Rozansky–Witten Theory, Localised Then Tilted

The paper has two parts, in the first part, we apply the localisation technique to the Rozansky–Witten theory on compact hyperkähler targets. We do so via first reformulating the theory as some supersymmetric sigma-model. We obtain the exact formula for the partition function with Wilson loops on $$S^1\times \Sigma _g$$ S 1 × Σ g and the lens spaces, the results match with earlier computations using Feynman diagrams on K3. The second part is motivated by a very curious paper (Gukov in J Geom Phys 168, 104311, 2021), where the equivariant index formula for the dimension of the Hilbert space of the Rozansky–Witten theory is interpreted as a kind of Verlinde formula. In this interpretation, the fixed points of the target hyperkähler geometry correspond to certain ‘states’. We extend the formalism of part one to incorporate equivariance on the target geometry. For certain non-compact hyperkähler geometry, we can apply the tilting theory to the derived category of coherent sheaves, whose objects label the Wilson loops, allowing us to pick a basis for the latter. We can then compute the fusion products in this basis and we show that the objects that have diagonal fusion rules are intimately related to the fixed points of the geometry. Using these objects as basis to compute the dimension of the Hilbert space leads back to the Verlinde formula, thus answering the question that motivated the paper.

Thermal–hydraulic analysis of a solar air heater fitted with a wire-roughened absorber plate

This study is to evaluate heat transmission and friction in a rectangular solar air heater with a V-shaped wire rib roughness on the absorber plate that operates in fully formed turbulent flow. Additionally, studies are performed to generate prediction equations for the average friction factor, Stanton number, and efficiency index. The Reynolds number [Formula: see text]–[Formula: see text], angle of attack [Formula: see text]20[Formula: see text]–90[Formula: see text]), relative roughness pitch [Formula: see text]–[Formula: see text], relative roughness height [Formula: see text]–[Formula: see text], and the aspect ratio [Formula: see text]–[Formula: see text] was varied. The efficiency index [Formula: see text] is commonly employed as a thermo-hydraulic performance metric. It is computed as [Formula: see text]. The wire roughness and airflow parameters [Formula: see text] are optimized to maximize heat transfer while retaining minimal friction losses. On the basis of resemblance criteria, average Stanton numbers, average Nusselt numbers, and even average friction factors are derived. The results are compared to those obtained with a smooth absorber duct under similar airflow circumstances in order to assess the increase in heat transfer coefficient and friction factor. The [Formula: see text], and [Formula: see text] have a significant influence on thermo–hydraulic performance, according to these studies. With [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], the optimal configuration geometry for wire roughness and solar air heater duct is identified.

Diversity of echinoderms of class echinoidea and holothuroidea in waingapu old pier, east sumba regency

Echinoderms are in habitats in coastal waters because is a biota that can maintain the sustainability and the balance of the coral reef ecosystem. Human activity in utili zing Echinoderms, namely in Echinoidea and Holothuroidea can affect life his life. The purpose of this study was to determine the diversity of phyla Echinoderms class Echinoidea and Holothuroidea at the Harbor Waingapu Old Pier and its use as a medium Biology learning. The research method used is purposive sampling and analyzed using the approach quantitative descriptive with the Shannon diversity index formula Wiener. Echinoderm samples were calculated using the technique quadratic transects with a plot size of 2 x 2 meters are placed perpendicularly in the direction of 50 meters using a plot of 30 plot. Environmental factors measured are temperature, salinity, degrees acidity (pH) and levels of oxygen (DO). Measurements are taken at each observation station. The results showed 11 species Echinoderms are divided into 2 classes, namely Diadema setosum, Diadema savignyi, Tripneustes gratilla, Strongylocentrotus droebachiensis, Echinocardium flavescens, Clypeaster subdepressus, and Mespilia globulus from the class Echinoidea. Holothuria atra, Holothuria scraba, Euapta godeffroyi and Chiridota rigida from the class Holothuroidea. The diversity index obtained includes medium category with a value of H = 1.696.

