Search NASA⌕ Search

SEARCH · Search NASA

Results for “engineering data”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 577 records · Page 32

Economic and Environmental Assessment of Biological Conversions of Agile BioFoundry (ABF) Bio-Derived Chemicals

Bio-derived chemicals are an essential part of the growing bioeconomy. They possess the potential to boost a new domestic bioproduct industry, improve the sustainability of integrated biomanufacturing, and reduce U.S. dependence on fossil energy. The Agile BioFoundry (ABF) consortium, a Department of Energy (DOE)-sponsored collaboration, is investigating biobased pathways to produce advantaged products including advanced biofuels, fuel intermediates, and bioproducts. ABF is integrating advanced computational tools for biological engineering, process design and data analysis, and economic/sustainability modeling tools into a comprehensive and dynamic platform for biomanufacturing of microbes and using them to produce key metabolic intermediates or beachhead molecules which may be derivatized into several distinct bioproducts of industrial interest. In this presentation, we first discuss a methodology to select a single exemplar product molecule to represent each beachhead pathway based on similarities with other end-molecule options (yields/titers/rates, fermentation operation mode, oxygen requirements, general separations challenges, etc.), in order to maintain a reasonable number of cases for rigorous process simulation. We then use techno-economic analysis (TEA) and life-cycle analysis (LCA) to highlight sensitivities and trends around economic performance and environmental footprint, reflecting examples for two selected ABF technology pathways to bio-derived chemicals: 1) adipic acid production via muconic acid fermentation from mixed sugars with Pseudomonas putida and 2) cineole via geranyl diphosphate with Rhodosporidium toruloides. We present multi-variable scan plots highlighting key drivers on costs and greenhouse gas emissions in order to identify the parameter space in which each pathway could ultimately achieve economic and environmental sustainability meeting or exceeding commodity product benchmarks, thus prioritizing future R&D focus areas.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Nuclear Requalification of the New ATR Core

The Advanced Test Reactor (ATR) creates a unique high neutron flux materials testing environment that subsequently causes neutron embrittlement damage to its beryllium reflector eventually requiring a replacement during a reactor Outage. Concurrently, a piece-for-piece core replacement is conducted to maintain reactor functionality called a core internals changeout (CIC). Once changeout is complete, ATR Reactor Engineering utilizes previous CIC data to model and predict criticality scenarios for the new unirradiated core. However, CIC data has been inconsistently reported over the years making it difficult to find data trends that could be useful for the modeling and prediction process. So nuclear requalification testing is conducted using different flux and irradiation tests to accurately verify the models and to recalibrate nuclear monitoring instrumentation in the ATR core allowing for safe re-start of normal operations.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Integrating Risk in Humanoid Robot Control for Applications in the Nuclear Industry - 18230

This paper discuss the integration of risk into a robot control framework for decommissioning applications in the nuclear industry. Our overall objective is to allow the robot to evaluate a risk associated with several methods of completing the same task by combining a set of action sequences. If the environment is known and in the absence of sensing errors each set of actions would successfully complete the task. In this paper, instead of attempting to model the errors associated with each sensing system in order to compute an exact solution, a set of solutions are obtained along with a prescribed risk index. The risk associated with each set of actions can then be compared to possible payoffs or rewards, for instance task completion time or power consumption. This information is then sent to a high level decision planner, for instance a human teleoperator, who can then make a more informed decision regarding the robots actions. In order to illustrate the concept, we introduce three specific risk measures, namely, the collision risk and the risk of toppling and failure risk associated with grasping an object. We demonstrate the results from this foundational study of risk-aware compositional robot autonomy in simulation using NASA's Valkyrie humanoid robot, and the grasping simulator HAPTIX. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Artificial Intelligence a D and D Enabler - 20552

The paper addresses the development of a specific search engine dedicated to Decommissioning and Dismantling (D and D) projects. The solution combines advanced model based system engineering methodologies and a data centric approach. It is based on an appropriate use of the last Natural Language processing techniques, the most innovative artificial intelligence algorithms and open source framework to handle large volume and diversity of data met in the case of a nuclear infrastructure we have to dismantle. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Searching for Strongly-Interacting Dark Matter with the Heavy Photon Search Experiment

