Search NASA⌕ Search

SEARCH · Search NASA

Results for “Structural Optimization”

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 1,315 records · Page 73

Simultaneous suppression of lignin, tricin and wall‐bound phenolic biosynthesis via the expression of monolignol 4‐ O ‐methyltransferases in rice

Summary Grass lignocelluloses feature complex compositions and structures. In addition to the presence of conventional lignin units from monolignols, acylated monolignols and flavonoid tricin also incorporate into lignin polymer; moreover, hydroxycinnamates, particularly ferulate, cross‐link arabinoxylan chains with each other and/or with lignin polymers. These structural complexities make grass lignocellulosics difficult to optimize for effective agro‐industrial applications. In the present study, we assess the applications of two engineered monolignol 4‐ O ‐methyltransferases (MOMTs) in modifying rice lignocellulosic properties. Two MOMTs confer regiospecific para ‐methylation of monolignols but with different catalytic preferences. The expression of MOMTs in rice resulted in differential but drastic suppression of lignin deposition, showing more than 50% decrease in guaiacyl lignin and up to an 90% reduction in syringyl lignin in transgenic lines. Moreover, the levels of arabinoxylan‐bound ferulate were reduced by up to 50%, and the levels of tricin in lignin fraction were also substantially reduced. Concomitantly, up to 11 μmol/g of the methanol‐extractable 4‐ O ‐methylated ferulic acid and 5–7 μmol/g 4‐ O ‐methylated sinapic acid were accumulated in MOMT transgenic lines. Both MOMTs in vitro displayed discernible substrate promiscuity towards a range of phenolics in addition to the dominant substrate monolignols, which partially explains their broad effects on grass phenolic biosynthesis. The cell wall structural and compositional changes resulted in up to 30% increase in saccharification yield of the de‐starched rice straw biomass after diluted acid‐pretreatment. These results demonstrate an effective strategy to tailor complex grass cell walls to generate improved cellulosic feedstocks for the fermentable sugar‐based production of biofuel and bio‐chemicals.

4-O-methylated↗

Data for Simultaneous Suppression of Lignin, Tricin and Wall-Bound Phenolic Biosynthesis via the Expression of Monolignol 4- O -Methyltransferases in Rice

Grass lignocelluloses feature complex compositions and structures. In addition to the presence of conventional lignin units from monolignols, acylated monolignols and flavonoid tricin also incorporate into lignin polymer; moreover, hydroxycinnamates, particularly ferulate, cross-link arabinoxylan chains with each other and/or with lignin polymers. These structural complexities make grass lignocellulosics difficult to optimize for effective agro-industrial applications. In the present study, we assess the applications of two engineered monolignol 4- O -methyltransferases (MOMTs) in modifying rice lignocellulosic properties. Two MOMTs confer regiospecific para-methylation of monolignols but with different catalytic preferences. The expression of MOMTs in rice resulted in differential but drastic suppression of lignin deposition, showing more than 50% decrease in guaiacyl lignin and up to an 90% reduction in syringyl lignin in transgenic lines. Moreover, the levels of arabinoxylan-bound ferulate were reduced by up to 50%, and the levels of tricin in lignin fraction were also substantially reduced. Concomitantly, up to 11 μmol/g of the methanol-extractable 4- O -methylated ferulic acid and 5–7 μmol/g 4- O -methylated sinapic acid were accumulated in MOMT transgenic lines. Both MOMTs in vitro displayed discernible substrate promiscuity towards a range of phenolics in addition to the dominant substrate monolignols, which partially explains their broad effects on grass phenolic biosynthesis. The cell wall structural and compositional changes resulted in up to 30% increase in saccharification yield of the de-starched rice straw biomass after diluted acid-pretreatment. These results demonstrate an effective strategy to tailor complex grass cell walls to generate improved cellulosic feedstocks for the fermentable sugar-based production of biofuel and bio-chemicals.

