Christie Maddock, PhD, FHEA, MRAeS

Search results

• 2023

  A multi-fidelity model management framework for multi-objective aerospace design optimisation

  Parsonage, B. & Maddock, C., 7 Feb 2023, In: Frontiers in Aerospace Engineering. 2, 21 p., 1046177.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Sampling 100%
  • Reentry 83%
  • Computational efficiency 69%
  • Physics 61%
  • Aerodynamics 57%
  2 Downloads (Pure)

• Implementing life cycle sustainability assessment for improved space mission design

  Wilson, A. R., Vasile, M., Maddock, C. & Baker, K., 18 Jan 2023, (E-pub ahead of print) In: Integrated Environmental Assessment and Management. p. 1-21 21 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • life cycle 100%
  • sustainability 74%
  • life cycle assessment 34%
  • circular economy 13%
  • economy 13%
  4 Downloads (Pure)
• 2022

  Multi-fidelity and multi-disciplinary approach for the accurate simulation of atmospheric re-entry

  Peddakotla, S. A., Morgado, F., Thillaithevan, D., O'Driscoll, D., Santer, M., Maddock, C., Vasile, M. & Fossati, M., 19 Sep 2022. 13 p.

  Research output: Contribution to conference › Paper

  Open Access

  File

  • Reentry 100%
  • Structural analysis 86%
  • Flight dynamics 50%
  • Thermoanalysis 44%
  • Dynamic analysis 38%
  36 Downloads (Pure)

• Ecospheric life cycle impacts of annual global space activities

  Wilson, A. R., Vasile, M., Maddock, C. A. & Baker, K. J., 15 Aug 2022, In: Science of the Total Environment. 834, 11 p., 155305.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Life cycle 100%
  • life cycle 94%
  • Industry 85%
  • Sustainable development 41%
  • Ecodesign 28%
  4 Citations (Scopus)

  29 Downloads (Pure)

• Multi-objective optimisation under uncertainty with unscented temporal finite elements

  Ricciardi, L. A., Maddock, C. & Vasile, M., 1 Mar 2022, Evolutionary Algorithms in Engineering Design Optimization. Greiner, D., Gaspar-Cunha, A., Hernández-Sosa, D., Minisci, E. & Zamuda, A. (eds.). Basel: MDPI Multidisciplinary Digital Publishing Institute, p. 187-208 22 p.

  Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed) › peer-review

  Open Access

  File

  • Multi-objective Optimization 100%
  • Multiobjective optimization 76%
  • Uncertainty 68%
  • Finite Element 64%
  • Transcription 27%
  4 Downloads (Pure)
• 2021

  Multi-objective optimisation under uncertainty with unscented temporal finite elements

  Ricciardi, L. A., Maddock, C. A. & Vasile, M., 24 Nov 2021, In: Mathematics. 9, 23, 22 p., 3010.

  Research output: Contribution to journal › Special issue › peer-review

  Open Access

  File

  • Multi-objective Optimization 100%
  • Multiobjective optimization 76%
  • Uncertainty 68%
  • Finite Element 64%
  • Transcription 27%
  11 Downloads (Pure)

• Design optimisation and analysis of very high power transportation system to Mars

  Maddock, C., Parsonage, B., Ricciardi, L. A., Vasile, M. & Cohen, O., 25 Oct 2021. 10 p.

  Research output: Contribution to conference › Proceeding › peer-review

  Open Access

  File

  • Mars 100%
  • High Power 78%
  • Trade-offs 44%
  • Design 40%
  • Nuclear propulsion 34%
  16 Downloads (Pure)

• Segmentation-driven spacecraft pose estimation for vision-based relative navigation in space

  Kajak, K. M., Maddock, C., Frei, H. & Schwenk, K., 25 Oct 2021, IAF Astrodynamics Symposium 2021. 12 p. (Proceedings of the International Astronautical Congress, IAC; vol. C1).

