A note on tameness of families having bounded variation

p-Lambda-bounded variation

A characteriation of continuity of the $p$-$Lambda$-variation function is given and the Helly's selection principle for $Lambda BV^{(p)}$ functions is established. A characterization of the inclusion of Waterman-Shiba classes into classes of functions with given integral modulus of continuity is given. A useful estimate on modulus of variation of functions of class $Lambda BV^{(p)}$ is found.

A Note on Families of Stable Matrices

Many topological properties of the whole family of stable polynomials and matrices have been studied in a number of publications (see e.g., [1,3–7,11,12]). The present paper continues these investigations with the aim of strengthening these results in the sense that instead of simple-connectivity we show stronger property of contractibility of the various families of stable matrices from this p...

A note on traces of set families

A family of sets F ⊆ 2[n] is defined to be l-trace k-Sperner if for any l-subset L of [n] the family of traces F|L = {F ∩L : F ∈ F} does not contain any chain of length k+ 1. In this paper we prove that for any positive integers l′, k with l′ < k if F is (n−l′)-trace k-Sperner, then |F| ≤ (k − l′ + o(1)) ( n bn/2c ) and this bound is asymptotically tight. AMS subject classification: 05D05

A Note on Bootstrapping Intuitionistic Bounded Arithmetic

This paper, firstly, discusses the relationship between Buss’s definition and Cook and Urquhart’s definition of BASIC axioms and of IS 2 . The two definitions of BASIC axioms are not equivalent; however, each intuitionistically implies the law of the excluded middle for quantifier-free formulas. There is an elementary proof that the definitions of IS 2 are equivalent which is not based on reali...

A note on power bounded matrices