Monochromatic sequences whose gaps belong to {d, 2d, …, md}

Avoiding Monochromatic Sequences With Special Gaps

For S ⊆ Z+ and k and r fixed positive integers, denote by f(S, k; r) the least positive integer n (if it exists) such that within every r-coloring of {1, 2, . . . , n} there must be a monochromatic sequence {x1, x2, . . . , xk} with xi − xi−1 ∈ S for 2 ≤ i ≤ k. We consider the existence of f(S, k; r) for various choices of S, as well as upper and lower bounds on this function. In particular, we...

Implementation and aspiration gaps: whose view counts?

2068 www.thelancet.com Vol 388 October 29, 2016 The Lancet’s Maternal Health Series paints a sobering picture of the state of maternal health today. The Series focuses on the “mismatch between burden and coverage”, which “exposes a crucial gap in quality of care” and spotlights the millions of pregnant women and adolescents who never get access to services at all. But 30 years after the start o...

On Certain Equations in Matrices Whose Elements Belong to a Division Algebra*

Profinite Identities for Finite Semigroups Whose Subgroups Belong to a Given Pseudovariety

We introduce a series of new polynomially computable implicit operations on the class of all finite semigroups. These new operations enable us to construct a finite pro-identity basis for the pseudovariety H of all finite semigroups whose subgroups belong to a given finitely based pseudovariety H of finite groups.

Exact sequences of extended $d$-homology

In this article, we show the existence of certain exact sequences with respect to two homology theories, called d-homology and extended d-homology. We present sufficient conditions for the existence of long exact extended d- homology sequence. Also we give some illustrative examples.