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Improved temperature dependence of rate coefficients for rotational state-to-state transitions in H 2 O + H 2 O collisions

Aims. We present an improved database of temperature-dependent rate coefficients for rotational state-to-state transitions in H 2 O + H 2 O collisions. The database includes 231 transitions between the lower para-states of H 2 O and 210 transitions between its lower ortho-states (up toj= 7) and can be employed in cometary and planetary applications up to the temperature of 1000 K. Methods. We developed and applied a new general method that allows the generation of rate coefficients for excitation and quenching processes that automatically satisfy the principle of microscopic reversibility and also helps to cover the range of low collision energies by interpolation of cross sections between the process threshold and the computed data points. Results. We find that in the range of intermediate temperatures, 150

Astronomy & Astrophysics↗

Dispatching Grid-Forming Inverters in Grid-Connected and Islanded Mode

This paper explores the dispatchability of grid-forming (GFM) inverters in grid-connected and islanded mode. GFM inverters usually use droop control to automatically share power with other GFM sources (inverters and synchronous generators) and follow the change in the load demand; however, they can be dispatched like their grid-following (GFL) counterparts to output the target active and reactive power. This will help grid operators better manage their inverter-based resources (IBRs) to improve operation efficiency and reliability; therefore, this paper proposes an innovative concept of dispatching GFM sources (inverters and synchronous generators) to output the target power in both grid-connected and islanded mode by adjusting their droop intercepts. The fundamental principle is that the GFM inverter's active and reactive power is dictated by its frequency and voltage, and thus dispatching the active and reactve power of a GFM inverter can be achieved through dispatching its frequency and voltage. Moreover, the concept distinguishes the dispatch rules for grid-connected and islanded mode. Finally, the concept is validated with an example microgrid system with two GFM inverters, one diesel generator, one GFL inverter, and the load in both grid-connected and islanded mode. This pioneering work results in practical guidance for the development of energy management systems for future electric grids with GFM and GFL inverters.

dispatching↗

Autonomous Voltage Response for Distributed Energy Resources

An implementation of stable droop voltage response for distributed energy resources (DER) is described. The key point is to use a new “autonomously adjusting reference voltage” as described in IEEE Standard 1547-2018. Examples include battery voltage response, a photovoltaic inverter at the end of a long secondary circuit, and 18 photovoltaic inverters on a distribution lateral. Default inverter settings are proposed for DER that would mitigate voltage fluctuations, with or without communications.

Automatic voltage control, distributed power gener↗

User’s Manual for RESRAD-RDD&IND Code Version 2: Vol. 2—User’s Guide for RESRAD-RDD&IND Code

Version 2.0 of the RESRAD-RDD&IND computer code is designed to support the implementation of protective action guides (PAGs) after a nuclear emergency incident including a radiological dispersal device (RDD) and/or an improvised nuclear device (IND) incident (EPA 2017). Eight different group types, addressing various decisions, are available for selection. The RESRAD-RDD&IND code calculates radiological doses, stay times, etc., for the selected group that the user wishes to focus on. (That is, the results for all the groups are not calculated simultaneously, and the input for those other groups do not matter, although some parameter values are shared between groups.) Version 2.0 has a user-friendly interface so that the RESRAD-RDD&IND code can be used with minimal training. For example, the user can select the major characteristics of the problem-event type, source term, and decision type from the left side of the interface and then calculate the results with the default assumptions for the exposure scenarios. More in-depth analysis would include specifying site-specific exposure scenario characteristics in the right side of the interface. The procedures for data entry and results viewing are self-explanatory. This is because common window maneuvering features and text instructions were incorporated in the interface design. General and context-specific help are available to aid users entering parameter values, as well. The RESRAD-RDD&IND computer code gives the user the option to select either an RDD or IND incident for analysis. For an RDD event analysis, 11 radionuclides (Am-241, Cf-252, Cm-244, Co-60, Cs-137, Ir-192, Po-210, Pu-238, Pu-239, Ra-226, and Sr-90) are included. These 11 radionuclides are the radionuclides most likely used for an RDD. More than 90 radionuclides can be selected for an IND event analysis. Initial default concentrations are provided for 44 radionuclides for a uranium-fueled IND event. These 44 radionuclides are those that would contribute significantly to the radiation dose associated with a uranium-fueled bomb detonation. The radionuclides generated from ingrowth of these 44 initial radionuclides are also automatically included in the analysis. Pu-239, Cs-134m, Ru-105, and Rb-89 and their progeny can be selected for analysis if they are detected and their concentrations are determined. This user’s guide, which is Volume 2 of the User’s Manual for RESRAD-RDD&IND Code Version 2, provides instructions to users on how to install the RESRAD-RDD&IND code, navigate the interface, and use the various features, including those discussed above, to set up an analysis and view/print the results in text outputs. Volume 1 of the User’s Manual for RESRAD-RDD&IND Code Version 2 (Yu et al. 2026), which contains descriptions of the methodology and theoretical basis for dose modeling and the mathematical equations implemented in the code, can be accessed and viewed through the Help menu in the code or can be downloaded from the RESRAD website (https://resrad.evs.anl.gov).

