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We introduce real Loesungen as an analogue of real roots. For each mutation sequence of an arbitrary skew-symmetrizable matrix, we define a family of reflections along with associated vectors which are real Loesungen and a set of curves on a Riemann surface. The matrix consisting of these vectors is called L-matrix. We explain how the L-matrix naturally arises in connection with the C-matrix. Then we conjecture that the L-matrix depends (up to signs of row vectors) only on the seed, and that the curves can be drawn without self-intersections, providing a new combinatorial/geometric description of c-vectors.

Greenhouse gases released by agriculture account for 19% of global greenhouse gas emission. Moreover, the abuse of pesticides and fertilizers is a fundamental cause of soil and water pollution. Finding sustainable countermeasures for these problems requires completely new approaches and the integration of knowledge. Precision agriculture (PA) is a technology that reduces environmental pollution with minimal input (e.g., fertilizer, herbicides, and pesticides) and maximize the production of high-quality crops by monitoring the conditions and environment of farmland and crops. However, the lack of data—a key technology for realizing PA—remains a major obstacle to the large-scale adoption of PA. Herein, we discuss important research issues, such as data managements and analysis for accurate decision-making, and specific data acquisition strategies. Moreover, we systematically review and discuss electrochemical sensors, including sensors that monitor the plant, soil, and environmental conditions that directly affect plant growth.

We introduce the Korea Institute of Science and Technology-Novel Materials Discovery (KISTNOMAD) platform, a materials data repository. We describe its functionality and novel features from an academic viewpoint. It is a data repository designed for computational material science, especially focusing on managing and sharing the results of molecular dynamics simulation results as well as quantum mechanical computations. It consists of three main components: a database, file storage, and web-based front end. The database hosts material properties, which are extracted from the computational results. The front end has a graphical user interface and an open application programming interface, which allow researchers to interact with the system more easily. KIST-NOMAD’s panel displays the searched results on a well-organized and research-oriented web page. All the open access data and files are available for downloading in comma-separated value format as well as zipped archives. This automated extraction function was developed by utilizing database parsers and JSON scripts. KISTNOMAD also has an efficient option to download simulation and computation results on a large-scale. All of the above functions are designed to satisfy academic and research demands, and make highthroughput screening available, while incorporating machine learning for computational material engineering. We finally stress that the repository platform is user-driven and user-friendly. It is clearly designed to follow the modern big-data architecture and re-use principles for scientific data, such as being findable, accessible, and interoperable.

We extend the usual notion of fully commutative elements from the finite Coxeter groups to the complex reflection groups. We decompose the sets of fully commutative elements into natural subsets according to their combinatorial properties, and investigate the structure of these decompositions. As a consequence, we enumerate and describe the form of these elements for the complex reflection groups.

The application of electrocatalysts with high activity to a practical water electrolysis cell is a crucial challenge for the production of pure hydrogen and commercialization of the water electrolyzer. Herein, a nanosized Cu0.5Co2.5O4 catalyst synthesized by co-precipitation by adjusting pH is applied to the anion exchange membrane water electrolysis (AEMWE) cell as an anode, which is demonstrated to have higher efficiency and stability than noble metal-based anodes. The composition (Cu/Co) and morphology of Cu0.5Co2.5O4 change as the pH increases and then nanoparticles are formed at pH 11, where oxygen vacancies are formed by the etching of Cu. In the density functional theory study, the electronic structure of Co modified by Cu in the Co3O4 lattice leads to an optimal adsorption strength, resulting in a free energy diagram in which the potential of Cu0.5Co2.5O4 (1.756 V vs. reversible hydrogen electrode, RHE) is more thermodynamically favorable than that of Co3O4 (1.951 V vs. RHE). The Cu0.5Co2.5O4 catalyst has a recorded overpotential of 285 mV at 10 mA cm−2 in 1 M KOH. Furthermore, the AEMWE cell using Cu0.5Co2.5O4 as an anode exhibited a current density of 1.3 A cm−2 at 1.8 V, which is the highest performance among the reported papers and maintains around 80% energy conversion efficiency for 100 hours.

