In this paper, the generalized BMO martingale spaces are introduced as the dual spaces of martingale Hardy–Lorentz–Karamata spaces Hs p,q,b, which completes the very recent result [Quart. J. Math. 65 (2014), 985–1009] in the case 0 < p ≤ 1, 1 < q < ∞. Moreover, by duality we obtain a new John–Nirenberg theorem when the stochastic basis is regular.

In this note, we prove a generalization of the ‘strange formula’ of Freudenthal and de-Vries for compact homogeneous spaces with positive Euler characteristic. As a corollary, we obtain a new proof of the original formula. We also apply our results to computing a topological invariant used to study hyper-Kähler structures.

We describe the bifurcation diagrams of plane-to-plane map-germs of corank 2 up to Aecodimension 4, and draw some new pictures. Two applications are presented: First, we study the affine differential geometry of crosscaps in 3-space by means of analyzing singularities of projections of the singular surface to the plane. Secondly, we give some new examples of generic two-dimensional bifurcation…

We present a new approach to measuring crustal thickness and bulk properties from teleseismic data. In contrast to the traditional H − k stacking approach, which involves receiver-function deconvolution followed by stacking along expected arrival-time curves, we eliminate the deconvolution step and generate synthetic transfer functions predicting the relationship between the vertical and …

Hydraulically induced microseismicity is used to study high-frequency attenuation properties (6–72 Hz) in an enhanced geothermal system. Intrinsic and scattering attenuation are separated by jointly inverting seismogram envelopes for structural parameters, source and site effects. Modelling of synthetic envelopes is based on radiative transfer theory. To speed up inversion, an analytical solu…

The measure of non-compactness of operators between complex interpolation spaces is studied. An estimate of this measure, under the Calderón approximation condition, is proved. Examples of Banach couples satisfying the mentioned condition are provided. An estimate of the essential spectral radius of an operator under complex interpolation is also given.

In TESOL teacher mentoring, giving advice can be conceptualized as a continuum, ranging from directive to facilitative feedback. The goal, over time, is to lead toward the facilitative end of the continuum and specifically to catalytic interventions that encourage self-reflection and autonomous learning. This study begins by examining research on the mentor’s advicegiving role. Next, the expe…

Let X be an L1-predual, non-separable in general. We show that the intrinsic Baire classes of X can be identified with the spaces of odd Baire functions on the set ext BX∗ of the extreme points of the dual unit ball BX∗ in the case when ext BX∗ satisfies some topological assumptions. This generalizes results of Lindenstrauss andWulbert from [On the classification of the Banach…

We provide, in a wide range of the parameters, an estimate for the mean-value over sifted integers of certain arithmetic functions with Dirichlet series analytically close to 1/ζK(s), where K is a number field and ζK its Dedekind zeta function.

We develop a new method referred to as the AR-z spectrum for detecting harmonic signals with exponential decay/growth contained in a noisy time-series by extending the auto regressive (AR) method of Chao & Gilbert. The method consists of (i) ‘blindly’ forcing one 2nd-order AR fit to the signal content in the frequency domain for any chosen frequency whether or not there is truly a signal; (…