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Dispatching Grid-Forming Inverters in Grid-Connected and Islanded Mode: Preprint

This paper explores the dispatch-ability of grid-forming (GFM) inverters in grid-connected and islanded mode. Grid-forming (GFM) inverters usually use droop control to automatically share power with other GFM sources (inverters and synchronous generator (SG)) and follow the change of the load demand. However, they can be dispatched like their grid-following (GFL) counterparts to output the target active and reactive power. This will help the grid operator better manage their inverter-based resources (IBRs) for improved operation efficiency and reliability. Therefore, this paper proposes an innovative concept of dispatching GFM sources (inverters and SG) to output the target power for both grid-connected and islanded mode by adjusting their droop intercepts. The fundamental principle of doing so is that the GFM inverter's active and reactive power is dictated by its frequency and voltage, thus, dispatching active and reactve power of a GFM inverter can be achieved through dispatching its frequency and voltage. Moreover, the concept distinguishes the dispatch rules for grid-connected and islanded mode. Finally, the concept is validated with an example microgrid system with two GFM inverters, one diesel generator, one grid-following inverter and loads in both grid-connected and islanded mode. This pioneering work results in a practical guidance for power system energy management system (EMS) development to control a future grid with GFM and GFL inverters.

droop control↗

Model America - data and models of every U.S. building

The 5-year goal of the 'Model America' concept was to generate a model of every building in the United States. This data repository delivers on that goal. Oak Ridge National Laboratory (ORNL) has developed the Automatic Building Energy Modeling (AutoBEM) software suite to process multiple types of data, extract building-specific descriptors, generate building energy models, and simulate them on High Performance Computing (HPC) resources. For more information, see AutoBEM-related publications (bit.ly/AutoBEM). There were 125,714,640 buildings detected in the United States and this dataset contains 122,930,327 (97.8%) buildings which resulted in a successful simulation. Future, annual updates have been proposed that may include additional buildings, data improvements, or other algorithmic enhancements. This dataset of 122.9 million buildings includes: Models (state_county.zip) - OpenStudio (v3.1.0) and EnergyPlus (v9.4) building energy models. Please note that the download requires the free Globus Connect Personal (https://www.globus.org/globus-connect-personal); Each model has approximately 3,000 building input descriptors that can be extracted. Please see the EnergyPlus(v9.4) 2,784-page Input/Output Reference Guide (https://energyplus.net/sites/all/modules/custom/nrel_custom/pdfs/pdfs_v9.4.0/InputOutputReference.pdf) for everything that can be retrieved or simulated from these models. These models were derived from the following metadata, which is not included in this dataset: 1. ID - unique building ID 2. County - county name 3. State - state name 4. CZ - ASHRAE Climate Zone designation 5. Clim_Zone - text label of climate zone 6. est_year - estimated year of construction 7. est_commercial - estimated building type (0=residential, 1=commercial) 8. Centroid - building center location in latitude/longitude (from Footprint2D) 9. Footprint2D - building polygon of 2D footprint (lat1/lon1_lat2/lon2_...) 10. Height - building height (meters) 11. Area2D - footprint area (ft2) 12. BuildingType - DOE prototype building designation (IECC=residential) as implemented by OpenStudio-standards 13. WWR_surfaces - percent of each facade (pair of points from Footprint2D) covered by fenestration/windows (average 14.5% for residential, 40% for commercial buildings) 14. NumFloors - number of floors (above-grade) 15. Area - estimate of total conditioned floor area (ft2) 16. Standard - building vintage. These models are made free and openly available in hopes of stimulating any simulation-informed use case. Data is provided as-is with no warranties, express or implied, regarding fitness for a particular purpose. We wish to thank our sponsors which include Oak Ridge National Laboratory (ORNL) Laboratory Directed Research and Development (LDRD), U.S. Dept. of Energy's (DOE) Building Technologies Office (BTO), Office of Electricity (OE), Biological and Environmental Research (BER), and National Nuclear Security Administration (NNSA). This research used resources of the Argonne Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC02-06CH11357. Please cite as: New, Joshua R., Adams, Mark, Bass, Brett, Berres, Anne, and Clinton, Nicholas (2021). 'Model America - data and models of every U.S. building. [Data set].' Constellation, doi.ccs.ornl.gov/ui/doi/339, April 14, 2021

