Let I ⊆ P(ω) be an ideal. We continue our investigation of the class of spaces with the I-ideal convergence property, denoted (I). We show that if I is an analytic, non-countably generated P-ideal then (I) ⊆ s₀. If in addition I is non-pathological and not isomorphic to , then (I) spaces have measure zero. We also present a characterization of the (I) spaces using clopen covers.
In this article we analyze the relationship between the growth and stability properties of coercive polynomials. For coercive polynomials we introduce the degree of stable coercivity which measures how stable the coercivity is with respect to small perturbations by other polynomials. We link the degree of stable coercivity to the Łojasiewicz exponent at infinity and we show an explicit relation between them.
We study distribution of the zeros of the Alexander polynomials of knots and links in S³. After a brief introduction of various stabilities of multivariate polynomials, we present recent results on stable Alexander polynomials.
The article is a survey on problem of the theorem of Hurwitz. The starting point of explanations is Schur's decomposition theorem for polynomials. It is showed how to obtain the well-known criteria on the distribution of roots of polynomials. The theorem on uniqueness of constants in Schur's decomposition seems to be new.
We give some subordination results for new classes of normalized analytic functions containing differential operator of non-Bazilevič type in the open unit disk. By using Jack's lemma, sufficient conditions for this type of operator are also discussed.
It is shown that product weakly measurable lower weak semi-Carathéodory multifunction is superpositionally measurable.
In this paper we give an alternative proof of our recent result that totally unrectifiable 1-sets which satisfy a measure-theoretic flatness condition at almost every point and sufficiently small scales, satisfy Besicovitch's 1/2-Conjecture which states that the lower spherical density for totally unrectifiable 1-sets should be bounded above by 1/2 at almost every point. This is in contrast to rectifiable 1-sets which actually possess a density equal to unity at almost every point. Our present method...