Prediction of Road Network Traffic State Using the NARX Neural Network

To provide reliable traffic information and more convenient visual feedback to traffic managers and travelers, we proposed a prediction model that combines a neural network and a Macroscopic Fundamental Diagram (MFD) for predicting the traffic state of regional road networks over long periods. The method is broadly divided into the following steps. To obtain the current traffic state of the road network, the traffic state efficiency index formula proposed in this paper is used to derive it, and the MFD of the current state is drawn by using the classification of the design speed and free flow speed of the classified road. Then, based on the collected data from the monitoring stations and the weighting formula of the grade roads, the problem of insufficient measured data is solved. Meanwhile, the prediction performance of NARX, LSTM, and GRU is experimentally compared with traffic prediction, and it is found that NARX NN can predict long-term flow and the prediction performance is slightly better than both LSTM and GRU models. Afterward, the predicted data from the four stations were integrated based on the classified road weighting formula. Finally, according to the traffic state classification interval, the traffic state of the road network for the next day is obtained from the current MFD, the predicted traffic flow, and the corresponding speed. The results indicate that the combination of the NARX NN with the MFD is an effective attempt to predict and describe the long-term traffic state at the macroscopic level.

Maqashid sharia-based mosque empowerment index

Purpose This study aims to formulate an index formula for mosque empowerment based on Maqashid Syariah as a measuring tool for the level of mosque empowerment. Design/methodology/approach This study uses a qualitative and quantitative approach (mixed method). Data collection techniques are carried out by in-depth interviews with experts consisting of academics, practitioners, scholars and regulators. The data analysis technique uses the Analytical Network Process (ANP) with Super Decision 2.10 software to construct the index model structure. Findings The results indicate that the mosque has a multi-field role, including in the fields of worship, social, education, politics, economy and culture. This study produces an index of mosque empowerment based on Maqashid Syariah, composed of sic criteria, namely, elements of Maqashid Syariah; protect religion, soul, mind, lineage, property and environment. The weighting results of the criteria indicate that maintaining religion is the main criterion with a weighted value of 0.209. Each of these criteria consists of five indicators. Of all indicators, environmental safety is the top priority, with a weighted value of 0.056. Originality/value This study is the first comprehensive study that discusses the mosque empowerment index by weighting the ANP method to produce an index of mosque empowerment based on Maqashid Syariah.

An inventory of the biodiversity of Kare Caves for the development of ecotourism karst district Pamotan Rembang

The karst area is a unique ecosystem area and has a wealth of abundant potential resources. On the one hand, it is vulnerable to environmental exploitation to improve the economy. Kare Cave is a non-natural formed cave located in a karst topography. The beauty of Kare Cave has the potential to be developed into an ecotourism object. This study aims to determine the diversity of fauna and flora and identify ecotourism’s potential in Kare Cave, Pamotan District, Rembang Regency. This research used a quantitative descriptive study. Data were analyzed using the Shannon-Wienner Diversity Index formula. The diversity of flora and fauna in Kare Cave can be developed into ecotourism based on education and conservation with several efforts that must be developed, namely improving infrastructure and involvement of local communities. The fauna diversity index H’=1.35 and the flora diversity index H’=1.81, which means it is included in the medium category.

Analysis of biodiversity in the Pamotan Mudal spring area, Rembang Regency

The community’s need for clean water is increasing along with the increase in population. In fulfilling clean water, most will use surface water and underground water. Mudal spring is one of the springs located in Pamotan District, Rembang Regency, and has 80 liters/second discharge. The community uses the uses of springs to meet their needs, such as drinking water and irrigation. This study aims to determine the diversity of fauna and flora of the Mudal spring area and identify the use and conservation efforts of the springs by the community in Pamotan District, Rembang Regency. This research uses descriptive quantitative research. Data were analyzed using the Shannon-Wienner Diversity Index formula. There are ten types of fauna in the Mudal spring area with a diversity index H’=1.82 which is included in the medium category. As for flora, 17 species were found with a diversity index H’=1.83 which was included in the medium category. The conservation and utilization efforts carried out by the surrounding community for the Mudal spring are reasonable enough so that it is necessary to improve the concept of sustainable and environmentally sound management so that it remains by following with its function.

