In this paper, we generalize the ordinary basic model of the Progressive means by introducing the new notion of the extended Progressive means or the notion of the Progressive means with a moving sequence of partial sums. Afterwords we use this new concept to talk about a multiplier ωe(n, r, z, f) of the extended Progressive means and convex maps of the unit disk. The work presented gives more ...

We construct a new map from a convex function to a distribution on its domain, with the property that this distribution is a multi-scale exploration of the function. We use this map to solve a decadeold open problem in adversarial bandit convex optimization by showing that the minimax regret for this problem is Õ(poly(n) √ T ), where n is the dimension and T the number of rounds. This bound is ...

Keywords: Analytic functions Differential subordination Ma–Minda type starlike and convex functions Integral operators a b s t r a c t Two integral operators on the classes consisting of normalized p-valent Ma–Minda type starlike and convex functions are considered. Functions in these classes have the form zf ′ (z)/f (z) ≺ pϕ(z) and 1 + zf ′′ (z)/f ′ (z) ≺ pϕ(z) respectively, where ϕ is a conve...

Objectives: The aim of this study was to determine the prevalence of condensing osteitis lesions in Eastern Anatolian Turkish population. About condensing osteitis lesions, these were evaluated; sex, localization, side, age, shape and status of involved teeth (caries, restoration etc.). Methods: This retrospective study was carried out using panoramic radiographs of 962 patients who came to for...

A KKM space is an abstract convex space satisfying the KKM principle. We obtain variants of the KKM principle for KKM spaces related to weakly KKM maps and indicate some applications of them. These results properly generalize the corresponding ones in G-convex spaces and φA-spaces X,D; {φA}A∈〈D〉 . Consequently, results by Balaj 2004, Liu 1991, and Tang et al. 2007 can be properly generalized an...

In this paper, we introduce a novel model-based visibility measure for geometric primitives called visibility map. It is simple to calculate, memory efficient, accurate for viewpoints outside the convex hull of the object and versatile in terms of possible applications. Several useful properties of visibility maps that show their superiority to existing visibility measures are derived. Various ...

Given any generating set of any subgroup G of the mapping class group of a surface, we find an element f with word length bounded by a constant K depending only on the surface, and with the property that the minimal subsurface supporting a power of f is as large as possible for elements of G. In particular, if G contains a pseudo-Anosov map, we find one of word length at most K. We also find ne...

Probabilistic automata (PA) combine probability and nondeterminism. They can be given different semantics, like strong bisimilarity, convex bisimilarity, or (more recently) distribution bisimilarity. The latter is based on the view of PA as transformers of probability distributions, also called belief states, and promotes distributions to first-class citizens. We give a coalgebraic account of t...

We show that if Lr(X), 1 < r < ∞, has an asymptotically uniformly convex renorming of power type then X admits a uniformly convex norm of power type.