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

  Open Access

  File

  • navigation 100%
  • spacecraft 74%
  • Spacecraft 72%
  • segmentation 71%
  • Convolutional neural networks 63%
  7 Downloads (Pure)

• Sustainable Impact by Design

  Essex, J., Wellisch, G., Galbraith, A., Egea Alvarez, A., Cunningham, M. R., Giovelli, N., Ivaturi, A., Li, R., Maddock, C., Somorin, T., Yue, H., Hendry, P., Hendry, M., Essex, W., Caccavale, E. & Johnson, M. P., 30 Sep 2021, 70 p. Glasgow : University of Strathclyde.

  Research output: Other contribution

  Open Access

  File

  • staff 100%
  • climate change 93%
  • sustainability 40%
  • funding 37%
  • learning 18%
  32 Downloads (Pure)

• Multi-stage multi-fidelity information correction for artificial neural network based meta-modelling

  Parsonage, B. & Maddock, C., 5 Jan 2021, 2020 IEEE Symposium Series on Computational Intelligence. Piscataway, NJ: IEEE, p. 950-957 8 p.

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

  Open Access

  File

  • Metamodeling 100%
  • Artificial Neural Network 72%
  • Fidelity 70%
  • Surrogate 34%
  • Neural networks 34%
  1 Citation (Scopus)

  19 Downloads (Pure)
• 2020

  Robust trajectory optimisation of a TSTO spaceplane using uncertainty-based atmospheric models

  Ricciardi, L., Maddock, C. & Vasile, M., 1 Apr 2020, 23rd AIAA International Space Planes and Hypersonic Systems and Technologies Conference. Reston, VA., AIAA 2020-2403

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

  Open Access

  File

  • Trajectory Optimization 100%
  • Robust Optimization 87%
  • Uncertainty 55%
  • Ascent 54%
  • Multi-objective Optimization 53%
  3 Citations (Scopus)

  19 Downloads (Pure)
• 2019

  Multidisciplinary design analysis of a semi-reusable two-stage-to-orbit small payload launch system

  Maddock, C., Ricciardi, L. A., Toso, F. & Vasile, M., 24 Oct 2019. 1 p.

  Research output: Contribution to conference › Poster

  Open Access

  File

  • Orbits 100%
  • Orbit 86%
  • Design 70%
  • Rockets 60%
  • Global optimization 59%
  59 Downloads (Pure)

• Aerodynamic database development for a future reusable space launch vehicle, the Orbital 500R

  Stindt, T., Merrifield, J., Fossati, M., Ricciardi, L. A., Maddock, C. A., West, M., Kontis, K., Farkin, B. & McIntyre, S., 3 Oct 2019. 8 p.

  Research output: Contribution to conference › Paper

  File

  • Launch vehicles 100%
  • Mach number 71%
  • Aerodynamics 71%
  • Hypersonic flow 20%
  • Supersonic flow 18%
  58 Downloads (Pure)

• Aerodynamic analysis of a TSTO spaceplane

  Fossati, M., Ricciardi, L. A., Merrifield, J., Peddakotla, S. A., Stindt, T., Maddock, C., Vasile, M. & Kontis, K., 30 Sep 2019.

  Research output: Contribution to conference › Speech › peer-review

• Robust multi-objective optimisation of a descent guidance strategy for a TSTO spaceplane

  Ricciardi, L. A., Maddock, C. A., Vasile, M., Stindt, T., Merrifield, J., Fossati, M., West, M., Kontis, K., Farkin, B. & McIntyre, S., 30 Sep 2019. 8 p.

  Research output: Contribution to conference › Paper › peer-review

  Open Access

  File

  • Multiobjective optimization 100%
  • Transcription 24%
  • Trajectories 14%
  29 Downloads (Pure)

• Robust trajectory optimisation of a TSTO spaceplane using uncertainty-based aerodynamic models

  Fossati, M., Maddock, C., Vasile, M., Kontis, K., Merrifield, J., Ricciardi, L. A., Stindt, T. & Farkin, B., 30 Sep 2019.