The Heavy Photon Search Experiment (HPS) is a fixed-target experiment at Jefferson Lab’s Hall B, designed to explore a hidden sector (HS) of particles containing dark matter and a new force mediator known as the “heavy photon” (A'). The A' is a massive spin-1 gauge boson associated with a new U (1)D symmetry in the HS that kinetically mixes with the Standard Model () photon with a weak coupling strength parameterized by ¿, with ¿2 ~ 10-2 -10-10. HPS utilizes a high-intensity electron beam on a thin tungsten target to produce heavy photons in the MeV-GeV mass range via “dark bremsstrahlung,” a process analogous to SM bremsstrahlung but suppressed by ¿2. The A' can decay resonantly to SM leptons, allowing HPS to conduct both mass resonance searches for prompt decays (large ¿) and displaced vertex searches for long-lived particles (small ¿). In addition to the minimal A' model, HPS probes more complex extensions such as the QCD-like strongly-interacting massive particles (SIMPs) HS containing “dark” pions (pD) and vector mesons (VD), with pD as dark matter candidates. These particles introduce new thermal dark matter freeze- out scenarios and visible signals through long-lived VD decays to SM leptons, which are accessible to HPS. This analysis conducted a displaced vertex search for VD ¿ e-e+ in the mass range 30 MeV to 124 MeV and ¿ between 10-6 < ¿ < 10-2 using data from the 2016 Engineering Run (10.753 nb-1) at 2.3 GeV. Unlike the minimal A' search, SIMP signal kinematics required new approaches to signal normalization and SM background rejection. The strongest signal evidence was a local p-value of 0.01317 for mVD = 119 MeV, corresponding to a global significance of 0.9s. Although no signal was found, this search excluded a region of the SIMP parameter space at 90 % confidence. This work demonstrates HPS’s competitive capability to probe SIMP sectors within cosmologically significant parameters and introduces a new method for HPS displaced vertex searches using track vertical impact parameter cuts

Spellman, Alic [Univ. of California, Santa Cruz, C↗

Effect of Split-Injection Strategies on Engine Performance and Emissions under Cold-Start Operation

The recently concluded partnership for advancing combustion engines (PACE) was a US Department of Energy consortium involving multiple national laboratories focused on addressing key efficiency and emission barriers in light-duty engines. Generation of detailed experimental data and modeling capabilities to understand and predict cold-start behavior was a major pillar in this program. Cold-start, as defined by the time between first engine crank and three-way catalyst light-off, is responsible for a large percentage of NOx, unburned hydrocarbon, and particulate matter emissions in light-duty engines. Minimizing emissions during cold-start is a trade-off between achieving faster three-way catalyst light-off, and engine out emissions during that period. In this study, engine performance, emissions, and catalyst warmup potential were monitored while the engine was operated using a single direct injection (baseline case) as well as a two-way-equal-split direct injection strategy. These injection strategies were analyzed at a range of cold-start-operation relevant retarded spark timings of up to 25 degrees after top dead center of firing (dATDCf). A stoichiometric 2-bar NIMEP steady-state condition was used for all cases to simulate cold-start operation. Significant improvement in engine stability was observed with the two-way-split injection strategy at the retarded spark timings allowing for up to 2.5x increase in exhaust heat rate when engine operation is stability constrained. Similar fuel-loss-to-oil trends with exhaust heat rate were observed for both single and two-way-split injection strategies. However, the two-way split injection was observed to produce higher NOx emissions per unit exhaust heat rate. A single data point run with three-way-split direct injection at a very retarded spark-timing of 30 dATDCf pointed to further improvements in engine stability and reduction in fuel-loss-to-oil as compared to single injection strategy. Engine stability decreased as spark timing was initially retarded with a single injection but was observed to plateau and stabilize beyond spark timing of 10 dATDCf. Finally, for the two-way-split-injection strategy, retarding the start of injection (SOI) timing of the second injection led to a decrease in engine stability as well as an increase in soot emissions.

