We show that the Möbius function of an interval in a permutation poset where the lower bound is sum (resp. skew) indecomposable depends solely on the sum (resp. skew) indecomposable permutations contained in the upper bound, and that this can simplify the calculation of the Möbius sum. For increasing oscillations, we give a recursion for the Möbius sum which only involves evaluating simple ineq...

The total number of new tuberculosis (TB) cases notified in Singapore among citizens, permanent residents and foreigners rose by 46% from 2004 to 2010. During this period, the proportion of foreigners increased from 29% to 47% of the total case burden. In 2008, the TB incidence rate among Singapore citizens and permanent residents increased for the first time in ten years, despite the on-going ...

A module is said to be $PI$-extending provided that every projection invariant submodule is essential in a direct summand of the module. In this paper, we focus on direct summands and indecomposable decompositions of $PI$-extending modules. To this end, we provide several counter examples including the tangent bundles of complex spheres of dimensions bigger than or equal to 5 and certain hyper ...

We show that if X is an indecomposable P D 3-complex and π 1 (X) is the fundamental group of a reduced finite graph of finite groups but is neither Z nor Z ⊕ Z/2Z then X is orientable, the underlying graph is a tree, the vertex groups have cohomolog-ical period dividing 4 and all but at most one of the edge groups is Z/2Z. If there are no exceptions then all but at most one of the vertex groups...

The existence of large sets of 5-(14,6,3) designs is in doubt. There are five simple 5-(14,6,6) designs known in the literature. In this note, by the use of a computer program, we show that all of these designs are indecomposable and therefore they do not lead to large sets of 5(14,6,3) designs. Moreover, they provide the first counterexamples for a conjecture on disjoint t-designs which states...

Iterated Function Systems (IFSs) are among the best-known methods for constructing fractals. The sequence of pictures E0; E1; E2; : : : generated by an IFS fX; f1; f2; : : : ; ftg converges to a unique limit E , which is independent of the choice of starting set E0, but completely determined by the choice of the maps fi. Random context picture grammars (rcpgs) are a method of syntactic picture ...

We construct a new class of positive indecomposable maps in the algebra of d × d complex matrices. Each map is uniquely characterized by a cyclic bistochastic matrix. This class generalizes a Choi map for d = 3. It provides a new reach family of indecomposable entanglement witnesses which define important tool for investigating quantum entanglement.

We give a Decomposition Theorem for a family of Hopf algebras containing the well-know family of Taft Hopf algebras. Therefore, those indecomposable codes over this family of algebras (cf. [4]) is an indecomposable code over the studied case. We use properties of Hopf algebras to show that dual (in the module sense) of an ideal code is again an ideal code.

First, we give a complete description of the indecomposable prime modules over a Dedekind domain. Second, if R is the pullback, in the sense of [9], of two local Dedekind domains then we classify indecomposable prime R-modules and establish a connection between the prime modules and the pure-injective modules (also representable modules) over such rings.

In this paper, we classify the indecomposable non-nilpotent solvable Lie algebras with $N(R_n,m,r)$ nilradical,by using the derivation algebra and the automorphism group of $N(R_n,m,r)$.We also prove that these solvable Lie algebras are complete and unique, up to isomorphism.