Credibility of Digital Comic Media in Audio Visual Form on Style Topic for Elementary School Students

Lack of teacher creativity in learning to develop instructional media makes learning less effective. Therefore, it is necessary to develop media that can make students enthusiastic about learning, such as digital comics. This research produces a product in the form of Digital Comic media on elementary school student style whose validity has been tested. The model used is the ADDIE model with the stages of Analyze, Design, Development, Implementation, Evaluation. In this study, digital comic media used as research subjects were 2 media expert lecturers, 2 material experts, 2 teachers. The method and instrument of data collection in this study is to use the rating scale method. To measure the validity of digital comic media using an instrument to assess the validity of digital comic media. The results of the data that have been obtained will be analyzed using the Aiken validity index formula for expert data and the mean formula for respondents' data in order to determine the validity of digital comic media. The results of the media validity on the Aiken validity index analysis, the assessment of the experts, got a score of 0.95 from the material experts with the criteria of "high validity", 0.95 from the media experts with the criteria of "high validity", while the analysis of the assessment scores of the respondents used the formula. The mean obtained an average of 4.57 from the practical response with the predicate "very good" and 4.50 from the student response with "very good". So, digital comic media is very suitable for use during the learning process, especially science learning.

Spectral computation of reactive bi-directional hydromagnetic non-Newtonian convection flow from a stretching upper parabolic surface in non-Darcyporous medium

This paper presents a mathematical model for bi-directional convection magnetohydrodynamic (MHD) tangent hyperbolic nanofluid flow from the upper horizontal subsurface of a stretching parabolic surface to a non-Darcian porous medium, as a simulation of nanocoating. Chemical reaction, activation energy and thermo solutal buoyancy effects are included. The Darcy–Brinkman–Forchheimer model is deployed which permits the analysis of inertial (second order) porous drag effects. The Buongiorno nanoscale model is deployed which includes Brownian motion and thermophoresis effects. The dimensionless, transformed, nonlinear, coupled ordinary differential equations are solved by implementing the spectral relaxation method (SRM). Validation with previous studies is included. The numerical influence of key parameters on transport characteristics is evaluated and visualized graphically. Velocity is elevated (and momentum boundary layer thickness is reduced) with increasing wall thickness parameter, permeability parameter, Forchheimer parameter, Weissenberg (rheological) parameter and modified Hartmann (magnetic body force) number. Velocity enhancement is also computed with increment in stretching rate parameter, rheological power-law index, thermal Grashof number, and species (solutal) Grashof number, and momentum boundary layer thickness diminishes. Temperature is suppressed with increasing stretching rate index and Prandtl number whereas it is substantially elevated with increasing Brownian motion and thermophoresis parameters. Velocity and temperature profiles are reduced adjacent to the parabolic surface with larger wall thickness parameter for stretching rate index [Formula: see text]1, whereas the reverse behavior is observed for stretching rate index [Formula: see text]1. Nanoparticle concentration magnitude is depleted with larger numeric of Lewis number and the Brownian motion parameter, whereas it is enhanced with greater values of the stretching index and thermophoresis parameter. The nanoparticle concentration magnitude is reduced with an increase in chemical reaction rate parameter whereas it is boosted with activation energy parameter. Skin friction, Nusselt number and Sherwood number are also computed. The study is relevant to electromagnetic nanomaterials coating processes with complex chemical reactions.

Testing an inflationary era in curvature–matter coupling gravity

In this paper, we investigate the cosmological inflation in the context of a minimal matter–geometry coupling, which is based on the [Formula: see text] gravity theory, where [Formula: see text] is a generic function of the curvature scalar [Formula: see text] and the trace [Formula: see text] of the energy–momentum tensor. Assuming that the slow-roll inflation conditions hold true in [Formula: see text] gravity, we obtain the various inflation-related observables such as the tensor-to-scalar ratio [Formula: see text], the scalar spectral index [Formula: see text], the running [Formula: see text] of the spectral index and the tensor spectral [Formula: see text] for two specific [Formula: see text] models from the Hubble slow-roll parameters. To observe the viability of these models, a numerical analysis of such parameters has been done. The results showed that, by using the various values of free parameters, it is possible to obtain a viable compatible with the observational data.