We apply some of the latest techniques from machine-learning to the arithmetic of hyperelliptic curves. More precisely we show that, with impressive accuracy and confidence (between 99 and 100 percent precision), and in very short time (matter of seconds on an ordinary laptop), a Bayesian classifier can distinguish between Sato-Tate groups given a small number of Euler factors for the L-function. Our observations are in keeping with the Sato-Tate conjecture for curves of low genus. For elliptic curves, this amounts to distinguishing generic curves (with Sato-Tate group SU(2)) from those with complex multiplication. In genus 2, a principal component analysis is observed to separate the generic Sato-Tate group USp(4) from the non-generic groups. Furthermore in this case, for which there are many more non-generic possibilities than in the case of elliptic curves, we demonstrate an accurate characterisation of several Sato-Tate groups with the same identity component. Throughout, our observations are verified using known results from the literature and the data available in the LMFDB. The results in this paper suggest that a machine can be trained to learn the Sato-Tate distributions and may be able to classify curves much more efficiently than the methods available in the literature., Comment: 21 pages, 1 table, 5 figures

We study the critical energy dissipation in an atomic superfluid gas with two symmetric spin components by an oscillating magnetic obstacle. Above a certain critical oscillation frequency, spin-wave excitations are generated by the magnetic obstacle, demonstrating the spin superfluid behavior of the system. When the obstacle is strong enough to cause density perturbations via local saturation of spin polarization, half-quantum vortices (HQVs) are created for higher oscillation frequencies, which reveals the characteristic evolution of critical dissipative dynamics from spin-wave emission to HQV shedding. Critical HQV shedding is further investigated using a pulsed linear motion of the obstacle, and we identify two critical velocities to create HQVs with different core magnetization., Comment: 8 pages, 7 figures

In this paper we study special bases of certain spaces of half-integral weight weakly holomorphic modular forms. We establish a criterion for the integrality of Fourier coefficients of such bases. By using recursive relations between Hecke operators, we derive relations of Fourier coefficients of each basis element and obtain congruences of the Fourier coefficients, which extend known congruences for traces of singular moduli., 19 pages

Two configurations of single-walled carbon nanotube-based chemi-capacitive gas sensors were fabricated, i.e., horizontal and vertical. Further, their sensing properties for hexane and ammonia (NH3) vapor were characterized and compared with chemi-resistive-type sensing properties. Upon exposure to hexane and NH3 vapor, both capacitance and resistance varied as the analyte concentration increased. The sensing sensitivity measured along the horizontal direction increased with the device resistance. However, the capacitive sensing response along the vertical direction was independent of the number and fraction of semi-conductive single-walled carbon nanotubes. Furthermore, the vertical chemi-capacitive sensing response was dependent on the dipole moment of analytes.

A three-dimensional thermoelectric (TE) nanocomposite based on functionalized single-walled carbon nanotubes (f-SWCNTs), tellurium nanowires (Te NWs), and polymethyl methacrylate (PMMA) microbeads was fabricated by a hot compaction via solvent casting. We chose a minimum content of f-SWCNTs of 1 wt% for fabricating the nanocomposite based on percolation threshold. The nanocomposite containing 2 wt% f-SWCNTs and 48 wt% Te NWs exhibited an electrical conductivity of 0.93 S/cm, a Seebeck coefficient of 303 μV/K, a thermal conductivity of 0.23 W/mK and a figure-of-merit (ZT) of 0.01 at RT. The electrical conductivity of the nanocomposite were higher than that of the Te NW/PMMA nanocomposite. In contrast, the thermal conductivity value showed a trend opposite to that of the electrical conductivity. This is because the f-SWCNTs formed bridges between the Te NWs into the nanocomposite, resulting in heterostructured interfaces. We believe that this-type nanocomposite can be widely used for thermoelectric generators at low temperature.

The excitonic behavior in two-dimensional (2D) heterostructures of transition metal dichalcogenide atomic layers has attracted much attention. Here, we report, for the first time, the ultrafast beh...

A Cu–Co–P electrocatalyst for hydrogen evolution reaction (HER) was designed with a dendritic and porous foam structure. Fabricated by one-step electrodeposition with binary alloy on a hydrogen bub...

Given any Coxeter group, we define rigid reflections and rigid roots using non-self-intersecting curves on a Riemann surface with labeled curves. When the Coxeter group arises from an acyclic quiver, they are related to the rigid representations of the quiver. For a family of rank 3 Coxeter groups, we show that there is a surjective map from the set of reduced positive roots of a rank 2 Kac-Moody algebra onto the set of rigid reflections. We conjecture that this map is bijective.