  Research output: Contribution to conference › Speech › peer-review

• Direct solution of multi-objective optimal control problems applied to spaceplane mission design

  Ricciardi, L. A., Maddock, C. A. & Vasile, M., 30 Jan 2019, In: Journal of Guidance, Control and Dynamics. 42, 1, p. 30-46 17 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • optimal control 100%
  • Nonlinear programming 86%
  • Optimal Control Problem 65%
  • nonlinear programming 58%
  • Nonlinear Programming 54%
  11 Citations (Scopus)

  89 Downloads (Pure)
• 2018

  Conceptual design analysis for a two-stage-to-orbit semi-reusable launch system for small satellites

  Maddock, C. A., Ricciardi, L., West, M., West, J., Kontis, K., Rengarajan, S., Evans, D., Milne, A. & McIntyre, S., 30 Nov 2018, In: Acta Astronautica. 152, p. 782-792 11 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Small satellites 100%
  • Conceptual design 85%
  • Orbits 73%
  • Aircraft carriers 30%
  • Launch vehicles 23%
  4 Citations (Scopus)

  41 Downloads (Pure)

• The Strathclyde space systems database: a new life cycle sustainability assessment tool for the design of next generation green space systems

  Wilson, A. R., Vasile, M., Maddock, C. & Baker, K. J., 27 Sep 2018. 7 p.

  Research output: Contribution to conference › Paper › peer-review

  Open Access

  File

  • Sustainable development 100%
  • Life cycle 97%
  • Monopropellants 42%
  • Environmental management 39%
  • Environmental impact 26%
  107 Downloads (Pure)

• Multi-objective optimal control of re-entry and abort scenarios

  Ricciardi, L. A., Maddock, C. A. & Vasile, M., 8 Jan 2018.

  Research output: Contribution to conference › Proceeding

  Open Access

  File

  • Reentry 100%
  • Transcription 99%
  • Nonlinear programming 30%
  • Parameterization 30%
  • Polynomials 21%
  4 Citations (Scopus)

  38 Downloads (Pure)
• 2017

  Recent developments on the orbital-500R and the UK future small payload launcher programme

  Fossati, M., Maddock, C., Farkin, B., Kontis, K., West, M., Merrifield, J. & Evans, D., 24 Oct 2017.

  Research output: Contribution to conference › Speech › peer-review

• Conceptual design analysis for a two-stage-to-orbit semi-reusable launch system for small satellites

  Maddock, C., Toso, F., West, M., West, J., Kontis, K., Rengarajan, S., Evans, D., Milne, A. & McIntyre, S., 25 Sep 2017, 68th Proceedings of the International Astronautical Congress. Adelaide, South Australia, 14 p. IAC-17-D2.7.12

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

  Open Access

  File

  • Small satellites 100%
  • Conceptual design 85%
  • Orbits 73%
  • Aircraft carriers 40%
  • Launch vehicles 31%
  80 Downloads (Pure)

• Return and abort trajectory optimisation for reusable launch vehicles

  Toso, F. & Maddock, C., 2 Mar 2017, Proceedings of the 21st AIAA International Space Planes and Hypersonic Systems and Technologies Conference. Reston, VA, 11 p. AIAA 2017-2250. (International Space Planes and Hypersonic Systems and Technologies Conferences).

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

  Open Access

  File

  • Launch vehicles 100%
  • Trajectories 61%
  • Recovery 15%
  61 Downloads (Pure)

• Vehicle and mission design of a future small payload launcher

  Maddock, C. A., Toso, F., Ricciardi, L., Mogavero, A., Lo, K. H., Rengarajan, S., Kontis, K., Milne, A., Merrifield, J., Evans, D., West, M. & McIntyre, S., 2 Mar 2017, 21st AIAA International Space Planes and Hypersonic Systems and Technologies Conference. Reston, VA, 21 p. AIAA 2017-2224. (International Space Planes and Hypersonic Systems and Technologies Conferences).

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

  Open Access

  File

  • Aircraft carriers 100%
  • Launch vehicles 78%
  • Conceptual design 70%
  • Orbits 61%
  • Earth (planet) 58%
  5 Citations (Scopus)

  348 Downloads (Pure)

• Initial guess generation strategies for spaceplane trajectory optimisation

  Toso, F. & Maddock, C., 10 Jan 2017, (Accepted/In press) In: Transactions of the Japan Society for Aeronautical and Space Sciences. 8 p.