24 POWER TRANSMISSION AND DISTRIBUTION↗

Optimization of the moderators in the STS preliminary design

This report details the results for an optimization of the dimensions of the moderators in the preliminary design of the Spallation Neutron Source Second Target Station (STS). This study uses the optimization algorithms of Dakota and an unstructured mesh model for the moderators in MCNP. More details on the unstructured mesh model and the automated mesh generation can be found in [3]. Parallel to this effort, the same moderator geometries have been optimized using a constructive solid geometry (CSG) MCNP model. More details on this model and its results can be found in [4]. Three optimal designs are selected for each moderator: one that is optimized for maximum peak brightness, one for maximum time-integrated brightness, and one for a combination of peak and time-integrated brightness. The backbone of the optimization work flow is provided by Dakota. For each set of design parameters requested by Dakota, a new solid geometry is automatically built in Creo and SpaceClaim, and subsequently exported to Attila4MC to generate an unstructured mesh geometry for MCNP. After the MCNP calculation is finished, the objective function (e.g., brightness metric) is returned to Dakota. After the new design has been evaluated, a result-file is written, and Dakota proposes the next set of design parameters to be evaluated. The loop continues until a specified convergence criterion has been met. The design parameters of the cylindrical (upper) moderator include the hydrogen radius, the premoderator thickness (top, bottom, radial), the beryllium radius and the horizontal position of the moderator. The crucial design choice is the hydrogen radius. A radius of 62 mm is shown to provide the maximum time-integrated brightness. The maximum peak brightness occurs with a radius of 40 mm. A combined (middle) design, which balances peak and time-integrated brightnesses, is obtained with a hydrogen radius of 50 mm. The premoderator thicknesses and the beryllium radius are slightly larger in the design optimized for time-integrated brightness than in the design optimized for peak brightness. The sensitivity to these two parameters is relatively small close to the optimal configurations. The hydrogen vessel and vacuum vessel wall thicknesses are dependent on the radius of the liquid hydrogen due to structural integrity requirements. The increased wall thicknesses for larger vessels significantly penalize the time-integrated brightness, with the maximum obtainable value reduced by more than 10% relative to earlier studies which used fixed vessel wall thicknesses. The impact of the variable wall thicknesses is much less for the peak brightness and combined brightness designs. The design parameters of the tube (lower) moderator selected for the optimization are the tube length, the annular premoderator thickness, the beryllium radius and the horizontal position of the moderator. The tube length is the crucial parameter and is chosen large (210 mm) and small (125 mm) in the designs optimized for time-integrated and peak brightness respectively. A combined optimal design has a tube length of 170 mm. The premoderator thickness and the beryllium radius are chosen larger in the design optimized for time-integrated brightness.