42 ENGINEERING↗

Early arrival waveform inversion using data uncertainties and matching filters with application to near-surface seismic refraction data

We develop an early arrival waveform inversion (EAWI) technique for high-resolution near-surface velocity estimation by iteratively updating the P-wave velocity model to minimize the difference between the observed and calculated seismic refraction data. Traditional EAWI uses a least-squares penalty function and an acoustic forward-modeling engine. Conventional least-squares error is sensitive to data with low signal-to-noise ratio (S/N) and iterations of EAWI stop at a local-minimum data misfit or at the preassigned maximum number of iterations. These stopping criteria can result in overfitting the data. In addition, fitting the elastic field data with an acoustic modeling engine can introduce artifacts in velocity estimation, especially in land data with significant elastic effects. To overcome these challenges, we develop a robust EAWI (REAWI) method by (1) incorporating the data uncertainties into the penalty function and (2) mitigating the elastic effects using a matching filter workflow. The data uncertainties are estimated from waveform reciprocal errors. When full-waveform reciprocity is not available, trace interpolation is applied. The proposed method prevents closely fitting data with low S/N, avoids overall overfitting by stopping the iterations when a normalized chi-square ([Formula: see text]) waveform misfit of one is achieved, and is less affected by elastic effects. Numerical examples and application to near-surface refraction data at a groundwater contamination site suggest that the final REAWI models are more accurate than the corresponding EAWI models, at the same level of misfit. This is the first known application of a matching filter workflow to real land data. The final REAWI models satisfy an appropriate misfit between the real data and predicted elastic P-wave data, making this approach in this respect equivalent to elastic waveform inversion. We also develop a method to analyze model constraint by examining the energy of the wavefield Fréchet derivative thereby avoiding the influence of the data residuals in traditional Fréchet kernels.

Geochemistry & Geophysics↗

NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elements

Multiphysics problems that are characterized by complex interactions among fluid dynamics, heat transfer, structural mechanics, and electromagnetics, are inherently challenging due to their coupled nature. While experimental data on certain state variables may be available, integrating these data with numerical solvers remains a significant challenge. Physics-informed neural networks (PINNs) have shown promising results in various engineering disciplines, particularly in handling noisy data and solving inverse problems in partial differential equations (PDEs). However, their effectiveness in forecasting nonlinear phenomena in multiphysics regimes, particularly involving turbulence, is yet to be fully established. Here, this study introduces NeuroSEM, a hybrid framework integrating PINNs with the highfidelity Spectral Element Method (SEM) solver, Nektar++. NeuroSEM leverages the strengths of both PINNs and SEM, providing robust solutions for multiphysics problems. PINNs are trained to assimilate data and model physical phenomena in specific subdomains, which are then integrated into the Nektar++ solver. We demonstrate the efficiency and accuracy of NeuroSEM for thermal convection in cavity flow and flow past a cylinder. The framework effectively handles data assimilation by addressing those subdomains and state variables where the data is available. We applied NeuroSEM to the Rayleigh-B´enard convection system, including cases with missing thermal boundary conditions and noisy datasets. Finally, we applied the proposed NeuroSEM framework to real particle image velocimetry (PIV) data to capture flow patterns characterized by horseshoe vortical structures. Our results indicate that NeuroSEM accurately models the physical phenomena and assimilates the data within the specified subdomains. The framework’s plug-and-play nature facilitates its extension to other multiphysics or multiscale problems. Furthermore, NeuroSEM is optimized for efficient execution on emerging integrated GPU-CPU architectures. This hybrid approach enhances the accuracy and efficiency of simulations, making it a powerful tool for tackling complex engineering challenges in various scientific domains.

42 ENGINEERING↗

Digital Twin for Hydropower System Object Modeling: Alder Dam (FY2023)

