (C5), we explored the structure and property variations of its derivatives in which their C7 rings were gradually replaced with C6 rings. Wi...

If a ring element α = 1 − ab is Drazin invertible, so is β = 1 − ba. We show that the Drazin inverse of β is expressible by a simple formula (in generalization of “Jacobson’s Lemma”) in terms of the Drazin inverse and the spectral idempotent of α. The commutation rules αa = a β and b α = β b are extended to the Drazin inverses, and the spectral idempotents of α and β are shown to be isomorphic....