‎Let $I$ be an ideal in a regular local ring $(R,n)$‎, ‎we will find‎ ‎bounds on the first and the last Betti numbers of‎ ‎$(A,m)=(R/I,n/I)$‎. ‎if $A$ is an Artinian ring of the embedding‎ ‎codimension $h$‎, ‎$I$ has the initial degree $t$ and $mu(m^t)=1$‎, ‎we call $A$ a {it $t-$extended stretched local ring}‎. ‎This class of‎ ‎local rings is a natural generalization of the class of stretched ...

Acute increases in cellular protein O-linked N-acetyl-glucosamine (O-GlcNAc) modification (O-GlcNAcylation) have been shown to have protective effects in the heart and vasculature. We hypothesized that d-glucosamine (d-GlcN) and Thiamet-G, two agents that increase protein O-GlcNAcylation via different mechanisms, inhibit TNF-α-induced oxidative stress and vascular dysfunction by suppressing ind...

TNF-α is a proinflammatory cytokine and is an important mediator of maternal endothelial dysfunction leading to preeclampsia. In this study, we tested whether IL-10 protects against TNF-α-induced endothelial dysfunction in murine aorta. In in vitro experiments, aortic rings of C57BL/6 female mice were incubated in Dulbecco's modified Eagle's medium in the presence of either vehicle (distilled H...

we show  that a projective maximal submodule of afinitely generated, regular, extending module is a directsummand. hence, every finitely generated, regular, extendingmodule with projective maximal submodules is semisimple. as aconsequence, we observe that every regular, hereditary, extendingmodule is semisimple. this generalizes and simplifies a result of  dung and   smith. as another consequen...

PURPOSE To gain further insight into a possible role of biomechanical cues in glaucoma, the authors assessed the influence of extracellular matrix (ECM) elasticity on TGF-β2-induced changes in trabecular meshwork (TM) cells. METHODS Human TM cells derived from donor cornea rings were plated on rigid collagen-coated tissue culture plastic or polyacrylamide gels of different elasticity and trea...

OBJECTIVES Mitral annulus reconstruction is now a common surgical procedure for the treatment of mitral regurgitation. However, there are still controversies in the selection of materials for annuloplasty in the clinical controlled studies available. The purpose of the present systematic review of the literature is to address whether a flexible ring is superior to a rigid ring in terms of impro...

We determine which rings of the form Z[α] are generated by there units, where α is a root of the polynomial X4 −BX2 +D such that α and all its conjugates are complex.

Locally direct sums [W, Definition 3.15] appeared naturally in classification results for topological rings (see, e.g.,[K2], [S1], [S2], [S3], [U1]). We give here a result (Theorem 3) for locally compact Baer rings by using of locally direct sums. 1. Conventions and definitions All topological rings are assumed associative and Hausdorff. The subring generated by a subset A of a ring R is denote...

Rigid rod oligo(phenylene-ethynylene-butadiynylene)s (oPEBs), "half-rings" of two rigid rods connected via a molecular clamp unit, and shape-persistent macrocycles (cyclic "half-ring dimers") are synthesized and their self-assembled monolayers (SAMs) are investigated by scanning tunneling microscopy (STM) at the interface of 1,2,4-trichlorobenzene (TCB)/highly oriented pyrolytic graphite (HOPG)...