42 ENGINEERING↗

Power Converter Circuit Design Automation using Parallel Monte Carlo Tree Search

The tidal waves of modern electronic/electrical devices have led to increasing demands for ubiquitous application-specific power converters. A conventional manual design procedure of such power converters is computation- and labor-intensive, which involves selecting and connecting component devices, tuning component-wise parameters and control schemes, and iteratively evaluating and optimizing the design. To automate and speed up this design process, we propose an automatic framework that designs custom power converters from design specifications using Monte Carlo Tree Search. Specifically, the framework embraces the upper-confidence-bound-tree (UCT), a variant of Monte Carlo Tree Search, to automate topology space exploration with circuit design specification-encoded reward signals. Moreover, our UCT-based approach can exploit small offline data via the specially designed default policy and can run in parallel to accelerate topology space exploration. Further, it utilizes a hybrid circuit evaluation strategy to substantially reduce design evaluation costs. Empirically, we demonstrated that our framework could generate energy-efficient circuit topologies for various target voltage conversion ratios. Compared to existing automatic topology optimization strategies, the proposed method is much more computationally efficient --- the sequential version can generate topologies with the same quality while being up to 67% faster. Here, the parallelization schemes can further achieve high speedups compared to the sequential version.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Hierarchical Conditioning of Diffusion Models Using Tree-of-Life for Studying Species Evolution

A central problem in biology is to understand how organisms evolve and adapt to their environment by acquiring variations in the observable characteristics or traits of species across the tree of life. With the growing availability of large-scale image repositories in biology and recent advances in generative modeling, there is an opportunity to accelerate the discovery of evolutionary traits automatically from images. Toward this goal, we introduce Phylo-Diffusion, a novel framework for conditioning diffusion models with phylogenetic knowledge represented in the form of HIERarchical Embeddings (HIER-Embeds). We also propose two new experiments for perturbing the embedding space of Phylo-Diffusion: trait masking and trait swapping, inspired by counterpart experiments of gene knockout and gene editing/swapping. Our work represents a novel methodological advance in generative modeling to structure the embedding space of diffusion models using tree-based knowledge. Our work also opens a new chapter of research in evolutionary biology by using generative models to visualize evolutionary changes directly from images. We empirically demonstrate the usefulness of Phylo-Diffusion in capturing meaningful trait variations for fishes and birds, revealing novel insights about the biological mechanisms of their evolution. (Model and code can be found at imageomics.github.io/phylo-diffusion)

Khurana, Mridul↗

Microkinetic Modeling of the Transient CO 2 Methanation with DFT–Based Uncertainties in a Berty Reactor

The transient operation of methanation reactors can become desirable when coupled with fluctuating renewable energies in Power-to-Gas scenarios, which requires suitable kinetic approaches that can describe the transient catalytic phenomena. A combined experimental and theoretical investigation of the transient CO 2 methanation is conducted using concentration forcing to derive a suitable microkinetic model. Methanation experiments are performed with a Ni/SiO 2 catalyst in a Berty-type reactor at industrially relevant conditions. The microkinetics are based on previous work and were automatically constructed for the Ni(111) facet using the Reaction Mechanism Generator. A feasible set of energetic parameters of the microkinetic models was identified in a theory-constrained optimization procedure within the DFT uncertainty space that can accurately reproduce the experimental results on a first-principles basis. The microkinetic model unravels that the formation of H 2 O* and CH 3 * control the activity and selectivity of Ni(111) under the investigated conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Attosecond x-ray free-electron lasers utilizing an optical undulator in a self-selection regime

Accelerator-based x-ray free-electron lasers (XFELs) are the latest addition to the revolutionary tools of discovery for the 21st century. The two major components of an XFEL are an accelerator-produced electron beam and a magnetic undulator, which tend to be kilometer-scale long and expensive. A proof-of-principle demonstration of free-electron lasing at 27 nm using beams from compact laser wakefield accelerators was shown recently by using a magnetic undulator. However, scaling these concepts to x-ray wavelengths is far from straightforward as the requirements on the beam quality and jitters become much more stringent. Here, we present an ultracompact scheme to produce tens of attosecond x-ray pulses with several GW peak power utilizing a novel aspect of the FEL instability using a highly chirped, prebunched, and ultrabright tens of MeV electron beam from a plasma-based accelerator interacting with an optical undulator. The FEL resonant relation between the prebunched period and the energy selects resonant electrons automatically from the highly chirped beam which leads to a stable generation of attosecond x-ray pulses. Furthermore, two-color attosecond pulses with subfemtosecond separation can be produced by adjusting the energy distribution of the electron beam so that multiple FEL resonances occur at different locations within the beam. Such a tunable coherent attosecond x-ray sources may open up a new area of attosecond science enabled by x-ray attosecond pump/probe techniques. Published by the American Physical Society 2024