Biomass Analytics↗

Structure and electronic properties of rare earth DOBDC metal–organic-frameworks

In our report, we apply density functional theory (DFT) to investigate rare-earth metal organic frameworks (RE-MOFs), RE 12 (μ 3 -OH) 16 (C 8 O 6 H 4 ) 8 (C 8 O 6 H 5 ) 4 (RE = Y, Eu, Tb, Yb), and characterize the level of theory needed to accurately predict structural and electronic properties in MOF materials with 4f-electrons. A two-step calculation approach of geometry optimization with spin-restricted DFT and large core potential (LCPs), and detailed electronic structures with spin-unrestricted DFT with a full valence potential + Hubbard U correction is investigated. Spin-restricted DFT with LCPs resulted in good agreement between experimental lattice parameters and optimized geometries, while a full valence potential is necessary for accurate representation of the electronic structure. The electronic structure of Eu-DOBDC MOF suggested a strong dependence on the treatment of highly localized 4f-electrons and spin polarization, as well as variation within a range of Hubbard corrections (U = 1–9 eV). For Hubbard corrected spin-unrestricted calculations, a U value of 1–4 eV maintains the non-metallic character of the band gap with slight deviations in f-orbital energetics. When compared with experimentally reported results, the importance of the full valence calculation and the Hubbard correction in correctly predicting the electronic structure is highlighted.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Krylov subspace recycling for evolving structures

Krylov subspace recycling is a powerful tool when solving a long series of large, sparse linear systems that change only slowly over time. In PDE constrained shape optimization, these series appear naturally, as typically hundreds or thousands of optimization steps are needed with only small changes in the geometry. In this setting, however, applying Krylov subspace recycling can be a difficult task. As the geometry evolves, in general, so does the finite element mesh defined on or representing this geometry, including the numbers of nodes and elements and element connectivity. This is especially the case if re-meshing techniques are used. As a result, the number of algebraic degrees of freedom in the system changes, and in general the linear system matrices resulting from the finite element discretization change size from one optimization step to the next. Changes in the mesh connectivity also lead to structural changes in the matrices. In the case of re-meshing, even if the geometry changes only a little, the corresponding mesh might differ substantially from the previous one. Obviously, this prevents any straightforward mapping of the approximate invariant subspace of the linear system matrix (the focus of recycling in this work) from one optimization step to the next; similar problems arise for other selected subspaces. In this paper, we present an algorithm to map an approximate invariant subspace of the linear system matrix for the previous optimization step to an approximate invariant subspace of the linear system matrix for the current optimization step, for general meshes. This is achieved by exploiting the map from coefficient vectors to finite element functions on the mesh, combined with interpolation or approximation of functions on the finite element mesh. We demonstrate the effectiveness of our approach numerically with several proof of concept studies for a specific meshing technique.

42 ENGINEERING↗

Test cavity and Iris-to-Coax transition for tuning and high-power verification of SNS DTL iris couplers

The Spallation Neutron Source (SNS) Drift Tube Linac (DTL) employs iris couplers to efficiently deliver RF power into the accelerating structure. To support the development, tuning, and high‑power conditioning of these couplers prior to installation in the actual DTLs, a dedicated test cavity and an iris‑to‑coaxial transition structure have been designed. This work presents the electromagnetic design, simulation, and optimization of the test setup, enabling precise characterization of the iris coupler’s performance. The transition structure allows for tuning of the iris opening dimensions without requiring a waveguide taper or full‑size waveguide transitions, while maintaining impedance matching between the coaxial feed and the iris geometry to minimize reflection and power loss. During low‑power tests, the iris opening di-mensions can be evaluated using the iris‑to‑coax transi-tion attached to the test cavity. For high‑power condi-tioning, full‑size waveguides with ceramic vacuum win-dows are connected to the test cavity to replicate opera-tional conditions. Key design parameters were optimized using computer-aided simulation, and sensitivity studies were conducted to assess the impact of mechanical toler-ances on RF performance. The resulting test platform provides a reliable and efficient means for tuning and validating iris couplers, contributing to improved opera-tional stability in the SNS DTL.

