Fractional Loop Group and Twisted K-Theory

We study the structure of abelian extensions of the group $L_qG$ of $q$-differentiable loops (in the Sobolev sense), generalizing from the case of central extension of the smooth loop group. This is motivated by the aim of understanding the problems with current algebras in higher dimensions. Highest weight modules are constructed for the Lie algebra. The construction is extended to the current algebra of supersymmetric Wess-Zumino-Witten model. An application to the twisted K-theory on $G$ is discussed.Comment: Final version in Commun. Math. Phy

Bullseye dielectric cavities for photon collection from a surface-mounted quantum-light-emitter

Coupling light from a point source to a propagating mode is an important problem in nano-photonics and is essential for many applications in quantum optics. Circular "bullseye" cavities, consisting of concentric rings of alternating refractive index, are a promising technology that can achieve near-unity coupling into a first lens. Here we design a bullseye structure suitable for enhancing the emission from dye molecules, 2D materials and nano-diamonds positioned on the surface of these cavities. A periodic design of cavity, meeting the Bragg scattering condition, achieves a Purcell factor of 22.5 and collection efficiency of 80 %. We also tackle the more challenging task of designing a cavity for coupling to a low numerical aperture fibre in the near field. Using an iterative procedure, we show that apodized (non-periodic) rings can achieve a collection efficiency that exceeds the periodic Bragg cavity.Comment: 9 pages, 6 figure

Enhanced light collection from a gallium nitride color center using a near index-matched solid immersion lens

Among the wide-bandgap compound semiconductors, gallium nitride is the most widely available material due to its prevalence in the solid state lighting and high-speed/high-power electronics industries. It is now known that GaN is one of only a handful of materials to host color centers that emit quantum light at room temperature. In this paper, we report on a bright color center in a semi-polar gallium nitride substrate, emitting at room temperature in the near-infrared. We show that a hemispherical solid immersion lens, near index matched to the semiconductor, can be used to enhance the photon collection efficiency by a factor of $4.3\pm0.1$, whilst improving the lateral resolution by a factor equal to the refractive index of the lens

Palladium nanoparticles supported on fluorine-doped tin oxide as an efficient heterogeneous catalyst for Suzuki coupling and 4-nitrophenol reduction

Immobilization of palladium nanoparticles onto the fluorine-doped tin oxide (FTO) as support Pd/FTO, resulted in a highly active heterogeneous catalyst for Suzuki-Miyaura cross-coupling reactions and 4-nitrophenol reduction. The Pd/FTO catalyst has been synthesized by immobilization of palladium nanoparticles onto FTO via a simple impregnation method. ICP-MS analysis confirmed that there is 0.11 mmol/g of palladium was loaded successfully on FTO support. The crystallinity, morphologies, compositions and surface properties of Pd/FTO were fully characterized by various techniques. It was further examined for its catalytic activity and robustness in Suzuki coupling reaction with different aryl halides and solvents. The yields obtained from Suzuki coupling reactions were basically over 80%. The prepared catalyst was also tested on mild reaction such as reduction of 4-nitrophenol (4-NP) to 4-aminophenol (4-AP). Pd/FTO catalyst exhibited high catalytic activity towards 4-NP reduction with a rate constant of 1.776 min(-1) and turnover frequency (TOF) value of 29.1 hr(-1). The findings revealed that Pd/FTO also maintained its high stability for five consecutive runs in Suzuki reactions and 4-NP reductions. The catalyst showed excellent catalytic activities by using a small amount of Pd/FTO for the Suzuki coupling reaction and 4-NP reduction

Body appreciation around the world: Measurement invariance of the Body Appreciation Scale-2 (BAS-2) across 65 nations, 40 languages, gender identities, and age.

The Body Appreciation Scale-2 (BAS-2) is a widely used measure of a core facet of the positive body image construct. However, extant research concerning measurement invariance of the BAS-2 across a large number of nations remains limited. Here, we utilised the Body Image in Nature (BINS) dataset - with data collected between 2020 and 2022 - to assess measurement invariance of the BAS-2 across 65 nations, 40 languages, gender identities, and age groups. Multi-group confirmatory factor analysis indicated that full scalar invariance was upheld across all nations, languages, gender identities, and age groups, suggesting that the unidimensional BAS-2 model has widespread applicability. There were large differences across nations and languages in latent body appreciation, while differences across gender identities and age groups were negligible-to-small. Additionally, greater body appreciation was significantly associated with higher life satisfaction, being single (versus being married or in a committed relationship), and greater rurality (versus urbanicity). Across a subset of nations where nation-level data were available, greater body appreciation was also significantly associated with greater cultural distance from the United States and greater relative income inequality. These findings suggest that the BAS-2 likely captures a near-universal conceptualisation of the body appreciation construct, which should facilitate further cross-cultural research. [Abstract copyright: Copyright © 2023 The Authors. Published by Elsevier Ltd.. All rights reserved.