Hydropower is the world's largest source of renewable electricity, and hydropower plants are distributed all over the world. Typical major components of a hydropower plant are the governor, excitation, generator, thrust bearing, hydraulic turbine, transformer, the main lead, metering and control, tailwater depression, and dissolved oxygen. For each component, various measures are taken. The measurements are acquired by various heterogeneous systems, including standalone sensors, programmable logic controllers (PLC), Supervisory control and data acquisition (SCADA), Internet of Things (IoT), and data acquisition and integration platforms such as OSI/PI. The measured data are often archived within the plant by a data management platform, and many institutions have cloud-based archive systems, such as Hydropower Research Institution (HRI), U.S. Army Corps of Engineers (USACE), and Columbia River Data Access in Real Time (DART). Object Modeling is a general framework for designing information systems. It focuses on objects, the actions they perform, and the messages they send to one another to cause those actions to be taken. The major differences among object modeling, network modeling, data modeling, and process modeling are that in the first we focus on the actions in response to information, objects which form the system, the actions they perform, and how they pass information to one another, while in the second we concentrate on where, when and how much information is moved, while in the third we focus on what information is moved and where it is moved, while in the last we focus on how it is moved and when it is moved. Object modeling was developed basically as a method to develop object-oriented systems and to support object-oriented programming. It describes the static structure of the system. The object Modeling Technique is easy to draw and use. That is why we choose object modeling to connect physical hydropower plants to Digital Twin. It recognizes the objects and the relationship between them. It identifies the attributes and functions of each class. Dynamic Modeling: It explains how objects respond to events. Functional Modeling indicates the processes executed in an object and how data changes when it moves to objects. It has been used in many applications like telecommunication, transportation, etc.

13 HYDRO ENERGY↗

Experimental study of the impact of scavenging efficiency on diesel combustion in an opposed-piston two-stroke engine

The opposed-piston two-stroke (OP2S) engine is a promising alternative powertrain technology that can offer thermal and brake efficiency improvements over conventional four-stroke engines. In recent years, many of the technical barriers of the OP2S engine architecture have been overcome. However, there is still a need for fundamental studies to provide insight into the scavenging and combustion processes of the OP2S engine to help design and operate the most efficient combustion systems using this engine architecture. This work aims to provide such insights by analyzing experimental data collected on a 3-cylinder, 4.9 L OP2S engine. Specifically, a scavenging efficiency sweep, an engine speed sweep with a constant scavenging efficiency, and an engine speed with a constant pressure differential across the engine were studied in detail. It was found that in diesel combustion, as the scavenging efficiency decreased, the increase in temperature of the hot, internal residuals resulted in a significant increase in heat transfer. Despite lowering pumping losses, this resulted in an overall decrease in brake efficiency. When the bulk thermodynamic conditions of two different scavenging efficiency cases (67% and 72%) were matched at port closing, the lower scavenging efficiency case still displayed a 0.7 percentage point penalty in net thermal efficiency and an increase in engine-out indicated specific emissions of NOx of 18% due to residual stratification in the cylinder. The results presented in this work show that the optimal breathing strategy in diesel combustion on an OP2S engine architecture is one that results in a slightly under-scavenged environment at port closing. However, the results did show potential system-level efficiency benefits of decreasing scavenging efficiency, meaning that alternative fuels and combustion strategies without the constraints of diesel combustion could achieve system-level efficiency gains by running significantly under-scavenged.

Engineering↗

Capturing Historic Reliability Performance Through Graph Databases: A Model Based System Engineering Approach

With the goal of improving the performance and reliability of high dependable technological systems such as nuclear power plants, advanced monitoring and health management systems are employed to inform system engineers on observed degradation processes and anomalous behaviors of assets and components. This information is captured in the form of large amount of data which can be heterogenous in nature (e.g., numeric, textual). Such large data availability poses challenges when system engineers are required to parse and analyze them in order to track historic reliability performance of assets and components. This paper tackles directly this challenge by providing means to organize data in the form of a graph: a knowledge graph. The presented approach distinguish itself from current knowledge graph-based methods by the fact that model-based system engineering (MBSE) models are used to “put data into context”. In particular, MBSE models are used as skeleton of a knowledge graph; numeric and textual data elements, once processed, are associated to MBSE model elements. Thus, a knowledge graph captures both system architecture (though MBSE models) and health/performance data. Such feature opens the door to new data analytics methods designed to identify causal relations between observed phenomena.

