The unitary Cayley graph Xn has vertex set Zn = {0, 1,…, n-1} and vertices u and v are adjacent, if gcd(uv, n) = 1. In [A. Ilić, The energy of unitary Cayley graphs, Linear Algebra Appl. 431 (2009) 1881–1889], the energy of unitary Cayley graphs is computed. In this paper the Wiener and hyperWiener index of Xn is computed.

Giant colonic diverticulum (GCD), defined as diverticulum larger than 4 cm, is a rare entity. It is generally a manifestation of colonic diverticular disease and can have dramatic complications such as perforation, abscess, volvulus, infarction and adenocarcinoma. This report documents the case of a 63-year-old man coming to the Emergency Department with acute abdomen due to a perforation of a ...

Let q be a prime power, Fq be the field of q elements, and k, m be positive integers. A bipartite graph G = Gq(g, h, k,m) is defined as follows. The vertex set of G is a union of two copies P and L of two-dimensional vector spaces over Fq, with two vertices (p1, p2) ∈ P and [ l1, l2 ] ∈ L being adjacent if and only if p2 + l2 = p1l 1 . We prove that graphs Gq(k, m) and Gq′(k,m) are isomorphic i...

In contrast with Tennenbaum’s theorem [8] that says Peano Arithmetic (PA) has no nonstandard computable model, Shepherdson [6] constructed a computable nonstandard model for a very weak fragment of PA, called Open Induction (Iopen) in which the induction scheme is only allowed to be applied for quantifier-free formulas (with parameters). Since then several attempts have been made from both side...

Based on the Bezout approach we propose a simple algorithm to determine gcd of two polynomials which doesn’t need division, like Euclidean algorithm, or determinant calculations, Sylvester matrix algorithm. The needs only n steps for degree n. Formal manipulations give discriminant resultant any without needing division nor calculation.

0 binary, I-binary: The binary GCD algorithm ([lS]) and its improvement for multidigit integers (Gosper, see [12]). We compare the executron times of several algoixtliiiis for computing the G‘C‘U of arbitrary precasion iirlegers. These algorithms are the known ones (Euclidean, brnary, plus-mrnus), and the improved variants of these for multidigit compzltation (Lehmer and similar), as well as ne...

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...

Let F be an arbitrary topological vector space; we shall say that a subset S of F is quasi-convex if the set of continuous affine functionals on 5 separates the points of S. If X is a Banach space and T: X -* F is a continuous linear operator, then T is quasi-convex if T(U) is quasiconvex, where U is the unit ball of X. In the case when T is compact, T(U) is quasi-convex if and only if it is af...

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...