The classical Newtonian potentials, defined in terms of metrics, give rise to the basic family of kernels defining linear integral operators and posing the fundamental problems of linear harmonic analysis. When the binary character of a metric on a set is naturally generalized to the (k+1)-ary character of hypermetric on the set, we obtain families of kernels of k+1 variables leading to multilinear integral operators of order k or k-linear operators. In this paper we consider the problem of multilinear approximation to the multilinear identity through potentials built on hypermetrics in the general setting of spaces of homogeneous type.
This case series examines the histopathological, immunological, and therapeutic characteristics of 7 patients diagnosed with pemphigus herpetiformis (PH) at a tertiary hospital between 1989 and 2025. The most common clinical manifestation was pruritic annular lesions. Direct immunofluorescence was positive in all cases, whereas serological testing (enzyme-linked immunosorbent assay, indirect immunofluorescence, and immunoblotting) performed at 2 independent referral centers detected anti-desmoglein 1 antibodies in only 2 patients, with negative antigen-specific results in the remaining patients. An association between PH and malignancy was observed in 43% of cases, particularly with lung cancer, including the first reported case of PH associated with pancreatic cancer. These findings underscore the importance of recognizing this potential association to optimize patient management. Regarding treatment, conventional therapies such as corticosteroids and dapsone showed variable efficacy, whereas rituximab appeared less effective than in other pemphigus variants.
We prove that if a is a fixed uncountable cardinal and f = is a sequence of infinite cardinals where delta < w(3) and kappa(alpha )is an element of {w, lambda} for each ca < S in such a way that f(-1){w} is w(2)-closed in delta, then it is consistent that there is a scattered Boolean space whose cardinal sequence is f. (c) 2026 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Warm spells are becoming an increasingly important type of extreme event under climate change, particularly in mountain regions where they strongly influence snowmelt processes. This study analyses winter warm spells (WWS) in the Pyrenees over 1960-2024, focusing on their temporal evolution, associated impacts, and large-scale atmospheric drivers. Results show that WWS have become both more frequent and more intense, based on modelling S2M (1960-2024) and cross-validation with homogenized and reconstructed spatial interpolations of maximum air temperature in the Pyrenees CLIMPY (1981-2020), showing consistent positive WWS trends. Their occurrence has increased by approximately 0.4 days per decade since 1990, while maximum air temperature during events has risen significantly (0.24 degrees C per decade), with stronger trends in the southern Pyrenees. These events substantially enhance snowmelt, increasing mean daily melt from similar to 1.3 mm day(-1 )under average winter conditions to similar to 2.2 mm day(-1 )during WWS (similar to 65% increase). More than 50% of WWS are associated with circulation weather types characterized by anticyclonic southwesterly flow, which promotes subsidence and the advection of warm air masses. The increasing frequency of these circulation weather types during 1960-2024, together with thermodynamic warming under the same synoptic conditions, demonstrates that the observed intensification of WWS results from the combined influence of dynamic and thermodynamic processes. These results have important implications for winter snowmelt and for the environmental and socioeconomic sectors that depend on seasonal snow cover.
Anaerobic digestion of wastes and other organic substrates produces energy-rich biogas. Biochemical methane potential (BMP) is a substrate-specific metric that quantifies the maximum amount of methane that could be produced per unit of substrate. Although numerous guidelines describe BMP determination in detail and several automated commercial systems are available, many studies and peer-reviewed publications continue to report problematic and even obviously inaccurate results. This contribution introduces a comprehensive checklist for BMP testing that consolidates typical requirements, common challenges, potential pitfalls, and useful supporting resources to ensure BMP data are accurate, consistent, and of high quality.
