This work establishes a multivariable Wold-type decomposition for left-inverse commuting n-tuples of bounded linear operators, built on the hypothesis that each component admits a Wold-type decomposition. For pairs of operators, we obtain a complete analytic model: every left-inverse commuting analytic toral 2-isometric pair is unitarily equivalent to the pair of multiplication operators by co-ordinate functions (Mz1 , Mz2) acting on some epsilon-valued Dirichlet-type space D epsilon (& micro;1, & micro;2) associated with two finite positive operator-valued Borel measures & micro;1 and & micro;2 on the unit circle. An explicit functional model is further derived for the non-analytic case. (c) 2026 Published by Elsevier Inc.
Context The mountainous region accounts for around one-fourth of the terrestrial ecosystem, hosts 12% of the world's population, and contains more than half of the world's biodiversity hotspots. Most of the research relies on primary datasets to inform the assessment of relationships between ecosystem services in the Himalaya. This study quantified the gradient characteristics, spatiotemporal distributions, trade-offs, and synergies at multiple scales, and identified the driving factors for different ecosystem services in the Satluj River basin of the Himachal Himalaya from 1996 to 2023. The results showed significant regional heterogeneity of ecosystem services. The water yield value was 897.08 mm in 1996, 875.32 mm in 2011, and 886.22 mm in 2023. The total Carbon Storage (CS) value increased by 8.03 g C/m2 in 2011 and 17.98 g C/m2 in 2023 compared to 1996. The improvement in habitat quality value was 0.11 over the last three decades. Integrated value Ecosystem Services (ESs) have increased above 3000 m in the high-altitude Z3 and Z4 regions of the study area over time. The relationship between habitat quality and carbon storage showed a strong synergy. The leading drivers of ecosystem services in the Satluj River basin were precipitation (PRE), elevation, and Normalized Difference Vegetation Index(NDVI). Vegetation expansion had the greatest impact on the synergy between habitat quality and other ecosystem services at multiple scales. The highly significant synergy relationships among ESs were observed at altitudes of 1500–3000 m, PRE of 900–1050 mm, and NDVI values of 0.3–0.5. This study provides meaningful insights for decision-making of sustainable development and ecosystem management in the Himalaya.
Resistive Plate Chambers (RPCs) are widely employed in high-energy physics experiments due to their excellent timing resolution and high detection efficiency. Conventional RPC operation relies on freon-based gas mixtures having high Global Warming Potential (GWP), contributing significantly to greenhouse gas emissions. In this work, the performance of a single-gap glass RPC detector (30 cm & times; 30 cm) is studied using the standard gas mixture (C2H2F4 95%, i-C4H10 4.5%, SF6 0.5%) and eco-friendly alternatives based on CO2 and HFO gases. The detector was tested using cosmic muons, and its performance was evaluated in terms of efficiency, current-voltage characteristics, and timing resolution. The results show that eco-friendly gas mixtures achieve stable detector operation with high efficiency and only marginal degradation in timing performance, demonstrating their potential application to environmentally sustainable RPC operation.
For a graded ideal I in a graded ring, the deviation of I is defined as the difference between the minimal number of generators of I and its grade. In this article, we provide bigraded free resolutions of the symmetric algebras for specific classes of ideals of deviation two. Additionally, we study the regularity of powers of deviation two ideals generated by dsequences. In particular, we examine the powers of Huneke-Ulrich ideals and find bounds on their regularity. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Gaseous detectors are key components of particle detection in High Energy Physics experiments. The GEM is one such detector being used in HEP experiments due to its good timing and spatial resolution, and radiation tolerance. The optimal performance of gaseous detector depends on the choice of gases being used as ionising medium. Fluorine (F)-based gases, specially CF4 are commonly used in particle detectors as it leads to time resolution of a few nanoseconds(ns). But due to environmental concerns, F-based gases are no longer considered appropriate for detectors. As a result, there is need to find environment friendly alternatives while maintaining the performance of the detector. In this direction, we have studied the possibility of using HFO as a replacement for CF4 in Ar/CO2 based gas mixture in GEM detectors. We performed this study to evaluate the gain and timing resolution of the GEM detectors. The timing resolution of GEM detectors with only Ar/CO2 mixtures is around 10 ns. In our study, we evaluate the possibility of improving the timing resolution with the use of HFO.