97 - MATHEMATICS AND COMPUTING↗

Determining appropriate data analytics for transformer health monitoring - 107

Transformers are vital assets for the safe, reliable and cost-effective operation of nuclear power plants. The unexpected failure of a transformer can lead to different consequences ranging from a lack of export capability, with the corresponding economic penalties, to catastrophic failure, with the associated health, safety and economic effects. Condition monitoring techniques examine the health of the transformer periodically, with the aim to identify early indicators of anomalies. However, many transformer failures occur because diagnostic and monitoring models do not identify degraded conditions in time. Therefore, health monitoring is an essential component to transformer life cycle management. Existing tools for transformer health monitoring use traditional dissolved gas analysis based diagnostics techniques. With the advance of prognostics and health management (PHM) applications, we can enhance traditional transformer health monitoring techniques using PHM analytics. The design of an appropriate data analytics system requires a multi-stage design process including: (i) specification of engineering requirements; (ii) characterization of existing data sources and analytics to identify complementary techniques; (iii) development of the functional specification of the analytics suite to formalize its behavior, and finally (iv) deployment, validation, and verification of the functional requirements in the final platform. Accordingly, in this paper we propose a transformer analytics suite which incorporates anomaly detection, diagnostics, and prognostics modules in order to complement existing tools for transformer health monitoring. (authors)

42 ENGINEERING↗

Advanced Visualization for Scientific Data Analysis and Insight [Slides]

This talk will explore how we have used advanced visualization technologies to support analytical reasoning and knowledge discovery. Specifically, we will present several examples detailing some recent scientific successes using state-of-the-art immersive and high-resolution visualization at the National Renewable Energy Laboratory's Computational Science Center. On multiple occasions, we have observed scientists and engineers discover features in their data using advanced visualization technologies that they had not seen in prior investigations of their data on traditional desktop displays. We have embedded more information into our analytics tools, allowing engineers to explore complex multivariate spaces. We have observed how interactions seem to catalyze understanding.

97 MATHEMATICS AND COMPUTING↗

ActiveSpaces: Exploring dynamic code deployment for extreme scale data processing: ActiveSpaces: Exploring dynamic code deployment for extreme scale data processing

Managing the large volumes of data produced by emerging scientific and engineering simulations running on leadership-class resources has become a critical challenge. The data have to be extracted off the computing nodes and transported to consumer nodes so that it can be processed, analyzed, visualized, archived, and so on. Several recent research efforts have addressed data-related challenges at different levels. One attractive approach is to offload expensive input/output operations to a smaller set of dedicated computing nodes known as a staging area. However, even using this approach, the data still have to be moved from the staging area to consumer nodes for processing, which continues to be a bottleneck. In this paper, we investigate an alternate approach, namely moving the data-processing code to the staging area instead of moving the data to the data-processing code. Specifically, we describe the ActiveSpaces framework, which provides (1) programming support for defining the data-processing routines to be downloaded to the staging area and (2) runtime mechanisms for transporting codes associated with these routines to the staging area, executing the routines on the nodes that are part of the staging area, and returning the results. We also present an experimental performance evaluation of ActiveSpaces using applications running on the Cray XT5 at Oak Ridge National Laboratory. Finally, we use a coupled fusion application workflow to explore the trade-offs between transporting data and transporting the code required for data processing during coupling, and we characterize sweet spots for each option.

97 MATHEMATICS AND COMPUTING↗

FPGA-based computing system for processing data in size, weight, and power constrained environments

Technologies that are well-suited for use in size, weight, and power (SWAP)-constrained environments are described herein. A host controller dispatches data processing instructions to hardware acceleration engines (HAEs) of one or more field programmable gate arrays (FPGAs) and further dispatches data transfer instructions to a memory controller, such that the HAEs perform processing operations on data stored in local memory devices of the HAEs in parallel with other data being transferred from external memory devices coupled to the FPGA(s) to the local memory devices.