  Research output: Contribution to journal › Conference Contribution › peer-review

  Open Access

  File

  • trajectory optimization 100%
  • Trajectory Optimization 83%
  • Guess 62%
  • White noise 60%
  • trajectory 42%
  60 Downloads (Pure)
• 2016

  Spaceplane trajectory optimisation with evolutionary-based initialisation

  Maddock, C. A. & Minisci, E., 9 Dec 2016, 2016 IEEE Symposium Series on Computational Intelligence (SSCI). Piscataway, NJ.: IEEE, 8 p. 7850109

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

  Open Access

  File

  • Trajectory Optimization 100%
  • Initialization 81%
  • Propulsion 59%
  • Shooting 56%
  • Trajectories 45%
  3 Citations (Scopus)

  151 Downloads (Pure)

• Global solution of multi-objective optimal control problems with multi agent collaborative search and direct finite elements transcription

  Ricciardi, L. A., Vasile, M. & Maddock, C., 21 Nov 2016, 2016 IEEE Congress on Evolutionary Computation, (CEC). Piscataway: IEEE, p. 869-876 8 p. 7743882

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

  Open Access

  File

  • Transcription 100%
  • Global Solution 68%
  • Optimal Control Problem 59%
  • Finite Element 58%
  • Nonlinear programming 45%
  8 Citations (Scopus)

  51 Downloads (Pure)

• A commercially driven design approach to UK future small payload launch systems

  McIntyre, S., Fawcett, T., Dickinson, T., West, M., Maddock, C. A., Mogavero, A., Ricciardi, L., Toso, F., Kontis, K., Lo, K. H., Rengarajan, S., Evans, D., Milne, A. & Feast, S., 26 Oct 2016. 11 p.

  Research output: Contribution to conference › Paper

  Open Access

  File

  • Costs 100%
  • Hypersonic aerodynamics 50%
  • Reusability 49%
  • Air 47%
  • Takeoff 47%
  204 Downloads (Pure)

• How to launch small payloads? Evaluation of current and future small payload launch systems

  McIntyre, S., Fawcett, T., Dickinson, T., Maddock, C. A., Mogavero, A., Ricciardi, L., Toso, F., West, M., Kontis, K., Lo, K. H., Rengarajan, S., Evans, D., Milne, A. & Feast, S., 26 Oct 2016. 15 p.

  Research output: Contribution to conference › Paper

  Open Access

  File

  • Orbits 100%
  • Underdevelopment 69%
  • Evaluation 61%
  186 Downloads (Pure)

• Comparison of the emissions of current expendable launch vehicles and future spaceplanes

  Garner, R. J., Toso, F. & Maddock, C. A., 30 Sep 2016, p. 1-12. 12 p.

  Research output: Contribution to conference › Paper

  Open Access

  File

  • Launch vehicles 100%
  • Trajectories 61%
  • Upper atmosphere 61%
  • Ozone layer 35%
  • Environmental impact 21%
  1 Citation (Scopus)

  216 Downloads (Pure)

• Deployed payload analysis for a single stage to orbit spaceplane

  Toso, F. & Maddock, C. A., 30 Sep 2016. 11 p.

  Research output: Contribution to conference › Paper

  Open Access

  File

  • Orbits 100%
  • Flight paths 23%
  • Small satellites 22%
  • Trajectories 13%
  • Engines 12%
  2 Citations (Scopus)

  61 Downloads (Pure)

• Multi-objective optimal control of ascent trajectories for launch vehicles

  Ricciardi, L. A., Vasile, M., Toso, F. & Maddock, C. A., 13 Sep 2016, AIAA/AAS Astrodynamics Specialist Conference, 2016. Reston, VA, 14 p. 2016-5669. (AIAA Space Forum).

