We discuss 1-Ahlfors-regular connected sets in a metric space. We prove that such a set is ‘flat’ on most scales and locations. We give a quantitative version of this. This, together with work of I. Hahlomaa, gives a characterization of 1-Ahlfors regular subsets of 1-Ahlfors-regular curves in a metric space, generalizing in a way the Analyst’s (Geometric) Traveling Salesman theorems by P. Jones...

Using a portion of the Continuum Hypothesis, we prove that there is a Menger-bounded (also called o-bounded) subgroup of the Baire group Z, whose square is not Menger-bounded. This settles a major open problem concerning boundedness notions for groups, and implies that Menger-bounded groups need not be Scheepers-bounded.

to understand the rate of oxidation of sponge irons and its mechanisim, their physical and chemical properties are normally required. in this report attempt has been made to show the results of research on varius pellets and briqutts produced at ahwaz steel complex. in presenting these data, the rate of oxidation of these articles in air between 300 and 600 °c is also quotted and analysed. in a...

INTRODUCTION There have been a number of generalizations of metric spaces. One such generalization is Menger space introduced in 1942 by Menger[9] who used distribution functions instead of nonnegative real numbers as values of the metric. This space was expanded rapidly with the pioneering works of Schweizer and Sklar [11, 12]. Modifying the idea of Kramosil and Michalek [7], George and Veeram...

We study subgroups of Z which possess group theoretic properties analogous to properties introduced by Menger (1924), Hurewicz (1925), Rothberger (1938), and Scheepers (1996). We obtain purely combinatorial characterizations of these properties, and combine them with other techniques to solve several questions of Babinkostova, Kočinac, and Scheepers. We also show that, while the Menger Conjectu...

We study subgroups of Z which possess group theoretic properties analogous to properties introduced by Menger (1924), Hurewicz (1925), Rothberger (1938), and Scheepers (1996). The studied properties were introduced independently by Kočinac and Okunev. We obtain purely combinatorial characterizations of these properties, and combine them with other techniques to solve several questions of Babink...

The main goal of this paper is to present an alternative, real variable proof of the T(1)-Theorem for the Cauchy Integral. We then prove that the estimate from below of analytic capacity in terms of total Menger curvature is a direct consequence of the T(1)-Theorem. An example shows that the L 1-BMO estimate for the Cauchy Integral does not follow from L 2 boundedness when the underlying measur...

in this research, a novel formulation of sponge cake was studied. instant tea powder (itp) with high ester-catechins content was used to replace 0, 7.5, 12.5, and 17.5% of flour to make sponge cakes, hereafter referred to as the control, itp1, itp2, and itp3, respectively. the microbiological analysis and lipid oxidation experiments were conducted and the odor, flavor, color, chewiness, and ove...

In this paper, the concept of compatibility of type (A) and weak compatibility in Menger space has been applied to prove a common fixed point theorem for six self maps which generalizes the result of Pant et. al. [8].