Lee, Sung-Woo [ORNL] (ORCID:000000030915835X)↗

Facet Impact of CuMn 2 O 4 Spinel Nanocatalysts on Enhancement of the Oxygen Reduction Reaction in Alkaline Media

Surface-structure engineering represents an attractive strategy to optimize the energy conversion performance of nanocatalysts using their deliberately controlled exposed facets. To further exploit the potential of non-PGM-based spinel catalysts for alkaline oxygen reduction reaction (ORR), a cathodic fuel cell reaction, we hereby report a strategy of ORR improvement by controlling the crystallographic facets of ultra-small CuMn 2 O 4 spinel nanocatalysts through a developed colloidal synthesis approach. The synthesis of CuMn 2 O 4 nanocrystals with morphological control relies on the design and selection of the Cu-/Mn-precursors with striking discrepancies in reaction kinetics. Following carbon loading and an annealing post-treatment of the as-synthesized nanocatalysts, the exclusively {101} facet-exposed CuMn 2 O 4 spinel nano-octahedra exhibit improved electrocatalytic activity toward ORR in 1 M KOH, when compared to their spherical counterparts, exhibiting a mass activity (MA) of 37.6 A/g at 0.85 V. After 10,000 cycles of ORR durability test, the nano-octahedra still retain an MA of 24.5 A/g, which is twice that of the CuMn 2 O 4 spinel nanospheres. Structural characterizations after durability testing indicate that the MA decay is likely associated with a decrease in the Mn 3+ fraction and the emergence of Cu + on CuMn 2 O 4 nano-octahedral surfaces. Finally, as a paradigm, this synthesis approach could be extended to other Mn-based spinel nanocatalysts with precise shape control, enabling us to understand and establish the relationship between the surface lattice/valence state and electrocatalytic properties.

36 MATERIALS SCIENCE↗

Optimization of thermal barrier coating performance and durability over a drive cycle

A methodology to thermo-mechanically optimize a piston thermal barrier coating over a full drive cycle was established. The optimization objective was to minimize the heat transfer to the engine wall while maintaining structural integrity of the coating. Over 800 candidate materials were investigated and the optimization required more than one million non-road transient drive cycle calculations; real materials were investigated to ensure a realizable result and the existence of thermal and mechanical properties. High computational efficiency was achieved using a recently developed analytical heat transfer technique for multilayer engine walls. An uncoupled approach was utilized for the optimization, wherein the gas temperature and heat transfer coefficient profiles from a fully coupled and calibrated baseline model over the 20-min drive cycle were employed. The coating/piston interface temperature was constrained to be below the maximum piston service temperature limit. The durability was assessed using a recently developed analytical coating delamination framework for engine in-cylinder coatings based on the energy release rate when a crack forms. Results are presented for a mechanically unconstrained optimization and for cases constrained to three fixed levels of drive-cycle maximum energy release rate, and also constrained by the individual material’s toughness. The best-performing coating materials identified were verified using the fully coupled system-level model, which compared well to the uncoupled predictions. A study on the effect of adding a sealing layer to some high-performing, but porous, coatings showed a reduction in fuel consumption benefit and an increased exhaust temperature over the cycle, but the system still outperformed the uncoated case. The results of the study elucidate the importance of including engine performance and mechanical failure considerations in thermal barrier coating design.

Engineering↗

Link Budget Analysis of Interrogation of Surface Acoustic Wave Sensors in Metallic Tubular Structures

We report on loss mechanisms contributing to the link budget for interrogation of Surface Acoustic Wave (SAW) devices in metallic tubular structures. Impedance matching losses associated with a SAW device are minimized by design optimization and antenna coupling losses, and resulting propagation losses are measured in metallic tubular structures enabling prediction of interrogation distances with various antenna configurations.

Pingree, Richard↗

Link Budget Analysis of Interrogation of Surface Acoustic Wave Sensors in Metallic Tubular Structures

For presentation at, and publication in the proceedings of, the National Radio Science Meeting, Boulder, CO, January 9-13, 2024.In this paper, we report on loss mechanisms contributing to the link budget for interrogation of Surface Acoustic Wave (SAW) devices in metallic tubular structures. Impedance matching losses associated with a SAW device are minimized by design optimization and antenna coupling losses and resulting propagation losses are measured in metallic tubular structures enabling prediction of interrogation distances with various antenna configurations.

