2,5,10,13-Tetraazatricyclo [12,2,2,26,9] icosa-1(16),6,8,14,17,19-hexene-3,4,11,12-tetraone tetraoxime (1a) and 2,5,11,14-tetraazatricyclo [13,3,1,16,10] icosa-1(19),6,8,10(20),15,17-hexaene-3,4,12,13-tetraonetetraoxime (1b) were obtained from condensation of 1,4- and 1,3-phenylendiamine with dichloroglyoxime, respectively. The reaction of 1,2-phenylendiamine with dich...

We construct the first n-node degree-d ring-based network with worst-case greedy routes of length Θ(log n/ log d) hops. We study greedy routing over uni-dimensional metrics defined over n nodes lying in a ring. greedy routing in graph (V, E) with distance function δ : V × V → R entails the following decision: Given target node t, node u with neighbors N(u) forwards a message to v ∈ N(u) such th...

In this paper, a generalization of a group-magic graph is introduced and studied. Let R be a commutative ring with unity 1. A graph G = (V,E) is called R-ring-magic if there exists a labeling f : E → R−{0} such that the induced vertex labelings f : V → R, defined by f(v) = Σf(u, v) where (u, v) ∈ E, and f : V → R, defined by f(v) = Πf(u, v) where (u, v) ∈ E, are constant maps. General algebraic...

Using the notion of “belongingness ($epsilon$)” and “quasi-coincidence (q)” of fuzzy points with fuzzy sets, we introduce the concept of an ($ alpha, beta$)- fuzzyHv-ideal of an Hv-ring, where , are any two of {$epsilon$, q,$epsilon$ $vee$ q, $epsilon$ $wedge$ q} with $ alpha$ $neq$ $epsilon$ $wedge$ q. Since the concept of ($epsilon$, $epsilon$ $vee$ q)-fuzzy Hv-ideals is an important and ...

There are two independent mol-ecules (A and B) in the asymmetric unit of the title compound, C(19)H(23)NOS. In each mol-ecule, the seven-membered thiepine ring is bent into a slightly twisted V-shape. The dihedral angles between the mean planes of the two benzene rings fused to the thiepine ring are 75.7 (5) in mol-ecule A and 73.8 (4)° in mol-ecule B. In both mol-ecules, an intra-molecular O-H...

Method of secure evaluation of polynomial y = F(x1, ..., xk) over some rings on untrusted computer is proposed. Two models of untrusted computer are considered: passive and active. In passive model untrusted computer correctly computes polynomial F and tries to know secret input (x1, ..., xk) and output y. In active model untrusted computer tries to know input and output and tries to change cor...

The mol-ecule of the title compound, C(12)H(10)N(6), which is V-shaped due to the boat conformation of the dihydro-tetra-zine ring, has crystallographic C(2) symmetry. The dihedral angle between the planes of the two pyridine rings is 31.57 (3)°. Mol-ecules are linked by weak N-H⋯N and C-H⋯N hydrogen bonds, forming a two-dimensional polymeric structure.