Warner (1966), Hewitt and Ross (1970), Yap (1970), and Yap (1971) extended the so-called Ditkin's condition for the group algebra L\G) of a locally compact abelian group G to the algebras L(G) Π L(G), dense subalgebras of L{G) which are essential Banach LHO-modules, LKG) Π L(G)(1 ^ p < co) and Segal algebras respectively. Chilana and Ross (1978) proved that the algebra L^K) satisfies a stronger...

Introduction By spherical functions one usually means functions on the double coset space K\G/K, where G is a group and K is a subgroup of G. This is equivalent to considering functions on the homogeneous space G/K left invariant with respect to K. More generally, if V is a fixed irreducible representation of K, for example, finite-dimensional, one can look at functions on G/K whose left shifts...

for every positive integer k, a set s of vertices in a graph g = (v;e) is a k- tuple dominating set of g if every vertex of v -s is adjacent to at least k vertices and every vertex of s is adjacent to at least k - 1 vertices in s. the minimum cardinality of a k-tuple dominating set of g is the k-tuple domination number of g. when k = 1, a k-tuple domination number is the well-studied domination...

Functional RNAs that switch their activities in response to K(+) may sense the intracellular (100 mM) and extracellular (5 mM) K(+) concentrations and regulate their functions accordingly. Previously, we developed a quadruplex hammerhead ribozyme (QHR) whose conformational change, from a duplex to a G-quadruplex, triggered by K(+) results in expression of the activity. However, this QHR require...

A routine computation with the spectral sequence of the fibering (G2, T, G2/T) confirms the result of Borel4 that H*(G2) has a cyclic group of order two as torsion group in dimensions 6 and 9. 6. Let K be a connected subgroup of maximal rank in G. The inclusions T c K c G induce a fiberingfk: GIT -G/K of GIT over GIK with fiber KIT. If Pal, . . . , Pt are the planes through o in 2' which belong...

We use Cayley graphs to construct several dual-containing codes, all of which have sparse graphs. These codes’ properties are promising compared to other quantum error-correcting codes. This paper builds on the ideas of the earlier paper Sparse-Graph Codes for Quantum ErrorCorrection (quant-ph/0304161), which the reader is encouraged to refer to. To recap: Our aim is to make classical error-cor...

An (n, k) group code over a group G is a subset of G which forms a group under componentwise group operation and can be defined in terms of n — k homomorphisms from G to G. In this correspondence, the set of homomorphisms which define Maximum Distance Separable (MDS) group codes defined over cyclic groups are characterized. Each defining homomorphism can be specified by a set of k endomorpbisms...

‎for any integer $kgeq 1$‎, ‎a set $s$ of vertices in a graph $g=(v,e)$ is a $k$-‎tuple total dominating set of $g$ if any vertex‎ ‎of $g$ is adjacent to at least $k$ vertices in $s$‎, ‎and any vertex‎ ‎of $v-s$ is adjacent to at least $k$ vertices in $v-s$‎. ‎the minimum number of vertices of such a set‎ ‎in $g$ we call the $k$-tuple total restrained domination number of $g$‎. ‎the maximum num...

Given certain compactly supported functions g ∈ L2(Rd) whose Zd-translates form a partition of unity, and real invertible d×d matrices B, C for which ||CT B|| is sufficiently small, we prove that the Gabor system {EBmTCng}m,n∈Zd forms a frame, with a (non-canonical) dual Gabor frame generated by an explicitly given finite linear combination of shifts of g. For functions g of the above type and ...