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Model America: Data and Models for every U.S. Building

The 5-year goal of the “Model America” concept was to generate a model of every building in the United States. This data repository delivers on that goal with "Model America v1". Oak Ridge National Laboratory (ORNL) has developed the Automatic Building Energy Modeling (AutoBEM) software suite to process multiple types of data, extract building-specific descriptors, generate building energy models, and simulate them on High Performance Computing (HPC) resources. For more information, see AutoBEM-related publications (bit.ly/AutoBEM). There were 125,715,609 buildings detected in the United States. Of this number, 122,146,671 (97.2%) buildings resulted in a successful generation and simulation of a building energy model. This dataset includes the full 125 million buildings. Future updates may include additional buildings, data improvements, or other algorithmic model enhancements in "Model America v2". This dataset contains OSM and IDF zip files for every U.S. county. Each zip file contains the generated buildings from that county. The .csv input data contains the following data fields: 1. ID - the Unique Building Identifier (UBID), generated using the Pacific Northwest National Laboratory (PNNL) BuildingID framework 2. Centroid - building center location in latitude/longitude (from Footprint2D) 3. Footprint2D - building polygon of 2D footprint (lat1/lon1_lat2/lon2_...) 4. State_abbr - state name 5. Area - estimate of total conditioned floor area (ft2) 6. Area2D - footprint area (ft2) 7. Height - building height (ft) 8. NumFloors - number of floors (above-grade) 9. WWR_surfaces - percent of each facade (pair of points from Footprint2D) covered by fenestration/windows (average 14.5% for residential, 40% for commercial buildings) 10. CZ - ASHRAE Climate Zone designation 11. BuildingType - DOE prototype building designation (IECC=residential) as implemented by OpenStudio-standards 12. Standard - building vintage This data is made free and openly available in hopes of stimulating any simulation-informed use case. Data is provided as-is with no warranties, express or implied, regarding fitness for a particular purpose. We wish to thank our sponsors which include Oak Ridge National Laboratory (ORNL) Laboratory Directed Research and Development (LDRD), U.S. Dept. of Energy’s (DOE) Building Technologies Office (BTO), Office of Electricity (OE), Biological and Environmental Research (BER), and National Nuclear Security Administration (NNSA). Update (September 23, 2025): We corrected the ID field in all state-level.csv input files to ensure one-to-one consistency with the corresponding .osm and .idf output files. The schema and file structure are unchanged; only the values in the ID column were modified. No files were added or removed, and the .zip bundles (containing .osm / .idf) are unchanged. The corrected .csv inputs were re-extracted in March 2025 from the original data generated ~ 2021 (Theta supercomputer runs), and published here to align input IDs with model outputs. Update (September 6, 2026): The Model America dataset was updated to replace the previous building ID field with the Unique Building Identifier (UBID), using the Pacific Northwest National Laboratory (PNNL) BuildingID framework. UBIDs provide standardized, location-based identifiers for individual building footprints and improve interoperability with other building and geospatial datasets. The data files containing the previous building identifiers were updated to include UBIDs. This update standardizes building identification; the underlying Model America building characteristics and energy simulation results were not recomputed as part of this update.

54 ENVIRONMENTAL SCIENCES↗

MSTor 2023 : A new version of the computer code for multistructural torsional anharmonicity, now with automatic torsional identification using redundant internal coordinates

The MSTor program is a computer program for calculating partition functions and thermodynamic functions of complex gas-phase molecules with multiple torsions; the multi-structural approximation with torsional anharmonicity (MS-T) can be used based on either a coupled torsional potential or an uncoupled torsional potential. The program can also carry out calculations in the multiple-structure local harmonic (MS-LH) approximation or multi-structural local quasiharmonic (MS-LQ) approximation or by the dual-level MS-T method. Furthermore, the program package includes eight utility codes that can be used as stand-alone programs to help the user to generate the input files for the code or to generate comparison results. The 2023 version of MSTor includes a new capability, namely automatic identification of torsional modes with redundant internal coordinates.