Pingree, Rick↗

Rational Design of Pore Size and Functionality in a Series of Isoreticular Zwitterionic Metal–Organic Frameworks

The isoreticular expansion and functionalization of charged-polarized porosity has been systematically explored by the rational design of 11 isostructural zwitterionic metal-organic frameworks (ZW-MOFs). This extended series of general structural composition {[M 3 F(L1) 3 (L2) 1.5 ]·guests} n was prepared by employing the solvothermal reaction of Co and Ni tetrafluoroborates with a binary ligand system composed of zwitterionic pyridinium derivatives and traditional functionalized ditopic carboxylate auxiliary ligands (HL1·Cl = 1-(4-carboxyphenyl)-4,4'-bipyridinium chloride, Hcpb·Cl; or 1-(4-carboxyphenyl-3-hydroxyphenyl)-4,4'-bipyridinium chloride, Hchpb·Cl; and H 2 L2 = benzene-1,4-dicarboxylic acid, H 2 bdc; 2-aminobenzene-1,4-dicarboxylic acid, H 2 abdc; 2,5-dihydroxy-1,4-benzenedicarboxylic acid, H 2 dhbdc; biphenyl-4,4'-dicarboxylic acid, H 2 bpdc; or stilbene-4,4'-dicarboxylic acid, H 2 sdc). Single-crystal structure analyses revealed cubic crystal symmetry ( I -43 m , a = 31-36 Å) with a 3D pore system of significant void space (73-81%). The pore system features three types of pores being systematically tunable in size ranging from 17.4 to 18.8 Å (pore I), 8.2 to 12.8 Å (pore II), and 4.8 to 10.4 Å (pore III) by the choice of auxiliary ligands. All members of this series have noninterpenetrating structures and exhibit robust architectures, as evidenced by their permanent porosity and high thermal stability (up to 300 °C). The structural integrity and specific surface areas could be systematically optimized using supercritical CO 2 exchange methods for framework activation resulting in BET surface areas ranging from 1250 to 2250 m 2 /g. Most interestingly, as a structural landmark, we found the pore surfaces lined with charge gradients employed by the pyridinium ligands. This key feature results in significant adsorption of carbon dioxide and methane which is attributed to polarization effects. With this contribution we pioneer the reticulation of pyridinium building blocks into extended zwitterionic networks in which specific properties can be targeted.

36 MATERIALS SCIENCE↗

Record-quality GaAs two-dimensional hole systems

The complex band structure, large spin-orbit induced band splitting, and heavy effective mass of two-dimensional (2D) hole systems hosted in GaAs quantum wells render them rich platforms to study many-body physics and ballistic transport phenomena. Here we report ultra-high-quality (001) GaAs 2D hole systems, fabricated using molecular beam epitaxy and modulation doping, with mobility values as high as 5.8 × 10 6 cm 2 /(V s) at a hole density of p = 1.3 × 10 11 /cm 2 , implying a mean free path of ≃ 27 μm. In the low-temperature magnetoresistance trace of this sample, we observe high-order fractional quantum Hall states up to the Landau level filling ν = 12/25 near ν = 1/2. Furthermore, we see a deep minimum develop at ν = 1/5 in the magnetoresistance of a sample with a much lower hole density of p = 4.0 × 10 10 /cm 2 where we measure a mobility of 3.6 × 10 6 cm2/(V s). Finally, these improvements in sample quality were achieved by the reduction of residual impurities both in the GaAs channel and in the AlGaAs barrier material, as well as optimization in the design of the sample structure.

2-dimensional systems↗

Single-layered organic photovoltaics with double cascading charge transport pathways: 18% efficiencies

The chemical structure of donors and acceptors limit the power conversion efficiencies achievable with active layers of binary donor-acceptor mixtures. Here, using quaternary blends, double cascading energy level alignment in bulk heterojunction organic photovoltaic active layers are realized, enabling efficient carrier splitting and transport. Numerous avenues to optimize light absorption, carrier transport, and charge-transfer state energy levels are opened by the chemical constitution of the components. Record-breaking PCEs of 18.07% are achieved where, by electronic structure and morphology optimization, simultaneous improvements of the open-circuit voltage, short-circuit current and fill factor occur. The donor and acceptor chemical structures afford control over electronic structure and charge-transfer state energy levels, enabling manipulation of hole-transfer rates, carrier transport, and non-radiative recombination losses.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Atomic-Scale Quantification of Interfacial Binding between Peptides and Inorganic Crystals: The Case of Calcium Carbonate Binding Peptide on Aragonite