Napier, Matthew↗

Experimental validation of shock propagation through a foam with engineered macro-pores

The engineered macro-pore foam provides a new way to study thermonuclear burn physics by utilizing capsules containing deuterated (D) foam and filling tritium (T) gas in the engineered macro-pores. The implosion of a thermonuclear capsule filled with an engineered macro-pore foam will be complex due to the interaction of a shock wave with the engineered macro-pores. It is our goal to quantify how substantially complex foam structures affect the shape of shock and bulk shock speed. A cylinder-shape shock tube experiment has been designed and performed at the Omega Laser Facility. In order to examine how a foam structure will affect shock propagation, we performed several tests varying (1) engineered macro-pore size, (2) average foam density, and (3) with/without neopentane (C 5 H 12 ) gas. X-ray radiographic data indicate that shock speed through engineered macro-pore foams depends strongly on average foam density and less on pore size. In this work, experimental shock propagation data helped guide two numerical simulation approaches: (1) a 2D simulation with homogenizing foams rather than explicitly simulating engineered macro-pores and (2) a 2D toroidal-pore approximation adopting a toroidal-tube geometry to model engineered macro-pores.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DeepLynx Ecosystem 2025

Poor data integration and governance continue to plague complex engineering projects, resulting in missed cost, schedule, and performance targets. Departments operate in isolated systems with manual data exchange, creating fragmented information that compounds errors and leads to significant delays and cost overruns. The DeepLynx ecosystem addresses these challenges through an open-source, modular data management platform that transforms fragmented project data into an integrated digital thread. Built on a federated microservice architecture, the ecosystem comprises seven specialized tools centered around DeepLynx Nexus, a unified data catalog with hierarchical organization and graph-based navigation capabilities. The ecosystem includes: DeepLynx Stream for real-time timeseries data ingestion from industrial sources; DeepLynx Ingest for governed data uploads with formal review workflows; DeepLynx Lattice for ontology-based entity and relationship extraction; DeepLynx Run for workflow orchestration and secure AI/ML compute; DeepLynx Visualize for 3D digital twin visualization; and DeepLynx Insight for AI-assisted document analysis with traceable, grounded responses. Deployable in cloud, on-premise, or hybrid environments using containerized Docker applications and Helm charts, the DeepLynx ecosystem provides flexible infrastructure that adapts to organizational requirements. By consolidating project data into a unified data lake with role-based access controls and OAuth2 authentication, DeepLynx enables digital thread and digital twin capabilities that improve decision-making, reduce risk, and support complex engineering workflows throughout the project lifecycle.

42 - ENGINEERING↗

A comprehensive guide to CAN IDS data and introduction of the ROAD dataset

Although ubiquitous in modern vehicles, Controller Area Networks (CANs) lack basic security properties and are easily exploitable. A rapidly growing field of CAN security research has emerged that seeks to detect intrusions or anomalies on CANs. Producing vehicular CAN data with a variety of intrusions is a difficult task for most researchers as it requires expensive assets and deep expertise. To illuminate this task, we introduce the first comprehensive guide to the existing open CAN intrusion detection system (IDS) datasets. We categorize attacks on CANs including fabrication (adding frames, e.g., flooding or targeting and ID), suspension (removing an ID’s frames), and masquerade attacks (spoofed frames sent in lieu of suspended ones). We provide a quality analysis of each dataset; an enumeration of each datasets’ attacks, benefits, and drawbacks; categorization as real vs. simulated CAN data and real vs. simulated attacks; whether the data is raw CAN data or signal-translated; number of vehicles/CANs; quantity in terms of time; and finally a suggested use case of each dataset. State-of-the-art public CAN IDS datasets are limited to real fabrication (simple message injection) attacks and simulated attacks often in synthetic data, lacking fidelity. In general, the physical effects of attacks on the vehicle are not verified in the available datasets. Only one dataset provides signal-translated data but is missing a corresponding “raw” binary version. This issue pigeon-holes CAN IDS research into testing on limited and often inappropriate data (usually with attacks that are too easily detectable to truly test the method). The scarcity of appropriate data has stymied comparability and reproducibility of results for researchers. As our primary contribution, we present the Real ORNL Automotive Dynamometer (ROAD) CAN IDS dataset, consisting of over 3.5 hours of one vehicle’s CAN data. ROAD contains ambient data recorded during a diverse set of activities, and attacks of increasing stealth with multiple variants and instances of real (i.e. non-simulated) fuzzing, fabrication, unique advanced attacks, and simulated masquerade attacks. To facilitate a benchmark for CAN IDS methods that require signal-translated inputs, we also provide the signal time series format for many of the CAN captures. Our contributions aim to facilitate appropriate benchmarking and needed comparability in the CAN IDS research field.

97 MATHEMATICS AND COMPUTING↗