an injective map f : e(g) → {±1, ±2, · · · , ±q} is said to be an edge pair sum labeling of a graph g(p, q) if the induced vertex function f*: v (g) → z − {0} defined by f*(v) = (sigma e∈ev) f (e) is one-one, where ev denotes the set of edges in g that are incident with a vetex v and f*(v (g)) is either of the form {±k1, ±k2, · · · , ±kp/2} or {±k1, ±k2, · · · , ±k(p−1)/2} u {k(p+1)/2} accordin...

We show that every semi-artinian module which is contained in a direct sum of finitely presented modules in $si[M]$, is weakly co-semisimple if and only if it is regular in $si[M]$. As a consequence, we observe that every semi-artinian ring is regular in the sense of von Neumann if and only if its simple modules are $FP$-injective.

We answer the following question: Let P and Q be graded posets having some property and let ◦ be some poset operation. Is it true that P ◦Q has also this property? The considered properties are: being Sperner, a symmetric chain order, Peck, LYM, and rank compressed. The studied operations are: direct product, direct sum, ordinal sum, ordinal product, rankwise direct product, and exponentiation.

Let $R$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎Let $M$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎Then $M$ has a direct decomposition $M=oplus_{iin I} M_i$‎,‎where each $M_i$ is noetherian quasi-projective and each‎‎endomorphism ring $End(M_i)$ is local‎.

We define the notion of almost $n$-layered $QTAG$-modules and study their basic properties. One of the main result is that almost 1-layered modules are almost $(omega+1)$-projective exactly when they are almost direct sum of countably generated modules of length less than or equal to $(omega+1)$. Some other characterizations of this new class are also established.

This paper initiates the study of k-catalytic branching programs, a nonuniform model of computation that is the counterpart to the uniform catalytic space model of Buhrman, Cleve, Koucký, Loff and Speelman (STOC 2014). A k-catalytic branching program computes k boolean functions simultaneously on the same n-bit input. Each function has its own entry, accept and reject nodes in the branching pro...

Katsunori Kawamura1 College of Science and Engineering Ritsumeikan University, 1-1-1 Noji Higashi, Kusatsu, Shiga 525-8577,Japan Abstract We show that there exists a non-cocommutative comultiplication ∆φ and a counit ε on the direct sum of Cuntz algebras O∗ ≡ C⊕O2 ⊕O3 ⊕O4 ⊕ · · · . From ∆φ, ε and the standard algebraic structure, the C ∗-algebra O∗ is a bialgebra. Furthermore we show the follow...

Let T be a block lower triangular contraction, i.e., a contractive operator T = (ti,j) ∞ i,j=−∞ acting from a doubly infinite Hilbert space direct sum ⊕∞ j=−∞Kj into a doubly infinite Hilbert space direct sum ⊕∞ j=−∞ Lj . The operator ti,j , which maps Kj into Li, is the (i, j)-th entry in the operator matrix representation of T relative to the natural Hilbert space direct sum decompositions. I...

We prove lower bounds for the direct sum problem for two-party bounded error randomised multipleround communication protocols. Our proofs use the notion of information cost of a protocol, as defined by Chakrabarti et al. [CSWY01] and refined further by Bar-Yossef et al. [BJKS02]. Our main technical result is a ‘compression’ theorem saying that, for any probability distribution μ over the inputs...