Using a specific explicitly solvated interface model between a calcium carbonate binding peptide and crystalline aragonite, we investigate the electronic structure, atomic bonding, solvation effect, and the role of hydrogen bonding on the cohesion, stability, and functionality of this complex hybrid system using density functional calculation. The large interface model is strategically constructed using a stepwise procedure followed by ab initio molecular dynamics to obtain the optimal conformation. The calculated data on the electronic structure and bonding are analyzed in terms of three structural parts: aragonite, peptide, and water. Next, we focus on the binding between aragonite (001) surface and the peptide mediated by water. Finally, specific interatomic bonding between the amino acids in peptide and the (001) surface of aragonite is quantified. A single quantum mechanical metric, the total bond order density (TBOD), infers the dynamic interplay of different competing interactions. Four amino acids HIS1, ARG6, MET7, and TRP11 in the peptide sequence have strong interfacial Ca–O bonding and O···H hydrogen bonding between aragonite and peptide. The calculated Young’s modulus 33.37 GPa is in line with the measured value for nacre. Our approach for interfacial study between aragonite and a calcium carbonate binding peptide offers a broad perspective for probing complex interactions between the biomimetic interfaces. Finally, TBOD can be used as an effective parameter in ranking the efficacy of peptide–surface interactions and in providing a programmable design for bio-inspired material interfaces based on computational means.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Effects of social structure and management on risk of disease establishment in wild pigs

Contact heterogeneity among hosts determines invasion and spreading dynamics of infectious disease, thus its characterization is essential for identifying effective disease control strategies. Yet, little is known about the factors shaping contact networks in many 28 wildlife species and how wildlife management actions might affect contact networks. Wild pigs in North America are an invasive, socially-structured species that pose a health concern for domestic swine given their ability to transmit numerous devastating diseases 2 such as African swine fever (ASF). Using proximity loggers and GPS data from 48 wild pigs in Florida and South Carolina, USA, we employed a probabilistic framework to estimate weighted contact networks. We determined the effects of sex, social group, and spatial distribution (monthly home range overlap and distance) on wild pig contact. We also estimated the impacts of management-induced perturbations on contact and inferred their effects on ASF establishment in wild pigs with simulation. Social group membership was the primary factor influencing contacts. Between-group contacts depended primarily on space use characteristics, with fewer contacts among groups separated by >2 km and no contacts among groups >4 km apart within a month. Modeling ASF dynamics on the contact network demonstrated that indirect contacts resulting from baiting (a typical method of attracting wild pigs or game species to a site to enhance recreational hunting) increased the risk of disease establishment by ~33% relative to direct contact. Low-intensity population reduction (<5.9% of the population) had no detectable impact on contact structure but reduced predicted ASF establishment risk relative to no population reduction. Here, we demonstrate an approach for understanding the relative role of spatial, social, and individual-level characteristics in shaping contact networks and predicting their effects on disease establishment risk, thus providing insight for optimizing disease control in spatially- and socially-structured wildlife species.

59 BASIC BIOLOGICAL SCIENCES↗

Tensile properties, strain rate sensitivity, and activation volume of additively manufactured 316L stainless steels [Tensile properties of 316L stainless steels made by laser powder-bed-fusion additive manufacturing]

The tensile properties of additively manufactured (AM) metals and alloys are among the most important variables that impact the potential applications of these materials. Here we examine and report on the tensile properties of AM 316L stainless steels fabricated by the laser powder-bed-fusion (L-PBF) technique, via twelve sets of optimized laser processing parameters that produce materials with density >98.8 ± 0.10%. A heterogeneous microstructure is observed in all L-PBF samples, including microscopic features such as dislocations, cellular walls, elemental segregations, local misorientations, impurities, precipitates, and a large fraction of low-angle grain boundaries (2-10°, ~40–60%). The derived average grain size defined by high-angle grain boundaries (>10°) is ~30–50 μm. Tensile testing reveals a yield strength ranging from 552 to 635 MPa and a tensile-elongation-to-failure (TEF) of 0.09–0.42 for directly-printed samples, whereas these values are 592–690 MPa and 0.29–0.50 for samples machined from the as-built rectangular thin plates. In all samples, we observe a variation of tensile yield strength within ~15% but not the TEF, suggesting marginal microstructural changes despite a wide range of laser processing parameters. The large scatter of TEF in directly-printed samples originates from the sensitivity of thin gauge geometry (~2 mm 2 cross-section area) to the built-in flaws. We measured a substantially higher strain rate sensitivity (m~0.02–0.03) of L-PBF 316L compared to the coarse-grained counterparts (~0.006), together with a small activation volume of ~20–30b3 (where b is the Burgers vector of 316L). In conclusion, these deformation kinetics parameters suggest that the tensile plasticity of L-PBF 316L is controlled by a much finer microstructural length scale than the measured grain size, consistent with the high strength and juxtaposed nano- to macro-structures seen in these materials. Strategies to optimize the tensile properties of AM materials are discussed.

