In recent work we called a ring R a GGCD ring if the semigroup of finitely generated faithful multiplication ideals of R is closed under intersection. In this paper we introduce the concept of generalized GCD modules. An R-moduleM is a GGCD module if M is multiplication and the set of finitely generated faithful multiplication submodules of M is closed under intersection. We show that a ring R ...

Mesial temporal sclerosis (MTS) is the most common lesion in chronic, intractable temporal lobe epilepsies (TLE) and characterized by segmental neuronal cell loss in major hippocampal segments. Another histopathological hallmark includes granule cell dispersion (GCD), an architectural disturbance of the dentate gyrus encountered in approximately 50% of patients with mesial temporal sclerosis. R...

Gaucher's disease, a lysosomal storage disorder caused by mutations in the gene encoding glucocerebrosidase (GCD), is currently treated by enzyme replacement therapy using recombinant GCD (Cerezyme) expressed in Chinese hamster ovary (CHO) cells. As complex glycans in mammalian cells do not terminate in mannose residues, which are essential for the biological uptake of GCD via macrophage mannos...

PURPOSE To analyze conjunctival cytological features 1 month after pterygium excision using limbo-conjunctival autograft (LCA) with and without intraoperative mitomycin C and to assess tissue short-term evolution in both situations. METHODS Fifty-nine primary nasal pterygia from 59 patients were excised with LCA. Twenty-nine were treated with intraoperative mitomycin C 0.02% (MMC+) and 30 wer...

In Saccharomyces cerevisiae, expression of the transcriptional activator GCN4 increases at the translational level in response to starvation for an amino acid. The products of multiple GCD genes are required for efficient repression of GCN4 mRNA translation under nonstarvation conditions. The majority of the known GCD genes encode subunits of the general translation initiation factor eIF-2 or e...

Coppersmith, Franklin, Patarin, and Reiter have shown that given two RSA cryptograms xemodN; and (ax + b)emodN for any known constants a; b 2 ZN one can compute x in O(e log e) ZN -operations with some positive error probability. We show that given e cryptograms ci (ax + b i)emodN; i = 0; 1; :::e 1; for any known constants a; b 2 ZN ; where gcd(a;N) = gcd(b;N) = gcd(e!; N) = 1; one can determin...

Superficial granular corneal dystrophy (SGCD) is a variant of GCD that is restricted to involvement of the Bowman layer and the superficial corneal stroma. Superficial and classic GCD result from mutations in the human transforming growth factor –induced gene (BIGH3) on human chromosome 5 (5q31). We report an unusual case of a patient with SGCD in which the typical deposits of GCD were associat...

Let S = {x1,x2, . . . ,xn} be a set of positive integers, and let f be an arithmetical function. The matrices (S) f = [ f (gcd(xi,xj))] and [S] f = [ f (lcm[xi,xj])] are referred to as the greatest common divisor (GCD) and the least common multiple (LCM) matrices on S with respect to f , respectively. In this paper, we assume that the elements of the matrices (S) f and [S] f are integers and st...

This paper presents a regularization theory for numerical computation of polynomial greatest common divisors and a convergence analysis, along with a detailed description of a blackbox-type algorithm. The root of the ill-posedness in conventional GCD computation is identified by its geometry where polynomials form differentiable manifolds entangled in a stratification structure. With a proper r...

Giant colonic diverticulum (GCD), defined as a diverticulum larger than 4 cm, is a rare entity that is generally a manifestation of colonic diverticular disease. Because of its rarity and its variable and non-specific presentation, the diagnosis of GCD depends mainly on imaging findings. Knowledge of the spectrum of radiographic and CT features of the GCD is important in making the correct diag...