In this paper we introduce the concept of weakly prime ternary subsemimodules of a ternary semimodule over a ternary semiring and obtain some characterizations of weakly prime ternary subsemimodules. We prove that if $N$ is a weakly prime subtractive ternary subsemimodule of a ternary $R$-semimodule $M$, then either $N$ is a prime ternary subsemimodule or $(N : M)(N : M)N = 0$. If $N$ is a $Q$-...

in the present paper we introduce and study the notion of pairwise weakly lindelof bitopological spaces and obtain some results. further, we also study the pairwise weakly lindelof subspaces and subsets, and investigate some of their properties. it was proved that a pairwise weakly lindelof property is not a hereditary property.

By introducing the concepts of order almost Dunford-Pettis and almost weakly limited operators in Banach lattices, we give some properties of them related to some well known classes of operators, such as, order weakly compact, order Dunford-Pettis, weak and almost Dunford- Pettis and weakly limited operators. Then, we characterize Banach lat- tices E and F on which each operator from E into F t...

Let λ = (λ1, λ2, . . . , λl), λ1 ≥ λ2 ≥ . . . ≥ λl > 0, be a partition of n, λ ⊢ n, and let [λ] = {(i, j) ∈ Z : 1 ≤ i ≤ l, 1 ≤ j ≤ λi} be the corresponding Young diagram. The conjugate partition λ is defined by λj = max{i : λi ≥ j}. We will freely use implications such as i ≤ j ⇒ λi ≥ λj. The hook Hz ⊆ [λ] is the set of squares weakly to the right and below of z = (i, j) ∈ [λ], and the hook len...

Thaumatin-like proteins (TLPs) are induced by a variety of phytopathogens in many plants and several TLPs are allergenic. Previously, we isolated three TLP-encoding cDNAs (Cry j 3.1, Cry j 3.2 and Cry j 3.3) from a cDNA library derived from the pollen of Cryptomeria japonica D. Don. Here, we describe three new TLP cDNAs (Cry j 3.4, Cry j 3.5 and Cry j 3.6). We compared the sequences, the geneti...

In 2001, S. Bulman-Fleming et al. initiated the study of three flatness properties (weakly kernel flat, principally weakly kernel flat, translation kernel flat) of right acts $A_{S}$ over a monoid $S$ that can be described by means of when the functor $A_{S} otimes -$ preserves pullbacks. In this paper, we extend these results to $S$-posets and present equivalent descriptions of weakly kernel p...

Let $R$ be a commutative ring. The purpose of this article is to introduce a new class of ideals of R called weakly irreducible ideals. This class could be a generalization of the families quasi-primary ideals and strongly irreducible ideals. The relationships between the notions primary, quasi-primary, weakly irreducible, strongly irreducible and irreducible ideals, in different rings, has bee...

In this paper we introduce the notion of $varphi$-commutativity for a Banach algebra $A$, where $varphi$ is a continuous homomorphism on $A$ and study the concept of $varphi$-weak amenability for $varphi$-commutative Banach algebras. We give an example to show that the class of $varphi$-weakly amenable Banach algebras is larger than that of weakly amenable commutative Banach algebras. We charac...

For a bounded linear operator on Hilbert space we define a sequence of the so-called weakly extremal vectors‎. ‎We study the properties of weakly extremal vectors and show that the orthogonality equation is valid for weakly extremal vectors‎. ‎Also we show that any quasinilpotent operator $T$ has an hypernoncyclic vector‎, ‎and so $T$ has a nontrivial hyperinvariant subspace‎.

For a Banach algebra $A$, $A''$ is $(-1)$-Weakly amenable if $A'$ is a Banach $A''$-bimodule and $H^1(A'',A')={0}$. In this paper, among other things,  we study the relationships between the $(-1)$-Weakly amenability of $A''$ and the weak amenability of $A''$ or $A$. Moreover, we show that the second dual of every $C^ast$-algebra is $(-1)$-Weakly amenable.