36 MATERIALS SCIENCE↗

Effect of Alkylsilyl Side‐Chain Structure on Photovoltaic Properties of Conjugated Polymer Donors

Abstract Side‐chain engineering is an important strategy for optimizing photovoltaic properties of organic photovoltaic materials. In this work, the effect of alkylsilyl side‐chain structure on the photovoltaic properties of medium bandgap conjugated polymer donors is studied by synthesizing four new polymers J70 , J72 , J73 , and J74 on the basis of highly efficient polymer donor J71 by changing alkyl substituents of the alkylsilyl side chains of the polymers. And the photovoltaic properties of the five polymers are studied by fabricating polymer solar cells (PSCs) with the polymers as donor and an n‐type organic semiconductor (n‐OS) m ‐ITIC as acceptor. It is found that the shorter and linear alkylsilyl side chain could afford ordered molecular packing, stronger absorption coefficient, higher charge carrier mobility, thus results in higher J sc and fill factor values in the corresponding PSCs. While the polymers with longer or branched alkyl substituents in the trialkylsilyl group show lower‐lying highest occupied molecular orbital energy levels which leads to higher V oc of the PSCs. The PSCs based on J70 : m ‐ITIC and J71 : m ‐ITIC achieve power conversion efficiency (PCE) of 11.62 and 12.05%, respectively, which are among the top values of the PSCs reported in the literatures so far.

Bin, Haijun↗

Measuring the dynamic response of the thylakoid architecture in plant leaves by electron microscopy

The performance of the photosynthesis machinery in plants, including light harvesting, electron transport, and protein repair is controlled by structural changes of the thylakoid membrane system inside the chloroplasts. In particular, the structure of the stacked grana area of thylakoid membranes is highly dynamic, changing in response to different environmental cues such as light intensity. For example, the aqueous thylakoid lumen enclosed by thylakoid membranes in grana has been documented to swell in the presence of light. However, light-induced alteration of the stromal gap in the stacked grana (partition gap) and of the unstacked stroma lamellae have not been well characterized. Light-induced changes of the entire thylakoid membrane system including the lumen in both stacked and unstacked domains as well as the partition gap are presented here, and the functional implications are discussed. This structural analysis was made possible by development of a robust semi-automated image analysis method combined with optimized plant tissue fixation techniques for transmission electron microscopy generating quantitative structural results for the analysis of thylakoid ultrastructure.

59 BASIC BIOLOGICAL SCIENCES↗

A Kaczmarz-inspired approach to accelerate the optimization of neural network wavefunctions

Neural network wavefunctions optimized using the variational Monte Carlo method have been shown to produce highly accurate results for the electronic structure of atoms and small molecules, but the high cost of optimizing such wavefunctions prevents their application to larger systems. We propose the Subsampled Projected-Increment Natural Gradient Descent (SPRING) optimizer to reduce this bottleneck. SPRING combines ideas from the recently introduced minimum-step stochastic reconfiguration optimizer (MinSR) and the classical randomized Kaczmarz method for solving linear least-squares problems. We demonstrate that SPRING outperforms both MinSR and the popular Kronecker-Factored Approximate Curvature method (KFAC) across a number of small atoms and molecules, given that the learning rates of all methods are optimally tuned. For example, on the oxygen atom, SPRING attains chemical accuracy after forty thousand training iterations, whereas both MinSR and KFAC fail to do so even after one hundred thousand iterations.

97 MATHEMATICS AND COMPUTING↗