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

  Open Access

  File

  • ascent trajectories 100%
  • launch vehicles 66%
  • optimal control 56%
  • Launch vehicles 50%
  • Trajectories 31%
  10 Citations (Scopus)

  67 Downloads (Pure)
• 2015

  Optimisation of ascent and descent trajectories for lifting body space access vehicles

  Toso, F., Riccardi, A., Minisci, E. & Maddock, C. A., 14 Oct 2015, p. 1-12. 12 p.

  Research output: Contribution to conference › Paper

  Open Access

  File

  • Trajectories 100%
  • Takeoff 78%
  • Landing 71%
  • Orbits 63%
  • Natural language processing systems 43%
  5 Citations (Scopus)

  213 Downloads (Pure)
• 2012

  Design of a formation of solar pumped lasers for asteroid deflection

  Vasile, M. & Maddock, C., 1 Oct 2012, In: Advances in Space Research. 50, 7, p. 891-905 15 p.

  Research output: Contribution to journal › Article › peer-review

  File

  • solar-pumped lasers 100%
  • Asteroids 81%
  • asteroids 72%
  • asteroid 66%
  • deflection 65%
  56 Citations (Scopus)

  126 Downloads (Pure)

• Ascent trajectory optimisation for a single-stage-to-orbit vehicle with hybrid propulsion

  Pescetelli, F., Minisci, E., Maddock, C., Taylor, I. & Brown, R., Sep 2012.

  Research output: Contribution to conference › Paper

  File

  • Trajectory Optimization 100%
  • Ascent 82%
  • Hybrid vehicles 69%
  • Propulsion 59%
  • Orbits 57%
  14 Citations (Scopus)

  1014 Downloads (Pure)
• 2011

  Prediction of the aerodynamic performance of re-usable single stage to orbit vehicles

  Ahmad, A. O., Maddock, C., Scanlon, T. & Brown, R., 21 Sep 2011. 11 p.

  Research output: Contribution to conference › Paper

  File

  • Aerodynamics 100%
  • Reentry 85%
  • Gas 77%
  • Orbits 72%
  • Atmosphere 68%
  427 Downloads (Pure)
• 2010

  Orbital debris removal with solar concentrators

  Vasile, M., Maddock, C. & Saunders, C., 27 Sep 2010, p. Paper IAC-10.A6.4. 11 p.

  Research output: Contribution to conference › Paper › peer-review

  File

  • Solar concentrators 100%
  • Debris 74%
  • asteroid 74%
  • ice ridge 61%
  • thrust 60%
  12 Citations (Scopus)

  174 Downloads (Pure)

• The Suaineadh Project: a stepping stone towards the deployment of large flexible structures in space

  Vasile, M., Cartmell, M., Dejene, F. Z., Drysdale, T., Flores, M. A., Gulzar, M. Y., Ismail, N., Khalid, M. U., Li, M., Maddock, C., Mallol, P., Mathieson, A., McRobb, M., Öberg, J., Reynolds, P., Ritterbusch, R., Sandqvist, W., Summerer, L., Tanveer, M. U., Tibert, G., & 3 othersWhyte, G., Zafar, W. & Zhang, J., 27 Sep 2010, p. Paper IAC-10-C3.4. 12 p.

  Research output: Contribution to conference › Paper

  File

  • Flexible Structure 100%
  • Flexible structures 84%
  • Sensor 83%
  • hubs 68%
  • Wheel 55%
  3 Citations (Scopus)

  93 Downloads (Pure)

• Integrated 915 MHz dual-patch circularly polarized antenna for Suaineadh space web experiment

  Whyte, G., Murray, C., Maddock, C., Vasile, M. & Drysdale, T. D., 11 Jul 2010, Proceedings of the IEEE Symposium on Antennas and Propagation: CNC/USNC/URSI Radio Science Meeting. IEEE, p. 1-4 5 p. (Antennas and Propagation).

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

  • Antenna 100%
  • Rockets 88%
  • Patch 87%
  • Microstrip antennas 78%
  • Experiment 61%
  1 Citation (Scopus)

• Active orbital debris removal by enhanced solar light

  Vasile, M., Maddock, C., Saunders, C., Sorel, M. & Watson, I. A., 22 Jun 2010.