97 MATHEMATICS AND COMPUTING↗

Massive all-atom analysis of 2D materials with quantum properties (Final report)

Improvements in microscopy have enabled the acquisition of data at a scale that is difficult to process manually, making automated machine learning approaches to analyzing experimental images essential. In this project, we developed and applied machine learning (ML) workflows for atomic resolution scanning transmission electron microscopy (STEM) images. This development included improving both methodology as well as generating user-friendly codes. We developed machine learning architectures which, after training, automatically identify the location and types of defects throughout a material. We used these data to produce class-averaged images of 2D atomic coordinates with up to 0.3 pm precision, uncovering the structure and oscillations of long-range strain fields around point defects in WSe 2-2x Te 2x . We also resolved a long-standing problem in this field in the training of ML models, a lack of labeled experimental data, by developing a cycle-GAN that transformed simulated-generated labeled data into labeled data indistinguishable from experiment and therefore suitable for training. This removed the remaining parts of the ML data processing workflow where human intervention was still critical and therefore a bottleneck to working at scale. Codes have been developed and released for this full machine learning workflow. ML approaches to partially automate STEM acquisition were also developed. Finally we applied ML and other advanced data processing methods to several materials science problems in two-dimensional materials, including studying the evolution of hyperuniformity with defect concentration in WSe2, understanding phase transformations in transition metal dichalcogenides during in-situ heating in the STEM, and exploring how 2D interfaces transform from twisted into aligned structures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Robotic Assembly of SRF Cavity Pair

Superconducting Radio Frequency (SRF) cavities for particle accelerators require tight tolerances, ultrahigh vacuum, and strict cleanliness during assembly. As in the semiconductor industry, defects such as particles and residues are deleterious to performance, possibly rendering a cavity unfit for use. This problem is addressed primarily through cleanroom assembly during sensitive steps and rigorous chemical processing to prevent and remove such defects. Human workers are often the largest source of contamination, even with proper gowning and practices. The semiconductor industry has long integrated robots in cleanroom operation, but this has not occurred for SRF cavity production; SRF cavities, unlike wafers, are complex shapes, require more hands-on mechanical assembly, and are low-volume production items. At Jefferson Laboratory, a co-operative robot (cobot) has been setup to overcome these problems. Cobots are safe for use alongside human workers and can integrate new tools such as a 3D camera part detection and gripper for item manipulation. Therefore, cobots represent a promising avenue for reducing particulate generated during a variety of assembly tasks. A mockup of a cavity pair and coupler was setup and the cobot programmed to automatically pick up the coupler and place on the mating cavity flange. Particle counting methods were setup to measure human vs cobot assembly particulate generation inside a cavity mockup. Other potential uses will be discussed for further improving SRF cavity assembly steps, where a cobot can replace or assist a human operator, and what potential gains are expected.

Duzik, Adam [Thomas Jefferson National Accelerator↗

Seascape Interface Control Document (V.1)

This paper serves as the Interface Control Document (ICD) for the Seascape automated test harness developed at Sandia National Laboratories. The primary purposes of the Seascape system are: (1) provide a place for accruing large, curated, labeled data sets useful for developing and evaluating detection and classification algorithms (including, but not limited to, supervised machine learning applications) (2) provide an automated structure for specifying, running and generating reports on algorithm performance. Seascape uses GitLab, Nexus, Solr, and Banana, open source codes, together with code written in the Python language, to automatically provision and configure computational nodes, queue up jobs to accomplish algorithms test runs against the stored data sets, gather the results and generate reports which are then stored in the Nexus artifact server.

97 MATHEMATICS AND COMPUTING↗

Seascape Interface Control Document (V. 2)

This paper serves as the Interface Control Document (ICD) for the Seascape automated test harness developed at Sandia National Laboratories. The primary purposes of the Seascape system are: (1) provide a place for accruing large, curated, labeled data sets useful for developing and evaluating detection and classification algorithms (including, but not limited to, supervised machine learning applications) (2) provide an automated structure for specifying, running and generating reports on algorithm performance. Seascape uses GitLab, Nexus, Solr, and Banana, open source codes, together with code written in the Python language, to automatically provision and configure computational nodes, queue up jobs to accomplish algorithms test runs against the stored data sets, gather the results and generate reports which are then stored in the Nexus artifact server.

97 MATHEMATICS AND COMPUTING↗