Body appreciation around the world: Measurement invariance of the Body Appreciation Scale-2 (BAS-2) across 65 nations, 40 languages, gender identities, and age

Abstract The Body Appreciation Scale-2 (BAS-2) is a widely used measure of a core facet of the positive body image construct. However, extant research concerning measurement invariance of the BAS-2 across a large number of nations remains limited. Here, we utilised the Body Image in Nature (BINS) dataset – with data collected between 2020 and 2022 – to assess measurement invariance of the BAS-2 across 65 nations, 40 languages, gender identities, and age groups. Multi-group confirmatory factor analysis indicated that full scalar invariance was upheld across all nations, languages, gender identities, and age groups, suggesting that the unidimensional BAS-2 model has widespread applicability. There were large differences across nations and languages in latent body appreciation, while differences across gender identities and age groups were negligible-to-small. Additionally, greater body appreciation was significantly associated with higher life satisfaction, being single (versus being married or in a committed relationship), and greater rurality (versus urbanicity). Across a subset of nations where nation-level data were available, greater body appreciation was also significantly associated with greater cultural distance from the United States and greater relative income inequality. These findings suggest that the BAS-2 likely captures a near-universal conceptualisation of the body appreciation construct, which should facilitate further cross-cultural research

Exposure and connectedness to natural environments: An examination of the measurement invariance of the Nature Exposure Scale (NES) and Connectedness to Nature Scale (CNS) across 65 nations, 40 languages, gender identities, and age groups

Detachment from nature is contributing to the environmental crisis and reversing this trend requires detailed monitoring and targeted interventions to reconnect people to nature. Most tools measuring nature exposure and attachment were developed in high-income countries and little is known about their robustness across national and linguistic groups. Therefore, we used data from the Body Image in Nature Survey to assess measurement invariance of the Nature Exposure Scale (NES) and the Connectedness to Nature Scale (CNS) across 65 nations, 40 languages, gender identities, and age groups (N = 56,968). While multi-group confirmatory factor analysis (MG-CFA) of the NES supported full scalar invariance across gender identities and age groups, only partial scalar invariance was supported across national and linguistic groups. MG-CFA of the CNS also supported full scalar invariance across gender identities and age groups, but only partial scalar invariance of a 7-item version of the CNS across national and linguistic groups. Nation-level associations between NES and CNS scores were negligible, likely reflecting a lack of conceptual clarity over what the NES is measuring. Individual-level associations between both measures and sociodemographic variables were weak. Findings suggest that the CNS-7 may be a useful tool to measure nature connectedness globally, but measures other than the NES may be needed to capture nature exposure cross-culturally

Body appreciation around the world: Measurement invariance of the Body Appreciation Scale-2 (BAS-2) across 65 nations, 40 languages, gender identities, and age

The Body Appreciation Scale-2 (BAS-2) is a widely used measure of a core facet of the positive body image construct. However, extant research concerning measurement invariance of the BAS-2 across a large number of nations remains limited. Here, we utilised the Body Image in Nature (BINS) dataset - with data collected between 2020 and 2022 - to assess measurement invariance of the BAS-2 across 65 nations, 40 languages, gender identities, and age groups. Multi-group confirmatory factor analysis indicated that full scalar invariance was upheld across all nations, languages, gender identities, and age groups, suggesting that the unidimensional BAS-2 model has widespread applicability. There were large differences across nations and languages in latent body appreciation, while differences across gender identities and age groups were negligible-to-small. Additionally, greater body appreciation was significantly associated with higher life satisfaction, being single (versus being married or in a committed relationship), and greater rurality (versus urbanicity). Across a subset of nations where nation-level data were available, greater body appreciation was also significantly associated with greater cultural distance from the United States and greater relative income inequality. These findings suggest that the BAS-2 likely captures a near-universal conceptualisation of the body appreciation construct, which should facilitate further cross-cultural research