  Research output: Contribution to conference › Paper

• On the deflection of asteroids with mirrors

  Vasile, M. & Maddock, C., Jun 2010, In: Celestial Mechanics and Dynamical Astronomy. 107, 1-2, p. 265-284 20 p.

  Research output: Contribution to journal › Article › peer-review

  File

  • Asteroids 100%
  • Deflection 89%
  • Concentrator 88%
  • asteroids 88%
  • Mirror 85%
  35 Citations (Scopus)

  243 Downloads (Pure)

• On the Dynamics, Navigation and Control of a Spacecraft Formation of Solar Concentrators in the Proximity of an Asteroid

  Maddock, C. A., 23 Feb 2010, Glasgow. 292 p.

  Research output: Thesis › Doctoral Thesis

  • Solar concentrators 100%
  • Asteroids 91%
  • Spacecraft 62%
  • Navigation 53%
  • Solar radiation 46%
• 2009

  Conceptual design of a multi-mirror system for asteroid deflection

  Maddock, C., Vasile, M. & Summerer, L., 5 Jul 2009, p. 2009-k-04. 7 p.

  Research output: Contribution to conference › Paper › peer-review

  File

  • Conceptual Design 100%
  • Asteroids 74%
  • Deflection 66%
  • Mirror 63%
  • Conceptual design 58%
  108 Downloads (Pure)

• Designs of multi-spacecraft swarms for the deflection of apophis by solar sublimation

  Maddock, C., Vasile, M., McInnes, C. R., Radice, G. & Summerer, L., 27 Apr 2009.

  Research output: Contribution to conference › Paper › peer-review

  File

  • Sublimation 100%
  • Spacecraft 63%
  • Solar concentrators 33%
  • Asteroids 30%
  • Debris 25%
  38 Downloads (Pure)
• 2008

  Extension of the proximity-quotient control law for low-thrust propulsion

  Maddock, C. & Vasile, M., 29 Sep 2008. 9 p.

  Research output: Contribution to conference › Paper

  File

  • Solar Radiation 100%
  • Proximity 63%
  • Solar radiation 62%
  • Propulsion 54%
  • Quotient 45%
  3 Citations (Scopus)

  66 Downloads (Pure)

• Mirror formation control in the vicinity of an asteroid

  Vasile, M., Maddock, C. & Radice, G., 18 Aug 2008. 23 p.

  Research output: Contribution to conference › Paper

  File

  • Formation Control 100%
  • Asteroids 79%
  • Solar Radiation 67%
  • Mirror 67%
  • Mirrors 62%
  4 Citations (Scopus)

  225 Downloads (Pure)

• Design of optimal spacecraft-asteroid formations through a hybrid global optimization approach

  Maddock, C. & Vasile, M., Apr 2008, In: International Journal of Intelligent Computing and Cybernetics. 1, 2, p. 239-268 30 p.

  Research output: Contribution to journal › Article › peer-review

  File

  • Hybrid Optimization 100%
  • Asteroids 76%
  • Global optimization 60%
  • Global Optimization 60%
  • Spacecraft 52%
  18 Citations (Scopus)

  66 Downloads (Pure)
• 2007

  Optimal design for a NEO tracking spacecraft formation

  Maddock, C. & Vasile, M., 25 Sep 2007, IEEE Congress on Evolutionary Computing. IEEE, p. Paper 1728 8 p.

  Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed)

  File

  • spacecraft tracking 100%
  • near Earth objects 81%
  • asteroids 62%
  • spacecraft orbits 28%
  • ephemerides 27%
  68 Downloads (Pure)

• Comparison of single and multi-spacecraft configurations for NEA deflection by solar sublimation

  Maddock, C., Sanchez Cuartielles, J-P., Vasile, M. & Radice, G., 2007, New trends in Astrodynamics and Applications III. 1st ed. Vol. 886. p. 303-316

  Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed)

  File

  • spacecraft configurations 100%
  • asteroids 63%
  • sublimation 60%
  • deflection 49%
  • spacecraft 33%
  24 Citations (Scopus)

  52 Downloads (Pure)