In this paper, we introduce the concept of bipolar-valued fuzzification of ordered AG-groupoids and discuss some structural properties of bipolarvalued fuzzy two-sided ideals of an intra-regular ordered AG-groupoid.

We present first-principles studies of the adsorption of Sb and Ag on clean and Sb-covered Ag (111). For Sb, the substitutional adsorption site is found to be greatly favored with respect to on-surface fcc sites and to subsurface sites, so that a segregating surface alloy layer is formed. Adsorbed silver adatoms are more strongly bound on clean Ag(111) than on Sb-covered Ag. We propose that the...

We report an experimental (scanning tunneling microscopy) and theoretical (embedded atom method) study of a heterophase interface reconstruction between Ag(111) and Ru(0001). Despite the large 7% mismatch, the second layer of Ag from the Ru exhibits a hexagonal structure with Ag bulk spacing, providing a close match to bulk Ag. The first layer of Ag (next to Ru) is reconstructed in a highly sym...

1 Some Homework Exercises In introductory automata theory, one can nd a wealth of entertaining automata-theoretic puzzles such as the classical rst halves problem: Show that if A is a regular set, then so is the set of all rst halves of strings in A: FirstHalves(A) = fx j 9y jyj = jxj and xy 2 Ag : Once students master the basic pebbling technique for solving such problems, they can move on to ...

Let AG be the adjacency matrix of G. Let λ1 ≥ λ2 ≥ . . . ≥ λn be the eigenvalues of AG. Sometimes we will also be interested in the Laplacian matrix of G. This is defined to be LG = D−AG, where D is the diagonal matrix where Dvv equals the degree of the vertex v. For d-regular graphs, LG = dI −AG, and hence the eigenvalues of LG are d− λ1, d− λ2, . . . , d− λn. Lemma 1. • λ1 = d. • λ2 = λ3 = . ...

A design is additive under an abelian group G (briefly, G-additive) if, up to isomorphism, its point set contained in and the elements of each block sum zero. The only known Steiner 2-designs that are G-additive for some have size which either a prime power or plus one. Indeed they point-line designs affine spaces AG(n,q), projective planes PG(2,q), PG(n,2) sporadic example 2-(8191,7,1) design....

Some new families of caps in Galois affine spaces AG(N , q) of dimension N ≡ 0 (mod 4) and odd order q are constructed. Such caps are proven to be complete by using some new ideas depending on the concept of a regular point with respect to a complete plane arc. As a corollary, an improvement on the currently known upper bounds on the size of the smallest complete caps in AG(N , q) is obtained.

No regular hyperoval of the Desarguesian affine plane AG(2, 2), with h > 1, is inherited by a dual André plane of order 2 and dimension 2 over its kernel.

BACKGROUND To investigate the significance of monitoring the levels of the serum squamous cell carcinoma antigen (SCC-Ag) for the detection of recurrent disease in patients with cervical cancer treated by concurrent chemoradiotherapy. METHODS The records of 112 patients with cervical cancer were reviewed. Serum SCC-Ag levels were measured at regular follow-up visits. A SCC-Ag level of 2 ng/mL...