Effects of the Base Substrate and Dietary supplementson Growth Indices Florida Oyster Mushroom (Pleurotus florida)

Introduction: Oystermush rooms contain a wide enzymatic system to catalyze lignocellu lose and naturally live in organs of plants that are protein-rich. Agricultural and industrial wastes contain organic cellulosic materials such as cereal straw, sawdust and leaves that are suitable substrate for growth of oyster mushrooms. Previous studies have shown that dietary supplements increase growth indices of oyster mushrooms. Materials and Methods: Spawn of Florida oyster mushrooms wereprovided experimentally on grains of wheat. The experiment was conducted in the laboratory of the Agricultural College of Mehr Shar, Islamic Azad University of Karaj, Iran in 2011. Two factors were considered in this study substrate (A) and dietary supplements(B). Sugarcane bag asse (A1) and wheat straw (A2) were shed into polyethylene bags after they were pasteurized by boiling vapor and spawning was conducted according to wet weight of straw bags which was 4 kg. Supplements of Nitrogen werecottonseed powder, 2%soya flour, and urea0.5% that were added to substrate according to dry weight of substrate (1334 gr). Mushrooms were transferred to the laboratory after cropping in order to measure dry and wet weight. They were packed and dried in the oven during 24-72 hours at 60-70ºC. In order to estimate the biological efficiency, the produced crop was divided by weight consumed substrate that was multiplied by 100. A completely randomized factorial statistical experiment according to completely randomized design with 16 treatments and three replications was conducted. MSTAT soft ware was used for statistical analysis and the Dunkan test was used for comparing mean data with probability of 5%.Finally figures were drown using Excel. Results and Discussion: In wheat straw substrate mushrooms were produced with high biological efficiency and yield, because compared to sugarcane bagasse, wheat straw needs a shorter period for fermentation, contains more nutrients, catalyzed faster than sugarcane bagasse soit provided mycelium with the nutrient amount of biological efficiency that increased byadding dietary supplements there for ethe yield was higher than control. Temperature of substrate increased by combining urea, cotton seed powder and soya flour nitrogen supplements, and that large amount of nitrogen were released into the environment and high temperature substrate. So expansion of mycelium decreased and mushrooms with low biological efficiency and low yield were produced. The highest biological efficiency (23.03 %) and the highest yield (4/921 gr) were obtained through wheat straw that fed by cotton seed powder + soya flour (A2B6).The lowest biological efficiency (10.48 %) and the lowest yield (419 gr) were from control treatment (A1). Frequency of nitrogen in cotton seed powder is one of the most important reasons of increasing biological efficiency and yield. Another efficiency biologic factor was used in cultivation of fungi was C/N ratio, since nitrogen is a necessary factor for the activity of ligninoletic enzyme that is produced by basidiomycets. Cultivated fungi on wheat straw were wetter than mushrooms cultivated on sugarcane bagasse, because wheat straw has 10-15%water and sugarcane bagasse has 9% moisture. Wheat straw with cotton seed + powder soya flour (A2B6) and control treatment (A1) had the highest moisture (92.26%). Byaddition of dietary supplements in the surface of enriched substrate, fruit body density had increased in control, so mushrooms were less exposed to the air flow, but the combination of nitrogen supplements, the arrival of more nitrogen andsubstrate heat increased and that the mushrooms had less humid. In wheat straw substrate more number of body fruits was obtained in comparison with sugarcane bagasse substrate..418 numbers of body fruits obtained from wheat straw by cotton seed powder + soya flour (A2B6) and 163 mushrooms were obtained from control treatment (A1). Absorbable chemical compounds in the medium were used faster and the number of mushrooms in wheat straw substrate with cotton seed powder and soya flour (A2B6) increased while combination of supplements and heat due to entrance of nitrogen caused death of mycelium and decreasing number of mushrooms. The results analysis of variance, substrate effect and mean compare supplement effect was significant at 1% on biological efficiency. Yield, moisture, number of body fruit, mean interaction effect of substrate and supplement was significant at 0.05on biological efficiency, yield and moisture but mean interaction effect of substrate and supplement on the number of body fruit was significant at 1%. Conclusion: Medium has a deep impact on growth indices of Florida oyster mushrooms in such a way that obtained mushrooms from rich mediums had higher growth indices than control. The impact of dietary supplements on growth indices is different and by adding an appropriate amount of dietary supplements to medium increases growth indices