A direction-length framework is a pair (G, p), where G = (V ;D,L) is a ‘mixed’ graph whose edges are labeled as ‘direction’ or ‘length’ edges, and p is a map from V to R for some d. The label of an edge uv represents a direction or length constraint between p(u) and p(v). Let G be obtained from G by adding, for each length edge e of G, a direction edge with the same end vertices as e. We show t...

The knowledge of intramolecular dynamics, geometric confinement, and structure of surface-bound ligands are important factors for understanding surface chemistry, catalysis, and design of catalytically optimized nanoparticles. In this report, intramolecular dynamics of perdeuterated triphenylphosphine ligands, d15-(PPh3), bound to the surface of gold nanoparticles (AuNPs) are characterized by p...

BACKGROUND We hypothesized that annuloplasty ring implantation alters mitral annular strains in a normal beating ovine heart preparation. METHODS AND RESULTS Sheep had 16 radiopaque markers sewn equally spaced around the mitral annulus. Edwards Cosgrove partial flexible band (COS; n=12), St Jude complete rigid saddle-shaped annuloplasty ring (RSA; n=10), Carpentier-Edwards Physio (PHY; n=11),...

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...

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...

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...

An ideal I on a cardinal κ is called rigid if all automorphisms of P (κ)/I are trivial. An ideal is called μ-minimal if whenever G ⊆ P (κ)/I is generic and X ∈ P (μ)V [G] \ V , it follows that V [X] = V [G]. We prove that the existence of a rigid saturated μ-minimal ideal on μ+, where μ is a regular cardinal, is consistent relative to the existence of large cardinals. The existence of such an i...

Two kinds of ladder-type conjugated polymers were concisely synthesized by the formation single-stranded via Stille cross-couplings, followed nitrogen-directed electrophilic borylations at electron-rich aromatic rings. The resulting BN-annulated show good film-forming behaviors and high air thermal stability. Their structurally shape-persistent rigid backbones render them with π-extended conjug...