in this paper, we define the notions of ultra and involution ideals in $bck$-algebras. then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. specially, we show that in a bounded implicative $bck$-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower $bck$-semilattice, the not...

in this paper we investigate some hereditary properties of amenability modulo an ideal of banach algebras. we show that if (e) is a bounded approximate identity modulo i of a banach algebra a and x is a neo-unital modulo i, then (e) is a bounded approximate identity for x. moreover we show that amenability modulo an ideal of a banach algebra a can be only considered by the neo-unital modulo...

When solving a linear algebraic system Ax = b with GMRES, the relative residual norm at each step is bounded from above by the so-called ideal GMRES approximation. This worstcase bound is sharp (i.e. it is attainable by the relative GMRES residual norm) in case of a normal matrix A, but it need not characterize the worst-case GMRES behavior if A is nonnormal. Characterizing the tightness of thi...

The Finagle point (Wuffle et al., 1989), the yolk (McKelvey, 1986; Ferejohn et al., 1984) and the epsilon-core (Wooders, 1983; Salant and Goodstein, 1990; Tovey, 2010; Feld and Grofman, 1991) are three solution concepts that have been proposed to predict the outcome of majority voting in the Euclidean spatial model. Relationships among these three concepts are investigated in (Bra̋uninger, 2007)...

let $r$ be a commutative ring with identity. an ideal $i$ of a ring $r$is called an annihilating ideal if there exists $rin rsetminus {0}$ such that $ir=(0)$ and an ideal $i$ of$r$ is called an essential ideal if $i$ has non-zero intersectionwith every other non-zero ideal of $r$. thesum-annihilating essential ideal graph of $r$, denoted by $mathcal{ae}_r$, isa graph whose vertex set is the set...

in this note we consider the notion of intuitionistic fuzzy (weak) dual hyper k-ideals and obtain related results. then we classify this notion according to level sets. after that we determine the relationships between intuitionistic fuzzy (weak) dual hyper k-ideals and intuitionistic fuzzy (weak) hyper k-ideals. finally, we define the notion of the product of two intuitionistic fuzzy (weak) du...

in this paper, various elementary properties of vague rings are obtained. furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated.

We consider linear operators and equations with partial integrals in Banach ideal spaces, spaces of vector functions, continuous functions. study the action, regularity, duality, algebras, Fredholm properties, invertibility, spectral properties such operators. describe principal integrals. show that are essentially different compared to usual integral equations. obtain conditions for alternativ...

notions of strongly regular, regular and left(right) regular $gamma$−semigroupsare introduced. equivalent conditions are obtained through fuzzy notion for a$gamma$−semigroup to be either strongly regular or regular or left regular.

conclusions the radiological findings of the present study showed that the use of a coral-dcfgp mixture led to superior bone defect healing and rapid graft incorporation when compared to the use of solely coral or dcfgp. background currently, coral is used as an osteoconductive material. demineralized calf fetal growth plate (dcfgp) has also been used as a source of osteoinduction. objectives t...